J. Phys. Chem. 1985,89, 3967-3970
(I - C)-1
= I + c + c2 + ...
(11)
where C is the appropriate lower triangular matrix of the coefficients {c),in which all components of the leading diagonal are zero. It is easily shown by induction that C”is lower triangular, with all components of its leading diagonal and next lower (v 1) diagonals zero. The series given by the right-hand side of (1 1) for any component of thp inverse matrix therefore terminates. All coefficients of the c’s in C , and consequently in the required expressions for the a’s, are positive. Because of the difficulty of expressing (10) as a sum of products of c’s, application of this result is complicated, and we use it to calculate only the leading order term of B2 in
+
B2 = -(2~)~/~r~~(U,”/3)-~/~ exp(-/3Uo)[ 1 O ( p i ) ] (12) Two terms of this order in containing U T ,cancel en route to (12). It is not generally true that odd derivatives of U cancel, for inspection of (2) shows that B2 depends on both even and odd parts of U about r = ro; nevertheless this cancellation leads us to expect that some simplification of higher order terms takes place. The increase of the magnitude of B2 as the curvature &” decreases in (12) is in accordance with the graphical interpretation of (1) as the area under the curve of the integrand. The expansion in inverse powers of /3 in square brackets in (12) is probably asymptotic. The result (12) is obviously inapplicable to potentials with discontinuous gradient or curvature at r = ro,although evaluation of B2 for simple potentials of this type still shows a dominant factor exp(-@Uo) and a further factor powerlike in /3. For continuous but higher-order minima in which UJ2p)is the lowest nonzero differential coefficient of U at r,, we take
which reduces to (12) when p = 1. When V ( r ) has several well-deparated minima (by a distance >> (@V,(2P))-i’(2P) where UJ2P)refers to either of two adjacent turning points), contributions of the form (13) can be added for each minimum. Clearly the most negativk. minimum is dominant. Unfortunately the exponentially small error discussed below (4) may cause inaccuracy in this dominant term greater than all contributions from other minima. Similarly there is no point in including the effects of any positive minima, which are exponentially small compared to the (neglected) contribution from the tail of the potential at large r. The above analysis ignore quantum effects, which separate naturally into exchange statistical effects and dynamical wave effects; both depend on the form of U(r).3 The wave effects can be dealt with by regarding (1) as the leading term in an expansion of Bz, believed to be asymptotic, in ascending powers of ti2? The coefficient of each power is an integral similar to (1) which may similarly be approximated at low temperature, akhough the series is not useful below temperatures kT = 8’ fi2/mrO2. We now use these results to derive more simply the known low-temperature result for the Lennard-Jones 12,6 potential:
-
U(r) = M / r I 2 - N / r 6
(14)
where M and N are positive. This potential is of the type assumed, with
ra = (2M/h91/6, U, = -N2/4M
(15)
rozUo”= 1 8 p / M
(16)
and which is nonzero, so that p = 1. It follows from (12) that
Bo
-
- ‘ / ( 2 ~ ) ~ / ~ ( 2 M / hi/2(M/2/3N2) 9
exp(/3N2/4M)
(17)
in accordance with the low-temperature asymptotic approximation of the exact e x p r e s ~ i o n . ~ . ~
and find similarly that
B2 = -27rpI’(
3967
t)..[
-I/(Zp)
L/3Uo(2P)] (2P)!
exp(-/3Uo)
X
(3) Lieb, E. H.J . Math. Phys. 1967, 8, 43, formulas (1.2)-(1.7). (4) Reference 1, p 48. (5) Eptein, L. F.; Roe, G. M. J . Chem. Phys. 1951, l g , 1320. (6) Garrett, A. J. M. J . Phys. A . 1980, 13, 379.
Photochemical Processes in 2-Fluoroethanol in Solid Neon M. Rasanen, AT& T Bell Laboratories, Murray Hiil, New Jersey 07974
J. Murto, Department of Physical Chemistry, University of Helsinki, Meritullinkatu 1 C SF-001 70, Helsinki, Finland
and V. E. Bondybey* AT& T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: July 8. 1985)
FTIR study of 2-fluoroethanol in solid neon shows that, contrary to some previous reports, only the Gg’ and Tt conformers can be trapped. Infrared irradiation in either OH or CH stretching region results in a very efficient conversion of the initially present Gg’ form into the higher energy Tt conformers. The overall isomerization rate is essentially unchanged by deuteration of the OH group.
Introduction Studies of rotational isomers of simple hydrocarbons represent a field of considerable current Saturated hydrocarbons (1) Giinthard, Hs.H.J . Mol. Strucr. 1984, 113, 141. (2) Barnes, A. J. J. Mol. Srruct. 1984, 113, 161.
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and similar unbranched chain compounds are characterized by a potential with a 3-fold barrier with respect to rotation around the carbon-carbon single bond. Studies of this rotational isomerism were greatly assisted by the observations that (a) the in(3) Lotta, T.; Murto, J.; RisBnen, M.;Aspiala, A. J . Mol. Srrucr. 1984, 114, 333.
0 1985 American Chemical Society
Letters
3968 The Journal of Physical Chemistry, Vol. 89, No. 19, 1985 dividual rotamers can usually be independently trapped in lowtemperature matrixes and (b) in many cases the conformer interconversion can be accomplished by infrared light. Studies in our laboratory have indicated that this situation is more general than originally anticipated and permitted rather detailed investigations of the gauche and trans conformers of n - b ~ t a n eand ~,~ numerous other haloalkanes and ethers.6 A more complex situation arises in alkanes with polyatomic functional groups such as OH or NH2,'+ where one has to contend with the added possibility of rotation and isomerization associated with the orientations of these substituents. The situation in 2fluoroethanol (2-FE) is particularly interesting and, even though most extensively studied, still controversial. In this compound five distinct, nonequivalent rotamers are conceptually possible which are usually denoted Tt, Tg, Gt, Gg, and Gg', where the capital and lower case letters refer to configurations with respect to the C-C and C-0 bonds, respectively. The matrix spectra of 2-FE were first studied by Murto and co-workers1° and the work was later extended both by his group and numerous other investigator~."-~~ Consistent with expectations, the initially deposited spectra are due predominantly to the most stable, intramolecularly hydrogen-bonded Gg' isomer. Infrared irradiation results in the growth of additional bands, due to the less stable rotamers. The early studies have suggested that the infrared interconversions involved at least four of the five possible i~omers.'~ The extensive and careful studies by Shirk and co-workers involving monochromatic irradiation using F-center lasers yielded several interesting re~u1ts.l~In particular, they concluded, based on their observations, that the reactions occurring are mode specific, with OH excitation favoring rotation around the C O bond, while C H irradiation yielding preferentially rotation around the C C bond. In spite of these extensive studies, several puzzling questions seemed to remain. Ab initio calculations suggested that the barriers to O H rotation are rather 10w.I~ More importantly, use of increasingly sophisticiated calculations and more complete basis sets resulted in further lowering the isomerization barriers, raising some doubt about the feasibility of trapping the individual conformers. Furthermore, several studies in our laboratory failed to give any evidence of trapping the higher energy conformers in either ethanol or its deuterated derivatives, even though the OH isomerization barriers in these compounds should probably be quite comparable to those in fluoroethanol. In the present manuscript, in an attempt to clarify some of the remaining questions, we extend the previous work in two directions. In the first place, we obtain the spectra of 2-FE in solid neon. Matrix spectra of many organic molecules and, in particular, of species containing highly polar bonds are invariably susceptible to site effects which may complicate the spectra and make their interpretation more difficult. These effects are usually minimized in the nonpolarizable and weakly interacting neon matrix. In the second place, we carry out experiments with the d, compound and compare the spectroscopy and isomerization of 2-FE with that of its deuterium derivative.
(4) Rasanen, M.; Bondybey, V . E. Chem. Phys. Lett., 1984, 111, 515. (5) Risanen, M.; Bondybey, V. E. J . Chem. Phys. 1985,82, 4718.
( 6 ) Rasanen, M.; Schwartz, G. P.; Bondybey, V. E., in press. (7) Frei, H.; Ha, T. K.; Meyer, R.; Giinthard, Hs.H. Chem. Phys. 1977, 25, 271.
(8) Takeuchi, H.; Tasumi, M. Chem. Phys. 1983, 77, 21. (9) Nakata, M.; Tasumi, M. Chem. Lett. 1984, 945. (10) Perttila, M.; Murto, J.; Kivinen, A,; Turunen, K . Spectrochim. Acta, Part A 1978, 34, 9. (11) Pourcin, J.; Davidovics, G.; Bodot, H.; Abouaf-Marguin, L.; Gauthier-Roy, B. Chem. Phys. Lett. 1980, 74, 147. (12) Davidovics, G.; Pourcin, J.; Monnier, M.; Verlague, P.; Bodot, H.; Abouaf-Marquin, L.;Gauthier-Roy, B. J . Mol. Srruct. 1984, 116, 39. (13) Hoffman, W. F.; Shirk, J. S. Chem. Phys. 1983, 78, 331. (14) Hoffman 111, W. F.; Shirk, J. S. J. Phys. Chem., submitted for
publication.
(15) Murto, J.; Rasanen, M.; Aspiala, A,; Lotta, T. J . Mol. Strucr. 1984,
108, 99.
II
I
Icm-4 Figure 1. (a) Infrared absorption spectrum of 2-fluoroethanolin solid Ne (1:lOOO) (the sample contains -20% of 2-FE-4. (b) The same spectrum after a prolonged irradiation. The dotted and dashed lines show the transition characteristics of two of the filters available for selective irradiation of the CH or OH (OD) region, respectively.
Experimental Section 2-Fluoroethanol was a commercial sample (Aldrich); it was purified by repeated vacuum distillations. Residual water impurity which is not readily separated by distillation was removed with a molecular sieve (Fisher 4A (4 A)). The deuterated compound 2-fluoroethanol-0-d was prepared by exchange with DzO.The samples were mixed with the rare gas-neon in most studies at ratios of 1500-1:1500. IR spectra of the matrix samples on a CsI substrate at 4 K were obtained for freshly deposited samples and after varying lengths of infrared irradiation. The photolysis was accomplished by the globar source of a Nicolet MX-1 FTIR instrument either directly or through various combinations of band-pass and interference filters. Results and Discussion 2-Fluoroethanol Spectra and Isomerization. A typical spectrum of freshly deposited 2-fluoroethanol in solid neon (1500) is shown in Figure 1. The spectrum is quite simple and is readily interpreted in terms of the gauche conformer. In agreement with previous studies in heavier rare gases, when exposed to the globar radiation the original bands decrease in intensity and a new set of bands appears. The effect of prolonged irradiation is shown in Figure 1b. Previous studies using tunable infrared photolysis have come to the conclusion that the final products depended upon excitation ~ave1ength.l~In particular, excitation in the C H stretching region resulted in a rotation around the C-C bond yielding preferentially the Tt product while OH irradiation produced rotation around the C - 0 bond yielding mainly the Gt conformer. Although a tunable infrared source was not available for our studies we examined this question with the aid of band-pass interference filters. These permitted selective IR irradiation of the samples in the C H or OH stretching regions, respectively. Since radiation with 3 5 2000 cm-' was found to be ineffective in producing isomerization, the effect of each irradiation could be conveniently followed spectroscopically through a cutoff filter transmitting only 8 < 1500 cm-'. The main conclusion of these studies is that the same changes occur in the spectrum and the same final product is produced, regardless of whether the sample is subjected to the unfiltered globar radiation, or whether the C H or OH stretches are selectively excited. This behavior persists throughout the range of temperatures studied, down to -2.5 K. We conclude that only two species are involved, the most stable, hydrogen-bonded Gg' conformer which dominates the originally deposited spectrum and the higher energy Tt form in which the hydrogen bond is broken as a result of photolysis. As noted in the Introduction, these experimental observations are in agreement both with chemical intuition and with recent results of ab initio calculations which suggest16 that only two
rhe Journal of Physical Chemistry, Val. 89, NO. 19, 1985 3969
Letters
0.12 -
- OH 0
Gp
I
I
I
1
60
Ix)
183
240
300
360
4c-c 0.10
3200 2800 2400 G cm-1 Figure 2. Section of the infrared spectrum showing the OH, OD stretching region of a sample containing -60% 2-fluoroethanol-d,. Panel a shows the original deposit, while the panel b shows the effect of IR irradiation. It can be seen that the G --+ T conversion proceeds in the do and d, species at almost identical rates. 4000
3600
minima on the 2-fluoroethanol potential surface should be sufficiently stable to be capable of being trapped in the low-temperature matrix. While earlier calculations16 predicted the existence of several minima along the potential associated with the OH group rotation, recent more extensive work suggested that such minima are either absent or too shallow to accommodate stable vibrational levels. This view is also supported by several control experiments we have performed with ethanol and its deuterated derivatives. In all these species even at 2 K only one conformer was detected, confirming that rotation around the C-O bond into the most stable conformation occurs readily even in the cryogenic matrix. Search for selective chemical reactions was an extremely active area in the past decade. A clear demonstration that, by exciting selectively different modes, one can make different products would be a very exciting development. Unfortunately, our studies show that in the present system only one product is involved. Guest species, and in particular complex organic molecules, are often stabilized in the matrix in several distinct local environments or “sites” and such site effects are undoubtedly responsible for the previous conclusions that four conformers of 2-FE can be stabilized. One of the advantages of neon matrices is that they are less susceptible to site effects than the heavier rare gases. The 2-FE-neon matrix spectra are particularly simple and show unequivocally the presence of only two distinct conformers. Effect of Deuterium Substitution. Even in the absence of two different products one can speak, on a lower level, about bond selectivity if one can demonstrate that excitation of particular vibrational modes, or bonds, is more effective in accomplishing the chemical “reaction”, and that the energy is channeled into the reaction coordinate more efficiently than just by random, statistical energy redistribution. To explore this question, we have compared the isomerization rates of 2-FE in neon with that of its deuterated form, 2-FE-d. We have also tried to establish more quantitatively, using band-pass IR filters, the spectral regions responsible for the isomerization process. In neither compound was any reaction detected when only radiation with B 5 2400 cm-I reached the sample. With unfiltered T conversion proceeds for both compounds radiation, the G with a, within the experimental error of f2%, identical halftime of 140 min under our experimental conditions. This is exemplified by the spectra of a partially deuterated sample in Figure
-
-
(16) Murto, J.; Rasilnen, M.; Aspiala, A,; Homanen, L. J . Mol. Strucr. 1983, 72, 45.
Figure 3. Schematic showing the torsional potential of the 2-fluoroethanol. The bold arrows are used to show that excitation of either the OH (OD) or CH bond places the molecule well above the isomerization barrier.
2. Quantitative experiments with filtered light show that in the normal compound the O H absorption accounts for -45% of the total activity, with the remaining 55% being mainly due to absorptions in the C H stretching region. This ratio is in fair agreement with the relative integrated absorption intensities in the O H and C H stretching regions and suggests that excitation of either vibration is similarly effective in promoting the reaction. In the deuterated d, compound, the 0-D absorption accounts for only -25% of the total reactivity. This can be, at least partially, explained by the decrease in the OD absorption intensity relative to OH. Since the total isomerization rate remains unchanged, the decrease in the OD contribution must be balanced by a slight increase in activity in the CH-stretching region. 2-Fluoroethanol Torsional Potential and Rotamerization Mechanism. Accurate information about the 2-FE torsional potential is not available. If one assumes that the initial matrix deposits (-91% Gg’, 9 % Tt) represent room temperature partitioning between the G and T rotamers, one can calculate the Tt form to be -310 cm-’ higher in energy. Ab initio calculations at the MP-3 level predict a somewhat higher value of AEG,T 500 cm-I. The calculated energy barrier for the G T process is 1600-1700 cm-I, with that for the reverse process being lower by the AEG,T energy difference. This is consistent with the observations made here and in a previous study that irradiation near 1500 cm-I in the C H bending region is not effective in inducing the rotamerization. A simplified 2-FE torsional potential is shown in Figure 3. It is fairly clear that both the OH (OD) and C H quanta are energetically capable of accomplishing the rotamerization in both directions. Initially predominantly a G T process is observed. With broad-band irradiation the isomerization does not go on to completion, but to a final composition containing 14% Gg and 86% Tt conformer. This we interpret in terms of a photochemical equilibrium, where the rates of processes in both directions are equal. Since the integrated absorption intensities of the Gg’ and T t forms in the O H and C H stretching regions do not differ substantially, this implies that the reaction in the G T direction is a factor of -6 more efficient than the reverse, “downhill” process. One possible interpretation of this observation would be to assume that, in the higher energy form, the excitation places the molecule above the threshold for unrestricted IVR,17-21leading to loss of energy to “unreactive” low-frequency modes. This model would then require that in the more stable Gg’ conformer the
- -
-
-
-
-
(17) (18) (19) (20) (21)
Parmenter, C. S. J . Phys. Chem. 1982,86, 1735. McDonald, J. D. Annu. Reu. Phys. Chem. 1979, 30, 29. Smalley, R. E. J . Phys. Chem. 1982, 86,3504. Amirav, A.; Even, U.; Jortner, J . Chem. Phys. Lett. 1980, 71, 12. Bondybey, V . E. Annu. Reo. Phys. Chem. 1984, 35, 591.
J. Phys. Chem. 1985,89, 3970-3976
3970
excited molecule is below this threshold and the energy is coupled preferentially to the 9eactive” mode, presumably the skeletal torsion. The fact that excitation of OH, OD, or CH vibrations seems to be similarly efficient in inducing the isomerization is, however, not consistent with this model. An additional problem with “IVR threshold model” is that, while it could explain the observations in 2-FE, it could not be T process used for numerous related compounds where the G is also found to be more efficient but where the trans form is lower in energy. A convincing interpretation of this trend will undoubtedly require additional work, in particular studies using continuously tunable infrared radiation sources. Effect of the Matrix. In previous studies it was observed that the rates of fluoroethanol isomerization decreased with the decreasing mass of the rare gas host3 While very fast isomerization was observed in solid Xe, the rate decreased substantially in the lighter rare gases and was found to be slower by more than an order of magnitude in solid argon. This seemed to suggest a systematic dependence upon the mass or, perhaps, polarizability of the host matrix. By extrapolation one could therefore expect the rates to be even slower in solid neon, and some experiments
-
of Schrems22apparently led to the conclusion that no IR-induced process occurs in solid neon. Actually, we find that a remarkable reversal in the trend established in the heavy rare gases occurs, and the rates in neon are in fact faster than in xenon matrix. This observation would seem to suggest that the behavior of the guest molecules depends on the nature and detailed geometry of the trapping site, and the trends probably cannot be simply modeled by considering only the bulk properties of the host matrices. This is consistent with our recent studies of halopropanes where we observed that differences between isomerization rates in different matrix “sites” are often of comparable magnitude, or even larger, than those between different hosts.
Summary Study of the infrared spectra matrix isolated 2-FE shows clearly that only the Gg’ and T t species are trapped in the 4 K rare gas solids. Infrared excitation of the O H and CH bonds is equally effective in producing the Gg’ Tt rotamerization. The isomeriyation rate is unaffected by deuteration of the OH group.
-
(22) Schrems, 0 ,private communication
FEATURE ARTICLE State-testate Theory of Unlmolecular Reactlons‘ H. 0. Pritchard Centre f o r Research in Experimental Space Science, York Uniuersity, Downsview, Ontario, Canada M3J 1 P3 (Received: March 15, 1985)
In state-testate calculations for the thermal dissociation of N 2 0and C 0 2 ,a close approximation to the strong-collisionfalloff shape is found, even though randomization among states above threshold is not permitted. Allowing rapid randomization among all types of states above threshold causes the falloff to approach the strong-collision shape in the limit, but restriction of the randomization to only those states which are dissociative gives rise to the observed strict-Lindemann shape for the falloff.
We have seen, to date, only a handful of attempts to calculate the rate of a thermal unimolecular reaction as a sum over the rates of individual state-to-state processes. Among them are the calculation of the rates of dissociation of N 2 0 and C 0 2 by Yau2 and of N 2 0 and dioxetane by Lorquet et al.3 and the calculation of the rates of isomerization of methyl isocyanide by Clarkson4 and of H N C by Perk et aL6 Clearly, more such calculations will be forthcoming, but equally clearly, we can see that unless there is some simplifying feature (such as symmetry), the number of matrix elements required for any realistic calculation is going to ( 1 ) An abbreviated version of this paper was presented at the Symposium on The Interface between Theory and Experiment, Canberra, Australia, Feb 1985, to mark the retirement of Professor D. P.Craig, F.R.S. (2) Yau, A. W.: Pritchard, H. 0. Con. J . Chem. 1979, 57, 1731. (3) Lorquet, A, J.; Lorquet. J . C.: Forst, W. Chem. Phys. 1980, 51, 2.53, 261. (4) Clarkson, M. E., unpublished work (cf. ref 5). (5) pritchard. H. 0. ’Quantum Theory of Unimolecular Reactions*; Cambridge University Press: Cambridge, England, 1984. (6) Peric, M.: Mladenovic, M.: Peyerimhoff, S . D.; Buenker, R. J. Chem. Phys. 1984, 86, 85.
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be astronomical for molecules containing more than three atoms. It is the pufpose of this article to illustrate how such a state-testate calculation proceeds once the matrix elements between the initial reactant and final product states have been determined and to draw attention to some unresolved difficulties. The two isomerization studies are very similar: the former treats the methyl radical as a rigid mas’s and the energy levels and lifetimes are determined for the (MI,)-N--C bending/restricted rotation/free rotation with an empirical potential and a rigidbender Hamiltonian,’ whereas the latter solves for the same properties for H N C with a theoretically computed potential; both, however, make the same assumption that the isomerization reaction is irreversible, whereas the physical process itself is c y c l i ~ . ~ Of the dissociation reaction calculations, the earlier one2 is the simpler. It solves for the matrix elements connecting various initial (7) Bunker, P.R.; Howe, D. J. J . Mol. Spectrosc. 1980, 83, 288. (8) In fact, this assumption would not be necessary if the problem were to be treated fully, by including the reverse reaction from the product states (cf. ref 9 and 10). (9) Widom, B. J . Chem. Phys. 1971, 55, 44. (10) Quack, M. Ber. Bunsenges. Phys. Chem. 1984, 88. 94.
0 1985 American Chemical Society
