Kinetics of elementary reactions in low-temperature autoignition chemistry

Progress in Energy and Combustion Science 37 (2011) 371e421

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Progress in Energy and Combustion Science journal homepage: www.elsevier.com/locate/pecs

Review

Kinetics of elementary reactions in low-temperature autoignition chemistry Judit Zádor a, Craig A. Taatjes a, *, Ravi X. Fernandes b a b

Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories, Livermore, CA 94551-0969 USA Shock Wave Laboratory, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 February 2010 Accepted 29 June 2010 Available online 2 September 2010

Advanced low-temperature combustion concepts that rely on compression ignition have placed new technological demands on the modeling of low-temperature oxidation in general and particularly on fuel effects in autoignition. Furthermore, the increasing use of alternative and non-traditional fuels presents new challenges for combustion modeling and demands accurate rate coefficients and branching fractions for a wider range of reactants. New experimental techniques, as well as modern variants on venerable methods, have recently been employed to investigate the fundamental reactions underlying autoignition in great detail. At the same time, improvements in theoretical kinetics and quantum chemistry have made theory an indispensible partner in reaction kinetics, particularly for complex reaction systems like the alkyl þ O2 reactions. This review concentrates on recent developments in the study of elementary reaction kinetics in relation to the modeling and prediction of low-temperature combustion and autoignition, with specific focus placed on the emerging understanding of the critical alkylperoxy and hydroperoxyalkyl reactions. We especially highlight the power of cooperative theoretical and experimental efforts in establishing a rigorous mechanistic understanding of these fundamental reactions. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Chemical kinetics Theoretical kinetics Low-temperature combustion Autoignition Quantum chemistry Biofuels Peroxy radicals Hydroperoxyalkyl radicals Hydrocarbon oxidation

Contents 1. 2.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .372 Key reactions for autoignition and low temperature combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .372 2.1. Chain-propagation reactions of fuel molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 2.1.1. Abstraction reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 2.1.2. Addition reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 2.1.3. Substitution or metathesis reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 2.2. The reactions of carbon-centered organic radicals (R) with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 2.2.1. General features of alkylþO2 reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 2.2.2. “Formally direct” pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 2.2.3. Other hydrocarbon radical reactions with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 2.2.4. Oxygenated alkyl radical reactions with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 2.3. Reactions of the hydroperoxyalkyl radicals (QOOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 2.4. Other reactions of ROO and HO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 Key experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 3.1. “High-level” phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 3.2. Classical kinetics methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 3.3. Time-resolved kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 3.4. Coordinated theoretical and experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Key theoretical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 4.1. Reliability of ab initio rate coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 4.2. Level of theory needed to describe key autoignition reactions accurately . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 4.2.1. Electronic structure calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 4.2.2. Theoretical chemical kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

* Corresponding author. E-mail address: [email protected] (C.A. Taatjes). 0360-1285/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.pecs.2010.06.006

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J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

Recent progress on specific systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 5.1. AlkylþO2 reactions in alkane oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 5.1.1. The C2H5þO2 reaction and the concerted HO2 elimination pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 5.1.2. The reactions of propyl and higher alkyl radicals with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 5.1.2.1. PropylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 5.1.2.2. ButylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 5.1.2.3. NeopentylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 5.1.2.4. General RþO2 studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 5.2. AlkylþO2 reactions in naphthene oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 5.2.1. CyclopropylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 5.2.2. CyclohexylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 5.3. Reactions of resonance-stabilized hydrocarbon radicals with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 5.3.1. PropargylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 5.3.2. CyclopentadienylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 5.3.3. AllylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 5.3.4. IsobutenylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 5.3.5. BenzylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 5.3.6. XylylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 5.3.7. General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 5.4. The reaction of vinylic and aromatic radicals with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 5.4.1. Vinyl radical and its analoguesþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 5.4.2. PhenylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 5.4.3. Other aromatic radicalsþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 5.5. Reactions of oxygenated alkyl radicals with O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5.5.1. Radicals derived from alcoholsþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5.5.1.1. HydroxymethylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5.5.1.2. HydroxyethylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5.5.1.3. HydroxybutylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 5.5.1.4. Larger hydroxyalkyl radicalsþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 5.5.2. Radicals derived from ethersþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 5.5.3. Vinoxy radical and its derivativesþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 5.5.3.1. VinoxyþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 5.5.3.2. AcetonylþO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 5.6. The “second O2 addition” and other hydroperoxyalkyl reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 5.7. AlkylþHO2 reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 5.8. AlkylperoxyþHO2 reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 5.9. Addition of the HO2 radical to unsaturated compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 6.1. Pressure dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 6.2. Low-temperature chain branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

1. Introduction The modeling of combustion phenomena depends on an understanding of both chemistry and fluid mechanics, as well as a description of the interactions between them. The development of comprehensive detailed mechanisms for hydrocarbon oxidation has focused attention on the aspects of combustion where the details of the chemistry are most important, for example, pollutant formation and ignition phenomena. Comprehensive mechanisms and their development have been reviewed elsewhere [1e3], and recently in this journal by Battin-Leclerc [4], who also compared the treatment of many classes of elementary reactions in comprehensive mechanisms of different groups. This review concentrates on the fundamental kinetics of key elementary reactions needed for models of ignition chemistry, particularly the low-temperature region (less than w900 K) where reactions of peroxy and hydroperoxy radical species are important. We especially wish to highlight the ways in which improvements in computational chemistry extend experimental capabilities and enable increasingly detailed characterization of more and more complex reactions. The understanding of the elementary reactions that govern autoignition and low-temperature combustion has been developing over the course of decades. Earlier reviews, in particular those by

Pollard [5], Walker and Morley [6], and Robertson et al. [7] give thorough descriptions of the state of knowledge in low-temperature hydrocarbon oxidation chemistry up to about the mid-1990s. This review in one sense is a partial update of those more comprehensive reviews to account for recent investigations that have led to important changes in the understanding of many key reactions. However, we also concentrate on two important recent aspects of lowtemperature autoignition chemistry research. First, the technological context for ignition chemistry studies has been altered by the emergence of non-traditional and alternative fuels, the combustion kinetics of which have often had relatively little previous investigation, and by the development of advanced engines that rely on compression ignition to initiate volumetric combustion. Predictive modeling of new engine concepts for a changing fuel stream requires detailed understanding of the autoignition chemistry of a large set of organic molecules over a wide range of pressure and temperature. Second, rapid advances in quantum chemistry and theoretical kinetics have produced new opportunities for synergy between theoretical and experimental methods to derive reliable kinetics for elementary reactions. The direct involvement of rigorous computational chemistry in the interpretation and design of experimental kinetics investigations is a powerful emergent paradigm for detailed study of complex reaction systems such as those of autoignition.

J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

Nomenclature ARAS atomic resonance absorption spectroscopy B3LYP Becke 3-parameter exchange, Lee, Yang and Parr CASPT2 complete active space with second-order perturbation theory CASSCF complete active space self-consistent field theory CBS complete basis set extrapolation cc-pVDZ, -pVTZ, -pVQZ correlation-consistent double-, triple-, quadruple-zeta polarization (basis set) CCSD(T) coupled-cluster with single and double excitations and perturbative treatment of triple excitations CRDS cavity ringdown absorption spectroscopy CTST canonical TST CVTST canonical VTST DEE diethyl ether DFT density functional theory DME dimethyl ether ETBE ethyl t-butyl ether FM frequency modulation FTIR Fourier-transform infrared spectroscopy G2, G3 etc. Gaussian-two, Gaussian-three etc. ab initio MO theory for molecular electronic energy calculations GC gas chromatography GC-MS gas chromatographyemass spectrometry HF HartreeeFock IR-FM frequency modulation-infrared spectroscopy

2. Key reactions for autoignition and low temperature combustion In this section we first provide a basic outline of the elementary reactions that will be considered and then describe general features of each major type of reaction. As an illustration of each general reaction type we present a specific example from propane (CH3CH2CH3) or n_ Þ oxidation. This section provides an propyl radical ðCH3 CH2 CH 2 overview of the relevant chemistry and can be read independently from the more detailed discussion in subsequent sections. The primary homogeneous initiation reactions will not be treated in this review. Initiation in high-purity systems with no heterogeneous initiation chemistry is thought to occur by slow reactions such as the abstraction of H atom from a fuel molecule (“RH”) by molecular oxygen: RH þ O2/ R þ HO2

(1)

These reactions are endothermic and experimentally rather difficult to characterize, partly simply because they are slow and partly because reactions of the products rapidly overwhelm reaction (1). In fact it is chain propagation reactions, e.g., abstraction of an H atom from fuel species by OH (and to a more limited extent by HO2, O atom, H atom or CH3) that are largely responsible for the nature of the pool of hydrocarbon radicals that participate in the chemistry of low-temperature autoignition. Besides the overall rate coefficient for these reactions, the relative yields of the various possible products in a chemical reaction are also important. For instance, an _ H abstraction from propane can result in either CH3 CH2 CH 2 (n_ (i-propyl radical), and because these propyl radical) or CH3 CHCH 3 products have different subsequent chemistry, it is important to know their relative production. These are commonly expressed as branching ratios (i.e., ratios of the yields of specific products) or

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LIF laser-induced fluorescence ME master equation MEE methyl ethyl ether MP2 MøllerePlesset second order perturbation theory MPI multi-photon ionization MRCI multi-reference configuration interaction MS mass spectrometry MSC modified strong collider MTBE methyl t-butyl ether m-VTST microcanonical VTST mJ-VTST microcanonical and J-resolved VTST NIR-FM near-infrared frequency-modulation spectroscopy PIMS photoionization mass spectrometry QCISD(T) quadratic configuration interaction with single and double excitations and perturbative treatment of triple excitations QRRK quantum RRK RQCISD(T) restricted QCISD(T) RRHO rigid rotor and harmonic oscillator RRK RiceeRamspergereKassel RRKM RiceeRamspergereKasseleMarcus RS2C multi-reference RayleigheSchrödinger second-order perturbation theory TST transition-state theory VRC-TST variable-reaction-coordinate TST VTST variational TST ZPE zero-point energy

branching fractions (i.e., the fraction of the total reaction that forms a specific product). The site-dependence of H abstraction by OH from hydrocarbon species is relatively well understood, and structureeactivity relationships are able to predict the isomeric populations of radicals produced by many OH þ hydrocarbon reactions reliably, especially for saturated hydrocarbons [8,9]. For unsaturated fuels addition of radicals to fuel molecules can be a significant chain propagation reaction. Furthermore, other bimolecular channels can compete with abstraction and association. The reaction of OH with ethene _ CH OHÞ (CH2CH2), for example, can produce b-hydroxyethyl ðCH 2 2 radicals by addition to the double bond, vinyl radical _ þ water by H abstraction, or C2H4O (ethenol (vinyl alcohol, ðCH2 CHÞ CH2CHOH) or acetaldehyde (CH3CHO)) þ H atom by substitution or addition-elimination [10]. The nature of the products is important in determining not only the ignition chemistry, but also the formation of many combustion intermediates and partial oxidation products in real combustion systems [11,12]. The branching in many of these systems has been recently investigated by theory and experiment. The core low-temperature chemistry leading to autoignition is conveniently summarized for alkanes in Fig. 1. Central to this chemistry is the reaction of alkyl radicals, R, with molecular oxygen, where the overall reaction can lead to a variety of products: R þ O2 / ROO

(2a)

R þ O2 / alkene þ HO2

(2b)

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R þ O2 / cyclic ether þ OH

(2c)

R þ O2 / QOOH

(2d)

As HO2 is relatively unreactive, and as its removal reactions produce mostly H2O2, which is stable up to w1100 K, this channel is effectively chain-terminating at low temperatures. The emergence of this channel and the loss of the ROO chain carrier is partially responsible for the decreased reactivity with increasing temperature (the “negative temperature coefficient” (NTC) region) observed for many hydrocarbons. In many ways the most interesting avenue for the ROO radical is isomerization via internal H-atom abstraction to form a hydroperoxyalkyl radical, often denoted by QOOH: ROO % QOOH

The R þ O2 reactions display a rich kinetic behavior that changes with pressure and temperature; the complexity of this class of reaction alone has supported dozens of studies and engendered decades of controversy. Briefly, at low temperature and moderate pressures, the reaction of alkyl radicals with O2 proceeds largely but not exclusively by association to form an alkylperoxy radical (ROO). The chemistry of alkylperoxy radicals governs tropospheric oxidation of organic species. In combustion chemistry however, the R þ O2 reaction displays much more complex behavior. As the temperature increases, the alkylperoxy radical becomes thermally unstable and can suffer a number of fates that have differing consequences for the progress of autoignition. Of course, the ROO radical can simply dissociate back to form the alkyl and O2 reactants, removing the ROO chain carrier and “undoing” the initial reaction. Secondly, the ROO can produce HO2 and the conjugate alkene. This pathway is observed even at room temperature [13e17] but is quenched as the pressure increases. The mechanism of HO2 formation was long a subject of debate, as described in Section 5.1.1, but because of accurate theoretical work [18e20] corroborated by experiment [21e26] it is now known that the major means of HO2 production in these reactions is the direct elimination of HO2 from the ROO radical: ROO / alkene þ HO2

(3)

RH + OH - H2O alkyl radical

alkylperoxy radical

second O2 addition

The observation of cyclic ethers in low temperature hydrocarbon oxidation was the key to recognizing these isomerizations [27] and to the development of the mechanism to describe cyclic ether formation and to account for chain branching. The formation of the highly reactive OH radical makes this pathway extremely important for chain propagation, but the more important aspect of the isomerization is the ephemeral QOOH species itself.

alkyl hydroperoxyde ROOH + O2

ROO•

internal H abstraction hydroperoxyalkyl radical

These weakly bound species (none have ever been directly observed!) typically rapidly decompose to an OH radical and an oxygen heterocycle (reaction (2c)) or to HO2 and an alkene. The heterocycles include oxiranes (3-membered ring), oxetanes (4-membered ring), oxolanes (5-membered ring), and oxanes (6-membered ring), the simplest representatives of which are shown below:

R• + O2

(4)

+ HO2

chain branching RO• + OH

direct HO2 elimination HO2 + alkene

•QOOH + O2

chain propagation OH + O-heterocycle

•OOQOOH internal H abstraction HOO•Q-HOOH

ketohydroperoxide HOOQ-HO + OH chain branching

•OQ-HO + 2 OH Fig. 1. Schematic mechanism for low-temperature hydrocarbon oxidation and autoignition chemistry.

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As the QOOH is a substituted alkyl radical, with the unpaired electron formally located at a carbon atom, it is subject to attack by a second O2 molecule: QOOH þ O2 % OOQOOH

ROO þ R0 OO / products

375

(9)

(5)

This OOQOOH product can undergo isomerization (internal H abstraction) and dissociation to produce multiple radicals (e.g., 2 OH radicals and an oxy radical), providing a chain branching pathway at low temperature:

the branching between the radical (RO þ R0 O þ O2) and stable molecule (e.g., RHO þ R0 OH þ O2) channels has been investigated mostly for simple systems near 300 K [29]. The reactions of substituted ROO with HO2, and especially the possibility of thereby producing OH, ROO þ HO2 / RO þ OH þ O2

(10a)

OOQOOH % HOOQ-HOOH / OH þ ketohydroperoxide / OH þ OH þ OQ-HO

(6)

are currently of great interest as a possible explanation for the unexpectedly high tropospheric OH concentration in many lowNOx environments. Under tropospheric conditions the reaction of unsubstituted alkylperoxy radicals with HO2 essentially always produces alkylhydroperoxides and molecular oxygen [30,31]. In combustion models the reaction of ROO with HO2 is invoked as a source of hydroperoxide molecules, ROO þ HO2 / ROOH þ O2

The reaction sequence ROO þ RH / ROOH þ R

(7)

ROOH / RO þ OH

(8)

was earlier thought to be the source of chain branching in lowtemperature oxidation [5]. The abstraction of H atom from a stable molecule by an alkylperoxy radical is, however, extremely slow, and it is now generally thought that the QOOH reactions dominate lowtemperature chain branching [28]. Hence the formation and reactions of these QOOH molecules are central to autoignition chemistry. These reactions form the core of the low-temperature oxidation mechanism that leads to autoignition, and have received the most intense study. Nevertheless, there are other classes of reactions involving peroxy species that play an important role in the chemistry of autoignition. These reactions have not been thoroughly investigated in the context of combustion chemistry, but many of them have been studied for their tropospheric importance. One example is the self-reaction or cross-reactions of ROO radicals,

(10b)

which subsequently decompose via reaction (8). giving an overall reaction similar to (10a), but which will in general have a different pressure and temperature dependence. Kaiser [32,33] invoked reaction of ethylperoxy radicals with HO2 directly forming OH (i.e., according to mechanism (10a)) to describe the observed H2O and H2O2 in the 400 Ke700 K oxidation of propanal. Although these are crucial reactions to reproduce ignition delay times, the mechanisms of such reactions, their kinetics, and their branching fractions have had little investigation at temperatures relevant for low-temperature autoignition. Reactions of other radicals, e.g., alkyl radicals, with HO2 could also produce OH: R þ HO2 / RH þ O2

(-1)

R þ HO2 / RO þ OH

(11)

The first reaction is the reverse of the homogeneous initiation reaction (1), but the second channel provides conversion of HO2 to the more reactive OH, enhancing chain propagation. The reactions described above constitute a core set of key reactions for low temperature combustion and autoignition and recent progress in determining the kinetic parameters for such reactions is the subject of this review. Before discussing the major experimental and computational methods that have been applied

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to these reactions, and the recent progress on specific systems, it is useful to consider the important general features of each class of reaction. 2.1. Chain-propagation reactions of fuel molecules The balance among chain-propagation, chain-termination, and chain-branching pathways, and the details of the alkylperoxy and hydroperoxyalkyl radical chemistry that governs low temperature heat release and lays the groundwork for autoignition, both depend on the isomeric nature of the initial radical pool, which is determined principally by chain-propagation reactions of radicals (principally OH) with fuel molecules. The literature on such reactions is vast and beyond the capacity of this review, which will concentrate mainly on ROO, HO2, and QOOH chemistry. Nevertheless, we briefly consider some aspects of the various important types of these chain-propagation reactions of fuels, especially where they directly relate to themes of this review; low-temperature peroxy radical chemistry, complementarity of theory and experiment in determining accurate rate coefficients, and the kinetic challenges presented by modeling biofuel combustion. 2.1.1. Abstraction reactions The abstraction of H atoms from fuel species RH can produce various isomers of the radical R, with the strength of the preference for the more stable isomeric product depending on the abstracting reactant. These abstraction reactions, especially by the OH radical, have been very extensively investigated both for atmospheric and combustion applications, and abstraction reactions are well suited for rule-based rate constant estimation schemes [34e39]. The product branching for reactions of OH with alkanes is considered to be relatively well established, despite limited direct experimental measurements. Instead, assuming additivity of the abstraction rate constants at individual sites, structure-activity relationships have been developed that predict the kinetics and the isomer product ratios. For example, partial deuterium substitution was employed by Tully and coworkers [40,41] to investigate sitespecific hydrogen abstraction by OH from propane and isobutane. Assuming that the total rate constant was a sum of independent rate constants for individual abstraction sites (and that the kinetic isotope effect for each site depended only on the type of CeH bond), they derived effective rate constants for primary, secondary, and tertiary abstractions. Detailed computational work by Truhlar and coworkers [42] on the OH þ propane reaction essentially validated this additivity assumption. Cohen [43] employed transition-state theory (TST) to derive a set of groups that systematized OH attack on the possible CeH bonds in alkanes according to nearest- and next-nearest-neighbor interactions. A similar systematization can be carried out for the reactions of H atom with alkanes, as by Cohen [44] and by Baldwin and Walker [9]. Truong [45e52] has carried out an extensive computation and systematization of abstraction of H atom from alkanes (and some other species [45,51]) by many combustion-relevant radicals, including H [45,51,52], OH [46], CH3 [48], and O [47], employing a generalization of variational transition-state theory to reaction classes [49,50] as a means to compute accurate rate coefficients for a range of similar reactions. The power of combined theory and experiment is evident in the systematization of rate constants for abstraction reactions, which permits extrapolation of experimental results to unexplored conditions or indeed to unmeasured reactions. In a very recent example of this approach, Sivaramakrishnan and Michael [8] have improved the groups used by Cohen [43] and, in conjunction with new shock-tube measurements of OH reactions with large alkanes, have devised a group-additivity based scheme that captures the

reactions of OH with straight-chain and branched alkanes by 10 groups. Again, because the reaction rate coefficients are treated as sums of the reactions at each site in the alkane, and because the individual reaction sites are classified into groups, the decomposition of the total rate coefficients for the various alkanes into group contributions serves also to predict isomeric branching fractions. The work of Cohen [43] employed a transition-state-theory model coupled to the available rate constant measurements; the recent work of Sivaramakrishnan and Michael [8] takes this to a new level of precision with increased accuracy of computation and a more extensive dataset of experimental rate coefficients. Abstraction from other hydrocarbons is not as widely investigated as for alkanes. Reactions with unsaturated molecules must include the competition between addition and abstraction. Most of the experimental investigations of OH reactions with alkenes and aromatics have focused either on the high temperature region (above where alkylperoxy chemistry contributes) [53e56] or on tropospheric chemistry, where addition dominates. The measurements of Tully and coworkers are a notable exception [57e60]; for example, Tully characterized the mechanism change from association to production of bimolecular products in OH þ ethene [59] and measured the bimolecular channels (thought to be mostly abstraction) in the reactions of OH with ethene and 1-butene from 650 K to 901 K [57], and Tully et al. [58] analyzed the OH þ benzene and OH þ toluene reactions over an extended temperature range. Also, Walker and coworkers [61,62] added toluene and ethylbenzene to reacting H2/O2 mixtures at w772 K and characterized the reactions of H and HO2 with the aromatic species. As novel biofuels begin to be more broadly investigated and utilized, more extensive and reliable knowledge will be required for chain-propagation reactions with a wide range of fuel types, especially oxygenated compounds [63]. Group-additivity-based structure-activity relationships have also been developed for substituted hydrocarbons [64,65] although they are less thoroughly validated than those for alkanes or alkenes. Reactions with some proposed fuels, e.g., alkylfurans (shown below), have only recently been explored and may lie outside the established parameters of structure-activity relationships [66].

Furthermore, the overwhelming majority of the experimental measurements for abstraction reactions from substituted hydrocarbons have been carried out near 298 K, with temperaturedependent studies rarely reaching above w440 K [67e75]. Many detailed structure-activity relationships have been formulated in the context of tropospheric oxidation [76], but features that are important near 300 K and atmospheric pressure may be insignificant under conditions relevant for autoignition. For example, it has been proposed, based on quantum chemistry and canonical transition-state-theory, that the branching fractions in reactions of OH with alcohols and other oxygenated hydrocarbons are affected by weakly bound intermediates in the entrance channel [77,78]. More detailed theoretical kinetics and direct measurements of isomeric products may be needed to determine the consequences of such complexes for autoignition chemistry. Efforts to generate reliable rate constants for abstraction reactions of substituted hydrocarbons have utilized quantum chemistry and group additivity to derive rate rules. For example, Sumathi and Green [38] used CBS-Q evaluations of thermochemical parameters in producing rate rules for abstraction reactions of oxygenates, and Black et al. [79] employed

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CBS-QB3 calculations and isodesmic corrections to calculate thermochemistry of H-abstraction reactions in n-butanol. Relatively few systematic experimental studies of abstraction reactions with substituted hydrocarbons have focused on the temperatures relevant to autoignition. Reactions of OH with alcohols have been investigated by Tully and coworkers [80e82], and the regeneration of OH by decomposition of b-hydroxyalkyl radical products used to gain information on the isomeric branching.

The a CeH bond in alcohols is weaker than similar bonds in alkanes, and abstraction tends to favor that site [64]. Tranter and Walker [83,84] used reacting H2/O2 mixtures to investigate the abstraction reactions from ketones and ethers by H and OH and also followed the oxidation of the resulting radical products. In the case of butanone and pentan-3-one [84] they were able to deduce initial isomeric product ratios from analysis of the final oxidation products.

There have been several investigations of the reactions of OH with ethers that reach the temperature range relevant to autoignition. Tully and Droege [85] determined rate coefficients for OH þ dimethyl ether and OH þ diethyl ether, but only up to 442 K; Bonard et al. [86] measured OH þ dimethyl ether and OH þ methyl t-butyl ether up to 618 K and Arif et al. [87] studied OH þ dimethyl ether and OH þ methyl t-butyl ether up to 800 K.

Ogura et al. [88] developed a general model for OH reactions with ethers, employing a procedure based on comparison between reactions of ethers and “corresponding” alkanes, i.e., replacing the eOe linkage with eCH2e. By combining quantum chemical calculations and transition-state-theory with the available experimental data, they derived group values to predict general reactions of OH with ethers. Recent high-temperature measurements of OH þ dimethyl ether reaction [89] are in good agreement with these group value predictions. Another key area for biofuel combustion modeling is the initial radical attack on esters [90], because of the increasing utilization of fatty-acid methyl ester (FAME) biodiesel, e.g.:

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The abstraction in the long (C16eC18) alkyl or alkenyl chain of these esters is likely to be similar to the corresponding alkanes or alkenes, and, for example, the ignition delays for n-decane can be reasonably predicted by the oxidation model for methyl decanoate [91,92]. However, there are some differences in reactivity near the ester functionality that have been identified through product analysis in OH-initiated oxidation [93], with increased reactivity at the a CeH bond, similar to the preference for a abstraction observed in alcohols. Most of the measurements on OH reactions with esters have been carried out at relatively low temperatures, with little direct experimental data in the temperature range relevant for autoignition. There is a general need for experimental data on OH reactions with substituted hydrocarbons taken at higher temperatures, to validate proposed structure-activity relationships over a wider temperature range and specifically in the region relevant for autoignition chemistry. 2.1.2. Addition reactions The addition of HO2 [94e100] to alkenes forms b-hydroperoxyalkyl radicals, i.e., QOOH radicals with an eOOH on the carbon adjacent to the radical site. These radicals generally rapidly dissociate to form OH þ oxiranes [101].

Walker and co-workers have studied many of these reactions, which typically have substantial activation energies, tens of kJ mol1, and are relatively slow, with rate constants less than 1015 cm3 molecule1 s1 under low-temperature combustion conditions. Nevertheless, as a means of converting the unreactive HO2 radical to the more potent chain carrier OH, it plays an important role in low-temperature oxidation [6]. As experimental investigation of these reactions is difficult, recent progress has been mostly computational. Bozzelli and coworkers [98,99] have calculated the thermochemistry of some HO2 additions by quantumchemical means and estimated high-pressure limits for the reactions by using simple transition-state-theory-based kinetic models. Their computational results are able to predict the raw experimental results of Walker and coworkers, but they caution that the thermochemistry on which the experimental rate constant derivations rely is sometimes substantially different than that calculated by quantum chemistry [98,99,102]. Furthermore, quantum chemistry has shown [25,26,103e105] that the rapid formation of OH þ oxiranes from HO2 þ alkene association reactions relates to features of the b-hydroperoxyalkyl radicals, whose transition states for OH elimination tend to lie below that for isomerization to ROO, and does not necessarily support arguments that QOOH isomerization to ROO more generally cannot compete with the dissociation to OH þ cyclic ethers [5]. This question is of importance when interpreting experimental measurements of OH formation in alkyl þ O2 reactions and attempting to relate them to elementary isomerization rate constants [106e111], specifically for the neopentyl þ O2 system [112], where the isomerization will form a ghydroperoxyalkyl radical.

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be negligible in both reactions around room temperature [128,129]. However, neither study considered possible enol products. Quantitative experimental branching fractions for OH þ alkene reactions are still generally needed, particularly as a function of temperature. 2.2. The reactions of carbon-centered organic radicals (R) with O2 Addition of H or CH3 to an olefin produces an alkyl radical with the radical site adjacent to the addition site (as in the case of HO2 or OH addition), and is the reverse of thoroughly studied decomposition reactions of alkyl radicals. The association reactions are relatively straightforwardly parameterized; for example, Cvetanovi c laid a framework for a general understanding of the rates for addition of atoms [113,114] and radicals [115] to olefins. However, branching fractions can be problematic, particularly in the case of O atom addition (although O atom reactions are relatively unimportant in autoignition), as both triplet and singlet surfaces contribute [116]. 2.1.3. Substitution or metathesis reactions The reactions of OH, O, or H with unsaturated species [117], or of alkyl radicals with carbonyl species [118], for example, often have energetically accessible bimolecular product channels other than the abstraction discussed above. Formally these products can be thought of as arising from the formation of an excited adduct by addition of the radical to the double or triple bond, followed by dissociation of this adduct. Fig. 2 shows an example of such a reaction, that of OH reacting with propene [119]. The formation of bimolecular products, e.g. propanal þ H or ethenol þ CH3, requires surmounting barriers lying slightly above the energy of the reactants. Such products can be produced either by thermal dissocia_ _ tion of an initially formed CH3 CHCH 2 OH or CH3 CHðOHÞCH2 adduct or by sufficiently energetic reactive encounters that overcome the barrier before collisions stabilize the adduct. As can be seen from the potential energy surface, either mechanism could entail crossing of multiple transition states in a single elementary step, and is one example of the type of process that we refer to as “formally direct” pathways [24], described in more detail in subsequent sections. There have been few experimental determinations of branching fractions for such pathways, and most of the information on these addition-elimination reactions comes from theory. For example, Simmie and Curran [120] recently calculated thermochemistry and activation enthalpies for addition of H, CH3 and C2H5 to substituted ethenes and H addition to aldehydes. They used their quantum chemical calculations to draw qualitative kinetic conclusions about branching fractions to enols (OH is attached to one carbon atom of a C]C double bond) in the decomposition of hydroxyalkyl radicals. Reactions of OH with alkenes can produce enols [11,12], and numerous studies have considered the quantum chemistry and kinetics of ethene þ OH [10,117,121,122], and propene þ OH [119,123,124], as well as analogous reactions with aromatics, e.g. OH þ benzene / phenol þ H [125,126]. Such reactions of aromatics are related to the OH-initiated oxidation of aromatic species in the troposphere, which is a very active research topic. However, the experimental work is confined to near room temperature; see e.g., Noda et al. [127], where the displacement reactions of OH with benzene, toluene, and xylenes are quantified. Hoyermann and Sievert [128], employing mass spectrometry, found C2H4O þ CH3, CH2O þ C2H5, and C3H6O þ H channels in the reaction of OH þ propene at low pressure, and reported product ratios for (propanal:formaldehyde) and (acetone:acetaldehyde). In a similar study, Bartels et al. [129] measured products from OH þ ethene and found 44% formaldehyde þ methyl, 35% C2H4O þ H, and 21% stabilized hydroxyethyl radicals at 298 K and 2 Torr (1 Torr ¼ 133.3 Pa). The abstraction channel was reported to

2.2.1. General features of alkyl þ O2 reactions The features of the potential energy surface for ROO transformations are illustrated in Fig. 3 for the example of n-butyl radical reacting with O2 [26]. The well-depth for formation of an alkylperoxy radical from R þ O2 is typically about 30e35 kcal mol1, depending on the nature of the alkyl radical, with more substituted R forming somewhat stronger CeOO bonds [130]. The addition of O2 to an alkyl radical is barrierless; accurate computation of the association step by statistical methods requires implementation of variational methods [131], including a variational definition of the nature of the reaction coordinate [132e134]. Typical (high-pressure limiting) rate constants for the association step are w1011 to 1012 cm3 molecule1 s1 in the 600 Ke800 K region most relevant for peroxy radical chemistry [103e105]. Over this temperature range the equilibrium constant for the reversible association reaction shifts from favoring the ROO product to favoring the R þ O2 reactants. Slagle and coworkers [135e137] have reported investigations of many R þ O2 equilibria. Knyazev and Slagle reevaluated much of this data in 1998 [130] and their experiments are generally in reasonable agreement with quantum chemical determinations. Simmie et al. [138] recently undertook a systematic theoretical investigation of the thermochemistry of small alkylperoxy radicals and alkylhydroperoxides, confirming the general increase in ReOO bond strength with methyl substitution at the a-carbon proposed by Knyazev and Slagle. Resonance stabilization of the hydrocarbon radical reduces the strength of its bonds with molecular oxygen, and measurements have been carried out by similar methods of equilibria involving unsaturated hydrocarbon radicals [139e142]. Experimental and theoretical ReOO bond energies for several species are listed in Table 1. The direct elimination of HO2 from the ROO radical takes place via a 5-membered ring transition state in which the reaction coordinate is principally heavy-atom motion: the O-O moiety leaves the molecule, taking the H atom from the neighboring C atom as it goes. The transition state for direct HO2 elimination is unlike the transition states for the isomerization channels to form QOOH, which are more accurately described as an internal abstraction of a hydrogen atom by the unpaired electron on the terminal O atom The geometry of some representative transition states is shown in Fig. 4. The transition-state energy for the HO2 elimination lies several kcal mol1 below the R þ O2 entrance channel for alkyl þ O2 systems, and its energy above the ROO well depends little on the nature of the CeH bond involved (primary, secondary, or tertiary) [26], again in marked contrast to the isomerizations forming QOOH (see Table 2). This direct elimination channel is the dominant pathway for HO2 formation in the R þ O2 reactions. Details of this topic are presented in Section 5.1.1. Isomerization of the ROO radicals to form the hydroperoxyalkyl radicals QOOH also proceeds through ring-shaped transition states, as shown in Fig. 4. The isomerizations in alkyl radicals can be categorized according to the positions of the heavy atoms between which the H atom is transferred and the type of CeH bond being broken. As shown in Fig. 5, the atoms in the ring-shaped transition state are numbered beginning from the terminal O atom and proceeding down the carbon backbone; a 1,4 transfer hence refers to a five-membered (OeOeCeCeH) transition state. A letter is then

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379

Fig. 2. Schematic partial potential energy surface for the reaction of OH radical with propene (depicting only pathways initiated by addition of OH at the terminal carbon), taken from Zádor et al. [119], reproduced by permission of the PCCP owner societies.

added to designate the type of CeH bond being broken, primary, secondary, or tertiary. The barrier heights for these isomerizations depend on the size of the ring and on the strength of the CeH bond broken in the isomerization. Table 2 shows some literature recommendations for the activation energies of ROO / QOOH isomerization; those recommended by Walker [6,143] based on analysis of his group’s experiments, anchored to Hughes et al.’s [106,107] derivation of a rate coefficient for the neopentylperoxy / hydroperoxyneopentyl isomerization (see Section 2.1.2), and the estimates used by Curran et al. [144,145] in generating the Lawrence Livermore comprehensive mechanisms. These values are compared with available computed barrier heights. The activation energy for the reverse isomerization is equally important and is of course related to both the ROO 4 QOOH transition state energy and the thermochemistry of the QOOH relative to ROO. Because the QOOH has eluded direct detection, quantum chemical calculations of its thermochemistry are not merely the most reliable but the only determinations available. These computed values can differ substantially from estimates made in comprehensive mechanism construction [146]; the fate of QOOH, including reverse isomerization, is discussed in Section 2.3, and details of specific systems are treated in Section 5.6.

Fig. 3. Schematic potential energy surface for the reaction of n-butyl radical with O2 [26], showing the various isomerization pathways to hydroperoxybutyl radicals and the direct elimination of HO2 from n-butylperoxy. The dashed arrows are examples of formally direct pathways, traversing more than one transition state. Despite following an indirect multiple-transition-state path, they are correctly represented as a single kinetic step. The elimination of HO2, depicted by the bold contour, is not “formally direct,” as it traverses only one transition state. It is mechanistically direct, i.e. simply “direct.”

2.2.2. “Formally direct” pathways One important feature of the R þ O2 reactions that has been highlighted by pulsed-photolysis experiments over the last ten years is the substantial participation of reactive pathways that traverse more than one transition state in a single elementary step. Some of these pathways are depicted as the dashed arrows in Fig. 3. For example, HO2 þ an alkene can be formed directly from the R þ O2 reactants without stabilization in the ROO or QOOH well, or R þ O2 can be stabilized directly into the QOOH well without intervening ROO formation. These pathways have been termed “formally direct” by our group [25,103,105,147], a term that deserves some clarification. The term “formally direct” should not be confused with mechanistically direct pathways, such as the direct HO2 elimination from ROO, which traverses one transition state only. Formally direct pathways are single elementary steps, and hence appear as direct reactions in a rate equation model, but they are mechanistically “indirect,” proceeding over multiple transition states. Chemical activation systems are one case where formally direct reactions play a role, but “formally direct” is not equivalent to “chemical activation,” as other processes like thermal dissociation or isomerization can also take place across multiple transition states in a single elementary kinetic step. Rate coefficients for the formally direct pathways are elementary rate coefficients that can be defined rigorously from eigenvector-eigenvalue pairs in the solution to the master equation [148e150]. They are not the same as effective rate coefficients derived from the conventional approximate quasi-steady-state elimination of a short-lived intermediate in a multiple-step kinetics scheme. The formally direct pathways can impart a complicated pressure dependence to the branching fractions of a complex-mediated reaction, and the pressure dependence of the formally direct pathways is not captured by a quasi-steady-state approximation [148]. 2.2.3. Other hydrocarbon radical reactions with O2 Reactions of substituted and unsaturated hydrocarbon radicals with O2 have received less investigation, but may become more important as advanced engine designs require more detailed knowledge of autoignition chemistry for predictive modeling. Furthermore, the development of biofuels necessitates modeling of the ignition chemistry of an increasing range of substituted hydrocarbons; the biofuel field is not limited to production of alcohols or fatty-acid esters, but is increasingly aimed at designing biochemical pathways for the efficient conversion of biomass to a wide array of combustible organic molecules [151,152], many with nearly unexplored ignition or combustion chemistry.

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Table 1 Some recent theoretical and experimental determinations of ReOO bond dissociation energies for selected radicals. Radical

Alkyl and cycloalkyl radicals CH3

C2H5

n-C3H7 i-C3H7 (CH3)3C n-C4H9

sec-C4H9 (CH3)2CHCH2 (CH3)3CCH2 n-C5H11 cyclo-C3H5 cyclo-C6H11 Unsaturated/aromatic radicals C2H3

C6H5

2-Methylphenyl Resonance-stabilized radicals C3H3 C3H5 CH2C(CH3)CH2 CH2CHCHCHCH2 cyclo-C6H9 C6H5CH2 Xylyl Oxygenated radicals CH2CHO CH2C(O)CH3

CH3CHCHO CH3CHOH CH2CH2OH CH3OCH2

D0(ReOO) (kcal mol1)a Theory

Experiment

30.5 (QCISD(T)/CBS), 30.4 (CBS-APNO) [289] 30.4 (mean of CBS-QB3 and CBS-APNO, isodesmic corrections)c [138]

30.5  1.2 [289] 28.7  1.2b [511] 31.3  1.2b [130] 34.2  2 [130] 34.8  1.9c [511]

30.3 (CCSD(T)/TZ2P//CCSD(T)/DZP) [20] 33.9 [18,19] (33.5 adjust to model experiments [103]) 30.6 (UB3LYP/6-31G(d,p)) [502] 34.4 (CBS-Q) [398] 34.0 (CBS-QB3) [425] 33.3 (mean of CBS-QB3 and CBS-APNO, isodesmic corrections)c [138] 33.23 wCCSDT(Q)/CBS via focal point analysis [342] 34.9 wQCISD(T)/6-311þþG(3df,2pd) (33.9 adjust to model experiment [26]) 34.6  0.5 (CBS-QB3, isodesmic corrections) [138]; 34.8 (CBS-QB3) [512] 36.8 wQCISD(T)/6-311þþG(3df,2pd) [26] (34.8 adjust to model experiment [25]) 36.3  0.7 (CBS-QB3, isodesmic corrections) [138] 36.7 wQCISD(T)/6-311þþG(2df,2pd) [26] 37.8  0.7 (CBS-QB3, isodesmic corrections) [138] 33.2 wQCISD(T)/6-311þþG(2df,2pd) [26] 34.7 (CBS-QB3) [138] 34.7  1.0 (CBS-QB3, isodesmic corrections) [138] 35.2 wQCISD(T)/6-311þþG(2df,2pd) [26] 36.6  0.7 (CBS-QB3, isodesmic corrections) [138] 33.0 wQCISD(T)/6-311þþG(2df,2pd) [26] 34.6  0.5 (CBS-QB3, isodesmic corrections) [138] 38.1 (CBS-QB3) [110] 35.1 (“corrected” B3LYP)d [108] 36.9  0.9e (CBS-QB3) [429] 42.1 (wQCISD(T)/6-311þþG(3df, 2pd)) [318] 37.3 (wG2(MP2)) [105]

37.1  2.3 [130] 36.5  1.8 [130] 37.5  2.5 [511]

33.4 (PMP4//UHF) [154] 46.4 (G2M(RCC,MP2)) [445] 44 (CCSD(T)/CBS), 50.6 (MRCI þ Q/CBS) [448] 47.4 (G3) [458] 44.9 (G3B3) [160] 46.3 (G2M) [513] 50.2 (G3) [458] 48.6 (G3B3) [160] 48.7  3.1 (G3B3) [464] 19.2 CHCCH2eOO (18.2 adjusted to match Keq from experiment [158]), 20.1 CH2CCHeOO (MP2-corrected QCISD(T)) [159] 19.0 CBSQ//B3LYP/6-31G(d,p) [165] 21.7 (G3MP2) [102]

22.3 (CBS-QB3) [437] 22.9 (G3B3) [495,514] 22.3 para, 22.5 meta, 22.4 ortho (CBS-QB3) [441] 26.8 (G2) [187] 22.9 (CBS-QB3) [185] 28.9 (G2) [187] 25.0 (CBS-QB3) [186,188] 24.4 (QCISD(T)/cc-pVTZ) [189] 26.9 (G2) [187] 22.6 (CBS-QB3) [188] 37.5 (QCISD(T)/cc-pVNZ) [175] 37.4 (G3B3) [472] 33.5 (QCISD(T)/cc-pVNZ) [175] 33.8 (CBS-q), 34.1 (G2) [478] 29.3 (UB3LYP//6-311G(d,p)) [479] 36.5 (G2M(CC1)) [170]

17.2  1.0 [141] 13.4  1.2 [142] 19.2  1.0 [139] 21.8  1 [140]

23.4  1.2 [184] 24.1 (25.1)  0.5 [186]

Uncorrected results for 298.15 K (i.e., DrxnH298 (R þ O2 / ROO) ¼ D298(ReOO)) are given in italics; typical (DrxnH0  DrxnH298) corrections are w1 to 2 kcal mol1. Reported DfH298 (CH3OO) value converted to 0 K and combined with DfH0 (CH3) ¼ (150.0  0.3) kJ mol1 ( ¼ (35.85  0.07) kcal mol1) [515]. c Reported DrxnH298 (R þ O2 / ROO) converted to 0 K. d Ad hoc correction to B3LYP/6-31G(d) value of 31.3 kcal mol1: adjusted by the difference between B3LYP/6-31G(d) and wQCISD(T)/6-311þþG(3df,2pd) calculated energies of analogous stationary points in the n-propyl þ O2 system. e Reported DfH298 (ROO) ¼ -22.37 kcal mol1 combined with DfH298 (1-pentyl) ¼ (61.0  3.8) kJ mol1 ( ¼ (14.6  0.9) kcal mol1) from group additivity [516]. a

b

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381

Fig. 4. Representative transition state geometries for (a) direct HO2 elimination from ROO; (b) ROO 4 QOOH isomerization; (c) QOOH 4 OH þ oxetane; (d) HO2 elimination from QOOH. Note the longer CeO and less extended CeH bonds in the HO2 elimination transition state (a) compared to the transition state for ROO 4 QOOH isomerization (b).

Table 2 Relative barrier heights for ROO / QOOH isomerization and ROO / HO2 þ alkene elimination compared to the recommendations of Walker et al. [6] and Curran et al. [144,145]. Transition state

Recommended Ea [6]

[144,145]

ROO / QOOH isomerization 1,4p 36.6

29.7

1,5p

29.4

23.9

1,6p 1,7p 1,3s

25.1 21.5 42.1

21.1 23.9

1,4s 1,5s 1,6s 1,7s 1,3t 1,4t 1,5t 1,6t 1,7t

31.8 26.3 21.5 17.9 38.2 28.2 22.2 17.9 14.8

27.9 22.15 19.35 22.15 25.4 19.7 16.4 19.7

Cyclic ROO / QOOH isomerization 1,3scyclic 32.4 [271] 31.0 [436] 1,4scyclic 29.5 [271] 24.07 [436] 1,5scyclic 26.8 [271] 24.35 [436] 1,6scyclic HO2 elimination 1,4p 1,4s 1,4t 1,4hydroxylc 1,4paOH

Calculated DEz or DHz (ROO / transition state)

C2H5OO 38.2 [18] 36.4 [398] (37.8, well depth adjusted to experiment [103]); i-C3H7OO 35.4 [26] 35.3 [430]; sec-C4H9OO 37.0 [26] 35.3 [430]; t-C4H9OO 37.9 [26] 32.8 [98] 35.5 [430]; CH3CH(OH)OO 36.5 [472] 37.6 [175] n-C3H7OO 23.7 [26] 23.9 [512]; sec-C4H9OO 24.6 [26] 23.3 [430]; i-C4H9OO 24.3 [26] 23.7 [430]; neo-C5H11OO 22.6a [108] 23.8 [110] (22.8 adjusted to experiment [109]) n-C4H9OO 23.9 [26] 22.6 [429] 22.9 [430]; n-C5H11OO 23.8 [429] C2H5OO 42.1 [18,19] (41.7, well depth adjusted to experiment [103]); n-C3H7OO 40.9 [512]; n-C4H9OO 40.8 [429]; n-C5H11OO 40.8 [429] n-C3H7OO 33.6 [26] 32.1 [512] 31.9 [430], n-C4H9OO 33.4 [26] 31.9 [430], sec-C4H9OO 32.8 [26] 31.3 [430] n-C4H9OO 20.5 [429] 20.6 [430] 22.3 [26]; n-C5H11OO 20.0 [429] n-C5H11OO 19.4 [429]

iso-C4H9OO 29.7 [26] 28.4 [98] 28.7 [430]

cyclo-C5H9OO 40.6 [435]; cyclo-C6H11OO 39.2 [435] cyclo-C6H11OO 33.6 [105] 31.6 [435]; cyclo-C5H9OO 31.1 [435]; cyclo-C3H5 37.4 [318] cyclo-C6H11OO 27.2 [105] 25.1 [435]; cyclo-C5H9OO 24.4 [435] cyclo-C6H11OO 32.1 [105] 29.3 [435]

C2H5OO 30.9 [18] 30.5 [398] (30.5, well depth adjusted to experiment [25,103]); iso-C3H7OO 29.8 [26] (28.8 adjusted to experiment [25]); t-C4H9OO 30.2 [26] 27.5 [98]; sec-C4H9OO 30.7 [26]; CH3CH(OH)OO 30.4 [472] 32.0 [175] n-C3H7OO 29.7 [26] (31.1 adjusted to experiment [24,25,103]; sec-C4H9OO 30.9 [26]; cyclo-C6H11OO 31.8 (29.8 adjusted to experiment) [105]; cyclo-C3H5 46.0b [318] iso-C4H9OO 29.0 [26] CH3CH(OH)OO 11.4 [472] 14.0 [175] HOCH2CH2OO 27.6 [175]; (CH3)2C(CH2OH)OO 31.9 [111]

Other isomerizations 1,6benzylic ortho-xylylperoxy 23.0 [441] 22.6 [440] 1,5benzylic 2-methylphenylperoxy 26.5 [464] 1,3benzylic ortho-xylylperoxy 39.1 [441] 34.9 [440]; meta-xylylperoxy 38.6 [441] 32.1 [440]; para-xylylperoxy 38.5 [441] 32.8 [440]; 38.7 [437] benzylperoxy 32.8 [438] 1,5aromatic ortho-xylylperoxy 31.7 [441]; meta-xylylperoxy 31.9 [441]; para-xylylperoxy 31.7 [441]; benzylperoxy 32.4 [437] 1,4hydroxyl CH3CH(OH)OO 21.8 [472] 23.4 [175] 1,5hydroxyl HOCH2CH2OO 30.2 [175]; (CH3)2C(CH2OH)OO 21.9 [111]; (CH3)2C(OH)CH2OO 22.8 [111] HOCH2CH2OO 30.2 [175]; (CH3)2C(CH2OH)OO 28.4 [111] 1,4paOH CH3OCH2OO 17.7 (CBS-q) 20.1 (G2) [478] 25.0 [479] 21.8 [88] 22.5 [170] 1,5paeO CH3CH2OCH2OO 19.6 [88] 1,5saeO (CH3)2CHOCH2OO 17.9 [88] 1,5taeO 1,6paeO CH3OCH2CH2OO 21.6 [88] CH3CH2OCH2CH2OO 19.4 [88] 1,6saeO (CH3)2CHOCH2CH2OO 18.0 [88] 1,6taeO a Ad hoc correction to B3LYP/6-31G(d) value of 31.3 kcal mol1: adjusted by the difference between B3LYP/6-31G(d) and wQCISD(T)/6-311þþG(3df,2pd) calculated energies of analogous stationary points in the n-propyl þ O2 system. b Formation of cyclopropene þ HO2 from cyclopropyl þ O2 is endothermic. c Transition state to a weakly bound aldehyde/HO2 complex. A small additional barrier separates this complex from the separated products.

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Fig. 5. Notation for the transition states for ROO 4 QOOH isomerization up to 6-member rings and schematic depiction of the corresponding QOOH 4 OH þ cyclic ether transition states. The isomerizations are labeled according to the length. Note that it is not possible to form cyclic ethers from the products of a 1,3 internal H-atom transfer. The OH elimination from QOOH species formed in 1,4 isomerizations yields oxiranes, elimination from QOOH formed by 1,5 isomerizations to oxetanes, and the 1,6 ones to oxolanes. The 1,7 abstractions (not shown) lead to oxanes.

The oxidation of aromatic species or olefinic molecules can proceed via unsaturated (e.g., vinylic, allylic, or aromatic) hydrocarbon radicals. Many of these R þ O2 reactions are qualitatively different from reactions of saturated alkyl radicals, and do not display the ROO / QOOH pathways described above. For example, vinyl radicals [153e157], propargyl radicals [158,159], and aromatic radicals (phenyl [157,160], cyclopentadienyl [161]) tend to form CeC bond scission products, not HO2 or OH. The oxidation of alkylated aromatics will of course display a competition between the effects of the aromatic ring and the aliphatic side chain [162]. The formation of benzylic radicals is of particular interest because the reduced reactivity of resonance stabilized radicals with O2 can tend to inhibit ignition, an inhibition which is reduced when ortho-alkyl constituents permit internal “ROO % QOOH” isomerization pathways [163,164]. Allylic radicals form only weak ReOO bonds and tend to react mainly by an easily reversible association reaction [102,141,153,165,166]. Peroxy radicals formed from unsaturated hydrocarbon radicals with the radical site more remote from the unsaturation may have more facile isomerization pathways because of the possibility of internal abstraction of an allylic H atom, but isomerization where the ring transition state includes a double bond is thought to be disfavored [167]. 2.2.4. Oxygenated alkyl radical reactions with O2 Many biofuels are oxygenates, and describing their ignition chemistry therefore necessitates consideration of oxygenated radical reactions with O2. Again, the elementary kinetics of these reactions have largely been measured at temperatures relevant to tropospheric oxidation, where the peroxy radicals are the dominant chain carriers and are largely converted to alkoxy radicals by NO. As a result, relatively little has been directly measured concerning the dissociation and isomerization processes relevant to autoignition in oxygenated alkylperoxy radicals.

The peroxy radical chemistry related to low-temperature combustion of ethers, or at least dimethyl ether, has been studied in _ Þ radical reaction with O2 some detail. The methoxymethyl ðCH3 OCH 2 has been investigated experimentally by time-resolved absorption probing of products from photolytically initiated dimethyl ether oxidation [168e171]. Ogura et al. [88] devised rate rules for isomerization of ROO radicals derived from ether oxidation, using quantum chemistry calculations to predict the decrease in activation energy for internal hydrogen abstraction due to the eOe group (see Table 2). Tranter and Walker [83] measured the initial products in the oxidation of several ethers added to reacting H2/O2 mixtures at 753 K. They noted a reduced formation of ROO isomerization products relative to reactions of similar alkanes, which was attributed to more rapid thermal dissociation, by CeO bond fission, of the initial radicals derived from the ethers. Low-temperature autoignition chemistry of alcohols will proceed via hydroxyalkyl radicals and their reactions with O2. The OH substitution markedly affects the reactions of the resulting ROO species in a number of ways [172e174]. First, there is the possibility of (internal) abstraction of the hydroxyl H atom from the hydroxyalkyl-OO system. This internal abstraction can be very favorable; e.g., 1-hydroxyalkyl radicals predominantly form aldehydes upon reaction with O2. As shown in Table 2, the isomerization of ahydroxyalkylperoxy radicals via a “1,4hydroxyl” transition state has a very low barrier, and typically only a very small additional barrier separates the Q(O)OOH (which more resembles a weakly bound aldehyde.HO2 complex) from the aldehyde þ HO2 products [175].

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The facility of H atom transfer from the hydroxyl group may also have an considerable impact on OH-initiated oxidation of alkenes, as pointed out by Sun et al. [111] for OH-initiated isobutene oxidation and by da Silva et al. [176] for the tropospherically critical case of isoprene oxidation. Second, the a-CeH bonds are weakened, as can be seen by comparing the 1,4p isomerization in ethylperoxy to the analogous “1,4paeOH” isom_ so that, for example, b-hydroxerization in HOCH2 CH2 OO, yalkylperoxy radicals may preferentially eliminate HO2 to form an enol rather than a b-hydroxyalkene. To illustrate, in the _ oxidation of 1-hydroxy-2-methylprop-2-yl, ðCH3 Þ2 CCH 2 OH, the formation of isobutenol (2-methyl-1-buten-1-ol, (CH3)2C] CHOH) is substantially more favorable than formation of 2methyl-2-buten-1-ol, CH2]C(CH3)CH2OH [111].

Finally, the relative instability of the b-hydroxyalkyl radicals may limit their participation in autoignition chemistry, as they dissociate at low temperatures to OH þ alkenes [80,81], e.g.:

Esters are the other prominent class of biofuels, but there has been little direct study above room temperature of the elementary reactions of ester-derived alkyl radicals with O2. For the simple purpose of modeling ignition delays, the chemistry of the alkyl chain seems to dominate [91,92], although the negative temperature coefficient region appears to be affected by the ester functionality [177]. Modeling of the ignition chemistry of esters has been accomplished principally by estimated rate coefficients drawn by analogy with alkane systems e there is a pressing need for direct investigations of the elementary reactions of ester autoignition in the relevant temperature range. Reactions of oxy radicals (radicals with eO functional groups) with O2 are of limited importance in autoignition because of relatively rapid dissociation of most alkoxy radicals [178]. Nevertheless, it is possible that the hydroxyalkyl radicals formed by (even more rapid) isomerization of larger alkoxy radicals could play a role in the temperature range of low-temperature autoignition [178e182]. For example, Blin-Simiand et al. [182] have suggested isomerization and secondary oxidation of oxy radicals derived from the dissociation of ketohydroperoxides, based on their measurements of multiply keto-substituted hydroperoxide species in dodecane oxidation. Furthermore, resonance-stabilized radicals with substantial carbon-radical _ CHO) [183e185] character, such as vinoxy (formyl methyl, CH 2 and substituted vinoxy radicals such as acetonyl radical, _ CðOÞCH [186e189], are something of an exception to the CH 2 3 instability of oxy radicals. Such radicals may be formed in the oxidation of carbonyl-containing fuels [190] or may form in the decomposition of ketohydroperoxide products of QOOH þ O2 reactions [191].

383

2.3. Reactions of the hydroperoxyalkyl radicals (QOOH) The fate of hydroperoxyalkyl radicals QOOH is central to the modeling of autoignition. However these critical species have never been experimentally observed, so the information about their reactions and thermochemistry is entirely indirect or theoretical. The key processes for these species are dissociation (e.g., producing OH or HO2), isomerization back to the ROO form, and the critical chain-branching reaction with O2 (see Fig. 1). Understanding the balance between dissociation and isomerization may be key to experimentally determining the isomerization rate constant for the ROO / QOOH step. The extensive oxidation studies of Walker and coworkers [6], carried out by addition of alkanes to H2/O2 mixtures, has generated a systematic database of end-product branching from the initial oxidation steps of a series of alkanes, which can in principle be related to relative rates for the ROO / QOOH isomerization. An absolute measurement of any one isomerization rate coefficient would therefore yield absolute rate coefficients for the whole series. As described in Section 5.1.2, the absolute ROO / QOOH isomerization rate constants remain uncertain. At the present time, with no direct experimental means to detect QOOH, state-of-the-art kinetics theory is the most accurate means of determining reaction rate coefficients and thermochemistry of the QOOH species. The reaction of the QOOH radicals with O2, sometimes referred to as the “second O2 addition,” is the source of low-temperature chain branching. Calculations of hydroperoxypropyl [192], hydroperoxyethyl [193] and hydroperoxyneopentyl [110] radical reactions with O2 have been reported by Bozzelli and coworkers. For example, in the hydroperoxyneopentyl radical reaction with O2, Sun and Bozzelli [110] found an energetically accessible pathway to the chain-branching products, with barriers lying some 10 kcal mol1 below the reactants.

Such topography on the OOQOOH surface may imply rapid chainbranching reactions of QOOH with O2. Andersen and Carter [194e197] have calculated a number of chain-branching pathways related to the second O2 addition in dimethyl ether oxidation. Although DeSain et al. [108] saw indications of QOOH-related chain branching in the neopentyl oxidation, and Fernandes et al. [147] found strong circumstantial evidence of a fast QOOH þ O2 chain branching reaction in high-pressure cyclohexyl oxidation, the experimental characterization of this crucial step remains, as for all of QOOH chemistry, maddeningly indirect. The stabilized ketohydroperoxide intermediates of QOOH þ O2 have been observed in alkane oxidation systems by mass spectrometry and UV/IR spectroscopy [181,182,198]. However, recently Battin-Leclerc, Qi, and coworkers [28] provided additional experimental corroboration of the low-temperature chain-branching mechanism by observing, e.g., 4-hydroperoxybutan-2-one (below), with synchrotron photoionization mass spectrometric analysis of n-butane oxidation, directly sampled from a jet-stirred reactor.

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Besides confirming critical mechanistic assumptions about lowtemperature chain branching, these observations may open the way for direct interrogation of QOOH þ O2 kinetics via detection of the ketohydroperoxide products. 2.4. Other reactions of ROO and HO2 Although the isomerization and dissociation of ROO and QOOH are major pathways for autoignition chemistry, other reactions of the peroxy radicals are important in modeling low-temperature combustion and autoignition. Slow chain-propagating reactions such as the reactions of ROO [199] or HO2 [100] with fuel molecules can affect autoignition. As described in the introduction, the alkyl þ HO2 reactions could convert the relatively inert HO2 radicals to highly reactive OH radicals. Addition of the HO2 radical to the radical site of the alkyl radical forms a hydroperoxide molecule, which then can decompose; the possible bimolecular channels include the formation of RO þ OH. However, other possible product channels, like RH þ O2 or alkene þ H2O2, are chain-terminating. The branching among these channels remains somewhat speculative. Tsang and Hampson [200] recommend a dominant CH3 þ CH2O þ OH channel in the case of ethyl þ HO2, and Tsang proposes exclusively similar termolecular OH-forming channels in the reactions of propyl and butyl radicals with HO2 [201,202]. Essentially no direct experimental information on R þ HO2 reactions is available above room temperature, although Lodhi and Walker [166,203] derived rate coefficients for allyl þ HO2 based on modeling of 4,4-dimethylpent-1-ene oxidation between 673 K and 773 K. If one assumes that the alkyl radical and HO2 associate to form an excited alkylhydroperoxide, then breaking the OeO bond may be expected to be the dominant dissociation channel of the adduct [204]. The nature of the products of self-reactions and cross-reactions of alkylperoxy radicals is a subject of active study in tropospheric chemistry [205e210]. Under the low temperature and high-pressure conditions of autoignition, substantial ROO radical concentration can build up, lending potential importance to this reaction in autoignition chemistry. The reaction of two ROO species can proceed via a chainpropagating pathway producing two oxy radicals, ROO þ R0 OO / RO þ R0 O þ O2 or a chain-terminating pathway forming an alcohol and a carbonyl species, e.g., ROO þ R0 OO / ROH þ R-H¼O þ O2. The understanding of the mechanism of this reaction is by no means complete; Dibble [207] highlighted such reactions as one of the failures in quantum chemical investigations of atmospheric chemistry reactions. Direct experimental information on kinetics and branching fractions for ROO þ ROO reactions are largely absent above about 373 K [211,212]. However, studies of the temperature dependence of the branching fractions for several ROO self-reactions suggest that the radical channel increases in importance with increasing temperature [29]. Similarly, the reactions of alkylperoxy radicals with HO2 have been investigated primarily because of their importance in tropospheric chemistry [213e218]. Reactions of HO2 with ROO derived

from hydrocarbons, saturated or unsaturated, appear uniformly to produce the corresponding ROOH and O2, at least near room temperature. At higher temperatures the dissociation of the hydroperoxide (ROOH) product may also be feasible. For substituted ROO, ROOH þ O2 are not always the only products, and tropos_ or pherically relevant reactions of acetonylperoxy ðCH3 CðOÞCH2 OOÞ _ radicals with HO2 have been found to acetylperoxy (CH3 CðOÞOO) form OH radicals as products [215,216,219]. The potential significance of similar pathways in low-temperature combustion and autoignition of, for example, oxygenated biofuels, has not been thoroughly studied. Formerly it was assumed that the experimentally observed negative temperature dependence of ROO þ HO2 reactions indicated that it proceeded mainly via a hydrotetroxide (ROOOOH) intermediate. However, recent theoretical works [220e223] point out that this is not necessarily the case. At room temperature and slightly above, the main reaction channel is the formation of a weakly bound complex (ROO/HO2) followed by a concerted O2 elimination/hydrogen abstraction step on the triplet surface to form the ROOH þ O2 products. However, this may be the only aspect of the mechanism where there is a consensus. Fig. 6 shows a schematic of the reaction pathways, including the controversial portions. The role of weakly bound complexes will certainly be reduced at temperatures relevant to autoignition, but the possibility of reactions on the singlet surface and the kinetics and product branching fractions of the ROO þ HO2 reactions at elevated temperature appear to be almost completely unexplored. 3. Key experimental techniques The measurement of kinetics and branching fractions for the reactions of peroxy and hydroperoxy radical species that are at the core of the autoignition mechanism is experimentally challenging because of the inherent complexity of the “elementary” reactions, for example in the case of R þ O2; because of the difficulty in preparing and isolating individual reactions, for example in the case of QOOH reactions; and because of the small rate coefficients for many important reactions, for example reactions of HO2 or ROO with stable molecules. In the last decade investigations of these reactions have applied improvements in experimental methods and, more crucially, have exploited innovative capabilities in electronic structure theory and theoretical kinetics to relate, with increasing rigor, fundamental properties of potential energy surfaces to experimental observations. The most powerful combination is a tightlylinked simultaneous theoretical and experimental approach, in which the experimental measurements validate the emerging theoretical model and the computational results are used to design new experiments that best constrain that model. 3.1. “High-level” phenomena Modeling the overall phenomenon of autoignition is the technological application for the fundamental kinetics investigations considered here. Detailed measurements and careful modeling of chemistry effects on device-scale autoignition events, for example in HCCI engines [224e228], while not providing rate constant determinations, can be extremely useful in guiding research into elementary reactions. Similarly, the measurement of bulk reaction in rapid-compression machines [163,229e238], flow reactors [239e243] or jet-stirred reactors [4,28,244e248] has much in common with the classical kinetics methods described below, but these techniques have been more generally used to validate large mechanisms, and conditions have typically not been designed to isolate elementary reactions. Shock-tube techniques are of course the linchpin of high-temperature reaction kinetics [249,250], predominantly responsible for experimental data on elementary

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reactions for high-temperature oxidation [251e253], but less useful in the 600 Ke900 K region most important for the chemistry considered here. Shock tubes have also long been used for ignition delay measurements over a wide temperature range [249,254]; recent work [255e259] has continued to improve the precision and accuracy of such determinations, and they are extremely valuable validation tools for ignition models [260].

3.2. Classical kinetics methods The development of the mechanism of low-temperature oxidation and autoignition in terms of elementary reactions was accomplished mainly through systematic and thorough studies using what might be termed “classical kinetics” techniques, that is to say, analysis of stable species concentrations throughout the course of a well-controlled set of reactions. These studies have been reviewed previously [5,6]. The contributions of Baldwin, Walker and their coworkers [6,9,62,83,84,94,95,97,100,261e274] have been especially influential. They used several thermal initiation methods designed to isolate aspects of low-temperature combustion [6], and monitored the product concentrations gas-chromatographically. For example, they used aldehyde (RCHO) oxidation to initiate ethyl þ O2, 1-propyl þ O2, and 2-propyl þ O2 reactions over a wide temperature range, and employed the decomposition of tetramethylbutane/O2 mixtures as a means to produce HO2 radicals via the sequence

Of particular importance is their technique of adding very small amounts of hydrocarbons to thoroughly characterized reacting H2/ O2 mixtures at 753 K [261,262], which has enabled measurements of rate coefficients for OH, H, and HO2 attack on fuel species as well as generated the most systematic experimental data available on the subsequent R þ O2 reactions. The photolytically initiated oxidation of ethane and propane has been measured in a series of exceptionally thorough investigations by Kaiser and coworkers [13e16,275e277]. These experiments employed steady-state ultraviolet photolysis of Cl2/ alkane/O2 mixtures, with gas-chromatography/mass spectrometry (GC/MS) [13e15,275,276] or Fourier-transform infrared (FTIR) [16,277] spectroscopic analysis of the product concentrations. Particularly notable is the exquisite investigation of the ethyl þ O2 reaction [275] where Kaiser used the ratio of products

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from the competing ethyl þ O2 and ethyl þ Cl2 reactions to establish the onset of thermal production of HO2 þ ethene from stabilized ethylperoxy radicals. At low temperature the formation of ethene arises from chemical activation, i.e., the formally direct reaction

_ CH3 CH 2 þ O2 /HO2 þ C2 H4

(12)

As the temperature increases this channel is a larger fraction of the total reaction of ethyl with O2 and the ethene (or HO2) yield increases slowly with temperature [13,21,278,279]. However, as the _ temperature rises above the point where dissociation of CH CH OO 3

2

becomes fast relative to its other removal reactions, the major product of the C2H5 þ O2 reaction at low temperature no longer _ , and the yield of the bimocontributes to the removal of CH3 CH 2 lecular products, principally HO2 þ C2H4, jumps dramatically [13,21]. This increase in ethene yield is partially because of increased direct elimination of HO2 from the ethylperoxy radical _ back to reactants, and partly because of dissociation of CH3 CH2 OO followed by reaction (12). However, in Kaiser’s scheme this latter path is in competition with the reaction

_ CH3 CH 2 þ Cl2 /Cl þ C2 H5 Cl so that if ethene is formed via reaction (12) (including reactions of ethyl formed by redissociation of ethylperoxy radicals) then chloroethane must also be formed proportionally. Kaiser observed that the ratio of ethene to chloroethane product, a quantity he denotes as b, more than quadrupled between 450 K and 500 K, as shown in Fig. 7. This dramatic result demonstrates that an additional source of ethene e the dissociation of stabilized ethylperoxy radicals directly to HO2 and ethene e emerges at higher temperature. 3.3. Time-resolved kinetics Pulsed-photolysis methods were applied to reactions of alkyl radicals with O2 by several groups that employed photolysis to initiate the reactions and mass spectrometry to follow the course of the reactions [130,136,141,142,278e285]. Bayes and coworkers [280,282,284,285] investigated many R þ O2 reactions, but primarily near 300 K. Plumb et al. [286] used a discharge flow reactor and mass spectrometric analysis to the study the reaction of ethyl þ O2 at 295 K. The laser photolysis / photoionization mass spectrometry (PIMS) work of Slagle and Gutman and coworkers [130,136,278,279,283] has been the most influential such set of experiments for autoignition chemistry because of their systematic

Fig. 6. Schematic mechanism for the ROO þ HO2 reaction, based on Refs. [220,221,223].

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Fig. 7. Plot of the ratio (b ¼ C2H4 / C2H5Cl) in the photolysis of Cl2/ethane/O2 mixtures as a function of temperature [275]. The dotted line shows the predicted ratio if the only significant dissociation of ethylperoxy was to the ethyl þ O2 reactants and all of the C2H4 was produced in the formally direct chemical activation path, reaction (12). The solid line is the prediction of a kinetic model that includes the direct elimination of HO2 from the ethylperoxy radical. Reprinted with permission from reference [275]. Copyright 2002 American Chemical Society.

investigation of alkyl þ O2 % ROO equilibrium constants [130] and because of their thorough characterization of the product channels in the ethyl þ O2 reaction [278,279]. The technique employs pulsed-laser photolysis of a reactant mixture that is flowing through a temperature-controlled quartz tube. A small orifice in the side of the tube allows continuous sampling of the reacting mixture by a photoionization mass spectrometer. Recently Osborn, Taatjes and coworkers [287e292] have augmented the laserphotolysis PIMS methodology with tunable synchrotron photoionization and multiplexed mass spectrometry. The use of tunable synchrotron photoionization is a powerful method to gain isomeric selectivity in mass spectrometry that has proven exceptionally valuable in flame chemistry studies [11,293e301], but has just begun to be applied to chemical kinetic problems related to autoignition [28,116,175,288,291,302,303]. The simultaneous detection of “all” masses by dual-focusing sector mass spectrometry or time-of-flight mass spectrometry provides a multiplex advantage over a single-mass detector such as a quadrupole mass spectrometer, and also probes even unanticipated side reactions or unexpected reaction products. The synchrotron-PIMS kinetics machine acquires a threedimensional data set [291], measuring ion signal as a function of mass-to-charge ratio (m/z), time relative to the photolysis laser, and ionizing photon energy. Fig. 8 schematically portrays such a data set, taken for the reaction of ethyl radicals with O2, initiated by the photolysis of diethyl ketone. The data can be integrated over any one independent variable, as depicted by the two-dimensional slices in Fig. 8. Integrating over a range of photon energies gives a mass spectrum as a function of time (left vertical plane in Fig. 8). Further integration of this 2-D image over one value of m/z gives the familiar trace of a species concentration as a function of kinetic time (relative to the pulsed-photolytic initiation). Starting from the 3-D dataset and integrating over kinetic time (the horizontal plane in Fig. 8) yields a mass spectrum as a function of ionizing photon

Fig. 8. Schematic representation of the three-dimensional dataset [291] from laser photolysis/synchrotron PIMS study of diethylketone (m/z ¼ 86) photolysis in the presence of O2. The left vertical panel is integrated over photon energy, giving a timeresolved mass spectrum. The horizontal panel is integrated over a range of reaction times, giving a photoionization efficiency spectrum of the chemical constituents. The acetaldehyde (m/z ¼ 44) and ethanol (m/z ¼ 46) products of the ethylperoxy selfreaction are evident. The m/z ¼ 29 signal as a function of time and ionizing photon energy, shown as the right vertical panel, contains signal both from direct ionization of ethyl radical and from dissociative ionization of ethylperoxy radical [289]. Adapted from ref [291], reproduced by permission of the PCCP owner societies.

energy, that is, a photoionization efficiency spectrum for each mass. Such data can be used to identify isomeric species by their ionization energy and the shape of their photoionization spectra. Finally, the 3-D dataset integrated over a single mass (right vertical plane in Fig. 8) shows the change with time of the photoionization efficiency spectrum. These changes can reveal isomerization processes, for example [304], or distinguish direct ionization of reactants in the presence of dissociative ionization of a product species with a different kinetic behavior [289]. Some disadvantages of the mass-spectrometric detection are the limitation on pressure because of the need for diffusive mixing in the side-sampled reactor and the limitation on time resolution because of the velocity spread in the sampling beam [305,306]. Laser photolysis coupled with optical detection overcomes some of these difficulties but with considerable loss of generality. Such techniques are best suited for relatively fast reactions and for detection of a small set of product species. Maricq and coworkers [171,307] have used infrared laser absorption probing to follow product formation (formaldehyde, methyl formate, formic acid) in Cl-initiated oxidation of dimethyl ether. Pilling and coworkers [308] employed laser-photolytic initiation with absorption spectroscopy to characterize association of alkyl radicals with O2 [309,310] or laser-induced-fluorescence detection of OH to follow isomerization and dissociation of neopentylperoxy radicals [106,107]. Munk et al. [311] used pulse radiolysis and chemical activation methods for radical generation and UV-VIS absorption detection of the peroxy to study the ethyl þ O2 association reaction. Atkinson and Hudgens [312] employed laser photolytic Cl-initiated oxidation of ethane to study the association reaction, monitoring ethyl and ethylperoxy by cavity ringdown spectroscopy. Recently association reactions of alkyl and substituted alkyl radicals with O2 have also been investigated at high pressure. Delbos et al. [184] studied the vinoxy oxidation reaction at pressures up to 46 bar in the temperature range from 298-660 K using laser photolysis and LIF detection and derived equilibrium constants for

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the association. Hassouna et al. [186] carried out similar experiments (up to 10 bar pressure) and analysis for the 1-methylvinoxy (i.e., acetonyl) association with O2. Troe and coworkers [313e317] studied the association reactions of H, CH3 and CCl3 þ O2 at high pressures, recently to temperatures up to 950 K and to pressures up to 1000 bar in order to provide high temperature fall-off data and explore the high pressure limit. They used laser photolysis to generate the alkyl radicals in the presence of oxygen and employed conventional UVeVIS lamp absorption detection of the peroxy radicals to follow the reaction progress. One main problem in employing conventional UV-absorption spectroscopy lies in isolation of the particular reaction of interest because of the spectral overlap of multiple species in the same wavelength region. To solve this one needs to use “clean” radical precursors. The most common choice therefore is to use azo-alkanes for most small alkyl radicals if feasible and NH3 for H-atom generation in order to significantly reduce the influence of spectral overlap in the UVeVIS region. In the Taatjes lab at Sandia National Laboratories’ Combustion Research Facility [21e25,103e105,108,147,175,318,319], and by Tezaki and coworkers in Toyama [168e170], laser-photolytic Clinitiated oxidation of fuel molecules has been investigated by laser absorption or laser-induced-fluorescence detection of HO2 or OH products of the R þ O2 reactions. In Toyama the ROO radical has also been observed [170]. The absorption experiments have been carried out in a reaction cell specifically designed to provide long pathlength absorption with the overlap region between photolysis and probe lasers confined to a central temperature-controlled region of the reactor [320]. The laser-induced-fluorescence experiments used a traditional crossed-beam low-pressure cell [103,104] or a high-pressure LIF cell [147] based on a Göttingen design [321]. The synchronous start of reaction afforded by pulsedphotolytic initiation, combined with the time resolution of the optical detection, allows different product formation mechanisms to be kinetically distinguished. For example, Fig. 9 shows the evolution of HO2 from Cl-initiated oxidation of cyclopentane [23] at two temperatures. At low temperature the R þ O2 reaction makes a small amount of HO2 promptly by the formally direct path through chemically activated cyclo-C5H9OO. The HO2 is then consumed on a longer timescale by self-reaction and reaction with ROO. At higher temperatures HO2 is also formed on a second timescale, via the thermal dissociation of stabilized cyclopentylperoxy radicals. A similar kinetic discrimination of formally direct channels from sequential thermally activated channels has also been measured in OH formation, e.g. from neopentyl þ O2 [109] and cyclohexyl þ O2 [105], at pressures up to 20 bar [147]. 3.4. Coordinated theoretical and experimental approach Experimental constraints on investigations of R þ O2 or subsequent key steps in autoignition like the reactions of QOOH with O2 may preclude isolation of individual reactions. Rather, they require study of well-characterized small sets of reactions, still far fewer reactions than a comprehensive oxidation mechanism. This bridging region between isolated reactions and full “high-level” oxidation studies might be termed “sub-mechanism” chemistry (despite possible ambiguity arising from the multiple senses of the word “mechanism” in chemical kinetics and modeling). Additionally, even many “elementary” reactions that participate in the “submechanism,” like R þ O2, are too complex to be described by a simple rate coefficient. The cooperation of theory has become essential in extracting the fundamental chemistry from such experimental systems. In our view one of the most powerful strategies is to employ state-of-the-art quantum chemistry and rigorous theoretical kinetics to describe the key reactions of a system, place these computed rate coefficients into a kinetic

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Fig. 9. Production of HO2 in Cl-initiated oxidation of cyclopentane at two temperatures [23]. The HO2 concentration is normalized to the initial Cl atom concentration. At low temperatures the only HO2 produced is via a chemically activated cyclopentylperoxy radical; this formally direct channel results in prompt HO2 formation. At higher temperature this prompt HO2 persists, but an additional slower formation mechanism is observed that reflects thermal dissociation of the cyclopentylperoxy radical both back to cyclopentyl þ O2 reactants and on to HO2 þ cyclopentene products.

mechanism, and then to adjust fundamental features of the potential energy surface, principally energies of stationary points, within the estimated computational uncertainties in order to model the primary data of as many experiments as are available. As phenomenological rate constants within the reaction system are often correlated, adjusting stationary point energies rather than individual rate constants enforces internal consistency in the resulting model for the complex reactions. More importantly, the stationary point energies or other fundamental properties of the potential energy surface must be the same for all conditions, so validation of these global reaction characteristics rather than phenomenological rate constants gives fundamentally more reliable prediction for other temperatures or pressures. This strategy is however not as simple as it sounds. The approach of adjusting stationary point energies must be used with caution, first ascertaining that all relevant transition states have been characterized, for example, and paying careful attention to deficiencies and uncertainties in the quantum chemistry methods. Uncertainties in the quantum chemical characterization of the critical points come from various sources: often a large component is the inaccurate localization of the transition states, in addition to the inherent uncertainties of the quantum chemistry, and (as frequently occurs) multi-reference character. The estimation of uncertainties in quantum chemical methods is often carried out by comparison to “test sets.” Although the uncertainties in such model chemistries are not simply transferable to different sets they are generally sufficient to guide the adjustment of energies for the accuracy of the commonly used methods. More accurate methods may demand more careful uncertainty estimates. It is, moreover, imperative that the theoretical kinetics is sufficiently accurate to allow meaningful determinations of the stationary point energies. The following section describes the theoretical machinery required to make rigorous rate coefficient determinations.

4. Key theoretical methods Computational and theoretical methods have become an integral part of elementary chemical kinetics in the last two decades

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Fig. 10. The best strategy to increase the accuracy of the electronic structure calculations is to balance the level of electron correlation and basis set (diagonal yellow arrow, right side). The best strategy for accurate theoretical kinetics is to balance the levels of the microcanonical rate coefficient model and the collision model (diagonal blue arrow, left side). The accuracy of the calculated rate coefficient is increased most efficiently if the theoretical kinetics and the electronic structure calculations are also in balance (vertical green arrow)

due to the enormous advances in both quantum chemistry and reaction rate theory. Models have always been used by experimental kineticists to interpret their measurements. However, the easy access and widespread use of quantum chemistry program packages (e.g. Gaussian [322], MOLPRO [323], ACES II [324] etc.) has revolutionized kinetics studies. Presentation of, or reference to, the potential energy surface (PES) of the reaction under study has become a standard part of experimental publications. The synergy between theory and experiment is even more fundamental in a number of cases: it is impossible to analyze some kinetic traces without a sound theoretical background. Using advanced theoretical methods it is now possible to obtain ab initio rate coefficients. The fidelity of calculated rate coefficients approaches that of the experimental ones in some cases; by changing a very limited number of parameters complete agreement often can be achieved. However, the great advantage of the theoretical methods is that they enable the extrapolation of the kinetics data to the full pressure (103e108 Pa) and temperature (300e3000 K) range encountered in combustion studies. It is not merely arduous, but simply impossible to study an elementary reaction over the whole PeT parameter space experimentally. Furthermore, no direct experimental investigation of any of the ephemeral QOOH species has yet been accomplished, whereas there are already several calculations on their properties and reactions with oxygen [110,192e194,325,326]. Another area where theory is essential is the investigation of product branching fractions, because most experimental kinetics techniques follow the time dependence of only one species. In this section we describe a selected set of key theoretical methods typically used to study elementary reactions related to low-temperature autoignition. State-of-the-art theoretical schemes are presented as well as future directions and we also describe the theoretical challenges related to the different classes of reactions. 4.1. Reliability of ab initio rate coefficients Calculation of accurate rate coefficients requires accurate PES’s coupled to good reaction rate theory. There are two very important features of any kind of theoretical schemes. The first is the ability to assess errors due to the unavoidable simplifications and neglected effects. The second is the prediction of the next simplest and computationally cheapest modification with the largest improvement in accuracy. Quantum chemistry has a well-

established answer for these questions, which is usually depicted in a plot with two axes (see Fig. 10, right side). The level of electron correlation increases along the horizontal axis, which lists the electronic structure methods from the HartreeeFock (HF, no electron correlation) to the full configuration interaction (FullCI) method, where all types of correlations (static, non-dynamic and dynamic) are taken into account. The size of the applied basis set increases from top to bottom; at the bottom of each column the calculated values correspond to the complete basis set limit, CBS [327] (HF limit, MP2 limit etc.). It is also well known that the most efficient way to improve the accuracy of the calculated values is to balance the improvement in electron correlation and basis set. Focal point analysis [328e331], in particular, applies elaborate schemes to extrapolate to the FullCI/CBS limit, by (among other things) prescribing the elements and order of the horizontal and vertical axes. However, it should be emphasized that relative energies can still be reliably calculated with methods far short of Full-CI. Theoretical kinetics lacks such a straightforward roadmap for improvement, mainly because it is by nature a more complex problem. Even so, with some simplifications it is still possible to show the major challenges in analogy with quantum chemistry (see left side of Fig. 10). The horizontal axis shows the range of theoretical levels that can be used for the calculation of the microscopic rate coefficient, k(E) (or k(E,J) in the microcanonical, J-resolved case). These are variants of transition-state theory in the order of increasing sophistication level, ranging from RRK to variable-reaction-coordinate transition-state theory (VRC-TST [133,332,333]). A very different, non-statistical approach to obtain k(E) is to use trajectory calculations, which would give an alternative horizontal scale ranging from classical trajectories through semiclassical dynamics and quantum dynamics to quantum scattering theory. The vertical axis stands for the microcanonical models that describe the governing equations of a reaction at the microscopic level. Models for the collisional physics are represented as a set of differential equations describing the time-dependence of the microscopic populations, with terms accounting for TST (movement along the reaction coordinate) and for the energy transfer between the reaction species on the PES and the bath gas (movement “perpendicular” to the reaction coordinate). These models, starting from the simple Lindemann-Hinshelwood scheme, are approximations of the 2D (meaning energy and total angular momentum resolved) master equation (ME).

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Unlike in quantum chemistry, there are no rigorous schemes for systematic improvements of theoretical kinetics. However, it is still true that a balanced movement along the diagonal is the most desirable direction. It is even more important to point out that in order to obtain accurate rate coefficients, the whole of the electronic structure calculation (diagonal yellow arrow on the righthand side of Fig. 10) and the whole of the theoretical kinetics calculation (diagonal blue arrow on the left-hand side of Fig. 10) have to be balanced, and moving along their resultant direction (vertical green arrow in the center of Fig. 10) is optimal. Errors from electronic structure and errors from kinetic methodology should be comparable; too often high-level quantum chemistry is “thrown away” on qualitative kinetics calculations or detailed and rigorous theoretical kinetics is carried out with inaccurate characterization of the potential energy surface.

4.2. Level of theory needed to describe key autoignition reactions accurately It is not the purpose of this work to give a detailed overview of all the methods used in theoretical chemical kinetics for the calculation of rate coefficients. This topic is covered in extensive reviews and monographs of their own (see for instance references [148,149,334e338]). There are also reviews focusing on the aspects related to combustion chemistry [339,340], with probably the latest being that of Pilling [341]. Therefore, in this section we present only the major theoretical challenges encountered for our reactions of interest, and provide our somewhat subjective view on the appropriate level of theory required. 4.2.1. Electronic structure calculations The requirements for the electronic structure calculations are demanding, because 1 kcal mol1 inaccuracy in critical stationary point energies can lead to large errors (or uncertainties) in the calculated rate coefficient [342,343]. Often, the energy barriers of the various pathways differ by only a few kcal mol1; precise barrier heights are therefore indispensable for calculating branching ratios. Because most systems of interest have at least four, but usually more, heavy atoms, and there can easily be 10 or even more relevant stationary points on the PES, the cost of the electronic structure calculation has to be limited. For intermediate size systems it is common to aim for methods that have 2e3 kcal mol1 uncertainty; this is usually achieved by the combination of a geometry optimization using a lower level method and an energy calculation using a high-level one. Geometry optimization and frequency calculations are typically carried out with DFT (usually using B3LYP functional [344,345]) or MP2 [346] methods, and normally using d,p-polarized split valence Gaussian basis sets (e.g. 6-311þþG(d,p)). However, the recent comparative study by Harding et al. [343] strongly suggests that the CASPT2 method consistently gives better geometries and frequencies than two popular DFT methods. Vibrational frequencies are sometimes scaled when thermodynamic properties are calculated; however, it was shown that for ZPE correction the unscaled frequencies are more appropriate [347]. Accurate (within 23 kcal mol1) ab initio energies are usually obtained by QCISD(T) or CCSD(T) methods employing infinite-basis-set extrapolation schemes on Dunning’s correlation consistent basis sets [348]. The extrapolation method suggested by Martin [349] and Feller and Dixon [350],

EN ¼ Elmax  B=ðlmax þ 1Þ4 ; is popular. EN is the infinite-basis-set energy, B is a least-squares fit parameter (not needed for the extrapolation) and lmax ¼ n is the maximum component of angular momentum in the cc-pVnZ basis set.

Fig. 11. Comparison of various electronic structure calculations [356] against the benchmark calculations of Lynch and Truhlar [357]. The calculated barrier heights for each method are ordered by increasing absolute error relative to the benchmark calculation. The x-axis, “Nth smallest error,” refers to this ordering e e.g., the points at x ¼ 15 depict the 15th smallest error in the test set for each electronic structure method.

For larger systems, these methods are computationally too expensive, and often lower-level, so-called composite methods have to be used, such as G2(MP2) [351], G3 [352], G3B3 [353], CBS-q [354], CBS-Q [354], CBS-QB3 [355] etc. These complex energy calculations involve a series of pre-defined optimization and energy calculations. Some authors prefer to use their own highlevel energy correction schemes (see e.g. [26,105]), which are often slight modifications of the standard, above-mentioned composite methods, and are frequently referred to as “G2-like energies”. The estimation of uncertainties in quantum chemical calculations is not necessarily straightforward, but to give a sense of the magnitude of errors arising in the calculated energies employing typical methods we present the unpublished results of Senosiain et al. [356]. Lynch and Truhlar [357] have compiled a benchmark database of 20 hydrogen abstraction reactions, for which the classical (i.e. zero-point-exclusive) forward and reverse barrier heights are well known. Senosiain et al. [356] tested UB3LYP (U/R) MP2, (U/R)CCSD(T), and (U/R)QCISD(T) electronic structure methods, with augmented and non-augmented cc-PVTZ and cc-pVQZ basis sets extrapolated to the infinite basis-set limit, on 17 elements of the Lynch and Truhlar dataset. These single-point calculations were based on geometry optimizations at the UB3LYP//6-311þþG(d,p) or UMP2//6-311þþG(d,p) level of theory. A representative selection of the results is shown in Fig. 11. It was found that 3/4 of the RQCISD(T)//UB3LYP calculations have less than 1.4 kcal mol1 difference compared to the “exact” values. Interestingly, the RCCSD(T)// UB3LYP calculation performed slightly worse. The same trend is observed when the RQCISD(T)// UMP2 and the RCCSD(T)//UMP2 methods are compared, but the difference is smaller. Finally, energy calculations at the B3LYP and MP2 level of theory have a significantly larger error, reaching 10 kcal mol1 in some cases. The CCSD(T) method is in general thought to be “superior” to the QCISD(T) method, because QCISD(T) is a slightly truncated version of CCSD(T). However, the CCSD(T) wavefunction is still a truncated representation of the Full-CI limit; therefore, it is possible that the QCISD(T) method performs slightly better for certain problems. The typical error estimate of w2–3 kcal mol1 from the QCISD(T)/ cc-pVNZ or CCSD(T)/cc-pVNZ methods is valid only if the multireference character of the species is small. If the T1 diagnostic of Lee et al. [358] is greater than w0.02, the multi-reference character can introduce substantial errors, increasing with increasing magnitude of

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1. Barrierless entrance channel due to the radical-radical nature of the reactions. The oxygen molecule is considered as a radical in this context, because of its triplet electronic ground state. 2. At least one low-lying (i.e. below reactants) channel leading to bimolecular products on the PES. 3. Numerous wells. Most of the species belonging to them are isomers formed by internal H-transfer.

Fig. 12. Zero-point energy corrected potential energy diagram of the neopentyl þ O2 system, as used by Petway et al. [109]. At the transition states, the first number is DH298 from the CBS-Q calculations of Sun and Bozzelli [110], bold numbers are energies determined from comparison of multiple-well master equation simulations (Variflex [362]) to experimental data, and numbers in parentheses are those determined from comparison of modified strong collider (CHEMDIS [363]) calculations to the experiments. Units are kcal mol1. Adapted with permission from [109]. Copyright 2007 American Chemical Society.

the T1 diagnostic. This, unfortunately, happens relatively often, especially in the case of transition states. If these barriers are critical for the determination of the rate coefficient, multi-reference methods should be used, such as CASPT2 [359,360] or Davidson-corrected [361] MRCI calculations. The difficulty in the multi-reference calculations is the determination of the minimum required active space providing sufficient accuracy; inclusion of all valence electrons in the calculations for the types of reactions we are interested in is almost never feasible. Harding et al. [343] also note that a large active space is often required in order to cover the whole region of interest on the PES for reactions involving substantial change in the electronic structure relative to the reactants. Of course, these are the very reactions for which a multireference treatment is particularly vital. Despite all efforts to obtain accurate quantum chemical results, fine-tuning of the energies within the uncertainty limits is often unavoidable to reproduce the experimental results (see e.g. Knepp et al. [105]). Naturally, the form of reaction rate theory used is correlated with the magnitude and direction of the energy adjustments. For example, Petway et al. [109] have studied the oxidation of the neopentyl radical, both theoretically and experimentally. Fig. 12 shows the lowest energy pathway on the neopentyl þ O2 reaction. The zero-point corrected energies of the transition states were determined by three methods: (1) directly from the CBS-Q work of Sun and Bozzelli [110], (2) adjusting the barrier heights to the experiments using kinetics calculated via the multiwell approach implemented in the Variflex version 1.13 m [362] program, and (3) calculating rate coefficients with the modified strong collider method implemented in the CHEMDIS program [363]. It can be seen in Fig. 12 that the different methods resulted in substantially different energy estimates. The opposite is also true: whenever the energies on the PES are known to high precision, rate coefficients may vary significantly depending on the level of reaction rate theory used. For that reason, it is important to understand the various aspects of the theoretical kinetic methods used for the study of autoignition-related reactions. 4.2.2. Theoretical chemical kinetics The aim of theoretical chemical kinetics is to obtain pressure and temperature dependent macroscopic (thermal) rate coefficients from a well-characterized PES by combining microscopic rate coefficients [k(E) or k(E,J)] with a model of the collisional dynamics. In order to select the appropriate theoretical methods, three general characteristics of the PES’s encountered in R þ O2, R þ HO2, ROO þ HO2 and QOOH þ O2 reactions should be considered.

An often used, but not particularly accurate, approach to calculate k(E) is the quantum Rice-Ramsperger-Kassel (QRRK) method, which corrects for some of the shortcomings of the only qualitatively correct, classical RRK theory, e.g. it includes the zeropoint energy. One implementation of the QRRK theory was developed by Bozzelli and Dean [364]. Instead of representing the vibrational frequencies of the molecule by one frequency, their method uses three frequencies. However, considering the computational power that is currently easily and widely available, the various implementations of the superior Rice-Ramsperger-KasselMarcus (RRKM) theory are well within reach. There seems little reason to retain the more approximate methods such as QRRK except where very rapid evaluation of qualitatively accurate rate coefficients (e.g., without full quantum chemical characterization) is desired [365]. The RRKM theory assumes strong coupling between the various modes of a molecule or radical, i.e. that it is in microcanonical equilibrium. In the classical RRKM framework, k(E) is calculated from the TST formula:

kðEÞ ¼

N s ðEÞ hrðEÞ

where Ns ðEÞ is the number of states at the transition state at energies less than E, h is the Planck constant, and rðEÞ is the reactant density of states per unit energy in the case of unimolecular reactions, and per unit energy and unit volume in the case of bimolecular reactions. When tunneling is included, Ns(E) is obtained by the convolution of the density of states and the tunneling probability. When a reaction occurs over an energetic barrier, as for instance in the case of most isomerization reactions, the transition state can be located to a good approximation at the electronic saddle point. The rigid rotor and harmonic oscillator (RRHO) model for the state counting is usually a good approximation at not too high temperatures, except for the low-frequency torsional modes, which represent an intermediate case between a free rotor and a harmonic oscillator. Frequently a Pitzer-Gwinn-like approximation [366] is used, although sometimes the calculation of the Hamiltonian matrix in the basis of the wave functions of free internal rotation, and subsequent calculation of energy levels by direct diagonalization of the Hamiltonian matrix is employed [367]. In both cases, the relaxed hindering potential is fitted, typically by a Fourier series of appropriate order. Treating hindered rotors as harmonic oscillators leads to substantial errors in the rate coefficient calculations [368,369]. Because the TS structure cannot be located directly for a barrierless reaction, it must be determined variationally. The goal of variational transition-state theory (VTST) is to find a dividing surface separating the reactants from the products, such that the resulting reactive flux is minimized. This totalangular-momentum-resolved, microcanonical reactive flux, Ns ðE; JÞ is identified as the number of states for the transition state. Conventionally, the variational principle is applied to a one-parameter family of surfaces orthogonal to a predefined reaction coordinate using the RRHO formalism, but for barrierless reactions this approximation is poor, because the optimal dividing surface varies widely with E and J, and the relative motion of the fragments is of large amplitude. For quantitatively

J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

accurate results, calculations require not only the optimization of the dividing surface position along the reaction coordinate, but also the optimization of the definition of the reaction coordinate. The latter is achieved by varying the “pivot point” locations on the two reacting fragments to which the dividing surfaces (typically spheres) are tied. This principle forms the basis of variable-reaction-coordinate transition-state theory (VRC-TST) [132]. VRC-TST requires an accurate and yet efficient sampling of the orientation dependence of the interaction energies. For the direct evaluation of the association potential, multi-reference methods are needed; this is especially true for radical-radical reactions (including doublet-triplet systems such as the R þ O2), because spin contamination can be large at large intermolecular distances. CASPT2 energy evaluations in particular have proven to be highly suitable and accurate for this purpose for reactions of hydrocarbons [370e373]. The direct evaluation of the microcanonical, J-resolved number of states, the direct VRC-TST [132,332,333] generally gives a very good agreement with the experimental values, typically within 25% [370,372,373], and can reduce (i.e., improve, because of the variational principle) the rate coefficient by a factor of two or more [374,375] compared to the results of the canonical VTST (CVTST). Often, a dynamical correction factor of 0.85-0.9 is also applied to the results of the direct VRC-TST calculations, to account for recrossing of the critical surface [370,371,373]. Some implementations of the direct VRC-TST method are the work of Zheng et al. [376] on methyl radical association, and Georgievskii, Harding, and Klippenstein’s VaReCoF code [377]. Minimum energy paths or model potentials for barrierless reactions are less accurate, but are also often used. Typical model potentials are the Varshni [378,379] and the Morse potential. The flatness of the Varshni potential at large intermolecular separation makes it a more accurate representation of the real potential. More importantly, the conservation of the total angular momentum plays a key role in barrierless transition states, which implies that in order to obtain accurate results the VTST has to be done at the Jresolved, microcanonical level (mJ-VTST). An alternative way to calculate k(E) is the statistical adiabatic channel model (SACM) [380,381]. In this method the number of states is replaced by the number of adiabatic channels connecting the fragments to products. However, this method has been used less often in relation to the particular reactions treated in this review. Whenever canonical high-pressure rate coefficients [k(T)] are available from experiment, the inverse Laplace transform theory [382] can also be used to derive k(E), but this is not an ab initio method. Long-range transition-state theory [383] typically cannot be applied for problems in combustion, because even at room temperature the transition state is at smaller interfragment separation than the limits of applicability of this method. A further complication with barrierless reactions occurs when they lead to a weakly bound complex that is followed by a low-lying saddle-point barrier to the formation of an adduct, as for instance for the R þ HO2, ROO þ HO2 and OH þ alkene reactions:

391

In this case an effective two-transition state model at the microcanonical level can represent the effective number of states s Þ for the barrierless outer ðN s ðNeff outer Þ and the saddlepoint-type s Þ transition states [379,384e387]: inner ðNinner

1 1 1 1 þ s  s ¼ Ns Neff N N max outer inner Nmax is the maximum flux between the two transition states. This approach has been successfully applied in a number of cases, mostly for alkene þ OH reactions (e.g. [119,388e390]). RRKM theory is an essentially classical framework. Nonetheless, some quantum (i.e. non-classical) effects can be easily implemented, such as tunneling and non-adiabatic transitions. Due to the important internal H-transfer processes, and the relatively low autoignition temperatures, tunneling gives a significant contribution to the rate coefficients of autoignition reactions. To model tunneling in one dimension, most commonly asymmetric Eckart barriers are used [391], less often the Wigner formalism [392]. Note that the latter method is accurate only if tunneling correction is small. The reactants, transition states and products appearing in hydrocarbon reactions often have very low or no point group symmetry. The rotational symmetry number can be high, and numerous optical isomers can also exist, especially for branched carbon chains. The precise determination of the overall symmetry number [393,394] is very important, because since miscalculated factors directly translate into the calculated rate coefficients. As a result of barrierless entrance channels and multiwell PES with low-lying transition states, many of the reactions that are most important for autoignition have a complicated pressure and temperature dependence. By coupling a collisional energy transfer model to transition-state theory, a full model forming bimolecular products and/or stable intermediates can be constructed. A simplistic collisional energy transfer model is the modified strong collider (MSC) model [395,396], built upon the LindemanneHinshelwood model by introducing broadening. The MSC model is considerably less accurate than a full time-dependent ME, because it assumes that stabilization occurs via a single collision, and is essentially unsuitable for precise rate coefficient determinations. The steady-state ME [397e399] also has limitations, e.g., a fully rigorous description of processes involving multiple isomerization steps (i.e. formally direct pathways) is not possible, although rate coefficients can be obtained under auxiliary assumptions, some of which (e.g., irreversible isomerizations [398]) are often physically untenable. At heart, steady-state methods assume that there is only one chemically significant timescale in the system [399]. Distinguishing between the formally direct and the sequential pathways, for example, generally entails at least two chemically significant timescales. The steady-state assumption also imposes an incorrect distribution for the chemically activated tail of the well, which is mostly responsible for formally direct bimolecular product formation in chemically activated systems. In order to get quantitatively accurate results, the 1D, i.e. the total energy (E) resolved time-dependent and multiple-well, ME equation is needed. The solution of the 2D, i.e. total energy and total angular momentum (J) resolved, ME [400] is in principle still more accurate, although angular momentum considerations usually play a limited role. The 2D ME is also often computationally too expensive, except in the collisionless limit (P / 0). The time-dependent ME can be written in a compact form using vector formalism:

djwðtÞi ¼ GjwðtÞi dt

(13)

where jwðtÞi is the time-dependent scaled population vector of the energy levels, and the Hermitian transition matrix G describes the

392

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chemical exchange between different wells, reactants, and products, as well as the vibrational energy transfer. The downward energy transfer is almost always modeled using a single-exponential-down model in the following form:


P E; E0 ¼

1
expð  DE=aÞ; CN E0

E  E0

where P(E,E’) is the probability of the downward energy transfer between levels E’ and E, DE ¼ E0  E, a is the average downward energy transfer hDEdi, and CN(E0 ) is a normalization factor. The probability of the activating collisions (E > E0 ) is determined from detailed balance. Collisional energy transfer models are the least well understood parts of theoretical kinetic models, and as quantum chemistry becomes more precise, energy transfer may begin to carry the major portion of the uncertainty [335,401]. The energy transfer process can be studied by trajectory calculations ([402,403] and references therein), and in favorable cases by clever experiment [404e406]. Even though the single exponential formulation has inherent inaccuracies (e.g., classical trajectory calculations [335,402,407] and experimental measurements [404e406] show that P(E,E’) has a somewhat more complex functional form), relatively limited knowledge about these processes has hindered the adoption of more accurate parameterizations. In a recent study by Jasper and Miller [403], highly averaged direct classical trajectory simulations were used to calculate energy transfer parameters for the CH3 þ H / CH4 reaction. They found that the accurate treatment of energetics, transition-state theory and energy transfer leads to excellent agreement with experiments. Further development in this field remains necessary in order to generalize a physically rigorous description of energy transfer processes. There are various methods in the literature for solving the ME. These range from numerical integration to the eigenvalueeigenvector analysis of Eq. (13). The time-dependent master equation methodology of Miller and Klippenstein [148e150] is based on the diagonalization of the transition matrix and has two major advantages over other methods. Firstly, their method is able to assign rate coefficients not only to the chemical transformations happening between adjacent wells, but also to those components of the chemical reaction that proceed across several transition states without collisional stabilization in the intermediate wells. These formally direct channels, of which chemical activation pathways are a subset, appear naturally from the MillereKlippenstein mathematical formulation. Frequently formally direct pathways are not treated rigorously in complex chemical mechanisms; however, detailed modeling of experiments have shown that in some cases formally direct pathways are responsible for a large fraction of the reaction flux. In Fig. 13 the experimental and modeled OH concentration curves for the cyclohexyl þ O2 reaction are shown [105]. The full model contains both the formally direct and the conventional, sequential pathways; it can be seen very clearly that ignoring the formally direct rate coefficients would substantially change both the shape and the magnitude of the theoretical curve. Note again the kinetic discrimination of reaction mechanisms that is possible in photolytically initiated measurements e formally direct pathways produce bimolecular products on a shorter timescale than the sequential paths. Another difficulty arises if the timescale of a chemical transformation becomes indistinguishable from the timescale of collisional relaxation processes. This makes the extraction of the rate coefficient not merely difficult, but impossible, because the definition of the rate coefficient breaks down. This happens as the temperature

Fig. 13. Measured (open circles) and modeled OH concentration in pulsed-photolytic Cl-initiated oxidation of cyclohexane, taken from the work of Knepp et al. [105], reproduced by permission of the PCCP owner societies. The shape of the OH concentration profile shows an initial fast rise, attributed to the formally direct pathways, while the slower component is due to the somewhat delayed sequential steps.

increases and/or in the case of shallow wells. This problem is also rigorously addressed by the methodology of Miller and Klippenstein by recognizing that the merging of the timescales mean that two (or more) species on the PES are no longer distinguishable from each other, and should be treated as one “super-species”. There are numerous program packages available for the solution of the full collisional models, such as Variflex [408], MESMER [409], Multiwell [410,411], Polyrate [412], UNIMOL [413], ChemRate [414], and CHEMDIS [363]. To include the complicated pressure and temperature dependence of the thermal rate coefficients in comprehensive chemical kinetic models, an appropriate numerical representation of the data is needed. The fall-off shapes for association reactions, such as those imposed by the Lindemann-Hinshelwood scheme or the more accurate and widely used Troe formulae [415] generally are inadequate for multiwell problems. One commonly used method is to represent k(T,P) in a given temperature and pressure range by Chebyshev polynomials [416]. An other method is to fit an extended Arrhenius formula, or sometimes the sum of two extended Arrhenius formulas, to a series of k(T,P ¼ constant) functions, and use logarithmic interpolation for pressures not on the pressure grid. Advantages of the logarithmic interpolation method are its simplicity and the fact that the pressure grid can be arbitrarily refined by adding more functions to already existing sets. The CHEMKIN-PRO program package [417] used to simulate complex chemical mechanisms can use both formalisms to parameterize rate coefficients. 5. Recent progress on specific systems In the following sections we present an overview of the recent literature in theoretical and experimental kinetics of reactions important for low-temperature combustion and autoignition. Only reactions initiated by R radicals directly derived from fuel molecules are considered in any detail, and then usually only if these reactions produce OH or HO2 radicals under the conditions relevant to low-temperature autoignition chemistry. The radical also has to be relatively stable; therefore, for instance the reactions of _ are excluded. The overview of recent the acetyl radical ðCH3 COÞ

J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

theoretical kinetic studies with these selection criteria is presented in Table 3. Because of the central role of the direct HO2 elimination pathway, where the various R þ O2 reactions are discussed we present only theory that was published after the detailed understanding of this channel. In practice, this corresponds to theoretical results published after approximately the year 2000. Furthermore, we concentrate on experimental results published after the mid-1990s, i.e., after the comprehensive reviews of Walker and Morley [6] and Robertson et al. [7]. An overview of recent (post-1995) experimental investigations that probe the elementary kinetics of autoignition-relevant peroxy radical reactions is given in Table 4. Section 5 is structured according to the different reaction types and the reacting species, starting with R þ O2 reaction in alkanes (Section 5.1), cycloalkanes (Section 5.2) and unsaturated compounds (Section 5.3 for resonance stabilized radicals, Section 5.4 for other unsaturated hydrocarbon radicals). In Section 5.5 reactions of oxygen-containing radicals are discussed. Section 5.6 gives an overview of the QOOH þ O2 studies, followed by the detailed discussions of the alkyl þ HO2 (Section 5.7), alkylperoxy þ HO2 (Section 5.8) and unsaturated compounds þ HO2 (Section 5.9) reactions. 5.1. Alkyl þ O2 reactions in alkane oxidation 5.1.1. The C2H5 þ O2 reaction and the concerted HO2 elimination pathway The ethyl þ O2 reaction is the most studied from the R þ O2 reaction family, and is sometimes considered to be a “combustion archetype” [342]. On the other hand, due to the shortness of the carbon “chain”, the ethyl radical lacks a very important degree of freedom: it cannot form the energetically favored, 6member ring transition state for internal H-abstraction (see Fig. 5). This transition state is very important for real hydrocarbon fuels; therefore, in our opinion the n-propyl radical reaction with O2 is a more useful combustion archetype, and nbutyl radical oxidation is even better, since in the latter case it is also possible to form an oxolane (often the most prominent oxygen heterocycles observed [418,419]), via a (1,6p) isomerization and subsequent OH elimination:

Even so, the amount of theoretical work on the ethyl þ O2 reaction is overwhelmingly detailed, and the majority of the conclusions and methodological approaches can directly be applied for larger hydrocarbons. There had been substantial controversy about the PES of this reaction; the historical account on this topic is reviewed by Rienstra-Kiracofe et al. [20]. Briefly, experimental evidence has shown that the major bimolecular product channel is C2H4 þ HO2 and that the rate coefficient has negative temperature dependence. Direct abstraction of the H-atom was ruled out fairly consistently based on product studies. By the 1990s, the two “competing” mechanisms in the literature were the ethylperoxy b-hydrogen transfer with CeO bond rupture

393

(14)

and the direct elimination of HO2 from the ethylperoxy radical.

(15)

The final HO2 elimination steps in the above two reaction series are related to very different transition-state structures (see Fig. 4 and Section 2.2.1). The problem was further complicated by the experimental evidence showing that the putative reverse of (14), the reaction of C2H4 with HO2, eventually forms oxirane þ OH. In the absence of accurate electronic structure calculations, reaction scheme (14) was favored. Wagner et al. [278] suggested a barrier height of 2.4 kcal mol1 based on the analysis of experimental data and assuming mechanism (14). It took almost a decade to settle the barrier heights of the mechanisms (14) and (15), with significant contributions from Quelch et al. [420,421], Green [422], Shen et al. [423] and Ignatyev et al. [424]. The details of the reconciliation of the forward and reverse rate coefficient determinations are discussed in the context of HO2 addition reactions, Section 5.9 below. For the ethyl þ O2 reaction, Rienstra-Kiracofe et al. [20] in 2000 concluded that the direct elimination mechanism (15) is the only operative mechanism at low temperatures. They used CCSD and CCSD(T) ab initio methods employing DZP, TZ2P and TZ2Pf basis sets, and arrived at a barrier height of 0.9 kcal mol1 (relative to the reactants) for the concerted elimination. At the same time, Miller et al. [18,19] conducted master equation calculations on this reaction. They optimized the geometries and obtained vibrational frequencies using B3LYP/6-311þþG(d,p) for the reactants, stable intermediates and transition states, and calculated the energies at these geometries using a variant of the G2 method. The association rate coefficient was calculated by assuming a Varshni potential along the reaction coordinate and separating the conserved and transitional modes; the latter is described in terms of a set of internal angles. They found the transition state of the concerted elimination to be 3 kcal mol1 below the reactants. More importantly, using this value gave an excellent agreement between the experimental and the calculated high-pressure limit rate coefficient, and also successfully reproduced the pressure dependence of the association rate coefficient. One important finding of these papers was that the rate coefficient is very sensitive to the barrier height: using the 0.9 kcal mol1 value of Rienstra-Kiracofe et al. [20] gave a factor of seven too low rate coefficient compared to the experimental values. The new theoretical understanding of the HO2 channel in the ethyl þ O2 reaction was validated against a series of detailed experiments. Clifford et al. [21] probed HO2 formation in Cl-initiated ethane oxidation and could kinetically distinguish two

Referencea

394

Table 3 Overview of recent theoretical chemical kinetics studies relevant to low-temperature autoignition. Electronic structure calculationc

Collisional model

G2-like//B3LYP G2-like//B3LYP CBS-Q G2-like//B3LYP CBS-QB3 QCISD(T)//B3LYP QCISD(T)//B3LYP CBS-q QCISD(T)//B3LYP CBS-Q From Sun 2004 [110] CBS-QB3 G2(MP2)-like//B3LYP CBS-QB3 CBS-Q CBS-q CBS-QB3, G3(MP2) CBS-QB3 Elaborated CASPT2 Elaborated CASPT2 CBS-QB3 PMP4(SDTQ)//MP2 G2M(RCC,MP2) QCISD(T)//B3LYP CCSD(T)//B3LYP G3B3 G2MS G3B3 CBS-QB3 Various versions of G2M//B3LYP

tdME/(EV, ODE) RRKM/RRHO tdME/EV RRKM/RRHO MSC, ssME QRRK tdME/EV RRKM/RRHO MSC QRRK tdME/EV RRKM/RRHO tdME/EV RRKM/RRHO ssME QRRK Based on analogy with propyl þ O2 (same work) ssME QRRK tdME, MSC RRKM/RRHO, QRRK e QRRK tdME/EV RRKM/RRHO e CTST ssME QRRK ssME QRRK ssME QRRK ME RRKM/RRHO e CTST e CTST ME RRKM/RRHO Activation scheme RRKM/RRHO ssME RRKM/RRHO tdME/EV RRKM/RRHO e RRKM/RRHO e e ME e ME QRRK Stochastic ME TST Weak-collision ME Multiconformer TST

Schocker 2007 [471] Zádor 2009 [175] da Silva 2009 [472] Sun 2007 [111] Yamada 1998 [477] Yamada 2000 [478] Andersen 2008 [502] Bozzelli 2002 [193] Sun 2004 [110] Zheng 2005 [325] Andersen 2008 [197]

Ethyl Ethyl Ethyl Ethyl Ethyl Propyl Propyl t-Butyl Butyl Neopentyl Neopentyl n-Butylperoxy and n-pentylperoxy isomerization Cyclohexyl Cyclohexylperoxy and cyclopentylperoxy isomerization Allyl Allylic isobutenyl Allylic isobutenyl Benzyl Benzylperoxy isomerization Xylylperoxy isomerization Xylyl Vinyl Vinyl Vinyl Cyclohexadienyl Phenyl (association only) Naphthyl (association only) Methylphenyl Hydroxymethyl Hydroxymethyl,1-hydroxyethyl, 2-hydroxyisopropylhydroxycyclohexyl Hydroxymethyl 1-Hydroxyethyl, 2-hydroxyethyl 1-Hydroxyethyl 2-Hydroxy-1,1-dimethylethyl, 2-hydroxy-2-methylpropyl CH3OCH2 CH3OCH2 CH3OCH2 Hydroperoxyethyl Hydroperoxy-neopentyl 2-Hydroperoxy-methyl-2-propenyl CH2OCH2OOH

G3//B3LYP QCISD(T)//B3LYP G3B3 CBS-Q CBS-q CBS-q and G2 B3LYP//B3LYP CBS-Q//B3LYP B3LYP//B3LYP CBS-QB3 and G3(MP2) B3LYP//B3LYP

tdME tdME/EV ME ssME ssME ssME stochastic tdME, ssME ssME ssME ssME stochastic tdME and ssME

RRKM/RRHO RRKM/RRHO RRKM/RRHO QRRK QRRK QRRK RRKM/RRHO QRRK QRRK QRRK RRKM/RRHO

R þ HO2, R ¼ Zhu 2001 [519] Jasper 2009 [493] Anglada 2006 [220] Hou 2005 [221]

Methyl Methyl Methylperoxy Ethylperoxy

G2M QCISD(T)//B3LYP CASPT2//CASSCF CCSD(T)//B3LYP

tdME/inversion tdME/EV e tdME

RRKM/RRHO RRKM/RRHO TST RRKM/RRHO

Alkene þ HO2, alkene ¼ Chen 2000 [99]

Ethene, propene, isobutene

CBS-Q

e

CTST

R þ O2 , R ¼ Miller 2000 [19] Miller 2001 [18] Sheng 2002 [398] DeSain 2003 [103] Carstensen 2005 [425] DeSain 2001 [26] DeSain 2003 [103] Chen 1999 [98] DeSain 2001 [26] Sun 2004 [110] Petway 2007 [109] Zhu 2007 [429] Knepp 2007 [105] Sirjean 2009 [435] Lee 2005 [165] Chen 2000 [102] Zheng 2005 [325] Murakami 2007 [437] Canneaux 2008 [438] Canneaux 2009 [440] Murakami 2009 [441] Carpenter 1995 [154] Mebel 1996 [445] Klippenstein 2003 [449] Estupiñán 2003 [456] de Silva 2008 [160] Park 2009 [462] da Silva 2007 [464] Dibble 2002 [467] Hermans 2005 [469]

a

d

Tight TS

Loose TSe

Tf

HRg

mJ-VTST/Varshni mJ-VTST/Varshni VTST/B3LYP mJ-VTST/Varshni From Miller 2000 [19] VRC-TST/B3LYP VRC-TST/B3LYP Literature kN

e E e E W E E

PG PG PG PG DI PG PG PG

Literature kN Literature kN e dVRC-TST//CASPT2 e e Literature kN Literature kN CVTST e e CVTST Approximation e dVRC-TST TST CVTST CVTST CVTST/O3LYP Inverse Laplace transform VTST/B3LYP

e E W E W e E W e W W e e e E e e e W e e

DI PG DI PG [517] DI PG DI e e e e DI e PG e DI PG DI e [518]

mJ-VTST/B3LYP

e E E e e e e e e W e

e PG DI DI PG PG e PG DI DI e

dVRC-TST/CASPT2 Canonical 2TST mJ-VTST/Morse

e E E E

e PG e e

e

e

PG, DI

dVRC-TST/CASPT2 CVTST/B3LYP CTST e From C3H7 þ O2 mJ-VTST/Varshni Based on ethyl Literature kN Literature kN mJ-VTST /Varshni

mJ-VTST/Varshni

Only the first author is listed, all papers have multiple authors. When not stated explicitly, all isomers are considered. Only the main method is listed. Some or all of the values are often refined based on experimental enthalpy values, multi-reference calculations for key stationary points, high-level corrections etc, or adjusted to match experiment traces of some observed species. d tdME: time-dependent ME; ssME: steady-state ME; ODE: ordinary differential equation based solution of the ME; EV: eigenvalue-eigenvector based solution of the ME. e dVRC-TST: direct VRC-TST; 2TST: two-transition-state theory. f Tunneling correction. E: Eckart-type; W: Wigner-type. g Hindered rotor treatment. PG: PitzereGwinn approximation; DI: direct integration over the energy levels of the intramolecular rotational potential. b c

J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

Chemical systemb

J. Zádor et al. / Progress in Energy and Combustion Science 37 (2011) 371e421

395

Table 4 Overview of recent experimental studies of elementary kinetics of RO2 and QOOH reactions under conditions relevant to autoignition. Tropospherically targeted studies of similar reactions are not generally included, although some studies (italicized) that probe only temperatures below 400 K are included, if they provide important mechanistic information. Referencea

Reaction system

Method of initiation

Detection technique

Alkyl þ O2 reactions Atkinson 1997 [312] Clifford 2000 [21] DeSain 2001 [22] DeSain 2001 [26] Kaiser 1998[14,16] Kaiser 2002 [275] DeSain 2003 [103,104] DeSain 2003 [108] Hahn 2004 [316] Luther 2004 [317] Herbon 2005 [251] Srinivasan 2005 [253] Estupiñán 2005 [24] Estupiñán 2007 [25] Fernandes 2006 [314] Petway 2007 [109] Fernandes 2008 [315]

C2H5 þ O2 C2H5 þ O2 C3H7 þ O2 Propyl þ O2, butyl þ O2 C3H7 þ O2 C2H5 þ O2 Ethyl þ O2, propyl þ O2 Neopentane oxidation H þ O2 (þM) / HO2 (þM) CCl3 þ O2 CH3 þ O2 CH3 þ O2, H2CO þ O2, OH þ O2 n-C3H7 þ O2, i-C3H7 þ O2 C2D5 þ O2, C3D7 þ O2 CH3 þ O2 (þM) / CH3O2 (þM) Neopentane oxidation H þ O2 (þM) / HO2 (þM)

Laser photolysis Laser photolysis Laser photolysis Laser photolysis UV-photolysis UV-photolysis Laser photolysis Laser photolysis Laser photolysis Laser photolysis Thermal Thermal Laser photolysis Laser photolysis Laser photolysis Laser photolysis Laser photolysis

UV-CRDS IR-FM IR- FM IR-FM GCeMS GCeMS OH-LIF IR-FM and OH-LIF UV-absorption UV-absorption OH-absorption, O-ARAS OH- absorption IR- FM IR- FM UV-absorption OH-laser absorption UV-absorption

Cycloalkyl þ O2 reactions Handford-Styring 1995 [270] Handford-Styring 2001 [271] DeSain 2001 [23] Handford-Styring 2002 [272] DeSain 2003 [318] Knepp 2007 [105] Fernandes 2009 [147]

H, OH þ cyclopentane and cyclopentyl HO2 þ cyclohexane Cyclopentyl þ O2 HO2 þ cyclopentane and propane c-C3H5 þ O2 Cyclohexyl þ O2 Cyclohexyl þ O2

Thermal Thermal Laser photolysis Thermal Laser photolysis Laser photolysis Laser photolysis

GC GC IR- FM GC IR-FM, UV-laser absorption and FTIR IR- FM and UV-laser absorption OH-LIF

Unsaturated /aromatic radical þ O2 reactions Knyazev 1995 [450] Vinyl þ O2 Eng 1998 [252] Toluene and p-xylene oxidation Scott 2002 [62] Toluene, ethylbenzene oxidation Ellis 2003 [61] Toluene, ethylbenzene oxidation Eskola 2003 [443] Vinyl þ O2 Choi 2004 [454] Phenylvinyl þ O2 Park 2009 [455] Phenylvinyl þ O2 Estupiñán 2005 [456] Cyclohexadienyl þ O2 Meloni 2008 [288] Cycloalkene oxidation Park 2009 [462] C10H7 þ O2 Oguchi 2009 [453] Vinyl þ O2

Laser photolysis Thermal Thermal Thermal Laser photolysis Laser photolysis Laser photolysis Laser photolysis Laser photolysis Laser photolysis Laser photolysis

PIMS UV-absorption GC GCeMS PIMS CRDS MS UV-absorption Synchrotron-PIMS VIS-CRDS LIF

Oxygenated radical þ O2 reactions Hoyermann 1996 [473] Maricq 1997 [307] Sehested 1997 [476] Hack 2000 [474] Tranter 2001 [83] Tranter 2001 [84] Rosado-Reyes 2005 [171] Suzaki 2006 [168] Delbos 2006 [184] Suzaki 2007 [169,170] Schocker 2007 [471] Zádor 2009 [175]

Laser photolysis Laser photolysis Pulse radiolysis Laser photolysis Thermal Thermal Laser photolysis Laser photolysis Laser photolysis Laser photolysis Laser Photolysis Laser photolysis

Mass spectrometry UV- and IR-laser absorption UV-absorption MPI/MS GCeMS GCeMS IR-laser absorption NIR-FM and UV-laser absorption CH2CHO-LIF NIR-FM and UV-absorption NIR-absorption Synchrotron-PIMS

a

CH2OCH3 þ O2 DME oxidation CH3OCH2 þ O2 t-C4H9OCH2 þ O2 H and OH þ ethers (DME, MEE, DEE, MTBE, ETBE) OH þ propanone, butanone and pentan-3-one DME oxidation DME oxidation CH2CHO þ O2 DME oxidation CH2OH þ O2 Hydroxyethyl þ O2

Only the first author is listed, all papers have multiple authors.

timescales for HO2 production. They assigned the shorter timescale to the formally direct pathway from ethyl þ O2 and the longer timescale to dissociation of the stabilized alkylperoxy radical. The phenomenological rate coefficients and branching fractions they derived were in close agreement with the master equation results of Miller and coworkers [18,19]. Kaiser [275] continued his earlier investigations of ethyl þ O2 [13,15,276,277], completing his tour de force study of the mechanism of this reaction. He had previously [13] measured the rapid increase in ethene yield with increasing temperature that accompanies the onset of thermal dissociation of ethylperoxy radicals; in 2002 [275] he used the competition between chlorination and oxidation to clearly identify the direct formation of ethene from ROO (see Fig. 7 and discussion in Section

3.2). The experiments of DeSain et al. [103,104], which probed OH formation, and those of Estupiñán et al. [25], which investigated the deuterated ethyl þ O2 system, included the much closer partnership between theory and experiment advocated in Section 3.4 above, employing master equation calculations in direct kinetic modeling of the experimental result and adjusting the stationary point energies to improve agreement with the body of experimental data. In 2002, Sheng et al. [398] revisited their earlier calculation [364] on the ethyl þ O2 reaction, now including the concerted elimination pathway. Their calculations were in some ways less sophisticated than those of Rienstra-Kiracofe [20] or Miller et al. [18,19]; Sheng et al. applied the CBS-Q//B3LYP/6-31G(d,p) method

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to calculate single point energies with scaled harmonic frequencies. The quantum chemical results were employed in a QRRK calculation for microscopic rate coefficients, and then coupled either to a MSC model or a steady state ME to calculate pressure-dependent rate coefficients, which were parameterized using Chebyshev polynomials. The association rate constant was computed using CVTST//B3LYP/6-31G(d,p) and a harmonic approximation. They obtained a 3.7 kcal mol1 energy (relative to ethyl þ O2) for the barrier to the concerted HO2 elimination channel, and were able to reproduce the experimental data of Kaiser [13] and Clifford et al. [21] satisfactorily. They also found only small differences between the rate coefficients derived from their steady state ME and those obtained with the MSC model. Fig. 14 shows the PES for the ethyl þ O2 reaction. The lowest energy OH-producing channel leads also to the formation of oxirane, and goes via the R þ O2 / ROO / QOOH / OH þ oxirane sequence, including a 5-member internal H-abstraction transition state. Although the amplitude and timescales for HO2 formation in the ethyl þ O2 reaction are quantitatively predicted by theory [25,103], the experimental OH profiles measured in the LIF experiments of DeSain et al. [103,104] were only qualitatively matched by the results of the time-dependent ME model. The authors attributed the residual differences (underprediction above 600 K and overprediction below 600 K) to auxiliary reactions, such as the addition of the second oxygen, ethyl þ HO2 and ethylperoxy þ HO2. Furthermore, these experiments used photolysis of CFCl3 as a Cl atom source for the Cl-initiated oxidation, and the reaction of the halomethyl photolysis coproduct with HO2 could have been a substantial source of OH [103], complicating the analysis of the data. Other attempts to model the DeSain et al. [103] experiments have also found difficulties e e.g., Carstensen et al. [425] found that the peak experimental OH concentration was closer to the modeled total OH yield than was the integrated experimental OH production e and it seems clear that more reliable experiments are needed. Huang et al. [426] have recently completed a reinvestigation of propane oxidation with an improved experimental technique, and now obtain excellent agreement with ME calculations. Future work will address the ethyl þ O2 system as well. In 2008, Wilke et al. [342] performed a definitive ab initio quantum chemistry calculation on the ethyl þ O2 PES. They optimized geometries using the CCSD(T)/cc-pVQZ method and applied the valence focal point approach to extrapolate the energies to the Full-CI limit, and also took into account core correlation, relativistic effects and diagonal Born-Oppenheimer corrections. Their final, zero-point corrected energy was in complete agreement with the value of Miller et al. [18,19]: 3.0 kcal mol1. This is an illustration showing that whenever one component from the experimental data/quantum chemistry/ theoretical kinetics triad is uncertain, accurate treatment of the other two components can yield an excellent determination for the third. A detailed description on the analysis of the ME computation and in particular the chemically significant timescales for this reaction is given in the “Examples” section of the paper of Miller and Klippenstein [149]. 5.1.2. The reactions of propyl and higher alkyl radicals with O2 Reactions of C3 and larger alkyl radicals can open up a new, energetically favorable pathway: the isomerization of the peroxy radical via a 6-member ring to form 3-hydroperoxyalkyl radicals (see Fig. 5). The reduced ring strain in the transition state results in this isomerization pathway lying well below the entrance channel, as illustrated in Fig. 15, which shows the calculated PES of for the npropyl þ O2 and the i-propyl þ O2 systems from the paper of DeSain et al. [103]. The 5-membered ring transition states (1,4p or 1,4s, also

Fig. 14. The C2H5 þ O2 PES employed in the study of DeSain et al. [103,104] to calculate rate coefficients. Transition state structures are analogous to the ones shown in Fig. 4. The H-abstraction by O2 is represented by the thin line. Modified and reprinted with permission from [103]. Copyright 2003 American Chemical Society.

see Fig. 5) from the propylperoxy radicals to the corresponding bhydroperoxypropyl isomers have somewhat lower energies relative to R þ O2 than does the 1,4 p isomerization of ethylperoxy to hydroperoxyethyl radical (see also Table 2), resulting in more isomerization to QOOH and higher OH branching fractions. A consequence of more facile isomerization is the increased concentration of the hydroperoxyalkyl radicals and thus a larger possibility of the second O2 addition pathways. Because n-

Fig. 15. PES of for the n-propyl þ O2 and the i-propyl þ O2 systems, adapted with permission from DeSain et al. [103]. Transition state structures are analogous to the ones shown in Fig. 4. Copyright 2003 American Chemical Society.

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propyl þ O2 is the smallest R þ O2 system that exhibits these important features, it is far more archetypical than ethyl þ O2 of the alkylperoxy and hydroperoxyalkyl chemistry that is critical to autoignition [319,427]. 5.1.2.1. Propyl þ O2. DeSain et al. [22] measured the HO2 production from the Cl-initiated oxidation of propane and noted a slightly increased “prompt” HO2 yield (related to the formally direct pathways) and a shorter time constant for the “delayed” HO2 (related to ROO dissociation) compared to the ethyl þ O2 system. In a later work DeSain et al. [26] calculated stationary point energies for the propyl þ O2 systems using MP2-corrected QCISD(T)/ 6-311G(d,p)//B3LYP/6-31G(d) quantum chemistry. For the barrierless entrance channels they employed VRC-TST//B3LYP/6-31G(d). Rate coefficients employed to describe the earlier Cl-initiated propane oxidation experiments [22] were calculated using a timedependent ME, and the stationary point energies in the propyl þ O2 reactions were adjusted to best match the available experimental data. This approach was further developed in the subsequent paper of DeSain et al. [103], where the ethyl þ O2 system was also studied. Rate coefficients via saddle points were calculated using conventional TST, while VRC-TST//B3LYP/6-31G(d) was applied for the barrierless processes. After minor adjustments the solution of the time-dependent RRKM/ME described the experimentally observed HO2 profiles well. As discussed above, discrepancies in the OH concentration were attributed to secondary chemistry, and the experiments also suffer from side reactions of photoproducts. Recent work by Huang et al. [426] remedies these experimental difficulties and removes the discrepancies between theory and experiment. The HO2 production in individual isomeric propyl þ O2 reactions was measured by Estupiñán et al. [24], who also carried out RRKM/ ME calculations, and adjusted the stationary point energies of the isomers (from the calculations of DeSain et al. [26]) independently. Based on their experiments and modeling they called into question the high-temperature rate constant given by Gulati and Walker [268] for the reaction i-propyl þ O2 / propene þ HO2, a conclusion strengthened in a subsequent paper [25] that investigated the Clinitiated oxidation of deuterated propane. 5.1.2.2. Butyl þ O2. Chen and Bozzelli [98] found the direct HO2 elimination pathway as well as a low-lying OH forming channel on the t-butyl þ O2 PES calculated at the CBS-q//MP2(full)631G(d) level of theory. Rate coefficients were calculated with a steady state ME methodology combined with QRRK calculations. DeSain et al. [26] measured HO2 formation from Cl-initiated oxidation of n-butane and isobutane, comparing the experimental results to rate expressions for butyl radical oxidation reactions that were derived from the rigorous ME rate constants for analogous reactions in the propyl þ O2 systems. They performed MP2-corrected QCISD(T)/6-31G(d)//B3LYP/631G(d) calculations on the stationary point energies for the four butyl radical isomer reactions with O2, but did not carry out any detailed kinetics evaluations. Rather, simple corrections were made to adapt the propyl þ O2 expressions for use in the butyl þ O2 systems, scaling pre-exponential factors based on numbers of participating H atoms and adjusting activation energies based on differences in calculated QCISD(T)/6-31G(d)// B3LYP/6-31G(d) barrier heights [26]. 5.1.2.3. Neopentyl þ O2. Because of the quaternary carbon atom, the concerted HO2 elimination pathway is absent in the neopentyl (2,2-dimethylprop-1-yl) radical reaction with O2 this makes this system an excellent candidate to study the ROO % QOOH isomerization pathway.

Hughes et al. [106,107] measured OH production in neopentyl þ O2 reactions, and the absolute values they derived for the neopentylperoxy / hydroperoxyneopentyl isomerization rate coefficient have been taken as benchmarks for ROO % QOOH isomerizations [6]. However, Curran and coworkers [112], in their modeling of neopentane oxidation, subsequently questioned the results, suggesting that both the forward and reverse isomerization rate constants could be substantially larger than Hughes et al. thought. Later, DeSain et al. [108] measured both OH and HO2 (formed in secondary reactions) in the Cl-initiated oxidation of neopentane. To model their results, they estimated the energetics of the neopentyl system by calculating B3LYP/6-31G(d) energies and made an ad hoc correction based on higher-level calculations of analogous reactions in the n-propyl þ O2 reaction. They also transferred the kinetic model from the n-propyl system, changing A-factors to account for the increased number of H atoms available for abstraction, and adjusting activation energies based on the comparison of B3LYP/6-31G(d) calculated energies of analogous stationary points in the n-propylperoxy and neopentylperoxy systems. The adjusted model agreed very well with the experimental results, suggesting that it may be feasible to build kinetic models for larger molecules based on the detailed models for smaller ones, but required a rather arbitrary assumption on the rate coefficient for the formally direct OH production. Nevertheless, their model matched their own experiments and those of Hughes et al. [106,107], with a rate for ROO / QOOH about sixty times larger than that inferred by Hughes et al., or roughly what Curran et al. [112] proposed. Furthermore, DeSain et al. [108] noted chain branching, with observed HO2 production exceeding the initial radical concentration that increased with increasing O2 concentration. They attributed this behavior to reactions of the QOOH radical with O2. Sun and Bozzelli [110] calculated the energetics of the neopentyl þ O2 system and carried out a kinetic analysis using steady state ME and QRRK analysis. They modeled the experiments of Hughes et al. [106,107], but with an isomerization rate coefficient eight times larger than Hughes et al. derived. The Sun and Bozzelli [110] results were incorporated in the work of Petway et al. [109] (see also Fig. 12), who re-measured OH production in the neopentyl þ O2 reaction and also carried out a more rigorous time-dependent ME analysis, using conventional TST and RRHO approximation for the isomerization pathways. They observed substantial differences for the calculated rate coefficients using different theoretical kinetics methods (factor of w4), but substantiated the proposal of DeSain et al. [108] that formally direct channels dominated production of OH. It also has to be noted that none of these theoretical works on the neopentyl þ O2

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reaction [108e110] applied full mJ-resolved VTST for the calculation of the association rate coefficient. However, it does appear that the experiments of Hughes et al. [106,107] may not directly yield the ROO / QOOH rate coefficient and that the isomerization may be substantially more rapid than they inferred. 5.1.2.4. General R þ O2 studies. Chan et al. [428] studied the isomerization of peroxy radicals containing up to 5 carbon atoms using the BHandLYP/6-311G(d,p) density functional. Arrhenius parameters for the internal H-abstraction reactions were also presented using conventional TST. According to their calculations the most facile isomerization process is via a 6-member ring with the H atom attached to a tertiary carbon atom (1,5t), however the absolute values of the activation energies are in substantial disagreement with experiment, and they recommend reducing the BHandLYP/6-311G(d,p) barriers by 6 kcal mol1. Zhu et al. [429] studied the n-butyl þ O2 and n-pentyl þ O2 reactions at the CBS-QB3 level of theory. In particular, kinetics for the intramolecular hydrogen shifts was investigated in a systematic manner, analyzing transition states belonging to 4 to 8-member rings using canonical TST. Tunneling was treated using Wigner’s method. They also found that the internal hydrogen abstraction is fastest in the case of the 6-member ring, and confirmed that the BHandLYP/6-311G(d,p) method employed by Chan et al. [428] overestimated the barrier heights. Part of the discrepancy in the Chan et al. paper might have arisen from an imprecise treatment of the A-factors. Most recently, Sharma, Raman, and Green [430] carried out a thorough and systematic investigation of the intramolecular hydrogen transfers in alkylperoxy and hydroperoxyalkylperoxy (OOQOOH) radicals, giving high-pressure limiting rate coefficients for representative isomerizations via 1,3 through 1,7 transfers. Several computational studies of ROO 4 QOOH barrier heights are compared in Table 2 to the recommended activation energies based on the experimental work of Walker and coworkers [6,143] and normalized to the determination of Hughes et al. [106,107] Differences between calculated barrier heights and the activation energies recommended by Walker and Morley [6] are displayed in Fig. 16 for various transitionstate ring sizes. There are systematic differences between the Walker and Morley recommendations and the calculations. The 1,4 barriers (except for the CBS-q//MP2(full)/6-31G(d) calculation of t-butylperoxy isomerization from reference [98], at 3.5 kcal mol1) are clustered w1 kcal mol1 above the Walker and Morley recommendation. The calculated barrier heights of the 1,5 transition states in contrast are 4e7 kcal mol1 below the Walker and Morley recommended Ea. This correlation holds for both primary and secondary H-atom transfer, suggesting that an inaccurate estimate of ring strain may be the major source of the discrepancy, and that hence the facility of 1,5 isomerization relative to 1,4 isomerization may be underestimated in the Walker and Morley recommendations. For the overall product branching ratio in an R þ O2 reaction the further isomerization of QOOH and the direct HO2 elmination pathways have to be considered as a whole, including entropic as well as energetic effects. Table 2 also lists the ROO / HO2 þ alkene barrier heights. The dissociation reaction QOOH / OH þ product is discussed in Section 5.5. As the formation of QOOH is critical to low temperature chain branching, it is informative to consider how large kinetic mechanisms of hydrocarbon oxidation model the isomerization process. The comprehensive oxidation models of the group in Nancy [4] use activation energies for the ROO % QOOH isomerizations closely modeled on the Walker [6] and Pilling [7] recommendations. The Lawrence Livermore (LLNL) modeling group led by Westbrook and

Fig. 16. Differences between calculated zero-point corrected barrier heights for alkylperoxy / hydroperoxyalkyl isomerizations (from Table 2) and the recommended activation energies from Walker and Morley [6] (open symbols) and from Curran et al. [144,145] (filled symbols), plotted as a function of the type of transition state (for the notation on the horizontal axis see Fig. 5).

Pitz employ a different set of activation energies, described by Curran et al. [144,145]. The differences between the calculated barrier heights and the Curran et al. activation energies are also shown in Fig. 16. In this case the agreement is good except for 1,4 isomerizations, again suggesting that the facility of 1,4 isomerizations is overestimated relative to 1,5 isomerizations. In this case the magnitude of the difference also appears to depend on the type of CeH bond broken in the isomerization. Both the Nancy and LLNL modeling strategies of course reproduce a wide range of experiments, illustrating how cancellation of errors in mechanisms can result in similar predictions from models that may have substantially discordant expressions for key reactions [431] (even for simple systems like methane combustion [432,433]). However, one of the key insights of the detailed theoretical kinetics work on these oxidation systems is that, for many or even most experiments, a major fraction of the products in fact involve the participation of formally direct pathways. The prime challenge for comprehensive modeling is thus not merely to accommodate the newest thermochemistry, but to accurately capture the fundamental, detailed, pressure-dependent mechanism of the elementary reactions. Note that neither the Nancy nor the LLNL mechanisms yet contain formally direct pathways in a systematic manner. Real fuels contain a vast number of hydrocarbons, for which the detailed exploration of the reaction mechanism and the determination of the rate coefficients is a task too great to accomplish anywhere in the near future. However, detailed knowledge about a few, smaller systems combined with systematic, but less detailed studies for larger ones might enable the correct representation of R þ O2 reactions in large chemical mechanisms. Qualitatively successful examples of simple extension of detailed results on smaller systems to model larger ones can be found in Refs. [26,108].

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5.2. Alkyl þ O2 reactions in naphthene oxidation Although the pathways are similar, the ring structure introduces important differences between the cyclic and acyclic alkyl radicals when reacting with oxygen. First, as shown by DeSain et al. in measurements of HO2 formation from Cl-initiated cyclopentane oxidation [23], the direct HO2 elimination pathway has a higher pre-exponential factor than in acyclic radicals. The increased pre-exponential factor arises because the lack of free rotation about the CeC bonds in the alkyl radical leads to smaller entropy loss in moving to the related transition state [23,105,319,434,435]. A similar increase should of course also occur for the isomerizations. Secondly, the constraint of the ring in the cycloalkyl radical affects the barrier heights for the ROO % QOOH isomerizations (see Table 2), the transition states for which are now bicyclic, for example:

The calculated energies for isomerization transition states in cyclohexylperoxy radicals [105,434,435] have a substantially different dependence on the ring size than in the acyclic alkylperoxy radicals, with an increased energy for the 1,6 isomerization over the 1,5 isomerization. This trend is different than that used in most comprehensive models [4,436], with the exception of the Milan group whose cyclohexane model was based on such ab initio calculations [434]. Finally, ring-opening pathways may be available, adding more complexity to the cycloalkyl þ O2 reactions. 5.2.1. Cyclopropyl þ O2 DeSain et al. [318] employed infrared absorption to probe both OH and HO2 formation in Cl-initiated cyclopropane oxidation, and used FTIR analysis of environmental-chamber experiments to determine that ethene and oxirane are the principal end products of the oxidation. They also investigated the cyclopropyl þ O2 reaction by using wQCISD(T,Full)/6-311þþG(3df,2pd)//B3LYP/6-31G(d) and wQCISD(T)/cc-pVNZ//B3LYP/6-311þþG(d,p) energetics to characterize the PES. The large ring strain of the cyclopropyl radical leads to various energetically accessible ring-opening pathways: acrolein þ OH, HOCO þ ethene and HCO þ oxirane (see scheme I below).

399

The HO2-elimination channel in this reaction is peculiar, not only in having a transition state above the entrance channel, but in that the product channel (HO2 þ cyclopropene) is endothermic. In the DeSain et al. work, rate coefficients were not determined. However, the authors point out significant inconsistencies between the theoretical PES and observed branching ratios. Substantial OH and HO2 formation was experimentally observed even at 298 K, and DeSain et al. [318] propose that the HO2 might arise from secondary reactions of HCO or HOCO coproducts of the oxirane and ethene observed as the dominant products in the environmental chamber experiments. However, the quantum chemistry [318] suggests that OH þ acrolein and stabilized cyclopropylperoxy radicals should be the dominant primary products. 5.2.2. Cyclohexyl þ O2 The cyclohexyl þ O2 reaction has received substantial attention. Silke et al. [436] created a comprehensive, low-temperature cyclohexane oxidation mechanism, where special emphasis was given to this reaction. Cavallotti et al. [434] characterized the cyclohexyl þ O2 PES; this work was further developed and combined with rigorous reaction rate theory in the paper of Knepp et al. [105]. Sirjean et al. [435] investigated the isomerization pathways of cyclohexylperoxy and cyclopentylperoxy at the CBS-QB3 level with isodesmic corrections (although they did not calculate the HO2 elimination pathways) and employed TST to generate recommended rate constants for both isomerization processes and the decomposition of the hydroperoxyalkyl radicals to cyclic ethers. Knepp et al. [105] measured the HO2 and OH production in Clinitiated oxidation of cyclohexane, using infrared frequencymodulation detection of HO2 and ultraviolet absorption probing of OH. They also performed detailed quantum chemistry (“G2(MP2)like”) on the cyclohexyl þ O2 stationary points, carried out multiple-well time-resolved master equation calculations for rate coefficients and applied direct VRC-TST//CASPT2/CBS for the entrance channel to calculate the mJ-resolved association rate coefficients. At larger intermolecular distances the pivot points were placed on the center of mass of the fragments, while at shorter distances (5e8 Bohr) the pivot points were located on the radical orbitals. One of the complications in the calculations was the existence of the various conformers; because conformational change is much faster than the chemical reactions of interest, the sum of the partition functions of the conformers was used to approximate the overall partition function. In order to match the experiments, barrier heights were adjusted within estimated

Scheme I

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uncertainty limits. In particular, the transition state from the 3hydroperoxycyclohexyl radical to form the ring-opening products hex-5-enal þ OH was found to have a large multi-reference component and a concomitantly large uncertainty. A substantial change to the energy of this transition state was required to obtain agreement with the hex-5-enal yields observed by HandfordStyring and Walker [271]. However, after adjustment, close agreement was obtained with the available data. The eigenvectoreeigenvalue based time-dependent ME methodology accounts correctly for the formally direct pathways, which were found to be prominent in both OH and HO2-forming channels in the experiments of Knepp et al. [105]. Fernandes et al. [147] utilized the same theoretical kinetics model to model their highpressure measurements of OH production in pulsed-photolytic Clinitiated cyclohexane oxidation. These experiments showed that formally direct pathways, including single-kinetic-step stabilization into QOOH wells from R þ O2, persist even for a relatively large molecule at realistic cylinder pressures for an internal combustion engine, implying that accurate modeling of pressure-dependent autoignition chemistry must include chemical activation and other formally direct processes. The Fernandes et al. [147] work also indicated the predictive force of rigorous theoretical kinetic models, even when applied at pressures more than two orders of magnitude higher than the original validating experiments. 5.3. Reactions of resonance-stabilized hydrocarbon radicals with O2 In resonance-stabilized radicals the radical orbital is delocalized among the carbon atoms, giving these radicals extra stability compared to ordinary radicals. Note that aromatic radicals like phenyl or naphthyl are not resonance-stabilized radicals: they have resonant stabilization of the aromatic ring but have localized radical orbitals. Their chemistry is similar to other non-resonance-stabilized radicals and they are treated in the next section. The simplest resonance-stabilized hydrocarbon radical is the propargyl radical, for which two resonance structures can be written:

The increased stability results in a decreased reactivity towards the oxygen molecule. Table 1 shows the substantially reduced well depths for resonance-stabilized radicals with O2. The smaller well depth also effectively raises subsequent barrier heights for isomerization, so peroxy radicals derived from resonance-stabilized radicals display reduced isomerization compared to peroxy radicals formed from non-resonance-stabilized radicals. In addition, the character of the transition state for the initial association of the radical with O2 is changed because the resonance stabilization is lost during the formation of the ReOO bond. Hahn et al. [159] compared the reaction path energies of various small radicals at the B3LYP/6-31G(d) level of theory, as shown in Fig. 17. They found that the character of these curves transition from barrierless to having a saddle point, as a function of increasing resonance stabilization energy. 5.3.1. Propargyl þ O2 Propargyl can be formed in flames at higher temperatures by the reaction of singlet methylene (1CH2) with acetylene, or by the abstraction of a hydrogen atom from allene or propyne. It plays a key role in PAH formation. However, its reaction with oxygen

Fig. 17. B3LYP/6-31G(d) minimum-energy pathways for the addition of molecular oxygen to five hydrocarbon radicals, taken from reference [159] e Reproduced by permission of The Royal Society of Chemistry.

[159] does not lead to OH or HO2 formation, therefore, its influence in autoignition processes is expected to be small. 5.3.2. Cyclopentadienyl þ O2 Cyclopentadienyl, c-C5H5, is a resonance-stabilized radical, formed during the decomposition of the phenoxy radical. Its reaction with O2 [161] is predicted to lead mainly to vinyl ketene þ formyl radical, and linear pentenal radicals. Again, the importance of this reaction in autoignition processes is expected to be small. 5.3.3. Allyl þ O2 Allyl radical is easily obtained by reaction of OH with propene [119].

Lee and Bozzelli [165] investigated the reaction of the allyl radical with oxygen using CBS-Q//B3LYP/6-31G(d,p) quantum chemistry calculations and steady-state ME coupled to QRRK analysis. They found an entrance barrier of 1.0 kcal mol1 above the reactants; note that the B3LYP/6-31G(d) calculations [159] shown in Fig. 17 have a submerged saddle point. Hahn et al. [159] noted that the entrance saddle point displayed substantial spin contamination, suggesting that multireference methods would be necessary for accurate determinations of the entrance channel characteristics. Lee and Bozzelli [165] found that the major bimolecular product channels for allyl þ O2 above 600 K produce allene þ HO2 via direct HO2 elimination from the corresponding ROO radical, and C2H2 þ CH2O þ OH via internal H abstraction. Moreover, the peroxy moiety can also add internally to the sp2 hybridized carbon atoms, leading to cyclic peroxy radicals. These, as Lee and Bozzelli [165] suggest, can further react with oxygen, and might conceivably contribute to chain branching. However, these processes are orders of magnitude less likely than the dominant channel of simple reversible addition, implying again limited effects on low-temperature autoignition processes.

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5.3.4. Isobutenyl þ O2 The isobutenyl radical is a methyl-substituted allyl radical, also having a resonance-stabilized character.

Chen and Bozzelli [102] studied the allylic isobutenyl radical þ O2 reaction with various quantum chemical methods (CBS-q//MP2(full)/ 6-31G(d), CBS-q//B3LYP/6-31G(d) and B3LYP/6-311 þ G(3df,2 p)// B3LYP/6-31G(d)). The existence of a barrier in the entrance channel was not determined unambiguously: the DFT method gave no barrier, the CBS-q calculations resulted in 1.5 kcal mol1, while the MP2 theory gave 12.2 kcal mol1; again it is likely that multireference methods are necessary for an accurate calculation. High-pressure limiting rate coefficients were calculated using ab initio calculation, literature, or referenced estimation techniques, and pressure-dependent rate coefficients were obtained by a steady-state master-equation/QRRK analysis. There is no low-energy pathway on the PES to bimolecular products, therefore the dominant decomposition channel of the ROO adduct is the re-formation of the reactants or isomerization to the related QOOH species. Zheng et al. [325] also investigated the same reaction at the CBS-QB3 level. They conclude that, apart from minor changes, the predictions of the higher level of theory agree well with the work of Chen and Bozzelli [102] on this PES.

401

The six-membered isomerization with abstraction at the ortho site on the ring, has a lower barrier, but must cross higher-energy transition states to reach bimolecular products.

Canneaux et al. [438] calculated the rate coefficient for the isomerization of benzylperoxy radical to the 1-hydroperoxybenzyl radical (whose fate is dissociation to benzaldehyde and OH) using 54 different levels of theory. They compared their results to the toluene oxidation experiments of Ellis et al. [61], who measured products of toluene addition to reacting H2/O2 mixtures at 773 K. Canneaux et al. [438] recommended the “elaborated CASPT2” (CASPT2/ANO-L-VDZP//B3LYP/cc-pVDZ) method e which yielded an isomerization rate constant 200 times larger than that of Murakami et al. e as giving the most reliable results for this isomerization. 5.3.6. Xylyl þ O2 The reactions of the isomeric xylyl radicals,

5.3.5. Benzyl þ O2 The benzyl þ O2 reaction was investigated by Murakami et al. [437] by CBS-QB3 methods and RRKM/ME calculations. The benzyl radical is also resonance stabilized:

e.g., metaxylyl,

However, the resonance energy is smaller and the first structure is most important in its reactions. Murakami et al. found that the redissociation of the adduct with O2 is fast. Among the bimolecular product channels the formation of benzaldehyde þ OH, which proceeds via a four-membered ring transition state has the highest branching fraction, supporting high-temperature autoignition mechanisms of toluene, but the formation of phenoxy and formaldehyde via a four-membered CeCeOeOe ring transition state was also predicted to be important.

with O2 and the isomerization pathways in the resulting xylylperoxy radicals are thought to be the basis of the “ortho effect” observed in the low-temperature ignition delay of xylenes [163,164], namely that the ortho-xylene is much more reactive than the meta- or para-isomers. High-temperature ignition experiments, where the peroxy radical chemistry is less significant, see little difference among the isomers [439]. Canneaux and coworkers [440] applied the CASPT2-based method that they advocated in the earlier benzylperoxy isomerization studies [438], in conjunction with canonical TST calculations and a Wigner-type tunneling correction, to derive high-pressure limiting values for isomerizations of the various methylbenzylperoxy radicals. In the ortho-xylylperoxy (2-methylbenzylperoxy) radical they found that the 1,6p isomerization (internal H-atom abstraction from the adjacent methyl group) was dominant, rather than the four-membered ring isomerization dominant in benzylperoxy and the other xylylperoxy radicals.

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As in benzylperoxy radicals, the six-membered ring transition state, for transfer of an H atom from the benzene ring, is lower in energy than the four-membered ring isomerization, but faces subsequent energy barriers to bimolecular products. Murakami et al. [441] carried out CBS-QB3 and RRKM/ME calculations on the xylene oxidations and also found a prominent role for the 1,6p isomerization pathway in ortho-xylylperoxy radicals. This facile isomerization may be the basis of the larger low-temperature reactivity of the orthoxylene isomer; it will increase the OH branching fraction in the orthoxylyl þ O2 reaction relative to the analogous reactions of the other isomers, and the QOOH radical formed may also react with O2 and provide a chain branching pathway. 5.3.7. General conclusions The reactions of resonance-stabilized radicals with O2 are relatively slow, because of the loss of resonance stabilization in the initial association step, and are moreover often effectively chainterminating reactions, forming HO2. The lack of reactivity makes these radicals inhibitors of autoignition, and fuels that readily form resonance-stabilized radicals (e.g., alkyl benzenes) are often resistant to autoignition. The presence of facile isomerization pathways, such as the “ortho effect” in xylene, can partially counteract the inhibiting effect of resonance stabilization. 5.4. The reaction of vinylic and aromatic radicals with O2 5.4.1. Vinyl radical and its analogues þ O2 _ The reaction of the vinyl radical ðCH2 CHÞ with oxygen is by far the most thoroughly studied reaction of an unsaturated hydrocarbon radical with O2, and it also provides a model for the ring opening pathways of aromatic radical þ O2 reactions. There are two competing pathways after the initial addition of the oxygen molecule. The reaction can either proceed via a 4-member (dioxetanyl) or a 3-member (dioxiranyl) ring, and the major bimolecular product channel, as observed in the pulsed-photolysis/PIMS experiments of Slagle et al. [442] and of Eskola and Timonen at low temperatures [443], is formaldehyde and the CHO radical:

Bozzelli and Dean [153] and Westmoreland [444] studied the vinyl þ O2 reaction theoretically, but considered only the 4-member ring TS. Carpenter [326] proposed, based on PM3/UHF and

PMP4(STDQ)/6-311G(d)//UMP/6-311G(d) calculations, that the lowest energy pathway corresponds to the 3-membered ring transition state. Qualitatively the reason for this is that no rotation around the double bond is needed at the transition state, while it is necessary for the formation of the 4-membered dioxetanyl structure. Carpenter [154] also studied the kinetics of the reaction using a simplified chemical activation scheme coupled to RRKM calculations to test the kinetic consequences of the proposed mechanism. The calculated barrier heights for the 4-membered ring is 13.5 kcal mol1 relative to the reactants (46.9 kcal mol1 above vinylperoxy) and for the 3-membered ring is 9.7 kcal mol1 relative to the reactants (23.7 kcal mol1 above vinylperoxy); according to the kinetic calculations, this results in the reaction via the 3membered ring being faster by w4 orders of magnitude than reaction over the 4-membered ring TS. Mebel et al. [445] used G2M(RCC,MP2) [446] quantum chemistry and explored the vinyl þ O2 PES in some detail. They also found that the lowest energy pathway proceeds via the 3-member ring transition state. The isomerization of the peroxy radical to the 3-member ring has a barrier 21.4 kcal mol1 below the reactants. The barrier height from the vinylperoxy well is 25.0 kcal mol1, in relatively good agreement with Carpenter [154]: they disagree substantially on the well depth for vinylperoxy. However, the further isomerization of the cyclic intermediate was calculated to be only 14.3 kcal mol1 below the entrance channel barrier (i.e., 32.1 kcal mol1 above vinylperoxy), making this transition state the bottle neck. The critical barrier height for the 4-member ring pathway was found to be 1.0 kcal mol1 relative to the reactants (45.4 kcal mol1 above vinylperoxy). Mebel et al. [445] found two other important pathways: one forming C2H3O þ O with a critical barrier height of 7.8 kcal mol1 relative to reactants, and the other forming C2H2 þ HO2, 3.5 kcal mol1 below the reactants. They applied a steady state kinetic model to calculate rate coefficients, combined with canonical VTST for the association step. The overall rate coefficient was found to be in good agreement with experiment. Carpenter [447] reinvestigated the critical isomerization barrier heights of the cyclic intermediate using CASPT2(23,15)/cc-pVTZ// CASSCF(23,15)/cc-pVTZ, and found that the first barrier in the formation of the 3-member cyclic compound has a higher barrier than the further isomerization step, contrary to the predictions of Mebel et al. [445]. He suggested this to be caused by the large multi-reference character of the transition states, and found 11.5 kcal mol1 largest difference between the single and multireference relative energies. Mebel and Kislov [448], however, carried out MRCI and CCSD(T)/CBS calculations and counter that the deficiency of the earlier single-reference calculations in fact lay with the 6-311 þ G(3df,2p) basis set, and advocated CCSD(T), with Dunning’s correlation-consistent basis sets [348], as an accurate method for vinyl þ O2. Probably the most complete theoretical kinetics calculation on the vinyl þ O2 reaction was carried out by Klippenstein et al. [449] incorporating high-level quantum chemistry for the stationary points, direct VRC-TST for the entrance channel flux, and multiwell time-dependent ME for the kinetics. Direct dynamics was also used to predict product state distributions. They used MP2-corrected QCISD(T)/cc-pVTZ energies at B3LYP/ 6-311þþG(d,p) geometries. In addition, for the key stationary points MRCI, RS2C and CASPT2 energies were also calculated. In the VRC-TST calculations the pivot point for the vinyl radical was located on the C atom, while there were two pivot points on the O2 molecule along the axis; the distance between the latter two was also varied. The VRC-TST calculations agree very well with the available experimental data (available up to w1000 K) for the addition rate coefficient. The results show that

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at low temperatures the dominant bimolecular product channel _ CHO is HCO þ CH2O, while at high temperature the CH 2 (vinoxy) þ O channel is the most important. However, the crossover temperature varies between w1200 and w2500 K depending on the barrier height belonging to the O-O fission, which was varied in the estimated (at least) 4 kcal mol1 uncertainty interval. Recent experimental investigations of the vinyl þ O2 reaction have focused on the branching among the various channels. Knyazev and Slagle [450] extended the temperature range of the earlier Slagle et al. [156] measurements, but did not detect products. However, they pointed out that the weak temperature dependence of the reaction up to 1005 K implied a bimolecular product channel that could compete with the back-dissociation of vinylperoxy to reactants. Low-resolution FTIR emission measurements following photolysis of vinyl radical precursors in the presence of oxygen [451,452] claimed to see CO, CO2, HCO, and CH2O as primary or secondary products of the reaction, but under conditions far too ill-characterized to be useful in determining branching fractions or detailed reaction mechanisms. Oguchi et al. [453] used laser-induced fluorescence detection and measured a significant yield at 298 K for the chain-branching vinoxy þ O channel, ranging from 0.14 at 100 Torr to 0.21 at 10 Torr. The room-temperature reaction of phenylvinyl radicals with O2 was measured by Choi et al. [454] by using pulsed photolysis / cavity ringdown. They observed rapid decomposition of the phenylvinylperoxy radical and also performed B3LYP/6-31 þG(d) calculations to rationalize their observations, finding that the phenylvinylperoxy should form benzaldehyde and HCO, analogously to the vinyl þ O2 reaction. Later work from the same group [455] extended the temperature range to 378 K and confirmed the production of benzaldehyde by mass spectrometry.

The cyclohexadienyl radical, c-C6H7, is an important intermediate in the oxidation of aromatic compounds. Its reaction with O2 was measured by Estupiñán et al. [456] between 302 K and 456 K and atmospheric pressure. They also calculated stationary points at the CCSD(T)/6-31G(d,p)//B3LYP/6-31D(d) level of theory. Kinetic parameters were estimated using TST. They found a 3.9 kcal mol1 barrier to form the peroxy adduct, but no barrier to the direct abstraction channel to form benzene þ HO2, and they ascribed the reaction to direct abstraction. 5.4.2. Phenyl þ O2 Although reactions of benzylic radicals (described above) are more important, understanding reactions of aromatic radicals with O2 is also relevant to predict the effect of aromatics on autoignition. Carpenter [326] suggested that the initial steps of the ring opening pathways in the phenyl þ O2 reaction are analogous to the initial steps of the vinyl þ O2 reaction, using PM3/UHF and PMP4(STDQ)/6-311G(d)//UMP/6-311G(d) level of theory:

403

Mebel and Lin [457] studied the structures of C6H5O2 isomers (minima on the phenyl þ O2 PES) and found the C6H4O(OH) isomers to be most stable, 105e110 kcal mol1 below reactants at the UMP3(PUMP3)//UHF/6-31G(d) level of theory. Sebbar and coworkers [458] investigated similarities among vinyl, phenyl, and dibenzofuranyl radical reactions with O2, applying DFT and ab initio methods (B3LYP/6-311G(d,p), G3MP2B3 and G3), and confirmed that smaller more easily computed systems like vinyl þ O2 can be useful surrogates for unraveling pathways in larger molecules. In line with the predictions of Carpenter [326], Barckholtz et al. [459] found that the lowest energy pathway (27.2 kcal mol1) is the formation of the 3-membered ring (dioxiranyl) radical in the oxidation of the phenyl radical using B3LYP/6-311 þG(d,p)//B3LYP/ 6-31G(d) stationary point calculations on the PES. They also found a low-energy barrierless chain-branching channel leading to phenoxy þ O atom. The internal hydrogen abstraction and the 4membered ring formation pathways are well above the energy of the reactants (by w40 kcal mol1). The authors describe the decomposition and rearrangement pathways on the PES, discussing the kinetics in terms of temperature-dependent Gibbs free energy diagrams. Fadden and Hadad [460] carried out a similar study on the decomposition pathways of the 2-oxepinoxy radical, which is a 7-member ring structure formed directly from the dioxiranyl radical. Sebbar et al. [157,461] studied the thermochemical properties of the phenyl þ O2 system using B3LYP/6-311G(d,p) level of theory and da Silva and Bozzelli [160] carried out a variational analysis on this reaction. They applied scaled O3LYP/6-31G(d) with RRHO approximation to calculate the variational k(T) and achieved moderate agreement with the available experimental data. 5.4.3. Other aromatic radicals þ O2 Other aromatic radicals may have similar reactions with O2, but these have had less study. Park et al. [462] have investigated the association reaction of naphthyl (C10H7) radicals with O2, probing the peroxy radical adduct by visible cavity ringdown spectroscopy and by mass spectrometry. They performed modified Gaussian-2 (G2MS [463]) calculations of the energies of the reactants, product, and association transition state, at geometries optimized with B3LYP/6-31 þG(d,p), and carried out 1D ME calculations with canonical VTST treatment of the association step, but did not consider bimolecular product pathways. Note that the major pathways of the vinyl þ O2 or phenyl þ O2 reactions produce neither OH nor HO2 radicals, in contrast to most other R þ O2 systems considered. The chain-branching channel in these reactions rather forms an oxy radical and O atom. Substituted

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aromatic radicals are expected to have more accessible reaction pathways, some of which can produce OH or HO2 radicals. For example, OH can abstract hydrogen in toluene either from the methyl group or from the aromatic ring, giving benzyl and methylphenyl radicals, respectively. Studies of the resonance-stabilized benzyl and xylyl radicals are described in Section 5.3.1. Methylphenyl radical is an aromatic non-resonance-stabilized radical. It is produced in toluene oxidation to a much lesser extent than benzyl radical because of the far stronger CeH bond in the aromatic ring compared to the CeH bond in the methyl group. The reaction of the methylphenyl radical with oxygen was studied by da Silva et al. [464] at the G3B3 level of theory using QRRK/steadystate ME analysis. The initial peroxy radical can barrierlessly dissociate to form 2-methylphenoxy þ O. The aromatic ring can also open forming conjugated methyl-dioxo-hexadienyl radicals. However, because the methyl hydrogens are benzylic, the barrier to internal (“1,5benzylic”) H abstraction in the 2-methylphenylperoxy radical is rather low (see Table 2). The hydroperoxybenzyl QOOH species formed in this isomerization can readily dissociate to form an OH radical and an o-quinone methide(see scheme II). 5.5. Reactions of oxygenated alkyl radicals with O2 With the emergence of alternative fuels, the combustion chemistry of oxygenated compounds gains more importance. Oxygenates add a new dimension to the already complex ignition chemistry due to the various substitution effects, which can dramatically alter branching fractions and open up new pathways. Many reactions of radicals derived from ethers and alcohols have been studied in some depth; one notable lack is investigations of the elementary reactions of radicals derived from methyl esters, despite the technological importance of biodiesel and the availability of many outstanding studies of the decomposition or overall oxidation of esters [177,237,418, 419,465]. 5.5.1. Radicals derived from alcohols þ O2 Alcohols are likely to remain the most prominent biofuels for the near future. An important difference between oxidation of hydroxyalkyl and simple alkyl radicals is that the barrier for the

direct HO2 elimination pathway is vastly lower for a-hydroxyalkylOO radicals than for unsubstituted alkylperoxy radicals. 5.5.1.1. Hydroxymethyl þ O2. Olivella et al. [466] mapped the PES of _ OHÞ þ O2 reaction at the CCSD(T)/ccthe hydroxymethyl ðCH 2 pVTZ//CASSCF/6-311G(d,p) level of theory and found only one lowlying channel, forming HO2 þ formaldehyde via the peroxy intermediate. Dibble [467] also studied this reaction at the CBS-QB3 level of theory. He used inverse Laplace transform to determine k(E) for the association channel, and the stochastic method of Barker [411,468] to obtain branching fractions. Absolute rate coefficients were not calculated. It was found that the direct HO2 elimination is fast and is the exclusive bimolecular product channel. The ROO / QOOH isomerization is slow due to the high barrier (13.7 kcal mol1). Hermans et al. [469] determined the energetics of the a-hydroxy-alkylperoxys with the G3 and G2M//B3LYP/cc-pVTZ methods and calculated the fate of these energized intermediates. _ The rate coefficient of the dissociation of the activated CH2 ðOHÞOO dissociation was determined. Ramírez-Ramírez et al. [470] used QCISD(T)/6-311þ G(2df,2p)//QCISD/6-31G(d) level of theory and found a saddle point along the entrance channel. However, most probably this is due to the high multi-reference character not captured appropriately by the applied methods. Moreover, this barrier was not found by other authors. Schocker et al. [471] reinvestigated the hydroxymethyl þ O2 reaction both theoretically and experimentally at the G3//B3LYP/631G(d) level of theory. They used microcanonical J-resolved VTST to calculate the association rate along a scaled B3LYP/6-31G(d) potential and using RRHO approximation. The calculated rate coefficient is in good agreement with the available low temperature (<600 K) data and shows a negative temperature dependence. However, at high temperatures (>1000 K) the experimental data has a positive temperature dependence, which cannot be rationalized based on the current theoretical model. The authors, in accordance with previous theoretical works, could not find a direct H abstraction channel, which would resolve the discrepancy at high temperatures. 5.5.1.2. Hydroxyethyl þ O2. Zádor et al. [175] measured product formation from hydroxyethyl þ O2 reactions using the laser-

Scheme II

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photolysis/synchrotron PIMS method, initiated both by the OH þ ethene reaction (forming 2-hydroxyethyl radical) and by Cl þ ethanol (forming both hydroxyethyl isomers). They observed CH2O, ethenol, and acetaldehyde products. Zádor et al. [175] also _ theoretically investigated the 1- and 2-hydroxyethyl (CH3 CHOH _ CH OH) þ O2 reactions. They determined high- and lowand CH 2

2

pressure limit rate coefficients along with branching ratios, which were also compared to multiplexed MBMS experiments. The 1hydroxyethyl þ O2 reaction has a low-lying exit channel leading to acetaldehyde þ HO2; the low barrier is responsible for the reaction having only very small pressure dependence. On the other hand, the 2-hydroxyethyl þ O2 PES has multiple competing pathways forming OH and HO2 radicals; the barriers lie w10 kcal mol1 below the entrance channel and close to each other, which makes the determination of the branching fraction very sensitive to the uncertainties in the quantum chemical calculations; in some cases uncertainties are significant, due to the multi-reference character. Zádor et al. used QCISD(T)/cc-pVNZ//B3LYP/6-311þþG(d,p) quantum chemistry for the stationary points coupled to a timedependent ME. The barrierless entrance channels were calculated using mJ-resolved direct VRC-TST at the CASPT(5e,5o)/cc-pVDZ level of theory, with corrections for geometry relaxation and the aug-ccpVDZ basis set. They obtained qualitative agreement with the experimental measurements, but the experiment showed higher formaldehyde production than the calculations predicted from 2hydroxyethyl þ O2, and the experiments could not observe hydroxyoxirane, predicted to be produced in similar or higher yields than formaldehyde. Zádor et al. [175] suggested that the transition states for these products, some of which have significant multi-reference character, may need to be adjusted or calculated at a higher level than the QCISD(T)/cc-pVNZ//B3LYP/6-311þþG(d,p) (or CASPT2/cc-pVQZ and Davidson-corrected MRCI/cc-pVQZ for multi-reference transition states) methods they employed. da Silva et al. [472] carried out calculations for the 1-hydroxyethyl þ O2 reaction using the G3B3 level of theory. For the highpressure limit rate coefficients they applied canonical TST, while for the pressure dependence they used RRKM calculations with ME analysis. The barrierless entrance channel was treated with canonical VTST using RRHO approximation. They calculate that even though the acetaldehyde þ HO2 channel dominates under low pressure conditions ethenol can also be formed. 5.5.1.3. Hydroxybutyl þ O2. Sun et al. [111] studied the reactions of isobutene-OH adducts with O2 in the context of the neopentane oxidation mechanism. The isobutene-OH adduct can also be derived easily from the i- and the t-butyl alcohols by hydrogen abstraction, therefore this study is discussed here, among the reactions of hydroxyalkyl radicals.

405

Sun et al. [111] calculated stationary points at the CBS-Q//B3LYP/ 6-31G(d,p) level of theory, and used QRRK and steady-state ME for the calculation of the temperature and pressure dependent rate coefficients. Numerous low-lying channels have been found that produce OH or HO2. Interestingly, unlike in unsubstituted alkylper_ oxy radicals, the 1,4aeOH isomerization of the ðCH3 Þ2 CðCH2 OHÞOO _ (with a transition state energy radical to ðCH3 Þ2 CðCHOHÞOOH 28.4 kcal mol1 above the ROO well) is found to be more favorable than the similar 1,4aeOH direct HO2 elimination with a barrier of 31.9 kcal mol1 [111]. This difference from alkylperoxy radicals (for which the elimination TS generally lies below the isomerization TS) reflects the independence of the HO2 elimination transition state on the strength of the CeH bond being broken, in contrast to the isomerization, for which the energy of the transition state is reduced because of the lowering of the CeH bond energy by the a-hydroxyl (Table 2). Another important property of radicals derived from alcohols that they may also produce OH radicals by simple thermal decomposition, i.e., b-hydroxyalkyl radicals form an alkene and an OH radical (see for instance the scheme for the butanols above). Theoretical calculations are available for the decomposition of hydroxyethyl [10] and hydroxypropyl [119] radicals. 5.5.1.4. Larger hydroxyalkyl radicals þ O2. Hydroxyalkyl radicals with greater separation between the radical site and the hydroxyl group have had much less study. Such radicals may occur in the oxidation of longer-chain alcohols or by isomerization of alkoxy radicals [178,180e182]. A series of investigations of hydroxyalkylperoxy radical isomerizations have been carried out based on microprobe sampling and off-line analysis of the hydroperoxide products of di-alkyl peroxide decomposition, followed by isomerization and oxidation of the resulting n-butoxy [179], n-pentoxy [180], and 2-hexoxy [181] radicals. Although the analysis requires a somewhat complicated mechanism, the competition between the isomerization of hydroxyalkylperoxy radical and its reaction with NO was employed to derive isomerization rate constants. The hydroxyalkylperoxy isomerizations that transfer the hydrogen from the carbon a to the hydroxyl group were found to have lower barriers than in analogous unsubstituted alkylperoxy radicals [181], presumably because of the weaker CeH bond. In general, the chemistry of the hydroxyalkyl radicals with O2 is changed from that of unsubstituted alkyl radicals principally by the weakening of the a CeH bond and the possibility of H-atom transfer from the hydroxyl group. 5.5.2. Radicals derived from ethers þ O2 The reactions of O2 with oxygenated radicals derived from ethers have been investigated extensively for dimethyl ether and to a limited degree for methyl t-butyl ether, which was used as an additive to gasoline. Hoyermann and coworkers measured reactions _ Þ [473] and t-butoxymethyl of methoxymethyl ðCH3 OCH 2 _  [474] radical with O2, and Langer et al. [475] studied ½ðCH3 Þ3 COCH 2 the association of molecular oxygen with alkyl radicals derived from F atom reaction with methyl t-butyl ether at room temperature. Sehested et al. [476] measured the rate constant for methoxymethyl þ O2 as a function of pressure at 296 K and at 18 bar pressure for 296 Ke473 K. They used a modified Lindemann mechanism to model the pressure dependence, inferring rate coefficients for the stabilization to ROO and the zero-pressure formation of OH þ 2 CH2O. Rosado-Reyes et al. [171] studied the Cl-initiated oxidation of dimethyl ether at temperatures up to 600 K, employing infrared absorption probing of the formaldehyde, methyl formate, and formic acid products. The methyl formate arises from secondary reactions of the methoxymethylperoxy radical, and the formic acid is observed only from thermal oxidation. Rosado-Reyes et al. [171] attributed formic acid production to an unknown secondary or

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tertiary reaction, assigning OH þ 2 CH2O as the sole primary bimolecular product channel of methoxymethyl þ O2. Yamada et al. [477,478] studied the methoxymethyl þ O2 system using QRRK/ME analysis and CBS-q or G2 energetics. The rate coefficient for the barrierless addition was taken from the C3H7 þ O2 reaction. The major bimolecular products are 2 CH2O þ OH, with barriers below the entrance channel. However, the authors had to decrease the barrier of QOOH dissociation by a somewhat surprising w3 to 6 kcal mol1 in order to match experimentally observed formaldehyde yields. Andersen and Carter [194e197,479] performed extensive hybrid density functional theory calculations on the mechanism of low-temperature dimethyl ether oxidation, uncovering a number of novel aspects of the chain branching following O2 _ 2OCH2OOH, which will be described further in the addition to CH following section, and characterized the association of methoxymethyl with O2 and the chain-propagating channel to 2 CH2O þ OH. In their theoretical kinetics work [196,197] they employed canonical TST, with RRKM/VTST for the barrierless reactions, as well as stochastic solution of the ME. They found an additional, lower-energy, transition state for formation of 2 CH2O þ OH from the QOOH, not discovered by Yamada et al. [477,478]. This transition state showed product formation initiated by OeO bond fission, with subsequent dissociation of the formaldehyde dimer. Andersen and Carter [479] pointed to this as an illustration both of the need for caution in adjusting stationary point energies without a through search for relevant transition states and of the potential deficiencies of the CBS-q and related methods for peroxy radical chemistry. Suzaki et al. [168,170] measured OH and HO2 formation in Clinitiated oxidation of dimethyl ether, finding a far greater OH yield (0.1e0.4) than in alkyl radical reactions with O2. They also observed a rapid production of HO2 which could not be described based on the mechanism of Yamada et al. [477,478]. They proposed that HO2 was produced both by secondary oxidation of the formaldehyde product and by reaction of HCO formed from the hydroperoxymethoxymethyl radical via OH transfer to form an HOQO species, Suzaki et al. [170] also carried out MRMP//CASSCF calculations on the various stationary points for the isomerization and dissociation, finding that the transition states for several unimolecular reactions of the QOOH, including dissociation to OH þ 2 CH2O and to CH2O þ CHO and H2O, lay close to one another in energy.

As discussed in Section 5.6, the calculated barrier heights for these transformations are substantially different than those in unsubstituted alkyl radical reactions, suggesting that the ether group stabilizes the transition state.

5.5.3. Vinoxy radical and its derivatives þ O2 _ CHOÞ can be formed in 5.5.3.1. Vinoxy þ O2. The vinoxy radical ðCH 2 combustion systems via the O þ C2H4, O þ C2H3, OH þ C2H2 reactions and is present in significant quantities during ethanol ignition. The vinoxy radical is essentially a carbon-centered radical, with relatively small resonance stabilization energy (w5 kcal mol1, see e.g. [480]) and with an appreciable stability (w40 kcal mol1 well depth [183]). Important substituted vinoxy radicals are the 1_ ) and 2-methylvinoxy methylvinoxy (acetonyl, CH3 CðOÞCH 2 _ radicals, both with a similar resonance stabilization ðCH3 CHCHOÞ energy. The small resonance energy results in relatively stable ROO radicals formed in their reaction with molecular oxygen. However, the outcome of the acetonyl þ O2 reaction is quite different from the other two, due to the absence of the weak a-carbonyl CeH bond. Gutman and Nelson [481] carried out an experimental investigation of the vinoxy þ O2 reaction using LIF for the detection of the vinoxy radical. They found small negative temperature dependence in the 295e476 K temperature, and slight positive pressure dependence in the 1.5e100 Torr (N2, SF6) pressure range. They estimated that the reaction reaches its high-pressure limit below 1 Torr, and hypothesized the formation of the CH2O þ CO þ OH “bimolecular” products via 1,4 internal hydrogen transfer from the carbonyl group. Lorenz et al. [482] also studied the reaction at 298 K and between 7.5 and 210 Torr of He, and identified OH as a reaction product with w20% yield at 20 Torr. The temperature dependence of the rate coefficient around room temperature was also determined. Zhu and Johnston [483] used cavity ring-down absorption experiments to measure the decay of the vinoxy radical in the pressure range 2.5e400 Torr. They observed a large glyoxal production, but the time-profile indicated that it is more likely to be a secondary product. They also detected formaldehyde, but could not quantify the signal unambiguously to support the products proposed by Gutman and Nelson [481]. Lee and Bozzelli [183] calculated thermodynamic properties and kinetic parameters on the vinoxy þ O2 potential energy surface at the CBS-Q level of theory using steady-state master equations. The main product channel is indeed CH2O þ CO þ OH via the carbonyl H atom abstraction and with a critical barrier height being w7 kcal mol1 below the energy of the reactants. The peroxy radical is bound by 27.5 kcal mol1, which is approximately halfway between the binding energy of a resonance-stabilized and an ordinary radical of similar size. CBS-Q predicts a small (w3 kcal mol1) barrier on the entrance channel (although as always multireference effects may play a role in radical-radical association), and the direct HO2 elimination has a high barrier (w20 kcal mol1), making this channel unimportant. Delbos et al. [184] studied the vinoxy þ O2 reaction in quasistatic and discharge flow reactors in the 298e660 K temperature, and 0.75 Torre46 bar pressure range by monitoring the vinoxy concentration using LIF. They also carried out QCISD(T), CCSD(T) and B3LYP energy calculations for the corresponding PES, and using steady-state approximations [397], obtained pressure-dependent rate coefficients. They found that the calculated entrance barrier height was unrealistically high given the experimentally observed weak temperature dependence; therefore, an assumed w0.25 kcal mol1 value was used in the model, resulting in a good agreement with the experimental results. Between 420 and 570 K a residual, more slowly decreasing component in the vinoxy timeprofile was observed in the experiments, which could be readily rationalized based on the R þ O2 % ROO equilibrium. Using OH LIF they determined that the OH radical is a product at low pressure. Yields were not quantified experimentally, but the model predicted a strongly decreasing OH yield with pressure, 58% at 7.5 Torr and 7% at 200 Torr, and T ¼ 298 K.

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5.5.3.2. Acetonyl þ O2. The acetonyl þ O2 reaction was studied by Cox et al. [484], who reported the rate coefficient at 1 bar and 298 K, along with the UV absorption spectra of the acetonyl and the adduct acetonylperoxy radicals. Oguchi [187] measured the rate coefficients of 1- and 2-methylvinoxy with O2 at 298 K in the ~ X ~ electronic pressure range 8e330 Torr using vinoxy LIF (B) transition) coupled to pulsed laser photolysis. Using RRKM theory and B3LYP calculations they calculated high-pressure limiting rate coefficients, and applying the Troe formalism, fall-off parameters were also obtained. It was found that both radicals react with oxygen in the investigated pressure range w10 times faster than the vinoxy radical. Hassouna et al. [186] also applied LIF to follow the decay of the acetonyl radical during its reaction with O2 in the temperature range 291e520 K and pressure range 0.042e10 bar. Similarly to the vinoxy case [184], in the temperature range 400e520 K they observed biexponential decays associated with the equilibration of the acetonylperoxy and the reactants. Stationary point on the PES of the reaction were explored using the composite G3MP2B3 and CBS-QB3 methods showing that the reaction has w2 kcal mol1 barrier on the entrance channel, but as in the study of Delbos [184], this is probably too high as well. Internal H abstraction from the CH3 group (1,5p) is the lowest-activationenergy isomerization from the acetonylperoxy well. Laser-induced fluorescence was also used in the work of Imrik et al. [485] to monitor the time-profile of the acetonyl radical in lowpressure discharge-flow experiments, which further established the fall-off behavior of this reaction. The authors point out that even though the resonance stabilization energy of the acetonyl radical (w4 kcal mol1 [480]) is much smaller than that of the prototype allyl radical (w12 kcal mol1), this difference is not reflected in different reactivity of these radicals towards O2. Another observation of the paper (in accordance with Oguchi et al. [187]) is that the pressuredependent region is shifted for both the allyl and the acetonyl radicals to higher pressures compared to the alkyl þ O2 reactions. Using the same experimental apparatus the acetonyl þ O2 reaction was further studied (Kovács et al. [189]), and both the supposed reaction product OH and the reactant acetonyl was monitored with LIF. The association rate coefficient was determined experimentally at 298 K in the pressure range 1e8 Torr and practically no OH production was found from this reaction under these conditions. In this work the PES of the reaction was also explored using various levels of theory up to QCISD/ aug-cc-pVDZ//QCISD/aug-cc-pVTZ. A small positive barrier was found in the entrance channel (although again it is possible that _ multireference effects could contribute) leading to CH3 CðOÞCH2 OO, followed by an only slightly higher barrier to the corresponding _ CðOÞCH OOH. The lowest energy pathway from QOOH isomer, CH 2 2 this QOOH species leads, over a substantial barrier, to the enol-ace_ which can dissociate to form the tonylperoxy, H2 C ¼ CðOHÞCH2 OO enol form of acetonyl and an O2 molecule.

The channel producing OH þ oxetan-3-one (above) has a slightly higher barrier. However, the most likely pathway for the acetonylperoxy radical is backdissociation under LTC conditions, with only a minor leak to bimolecular products. They observed a small but significant pressure dependence for the reaction between 1.33 mbar and 10.91 mbar, in at best qualitative agreement with the falloff behavior implied by the higher-pressure measurements of Oguchi et al. [187] and Hassouna et al. [186].

407

Kuwata et al. [185,188] studied the reactions of vinoxy, acetonyl, and 2-methylvinoxy radicals with molecular oxygen at the CBSQB3 level combined with RRKM / steady-state ME simulations. They also found small (2e4 kcal mol1), possibly spurious barriers to the addition. The well-depth of the peroxy radicals for all three cases is similar, w27 kcal mol1, but the lowest barriers for isomerization to a QOOH species are different for the three radicals. The values are 19.5 kcal mol1 for the vinoxyeOO, 18.6 kcal mol1 for 2methylvinoxyeOO (both 1,4aldehyde), and 26.1 kcal mol1 for acetonyleOO (1,5pb-carbonyl), measured from the bottom of the peroxy wells. The difference in barrier height reflects the weakness of the aldehydic CeH bond, and can explain the differences in the experimentally observed OH yields [184,189,483,486], as confirmed numerically by ME calculations. In general it appears that the effect of ethereal or carbonyl oxygen on the reactivity of radicals with O2 is more complex than a simple weakening of proximal CeH bonds. 5.6. The “second O2 addition” and other hydroperoxyalkyl reactions Despite its central importance, and despite years of effort, direct experimental investigation of the ephemeral QOOH species, including the second O2 addition reaction, has remained unattainable. Product channels and rate coefficients currently employed in comprehensive models therefore are mostly estimates, with a very few exceptions where direct theoretical kinetic calculations have been performed. To date the Bozzelli group [110,192,193,487,488] has been responsible for most of the direct computational information on the critical reactions of QOOH with O2; they studied hydroperoxypropyl [192], hydroperoxyethyl [193], 4-hydroperoxypent-2-yl [487,488] and hydroperoxyneopentyl þ O2 [110] reactions. The calculations on the hydroperoxypropyl þ O2 reaction [192] were carried out before the mechanism of direct HO2 elimination was understood; therefore, this pathway is missing in that work. Moreover, energies of the stationary points were obtained using empirical estimates, such as group additivity rules. However, the mechanism shows that the lowest pathway produces OH radical and leads to chain branching. Stationary points on the hydroperoxyethyl þ O2 PES were calculated at the CBS-Q//B3LYP/6-31G(d,p) level of theory [193]. Kinetic parameters were estimated by QRRK theory and microcanonical TST. The rate coefficient for the barrierless association process was assigned based on the ethyl þ O2 reaction. After the _ initial formation of OOCH 2 CH2 OOH, the internal hydrogen abstraction via a 5-member ring leads to rapid dissociation into OH and HOOCH2CHO. The direct HO2 elimination pathway is less exothermic, but the barrier is also below the entrance channel. In the work of Sun and Bozzelli [110] the hydroperoxyneopentyl þ O2 reaction (Scheme III) was investigated at the CBS-Q//B3LYP/6-31G(d,p) level of theory. The O2QOOH radical can either form bimolecular products or can isomerize to the corresponding HOOQeHOOH. The barrier heights of dissociation and isomerization were found to be the same within 1 kcal mol1. The bimolecular product can further dissociate, thus forming a second OH and leading to chain branching. Again, QRRK calculations combined with steady-state ME methodology were used to estimate pressure and temperature dependent rate coefficients for this system. Zheng et al. [325] investigated the second O2 addition to the 2hydroperoxymethyl-2-propenyl radical using B3LYP/6-311G(d,p) and G2(MP2) energies.

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This QOOH radical is formed in the oxidation of the resonancestabilized isobutenyl radical (see Section 5.3.1). One of the main differences is that there is a small barrier (1.5 kcal mol1) on the addition channel, commonly found for resonance stabilized radicals (see also Fig. 17). The lowest-energy pathway has only 3.2 kcal mol1 barrier and leads to the formation of two OH radicals. The reaction can also form cyclic products, although with higher activation energy. As in the other QOOH þ O2 calculations, Zheng et al. [325] also carried out QRRK calculations for the temperature and pressure dependence of the reaction. Andersen and Carter [194,196,197] studied the reaction of O2 _ OCH OOH radical derived from dimethyl ether, with the CH 2 2 employing UDFT-B3LYP calculations of the stationary points [194]. _ OCH OOH kinetics calculations, applying They also carried out CH 2 2 canonical transition-state theory and RRKM/VTST for high-pressure-limiting rate constants and determining pressure-dependent rate coefficients with stochastic master equation calculations _ [196,197]. After formation of an OOCH 2 OCH2 OOH radical by association with the “second O2”, isomerization by internal H atom transfer can occur with a barrier about 7 kcal mol1 below the þ O2 _ asymptote. The resulting “HOOQOOH” radical, HOOCH2 OCHOOH, very rapidly (in a few hundred fs [196,197]) dissociates to hydroperoxy methyl formate (HOOCH2OCHO, denoted HPMF) and OH. The subsequent fate of the HPMF determines the level of chain branching. Direct OeO fission, producing a second OH, and subse_ quent dissociation of the OCH 2 OCHO radical to formic acid and HCO, appears to be the most facile channel. However, Andersen and Carter [194,196,197] found that an unusual pathway could compete with this channel: a hydrogen transfer from the hydroperoxyl group to the central oxygen and subsequent CeO fission to produce formic acid and CH2OO, the simplest Criegee biradical. The Criegee intermediates (although only recently directly observed in the gas phase [292]) are well-known in ozonolysis [489] and are important atmospheric species, but Andersen and Carter’s work is the first time a role for them has been proposed in combustion. The major steps are summarized in Scheme IV. Asatryan et al. [487,488] carried out CBS-QB3 calculations for the 4-hydroperoxypent-2-yl þ O2 reaction. Because of the size of the system it includes many sorts of transition states for isomerization. The formation of OH þ CH3C(O)CH2CH(OOH)CH3, has the lowest (approximately 20 kcal mol1) barrier relative to the entrance channel, and subsequent dissociation of the ketohydroperoxide will lead to chain branching. Asatryan et al. [487,488] also found a pathway to a Criegee biradical, albeit with substantially higher barriers. The second O2 addition must compete with other, principally unimolecular, reactions of the QOOH radicals. The dissociation to form OH or HO2 is the other dominant reaction of QOOH. Using

BHandLYP/6-311G(d,p) density functional theory, Chan et al. [490] calculated barrier heights for the ring-closure processes of aliphatic QOOH radicals, i.e. for reactions producing a cyclic ether and an OH radical, and compared the rate of the QOOH / ROO isomerization to the rate of QOOH / OH þ cyclic ether reactions. Despite inaccuracies of the BHandLYP functional for QOOH [428], as discussed in Section 5.1.2, Chan et al. found that all QOOH species are more likely to equilibrate with the related ROO than to dissociate into OH and a cyclic ether, except for the b-hydroperoxyalkyl radicals. However, b-hydroperoxyalkyl radicals are those formed in the HO2 addition to alkenes, such as in 14Clabeling experiments [101] that were interpreted as showing the dominance of dissociation over isomerization in the QOOH systems [5]. It appears that this result is particular to the bhydroperoxyalkyl radicals and that ROO % QOOH isomerization is rather more facile in other cases. Wijaya et al. [491] investigated the OH formation pathways starting in various acyclic QOOH species (up to 6 carbon atoms) using a variety of quantum chemical methods (CBS-Q, CBS-QB3, QCISD, B3LYP, and BHandHLYP). Their general conclusion for the formation of the cyclic ethers is that dissociation of b-hydroperoxyalkyl radicals to the oxiranes (3-membered CeCeOe ring) is energetically and kinetically most favorable, followed by dissociation of g-hydroperoxyalkyl radicals to the oxolanes (5-membered CeCeCeCeOe ring) and then by dissociation of d-hydroperoxyalkyl radicals to oxetanes (4-membered CeCeCeOe ring). The barrier height is also correlated with the order of the carbon radical center: it is smaller for tertiary carbon radical, followed by the secondary and then by the primary ones. Of course the initial isomerization to form the QOOH species from ROO tends to favor QOOH radicals with a larger separation between radical and hydroperoxy group (b < d < g), which can lead to a preference for larger O-heterocycles in overall oxidation processes [418,419]. In another study Green et al. [492] had applied density functional theory and conventional transition-state theory to a series of such reactions for hydroperoxy alkyl radicals and found that the QOOH / HOQO isomerization was significant, but only about one-tenth the rate of the cyclization and decomposition to OH þ cyclic ether. A similar QOOH / HOQO reaction was invoked by Suzaki et al., [170] in the oxidation of dimethyl ether and supported by MRMP//CASSCF calculations. Green et al. [492] found with CBS/QB3 methods that the barrier for hydroxyl transfer in 2-hydroperoxyalkyl radicals was some 9 kcal mol1 higher than for the QOOH / oxirane þ OH dissociation, and in 3-hydroperoxyalkyl radicals hydroxyl transfer had a transition state about 6 kcal mol1 _ OCH OOH higher than that for QOOH / oxetane þ OH. If the CH 2 2 radical is most like a 3-hydroperoxyalkyl radical, the MRMP//CASSCF calculations of Suzaki et al. [170] suggest that oxygenation substantially facilitates this OH transfer.

Scheme III

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409

Scheme IV

5.7. Alkyl þ HO2 reactions Reactions of HO2 with the simplest R, the methyl radical [493,494], and the resonance-stabilized radicals benzyl [495] and cyclopentadienyl [161] have been investigated theoretically. Zhu and Lin [494] investigated the CH3 þ HO2 reaction, using RRHO approximation along a Varshni potential for the barrierless entrance and exit channels. The stationary points on the PES were characterized by the G2M//B3LYP/6-311G(d,p) method [446]. In 2009, Jasper et al. [493] reinvestigated the reaction (see the corresponding PES in Fig. 18) with higher-level quantum chemistry and much more accurate theoretical kinetics methods. Energies of the stationary points were calculated at the QCISD(T)/CBS//B3LYP/ 6-311þþG(d,p) level of theory, except for the highly multi-reference H abstraction channel on the singlet surface, where they applied CAS þ 1þ2 þ QC(4e,3o)/CBS//CASPT2(4e,3o)/aug-cc-pVTZ. They then used direct VRC-TST to calculate the microcanonical Jresolved reactive flux through the barrierless entrance channel, and the eigenvector-eigenvalue based solution of the time-dependent ME to obtain rate coefficients. Jasper et al. showed that the main bimolecular product channels are methoxy þ OH and CH4 þ 3O2. Due to the low-lying exit channels the pressure dependence of the total rate coefficient is predicted to be small. The experimental data on R þ HO2 is rather sparse. In very lowpressure reactor (VLPR) experiments, Dobis and Benson [496] observed no products from ethyl þ HO2 that would correspond to the radical product channels under their conditions and measured the rate coefficient for the chain-terminating C2H4 þ H2O2 products as 3  1012 cm3 molecule1 s1. They proposed an approximately equal role for the (unobservable in their experiments) C2H6 þ O2. The observed rate coefficient from the Dobis and Benson experiments is approximately an order of magnitude lower than that expected based on calculated total rate coefficients for similar systems CH3 þ HO2 [493] or benzyl þ HO2 [495]. In pulsedphotolysis / time-resolved mass spectrometry experiments, Ludwig et al. [497] directly measured the reaction of C2H5 þ HO2, finding a more realistic total rate coefficient of 5  1011 cm3 molecule1 s1, and observed a strong C2H5O product signal, suggesting that C2H5O þ OH is the major product. Although no detailed calculations have been reported, the kinetics for the reactions of higher aliphatic alkyl radicals with HO2 can be expected to be essentially analogous to CH3 þ HO2. The OH radical product is formed by the scission of the OeO bond; as the length of the alkyl chain is expected to have relatively small effects on this process, this channel likely dominates for most aliphatic R þ HO2 reactions. At low temperatures the ROOH molecule can also be stabilized. Simmie et al. [138] compared the bond energies of C1C4 hydroperoxides, and the difference between the weakest (methyl) and strongest (s-butyl) bond is w2 kcal mol1. The H2Oforming channel in CH3 þ HO2 has a 4-center transition state, where

the outer O atom in the breaking OeOH bond abstracts an H atom from the a-carbon. This transition state should also remain relatively unchanged as the alkyl chain gets longer. Finally, the possibility of roaming reactions [498,499] has to be considered, which might channel some fraction of the barrierless alkoxy þ OH products into the molecular (e.g., aldehyde þ H2O) bimolecular products. The benzyl þ HO2 [495] and cyclopentadienyl þ HO2 [161] reactions are calculated to produce OH þ benzoxyl or OH þ cyclopentadienoxy as the principal bimolecular products, with contributions from the chain terminating H2O-forming channels about two orders of magnitude lower. As these reactions convert relatively unreactive HO2 and resonance-stabilized radicals to more reactive radical products, it can be expected to accelerate chain propagation and enhance autoignition. 5.8. Alkylperoxy þ HO2 reactions Hou and Wang [222] and Anglada et al. [220] calculated stationary points on the methylperoxy þ HO2 reaction, and both studies found that the lowest energy pathway is a barrierlessly formed van der Waals well followed by a submerged barrier on the triplet surface. The resulting bimolecular product pair on the triplet surface is CH3OOH þ 3O2, expected to dominate around room temperature; the methyl hydroperoxide can decompose at the temperatures of autoignition to form a methoxy and a hydroxy radical (cf. Figs. 6 and 18). Hou and Wang [222] used CCSD(T)/ccpVDZ//B3LYP/6-311G(d,p) level of theory and obtained 7.65 kcal mol1 for the van der Waals well, and 3.76 kcal mol1 for the submerged barrier. The same values of Anglada et al. at the CASPT2/6-311 þ G(3df,2p) level of theory are 4.5 kcal mol1 and 3.8 kcal mol1, respectively. The structure of the weakly bound complex differs in the two studies: Hou and Wang found a 7member ring, while Anglada et al. a 6-member one. On the singlet surface both studies predicted positive barriers following the weakly bound complex, which is again formed in a barrierless process. Nevertheless, Hou and Wang [222] identified this with a hydrotetroxide structure, while Anglada et al. [220] found a 6-member ring hydrogen bonded structure (almost identical to the triplet one), which is then separated from the hydrotetroxide structure by a small barrier. Both authors found a pathway from the hydrotetroxide intermediate leading to OH, HO2 and the corresponding aldehyde. However, the tight and high transition state most probably prevents the formation of these products. Anglada et al. [220] also carried out a simple analysis of the kinetics at the canonical level, which reproduced the negative temperature dependence of the association rate coefficient for this reaction. However, the calculated and experimental rate coefficients differ significantly. The ethylperoxy þ HO2 reaction was studied by Hou et al. [221] at the RCCSD(T)/CBS//B3LYP/6-311G(d,p) level of theory, and by

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temperatures, with rate coefficients in the 5e20  1011 cm3 molecule1 s1 range.

5.9. Addition of the HO2 radical to unsaturated compounds

Fig. 18. Stationary points on the methyl þ HO2 PES, reproduced from the work of Jasper et al. [493], Copyright 2009, with permission from Elsevier.

Hasson et al. [223] at the CBS-QB3//B3LYP/6-311G(2d,d,p) level of theory. The general features of the more important triplet surface are very similar to the methylperoxy case, which suggests that similar results are to be expected for even longer hydrocarbon chains. All predicted product channels on the singlet surface proceed via a positive barrier and form OH either directly, or via unstable bimolecular products. Hou et al. [221] investigated the rate coefficients for both the triplet and the singlet surfaces using flexible-transition-state theory (essentially applying RRHO approximation) with a Morse potential, and using mTST for the tight transition states. The authors noted that the rate coefficient on the triplet surface is extremely sensitive to the level of theory used for the calculation of the submerged saddle point. In the absence of experimental evidence, the high temperature branching fractions are uncertain; however, the lowest energy pathways all produce OH radicals. The kinetic analysis of Hasson et al. [223] shows that ethyl hydroperoxide þ oxygen are the main products of the reaction. Du et al. [500] investigated a significantly larger system, the benzylperoxy þ HO2 reaction at the B3LYP/6-311þþG(3df,3pd)// B3LYP/6-311/G(d,p) level of theory. Even though the energetics is expected to exhibit significant uncertainties, the reaction was found to mainly happen again on the triplet surface producing C6H5OOH þ 3O2. The shallow well on the singlet surface is predicted to be the hydrotetroxide species. It is clear from this section that the channels found on the singlet surface are controversial; the major questions are presented schematically in Fig. 6. Moreover, calculated energies are also very sensitive to the level of theory applied; as Anglada et al. [220] point out, the substantial multi-reference character necessitates the use of multi-reference electronic structure methods for at least the critical barriers on the PES. The further theoretical kinetic investigation of this reaction type would be also very important to understand the anticipated complex pressure and temperature dependence. For the accurate determination of the rate coefficients an effective two-transition state model should be used; these kinds of models have been successfully applied to study OH þ alkene reactions (see e.g. [10,119,388,389]), which feature similar entrance channels with a van der Waals well and a submerged barrier. Work in this area is expected to continue especially as such reactions can effectively convert HO2 radicals into OH radicals at autoignition

The addition of HO2 radicals to alkenes directly yields bhydroperoxyalkyl radicals (QOOH) that then decompose to form OH þ oxiranes [6,100], which was one of the processes puzzled scientists in the quest for the direct HO2 elimination pathway. HO2 and the organic peroxy radicals have two low-lying electronic states, the ground 2A00 and the lowest excited 2A0 states. Based on the calculations of Quelch et al. [420,421] and Stark [501] the ground states of the ROO and HO2 radicals are correlated with each other, while the ground state of the QOOH radical correlates with the low-lying excited states of the ROO and HO2 radicals (see Fig. 19). Stark [501] put forward the idea that the addition of the hydroperoxy radical to olefins involves a conical intersection between the 2A00 and 2A0 surfaces. Before the details of the direct HO2 elimination from ROO radicals became clear, Pilling et al. [308] and Stark [501] proposed mechanisms based on these differentsymmetry states to explain the discrepancy between experimentally observed barrier heights for HO2 addition to ethene and for ethene þ HO2 formation from ethyl þ O2. However, Stark [501] suggested that experimentally deduced barrier for HO2 addition to ethene (marked with the circle in Fig. 19) would still need to be revised downward by w4 kcal mol1 to rationalize the ethyl þ O2 system based on conical intersections. The underlying discrepancy has since been resolved by the detailed calculations of the direct elimination channel [18e20,424], but the participation of statemixing in determining the shape of the potential energy surface for the ROO/QOOH systems remains an interesting, if perhaps academic, question. Andersen and Carter [502] recently used hybrid DFT and Born-Oppenheimer molecular dynamics to investigate the ethyl þ O2 % HO2 þ ethene reaction. They follow the vibronic interactions that mix the 2A0 and 2A00 states and in fact observe state mixing all along the reaction path. Chen and Bozzelli [99] used CBS-q//MP2(full)/6-31G(d) level of theory to study the HO2 addition to ethene, propene and isobutene, forming the corresponding QOOH radicals. They calculated thermodynamic properties and high-pressure limit rate coefficients, and compared their activation energies to those experimentally derived by Walker and coworkers based on observation of epoxide formation [94e96,100]. Chen and Bozzelli [99] report three-parameter Arrhenius fits rather than the two-parameter fits of Walker and coworkers, but fitting the Chen and Bozzelli recommendations to a simple Arrhenius form yields activation energies very similar to the experimental values. Fig. 20 displays a comparison of the calculated rate expression for HO2 addition to ethene from Chen and Bozzelli [99] and the experimental determination of Baldwin et al. [96]. The activation energies are essentially identical between 500 K and 1000 K, suggesting that the experiments in fact do probe the transition states for HO2 addition to alkenes to form QOOH. The resolution of the discrepancy between the activation energies for ethyl þ O2 / HO2 þ C2H4 and for the reaction of HO2 with C2H4 is partly that the two reactions are simply not each other’s reverse. Ethylperoxy radical preferentially dissociates via the lower-enthalpy transition state to direct elimination rather than over the higher barrier to QOOH formation. Both the elimination and isomerization transition states are relatively constrained. From the HO2 þ ethene asymptote, however, the competition is between the lower-enthalpy but low-entropy transition state to form ethylperoxy and the higher-enthalpy but _ CH OOH. Using the high-entropy transition state to form CH 2 2 thermochemistry from Sheng et al. [398] to calculate association

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Fig. 19. Schematic R þ O2 potential energy surface, based on ethyl þ O2, showing a rationalization of the shape of the PES in terms of interactions between 2A0 and 2A00 states. The OH þ oxirane channel is omitted for clarity. The ROO radical dissociates directly to form HO2 þ alkene, but the reaction of HO2 þ alkene proceeds not back to ROO but largely via the higher enthalpy but also higher entropy (by w10 cal mol1 K1 for ethylperoxy at 800 K [398]) transition state to form QOOH, which dissociates to an oxirane þ OH.

rates from their high-pressure rate coefficients for reverse dissociation reactions

_ CH3 CH2 OO/HO 2 þ C2 H 4

(16)

and

_ CH OOH/HO þ C H CH 2 2 2 2 4

(17)

yields a ratio of k16/k17 < 0.2 for the temperature range of Baldwin, Stout and Walker [96]; i.e., less than w20% of the HO2 þ ethene in those experiments reaches the ethylperoxy well. Stark [501] had argued in general against participation of ROO in the HO2 addition to alkenes based on the small yield of (Z)-but-2ene product from the HO2 addition to (E)-but-2-ene in the experiments of Stothard and Walker [503]. However, the topography of the 2-butyl þ O2 PES is qualitatively different from ethyl þ O2, in that the transition state for HO2 elimination from _ CH3 CHðOOÞCH 2 CH3 in fact lies above that for HO2 elimination _ from the QOOH species, CH3 CHðOOHÞCHCH 3 [26]. Therefore the production of ROO from HO2 addition to 2-butene is disfavored both by enthalpy and by entropy relative to formation of QOOH. Furthermore, as Pilling et al. [308] point out, under the high-O2 conditions of the Walker et al. experiments, any ROO radicals that dissociate to ethyl þ O2 can react again to regenerate HO2 þ ethene reactants, so that the portion of the reaction that may proceed through ROO is hidden from the end product measurements. The oxirane is formed not from ROO, but is produced directly and rapidly from the QOOH product of the HO2 addition to ethene. 6. Outlook The past decade has brought dramatic new insights into the fundamental chemistry that underlies low-temperature autoignition, but there remain many little-explored frontiers. First, there is the expansion in the number of fuel species that must be considered, because of the changing nature of the fuel stream. The potential increased use of biofuels will require balancing technological, environmental, and economic factors in deciding the most beneficial form of biofuel e e.g., using oxygenated bio-generated fuels like butanol or furans, biological generation of hydrocarbon fuels, use of biocrude in the refinery input stream e and fundamental research into the combustion of novel biomass-derived

411

Fig. 20. Comparison of calculated rate coefficients for HO2 þ C2H4 / CH2CH2OOH from Chen and Bozzelli [99] with the experimental determination of Baldwin, Stout and Walker [96] for the process HO2 þ C2H4 / (CH2CH2OOH) / oxirane þ OH.

molecules must be a part of this balance. Second, the improved understanding of the critical R þ O2 reaction in particular has increased attention to details of the subsequent reactions of QOOH and other reactions of peroxy radicals in the LTC region. Finally, the technological innovations in engine design continue to extend the range of conditions over which predictive combustion modeling is required., e.g. through increased dilution, higher pressures, and ultralean combustion. Investigation of several classes of reactions may prove central to developing increasingly accurate and predictive models of low- and intermediatetemperature autoignition chemistry. The details of the reactions of radicals derived from methyl and ethyl esters should be investigated. Besides the continuing and well-known questions along the direct line of the oxidation mechanism in Fig. 1, the crucial and complex chemistry among peroxy radicals remains incompletely understood. The product branching fractions in reactions of HO2 and ROO with alkyl radicals, for example, as well as HO2 þ ROO, need to be established. Progress in understanding the elementary reactions of autoignition will rely increasingly on the close collaboration of theory and experiment. The rigor of that collaboration will depend on methodological improvements in connecting experimental observables with fundamental physical characteristics on a potential energy surface. The strategy of tuning stationary-point energies within their uncertainties implicitly relies on the uncertainties in those energies dominating the uncertainty in the overall kinetics calculation. As available quantum chemistry calculations continue to improve e e.g., the recent exquisite work by Wilke et al. on ethyl þ O2 [342] e the demands on the theoretical kinetics (e.g., RRKM/ME) part of the calculation increase. For example, the details of energy transfer have long been considered in the “noise” of such calculations, but that will not long remain the case. More precise treatment of the form of the energy transfer function [504,505] in master equation calculations may be required, as well as theoretical work to follow details of energy transfer in larger systems [403]. In addition, the quantification and propagation of the various uncertainties in theoretical kinetics has yet to be undertaken in a rigorous and systematic fashion. The uncertainty in calculated stationary point energies is typically estimated based on performance against a set

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measurements, especially of branching fractions as a function of (high) pressure for key elementary reactions. One key future direction for research in elementary reactions of autoignition is a more general understanding of the formally direct pathways and the development of rate rules for predicting pressure-dependent rate coefficients in such systems. For example, Petway et al. [109] explored the ability of QRRK/MSC methods to approximate the formally direct rate coefficients in the neopentyl þ O2 system and found substantial disagreements with a more rigorous ME calculation. Clearly systematic and rapidly calculable rules for formally direct rate coefficients are desirable, but these will evidently have to be derived from master equation studies and validated by experiment. This will require theoretical consideration not only of thermochemistry and stationary points on the potential energy surfaces, but of energy transfer effects on branching fractions. Fig. 21. OH concentration vs. time profile from pulsed-photolytic Cl-initiated oxidation of cyclohexane at 586 K and 7.9 bar. The “spike” at early time is the signature of formally direct OH production in this system. A model (dotted line) for the R þ O2 chemistry built on stationary points validated at low pressure [105] matches the shape of the signal. However, inclusion of a rapid QOOH þ O2 chain-branching reaction (solid line) is required to model the amplitude. From reference [147], reproduced by permission of the PCCP owner societies.

of benchmarks, but these may not be completely relevant to the reactions of interest. As the contributions from energy uncertainties become comparable to other uncertainties there will be an increasing need for more precise estimates of quantum chemical error limits as well as for quantification of the uncertainties from theoretical kinetics approximations on the final rate constant determinations. Furthermore, two fundamental research thrusts seem to us to stand out in importance for solving the frontier problems in autoignition chemistry: understanding the pressure dependence of key reactions and learning the details of QOOH chain-branching chemistry. 6.1. Pressure dependence Possibly the broadest area for elementary chemistry research of importance to autoignition modeling is the area of the pressure dependence of the branching fractions of key reactions. Some automated mechanism generation methods have the machinery to incorporate pressure dependence and chemical activation [506e509], but comprehensive models in fact still rarely treat the pressure dependence of chemically activated reactions [4], although it can be demonstrated that the high pressure limit is only rarely obtained under combustion conditions [510]. The neglect of pressure dependence is partly because of the additional parameterization that is required, and partly because of the limited information on the pressure-dependent pathways. This lack of information is beginning to be addressed with master-equation calculations that have been validated at low pressure [25,103e105] and with time-resolved measurements of product formation at elevated pressure [147]. The measurements of Cl-initiated oxidation of cyclohexane at high pressure implied that formally direct pathways in cyclohexyl þ O2, both to bimolecular and unimolecular products, affect the pressure dependence even at tens of bar [147]. Fig. 21 shows the OH formed from Cl-initiated oxidation of cyclohexane at 7.9 bar. The formally direct pathways are captured well by a kinetic mechanism based on ME calculations that employed stationary point characteristics validated at low pressure [105]. However, matching the amplitude of the observed OH signal required postulating a rapid chain-branching reaction of QOOH with O2. There is a clear need for detailed experimental

6.2. Low-temperature chain branching As the picture of the reactions of alkyl radicals with O2 has come into sharper focus, the lack of knowledge about the subsequent chain branching reactions of the QOOH radicals becomes more obvious. The mechanism of the “second O2 addition” and related chemistry is at present the most important unanswered question for ignition chemistry research. As discussed above, if the theoretical understanding of these reactions is in its infancy, the experimental characterization must be said to be embryonic. The strategy of sub-mechanism studies may hold some promise in this area, as indirect indications of chain branching by QOOH have been observed [108,147]. The detection of ketohydroperoxide intermediates [181,182,198], particularly by molecular-beam sampling and photoionization [28] will doubtless play a role in these investigations. As calculations of the kinetics of the second O2 addition and the possible product pathways are beginning to become available, master equation analysis may provide insight into suitable reaction conditions for isolating the effects of the QOOH species. However, the real leap forward would be the direct detection of QOOH. Tunable synchrotron photoionization has been successful in detecting other elusive molecules [11,292], and it might also prove to be the answer for QOOH. The more stable ROO isomers often do not have stable cations [287,289] but many cations in the QOOH configuration are calculated to be bound. The huge remaining challenge is to make enough of the unstable QOOH to detect; the kinetics makes observation of QOOH in an actual hydrocarbon oxidation system a difficult proposition. The production of QOOH largely proceeds via the ROO well, and hence formation of QOOH is not rapid until higher temperature, where the dissociation and reverse isomerization of QOOH are also rapid. The equilibrium constant of the ROO % QOOH vastly favors the ROO species. Alternative schemes for producing QOOH directly, e.g., by HO2 addition to alkenes, may be preferable. Acknowledgements This work is supported by the Division of Chemical Sciences, Geosciences, and Biosciences, the Office of Basic Energy Sciences, the U. S. Department of Energy. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy, under contract DE-AC04-94AL85000. R.X.F. thanks the Cluster of Excellence “Tailor-Made Fuels from Biomass”, which is funded by the Excellence Initiative by the German federal and state governments to promote science and research at German universities. The authors thank Dr. Stephen J. Klippenstein (Argonne National Laboratory), Dr. James A. Miller and Dr. Ahren W. Jasper

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(Sandia National Laboratories) for helpful discussions and thank Dr. Kentaro Tsuchiya (AIST) for providing numerical values of the calculated energies from references [169,170].

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