Hydrogen atom abstraction by methyl radicals in methanol glasses at 15–100 K: evidence for a limiting rate constant below 40 K by quantum-mechanical tunneling

CHEMICAL

Volume 48, number 1

HYDROGEN ATOM ABSTRACTION

PHYSICS

15 May 2977

LETTERS

BY METHYL RADICALS

IN METHANOL

GLASSES

AT 15--t00 EC:

EVIDENCE FOR A LIMITING RATE CONSTANT BELOW 40 K BY QUANTUM-MECHANICAL Reggie L. HUDSON,

TUNNELING*

Masaru SHIOTANI**

and Ffrancon

WILLIAMS

Department of Chemistry, iJniversity of Tennessee. Knoxville. Tennessee 379 16. USA Received 14 February

1976

Rate constants for hydrogen atom abstraction by methyl radicals in methanol glasses have been measured from 100 to 15 K. The Arrhenius plot is nonlinear and the reaction rate constant appears to reach a limiting value below 40 K. The r+ suits are discussed in terms of simple models for quantum-mechanical tunneling in the solid state at low temperatures. Assuming that the methyl group rotation in methanol brings about a merging of the energy level distribution at the potential barrier, the observation of temperature-independent rate constants below 40 K may be attributable to a freezing out of this rotation such that tunneling occurs only from the zero-point vibrational level.

1. Introduction Previous reports from this laboratory and elsewhere have provided evidence that methyl radicals can abstract hydrogen atoms from acetonitrile [l] , methyl isocyanide [2], methanol [3], and 3-methylpentane [43 in the solid state at low temperatures. Since these reactions are characterized by low apparent activation energies, curved Arrhenius plots, and unusually large deuterium isotope effects, it has been argued [l-3] _ that hydrogen atom abstraction proceeds largely by quantum-mechanical tunneling under these conditions. Moreover, it has been shown that the results for the methyl radical-acetonitrile (crystal I) system can be accurately described in the range from 69 to 112 K by exact one-dimensional tunneling calculations for a gaussian barrier [S] _ The importance of quantum-mechanical tunneling in hydrogen-atom transfer reactions at Iow temperatures has also been demonstrated very cfearly in a recent study of the isomerization of steritally-hindered aryl radicals in solution [6].

* Research supported by the Division of Physical Research, U.S. Energy Research and Development Administration (document no. ORO-2968-107). ** On leave from Faculty of Engineering, Hokkaido University, Sapporo 060, Japan.

For such reactions involving the transfer of hydrogen, it was predicted by Bell in his 1935 paper on quantum tunneling that “at very low temperatures the reaction velocity will reach an almost constant value” [7] _ In the present work we have extended the study of the methyl radical - methanol reaction to much lower temperatures than before [3] and we fmd that the reaction rate constant appears to reach a limiting value below 40 K. As far as we are aware, this is the first observation in chemical kinetics of the anticipated situation [S] where the velocity of a reaction having an appreciable energy barrier (ca. 8.2 kcal mole-l in this case) shows virtually no dependence on temperature.

2. Experimental

As in the previous study [3], methyl radicals were conveniently generated ai the temperature of interest by dissociative electron attachment to methyl chloride, the electrons being produced by the photoionization of N,N,N’,N’-tetramethyl-p-phenylenediamine (TMPD). Spectrosil sample tubes (3 mm i-d.) were used, each tube containing approximately 0.2 ml of a sohtion of 0.2 mol 5%TMPD and 2 mol % CH,Cl in CHsOD. After degassing the solution, a transparent glass was produced by quickly cooling_the sample to 77 K. I95

CHEMICAL PHYSICS LETTERS

Volume 48, number 1

The source of UV radiation was the A-H6 mercury arc Iamp (George W. Gates and Co. Inc.) mounted in an air-cooled assembly with suitable optics (Oriel Optics C-60-53 universal lamp housing). The beam was focussed on the irradiation slots of the ESR cavity. Exposure times of about 1 min sufficed to produce intense signals from methyl radicals. In ah experiments the W irradiations were carried out in situ at the same temperature as that employed for the subsequent observation of methyl

radicaI

decay.

The temperature of the samp!e in the ESR cavity was regulated between 10 and 90 K by means of the

Heli-Tran LTD-3 11 OB 1 liquid transfer refrigerator system supplied by Air Products and Chemicals Inc. The transfer line was coupled to a 30 liter helium storage dewar (model USHefrom Minnesota Valley Engineering). An iron-doped gold versus chrome1 thermocouple was inserted next to the sample tube and the leads connected to an APD-ll direct digital temperature readout (Air Products and Chemicals Inc.). This arrangement allowed the sample temperature to be monitored continuously during the course of an experiment. ESR measurements were made using a Varian (V4502-15) X-band spectrometer system. Magnetic field strengths were determined by means of the WaIker/magnetrics precision NMR gaussmeter (model G-502) using a proton magnetic resonance probe inserted between the pole face and the cavity. Kinetic measurements on the decay of me’rhyl radicals were generahy made using line 3 (M, = -I/2) of the methyl radical ESR spectrum. In some experiments line 1 (MI = +3/2) was also scanned repetitively, similar results being obtained. The interval between consecutive scans was 0.5 to 1 min and the decay was monitored over IS to 25 min, depending on the temperature of the sample.

3. Results and discussion As in the previous study [3 1, we have treated the kinetics of methyl radical decay as a first-order reaction_ Actually, the plots of In c versus time show a slight decrease in slope as the reaction proceeds [3], and similar deviations have been observed for the decay of aIky1 radicals in a number of other organic glasses [4,9,1c)]. However, these decay plots are invariably 194

1.5 May 1977

found to be independent of the initial concentration of radicals [3,4,9,10] so the results are regarded as obeying composite first-order kinetics [IO]. The procedure followed in the present study was to calculate the slope of the first-order plot by the usual least-squares method with equal weighting for each of the data points. Despite the slight curvature as noted above, the correlation coefficients of the first-order plots were between 0.90 and 0.99 with the majority being above O-95, so we b&eve it is justified to use this procedurefor extracting the kinetic parameter. Before discussing our results, we wish to comment on the recent paper by Bol’shakov and ToIkatchev [I 1 J . These authors claim that the reaction of methyl radicals with methanol at 77 K is more closeIy obeyed by the relation c = co exp(-Kt lj2) than by the exponential decay c = co exp(--kt). However, since most of their results refer to water-methanol glasses of varying isotopic composition (CH,OH/CD,OD), it can be argued that in this case the methyl radicals are produced in nonhomogeneous microscopic environments_ Bearing in mind that the hydrogen atom abstraction from methanol is subject to extremeIy large deuterium isotope effects [3] and that the water molecules are unhkely to react [ 1 I ] , it is probable that a significant fraction of the methyl radicals are produced in relatively unreactive sites. Actually, an entire spectrum of reactivities would be expected in these circumstances, depending on the immediate environment of the methyl radicals, and consequently it is not surprising that first-order kinetics is not obeyedPursuing this point further, the deviation from firstorder kinetics in the case of the 100% methanol glass may also be attributable to the lack of complete homogeneity between the reactants. Since it is known that abstraction occurs almost entirely from the methyl hydrogens [3], the reaction wilI clearly have anisotropic character in a rigid glass, and therefore the existence of random orientations is bound to impart some degree of non-homogeneous kinetics. We believe that this is the correct explanation for the composite first-order kinetics which is observed [3,11 J . Accordingly, the decay constants reported here represent average values for all reaction orientations in the glassy matrix. The temperature dependence of the methanol reaction is shown in fig. 1. As expected for quantum tunneling, the Arrhenius plot shows considerable curvature below 100 K and the rate constant approaches a

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CHEMICAL PHYSICS LETTERS

15 May 1977

ergy are much lower than those predicted by the caIculations. A suitable fit could not be obtained with fured values of the parameters V, and 13over the entire temperature range, and a continuous adjustment in the value of p was needed in order to frt the low-temperature results. No improvement was achieved through the use of a parabolic instead of a gaussian barrier. The apparent failure of these tunneling calculations at very low temperatures can probably be traced to

I

5Q-

the assumption in the mode1 [5] Boltzmarm

distribution

of a continuous

of kinetic energies incident on

the barrier. As pointed out originally [S J , this is inconsistent with the use of the C-H stretching frequency for the A factor since in a vibrational ergies would be quantized according

2.0

‘II

I 2

1 3

I 4

1 5

1frx10*

Fig. 1. Arrhenius plot of first-order rate constants for hydragen-atom abstraction by methyl radicals in methanoI glasses. The data points represented by the open circles were obtained in a series of runs in which the samples were progressively cooled to the appropriate temperature. The filled circles are taken from ref. [ 31, and the other symbols refer to runs in which the sample temperature was attained during the heating part of the cycle. limiting value at very low temperatures. puter program described by Le Roy et

Using the com-

al. [!?I], a satisfactory fit was obtained to the experimental data between 60 and 85 K by tunneling calculations based on a gaussian barrier height V. of 8.4 kcal/moI [12], a frequency factor,4 of 8.5 X 1OL3s-l corresponding to the C-H stretching frequency in CH,OD [13], and a value of 28.5 a 0.5 for the dimensionless parameter p = 2rr2a(2pV0)1/2/h. In this latter expression, a (= 68.7 pm) is the length scaling factor in the gaussian expression V(x) = Vo exp(-x 2/a2) and P is taken as the mass of the hydrogen atom. In contrast to the good fit at higher temperatures, the results of the one-dimensional tunneling calculations using the above parameters differed appreciably from the experimental data below 60 K. In this region the experimentaI values of the apparent activation en-

model, the en-

to the C-II vibrational level spacing (8.1 kcal/mol). In this latter case, only the zero-point energy levels wouId be occupied at low temperatures and the mass points would undergo collisions at exactly the same height on the barrier. This situation would clearly result in temperatureindependent rate constants at low temperatures, as observed. Accepting the above explanation, the problem now becomes to reconcile the data at higher temperatures within the scope of a vibrational model. Since the vibrational energy spacing is much too large to allow a . significant population of excited levels at 60-85 K where the temperature dependence of the reaction is we11developed, the model would seem to be invahd for this region. However, if the internal rotation of the methyl group results in a smearing of the energy level distribution, a temperature dependence would set in, even at low temperatures. Therefore, the sudden freez-

could be the reason for the sharp transition to the region of temperatureindependent rate constants below 40 K. This hypothesis is consistent with NMR studies [ 14,151 which indicate that the onset of methyl group rotation in methanol occurs below 77 K. Further work is clearly needed to explore the quantitative ramifications of a vibrational model for the abstraction reaction [I6]. ing-out of this internal rotation

Acknowledgement We are very grateful to Professor R.J. I.e Roy for providing us with hi computer programs for cahdating tunneling factors and for his most helpful comments

Volume 48, nbmber

on the present work, sible effect of methyl

15 May 1977

CHEMICAL PHYSICS LETTERS

1 particularly in regard group rotation.

E-D. Sprague, K. Takeda, J.T. Wang and F. WiIIiams, Can

to the pos-

J. Chem. 52 (1974) 2840;

References [ 1] E.D. Sprague and F. Wiiiams, J. Am. Chem. Sot. 93 (197 1) 787. ]2] J-T. Wang and F. Williams, J. Am. Chem. Sot. 94 (1972) 2930. [ 3) A. Campion and F_ Williams, J. Am. Chem. Sot. 94 (1972) 7633. [4] E-D_ Sprague, J. Phys Chem. 77 (1973) 2066; M.A. Neissand J.E. Willard, J. Phys. Chem. 79 (i97.5) 783; M.A. Neiss, E.D. Sprague and J.E. Wilhrd, J. Chem. Phys. 63 (1975) 1118. [S] R.J. Le Roy, E.D. Sprague and F. Williams, J. Phys Chem. 76 (1972) 546;

J.T. Wang, Ph.D. thesis, University of Tennessee (1972). [6] G. Bruntorz, D. GriIler, LRC. Barclay and KU. Ingold, J. Am. Chem. Sot. 98 (1976) 6803. [7] R.P. Bell, Proc. Roy. Sot. 148 A (1935) 241 [8] R.P. Bell, Trans. Faraday Sot. 55 (1959) 1. [9] W-G. French and J-E. Willard, J. Phys. Chem. 72 (1968) 4604. [IO] J-E. Willard, Intern. J. Radiat. Phys Chem. 6 (1974) 325. [ 111 B.V. Bol’shakov and V.A. Tolkatchev, Chem. Phys. Letters 40 (1976) 468. [ 121 A.F. Trotmau-Dickenson

[ 131 [ 141 [ 151 [ 16 ]

and E.W.R. Steacie, J. Chem. Phys 19 (1951) 329. M. FaIk and E. Whalley, J. Chem. Phys. 34 (1961) 1554. A.H. Cooke and LE. Drain, Proc. Phys Sot. (London) A ( (1952) 894. H.S. Gutowsky and G-E. Pake, J. Chem. Phys 18 (1950) 162. R.J. Le Roy, private communication.

ERRATA R.H. Clarke, R.E. Connors, H.A. Frank and J.C. Hoch, Investigation of the structure of the reaction center in photosynthetic systems by optical detection of triplet state magnetic resonance, Chem. Phys. Letters 45 (1977) 523. Section 3, case (3). The heading and first line do not describe the case actually discussed in the text that follows them, which is a combination of case (1) and case (2). It should read (3) Dimer with all molecular axes parallel (or antiparallel) and two-fold rotation symmetry. The imposition of both a two-fold axis and a parallel (or antiparallel) axis structure on the dimer geometry...

Y. Kato and I. Nakano, Magnetic circular dichroism Eu(C2 H, SO,), - 9H20 due to magnetic dipole transitions, Chem. Phys. Letters 45 (1977) 359. The sign of the scale of all the ordinates figs. 2-4 rameters

in

and also that of the values of the Faraday padivided by D appearing in table 1 and page

362 should be reversed. Iowing discussion. 196

for 8~

of

This does not affect the fol-