The standard enthalpies of formation of 1- and 2-Adamantyl cations and radicals. An ab initio study

6 April 2001

Chemical Physics Letters 337 (2001) 327±330

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The standard enthalpies of formation of 1- and 2-Adamantyl cations and radicals. An ab initio study J.-L.M. Abboud a,*, O. Casta~ no b, J.Z. D avalos a, R. Gomperts c b

a Instituto de Quõmica Fõsica `Rocasolano', CSIC. C/Serrano 119, E-28006 Madrid, Spain Departamento de Quõmica Fõsica, Universidad de Alcal a, E-28871 Alcal a de Henares, Madrid, Spain c Silicon Graphics, Inc., One Cabot Road, Hudson, MA 01749, USA

Received 18 January 2001; in ®nal form 2 February 2001

Abstract The results of a G2(MP2) computational study involving 1- and 2-Adamantyl cations (1‡ ; 2‡ ) as well as 1- and 2-Adamantyl radicals (1 ; 2 ) are presented. They provide purely computational thermodynamic data for the following processes: (i) Ionization of 1 and 2 , (ii) Exchange of hydrogen atoms or hydride anions between Adamantyl radicals or cations and alkyl radicals or cations, respectively. These data, once combined with the experimental enthalpies of formation of iso-C3 H7 ; iso-C3 H7‡ ; tert-C4 H9 and tert-C4 H9‡ , allowed us to screen the available experimental data and to de®ne a self-consistent set of experimentally-based standard enthalpies of formation, Df H 0m , for Adamantyl species, namely: Df H 0m …1‡ ; g† ˆ 162:0  2:0; Df H 0m …2‡ ; g† ˆ 171:9  2:0; Df H 0m …1 ; g† ˆ 17:9  2:1, Df H 0m …2 ; g† ˆ 16:6  2:0 kcal mol 1 . Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction We have recently reported [1] that the standard enthalpy of formation of 1-Adamantyl cation (1‡ , Fig. 1) in the gas-phase ‰Df H 0m …1‡ ; g†Š as determined experimentally by thermochemical techniques and standard gas-phase equilibrium methods (high-pressure mass spectrometry, HPMS, and Fourier transform ion cyclotron resonance spectrometry, FT ICR) agrees within experimental error limits with the value obtained at the G2(MP2) level [2] using isodesmic reactions, such as the hydride-transfer between Adamantane (Ad±H) and tert-butyl cation, process (1):

*

Corresponding author. Fax: +34-91-564-2431. E-mail address: [email protected] (J.-L.M. Abboud).

tert-C4 H9‡ …g† ‡ Ad±H …g† ! iso-C4 H8 …g† ‡ 1‡ …g†:

…1†

We have also pointed out [1] the disquieting fact that the average value of Df H 0m …1‡ ; g† obtained by these methods, 162:0  2:0 kcal mol 1 (1 kcal ˆ 4.184 kJ) is signi®cantly di€erent from the experimental result (153  3 kcal mol 1 ) obtained by direct electron impact ionization of neutral molecules [3]. On account of the importance of carbocations [4,5] as well as of the special relevance of Adamantyl cations in physical organic chemistry [6±8], we have decided to further investigate these systems. While experimental work is presently under way in our laboratories, we present herein the results of a computational study involving 2-Adamantyl cation (2‡ ) as well as 1- and 2-Adamantyl

0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 1 2 - 3

328

J.-L.M. Abboud et al. / Chemical Physics Letters 337 (2001) 327±330 Table 1 G2(MP2) results for the species examined in this worka Species 1

)389.222028 ()389.230330)b

1‡

)388.994320 ()389.002809)b

2

)389.221192 ()389.229691)b

2‡

)388.976035 ()388.984762)b

Fig. 1. Positions 1 and 2 in Adamantane. 



radicals (1 ; 2 ), for which some experimental information is already available. Our purpose is to use the computational results as an independent source of information allowing the screening of experimental data and the de®nition of an internally self-consistent set of experimentally-based standard enthalpies of formation.

b

For the sake of consistency with our previous work [1,9], we have used the G2(MP2) methodology [2]. It is known that it provides standard enthalpies of hydride and halide exchanges [1,9] in excellent agreement with experiment, as it is also the case for the ionization energies of radicals, also shown to be essentially indistinguishable from the values obtained at the G2 and CBS-Q levels [10]. This is particularly important, because the size of some of the relevant Adamantyl derivatives so far precludes the use of the latter methods. The raw computational data, as obtained by means of the GA U S S I A N 98 package of programs [11], are collected in Table 1.

3. Discussion of results The computational results have been used to study the following processes: 3.1. Hydrogen atom exchange Consider reactions (2) and (3): tert-C4 H9 …g† ‡ Ad±H …g† ! 1 …g† ‡ iso-C4 H10 …g†;

Tert-C4 H9 Tert-C4 H9‡ Iso-C3 H7 Iso-C3 H7‡ Iso-C4 H10 C3 H 8 Ad±H(C10 H16 ) a

2. Computational methods

Dr H 0 …2†:

…2†

H298



)157.418686 )157.169341 )118.189858 )117.921140 )158.074000 )118.847500 )389.881580

All values in Hartree. E°(0 K).

iso-C3 H7 …g† ‡ Ad±H …g† ! 2 …g† ‡ C3 H8 …g†;

Dr H 0 …3†:

…3†

Using the data from Table 1 we get Dr H 0 …2† ˆ 2:66 and Dr H 0 …3† ˆ 1:72 kcal mol 1 . The combination of these data with the standard enthalpies of formation of tert-Bu (g) (13:6  1:7 kcal mol 1 , [10]), Ad±H (g) ( 32:0  0:9 kcal mol 1 , [1]), iso-C4 H10 (g) ( 32:25  0:50 kcal mol 1 , [1]), iso-C3 H7 (g) …22:0  0:5 kcal mol 1 , [12]) and C3 H8 (g) … 24:92  0:20 kcal mol 1 , [12]) yields values of, respectively, 16:5  2:0 and 16:6  1:4 kcal mol 1 for Df H 0m …1 ; g† and Df H 0m …2 ; g†. All these results seem to re¯ect the unfavorable in¯uence of strain on the stability of 1 and 2 , this e€ect being largest in the case of 1 . The value of Df H 0m …2 ; g† is in good agreement with Holmes and co-workers [3] experimental result, reported as 16 kcal mol 1 [15:7  3:1 kcal mol 1 using the `electron at rest' convention, with the appropriate thermal correction and allowing for the experimental uncertainties on Df H 0m …2‡ ; g† and IE(2 )]. The value of Df H 0m …1 ; g†, however, is somewhat di€erent from that determined in [3], 12  3 kcal mol 1 .

J.-L.M. Abboud et al. / Chemical Physics Letters 337 (2001) 327±330

3.2. Adiabatic ionization energies of 1-Ad and 2-Ad These magnitudes, respectively de®ned through Eqs. (4) and (5) are computed by using the 0 K total energies summarized in Table 1. 1 …g† ! 1‡ …g† ‡ e ;

IE…1 † ˆ Dr E0 …4; 0 K†; …4†

2 …g† ! 2‡ …g† ‡ e ;

IE…2 † ˆ Dr E0 …5; 0 K†: …5†

The values we obtain, 6.22 and 6.67 eV for IE(1 ) and IE(2 ) are in very good agreement with the experimental photoionization results of Kruppa and Beauchamp [13], 6:21  0:03 and 6:73  0:03 eV, respectively. Combination of the Df H 0m …1 ; g† and Df H 0m …2 ; g† values given above with the experimental IE(1 ) and IE(2 ) and the appropriate thermal corrections, as computed in this study [H298 E…0 K†, Table 1] provide standard enthalpies of formation for 1‡ and 2‡ of respectively 159:3  2:0 kcal mol 1 and 171:9  1:1 kcal mol 1 (or, respectively 160:7  2:0 and 173:4  1:1 kcal mol 1 taking the electron as a classical particle). Notice that: (i) Extremely close values are obtained if the computed IE values are used instead of the experimental ones, (ii) The value of Df H 0m …1‡ ; g† is in good agreement with the value, 162:0  2:0 kcal mol 1 from [1] and, (iii) Our computed Df H 0m …2‡ ; g† also agrees closely with the experimental datum obtained by Holmes and coworkers [3] (171  3 kcal mol 1 ). 3.3. Hydride exchange reactions We have already referred to our earlier studies on reaction (1). We now focus on reaction (6): iso-C3 H7‡ …g† ‡ Ad±H …g† ! 2‡ …g† ‡ C3 H8 …g† Dr H 0 …6†:

…6†

Data from Table 1 yields the purely computational Dr H 0 …6† ˆ 13:1 kcal mol 1 , which upon combination with the experimental standard enthalpies of formation for gaseous iso-C3 H7‡ , (192:1  1:0 kcal mol 1 , average of the values obtained respectively by: (i) TOF-PEPICO [14], and,

329

(ii) HPMS [15]) and the relevant neutral species, leads to Df H 0m …2‡ ; g† ˆ 171:9  1:4 kcal mol 1 , in good agreement with the purely experimental value based on appearance energies, as well as with the computational results given above. We now have two sets of thermodynamic data. One is purely experimental, while the other is of computational origin, although anchored to experimental values. In keeping with the spirit of the studies reported in [1] and [10], we now seek to use both sets of in order to determine for each state function a range of values simultaneously consistent with experiment and computation. The following results (in kcal mol 1 ) satisfy this condition: Df H 0m …1‡ ; g† ˆ 162:0  2:0 [1]; Df H 0m …2‡ ; g† ˆ 171:9  2:0; Df H 0m …1 ; g† ˆ 17:9  2:1,  0 Df H m …2 ; g† ˆ 16:6  2:0. To summarize, G2(MP2) calculations have provided purely computational thermodynamic data for the following processes: (i) Ionization of 1- and 2-Adamantyl radicals, (ii) Exchange of hydrogen atoms or hydride anions between Adamantyl radicals or cations and alkyl radicals or cations, respectively. These data, once combined with the experimental enthalpies of formation of iso-C3 H7 , iso-C3 H7‡ , tert-C4 H9 and tert-C4 H9‡ , allowed us to screen the available experimental data and to de®ne a set of experimentally-based standard enthalpies of formation for Adamantyl radicals and cations. Acknowledgements We thank Dr. R. Notario for valuable discussions. This work was supported by grants BQU2000-1497 and BQU2000-0646. of the Spanish CICYT and is dedicated to Prof. J.F. Liebman. References [1] H. Flores, et al., J. Phys. Chem. A 103 (1999) 7555. [2] L.A. Curtiss, K. Raghavachari, J.A. Pople, J. Chem. Phys. 98 (1993) 1293. [3] C. Aubry, J.L. Holmes, J.C. Walton, J. Phys. Chem. A 102 (1998) 1389. [4] G.K. Surya Prakash, P.v.R. Schleyer (Eds.), Stable Carbocation Chemistry, Wiley, New York, 1997.

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Chemistry WebBook, NIST Standard Reference Database Number 69, February 2000, National Institute of Standards and Technology, Gaithersburg MD, 20899 (http:// webbook.nist.gov). [13] G.H. Kruppa, J.L. Beauchamp, J. Am. Chem. Soc. 108 (1986) 2162. [14] T. Baer, Y. Song, C.Y. Ng, J. Liu, W. Chen, J. Phys. Chem. A 104 (2000) 1959. [15] J.E. Szulejko, T.B. McMahon, J. Am. Chem. Soc. 115 (1993) 7839.