Unimolecular reactions of the enolic tautomer of ionized acetic acid in

J . Phys. Chem. 1988, 92, 3336-3341

3336

ARTICLES Unimolecular Reactions of the Enolic Tautomer of Ionized Acetic Acid in the Gas Phase. An ab Initio and RRKM Studyt Rosa Caballol,* Josep M. Poblet,* Jose Pedro Sarasa, Departament de Quimica Fisica. Facultat de Quimica de Tarragona, Universitat de Barcelona, 43005 Tarragona, Catalunya, Spain

Santiago Olivella,**and Albert Sol8 Departament de Quimica Orgcinica and Departament de Quimica Fisica, Facultat de Quimica, Universitat de Barcelona, 08028 Barcelona, Catalunya, Spain (Received: June 23, 1987; I n Final Form: October 27, 1987)

Ab initio MO calculations, using basis sets including d-polarization functions and incorporating valence-electron correlation energy, have been used to determine structures and relative energies of stationary points on the C2H402'+potential energy surface which are relevant in the fragmentation processes of the enolic tautomer (1) of ionized acetic acid (2). It is found that 1 undergoes a rate-determining 1,3-hydrogen shift to 2 prior to OH' loss. The same stepwise mechanism is predicted for the losses of OH' and OD' from the 0-deuteriated ionized enol. In addition, it is established that the loss of H 2 0 from 1 takes place via a stepwise pathway involving the formation of the isomer 'CH2COOH2+(4) as the rate-determining step. Energy barriers of 52.4 and 51.0 kcal/mol for the rearrangement of 1 to 2 and of 1 to 4, respectively, are obtained at the MP3/6-3 lG* level, including the changes in zero-point vibrational energies. Rate-constant calculations based on the RRKM theory, using the ab initio calculated vibrational frequencies, lead to an activation energy of about 50 kcal/mol for both rearrangements.

+

Introduction There has been considerable experimental interest in rearrangement and fragmentation processes associated with the enolic tautomer (1) of ionized acetic acid (2) in the gas phase.'-6 It

+.

^I,

1

loss from 1, it was concluded2that this elimination does not proceed by direct fragmentation of the enolic ion to give the daughter ion 5 but by a prior rearrangement to 2, which fragments by OH' loss yielding the ion 6. On the basis of the larger activation energy

2

c:i,=

has been shown that the radical cation 1, formed by McLafferty rearrangement of ionized butyric acid (or homologues), generates important metastable peaks in its mass spectrum,'-3 corresponding to loss of OH' and H20. Similar metastable peaks appear in the mass spectrum of radical cation 2.1-3 From the ionization and appearance energies, Holmes and LossingS have found that the enolic ion 1 is 22 f 2 kcal/mol more stable than is ketonic tautomer 2. This remarkable reversal of the stability order of the radical cation keto/enol pair relative to the neutral pair seems to be a general feature of the cationic species.' The rearrangement of 1 to 2 requires a 1,3-hydrogen shift and this involves a relatively large activation energy, which has been estimated, from appearance energies and thermochemical data,3to be approximately 51 kcal/mol. Early experimental work by Levsen and Schwarz2 established that 1 loses OH' and H 2 0 in the approximate ratio 30:70 and that the H 2 0loss is a specific 1,2-elimination to give ionized ketene (3), without prior isomerization to 2. In a later s t ~ d ySchwarz ,~ et al. reported an approximate activation energy of 48 kcal/mol, determined from appearance potential measurements, for the H 2 0 loss from 1 and suggested that this process may involve the radical cation isomer 4 as a discrete intermediate. Regarding the OH' A contribution from- the Grup de Qurmica Quhtica del I.E.C. 'Departament de Quimica OjgPnica. 5Departament de Quimica Fisica.

0022-3654/88/2092-3336$01.50/0

w3-

:= #QE

5

+

c

0

6

estimated for the 1,3-hydrogen shift as compared with the approximate activation energy (-21 k ~ a l / m o l )determined ~ for the OH' loss from 2, the rearrangement of 1 to 2 prior to loss of OH' was proposed3 to be the rate-determining step of such a stepwise mechanism. Additional deuterium labelling experiments revealed that 0-deuteriated enol ions (la) show a preference to lose OD' rather than OH' (ratio ca. 2.4:1), reflecting a dominance of the rearrangement la 2b over la 2a due to a primary deuterium isotope effecL3 Subsequently, Holmes and Lossing5 reported the

-

-

+/OH CH 2- C

\

-------t

CE 3- C O

t

OH

(1) Holmes, J. L. Org. Mass Spectrom. 1973, 7, 341. (2) Levsen, K.; Schwarz, H . J . Chem. SOC.,Perkins Trans. 2 1976, 1231. (3) Schwarz, H.; Williams, D. H.; Wesdemiotis, C. J . Am. Chem. SOC. 1978, 100, 7052. (4) Griffin, L. L.; McAdoo, D. J. J . Phys. Chem. 1979, 83, 1142. ( 5 ) Holmes, J . L.; Lossing, F. P. J . Am. Chem. SOC.1980, 102, 3732. (6) McAdoo, D. J.; Hudson, C. E.; Griffin, L. L. J . Phys. Chem. 1984,88, 1481. (7) Heinrich, N.; Koch, W.; Frenking, G.; Schwarz, H. J. Am. Chem. SOC. 1986, 108, 593.

0 1988 American Chemical Society

The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3337

Enolic Tautomer of Ionized CH3COOH interesting observation that l a released 1.5 times as much translational energy upon losing OH' as upon losing OD*. They proposed that the greater energy release resulted from the selective suppression of the lower energy of two reaction paths, a low-energy stepwise process (e.g., 1 2 6 + OH'), and a higher energy concerted one, involving a concerted 1,3-hydrogen shift and C-OH bond cleavage:

--

2s

ia CH3-

C

/OD

\\o

+.

2b

This interpretation has recently been criticized by McAdoo et a1.,6 who argue that the observed isotope effect on the relative intensities of the OH' and OD' losses is about what would be expected if only the stepwise reaction were occurring. Moreover, these authors conclude that the internal energy is deposited differently in the intermediate acetic acid ions 2, depending on whether H or D is transferred from oxygen to carbon in the rearrangement of 1 to 2, and that this difference is maintained and reflected in the subsequent fragmentations. The observed larger translational energy released by l a in the loss of OH', as compared to the loss of OD*,was attributed to an insufficient density of states in the fragmenting ions to permit energy randomization between isomerization and decomposition. In light of the above results, it is felt that a rigorous theoretical study of the most relevant part of the CZH4O2" potential energy surface is clearly needed in order to ascertain the fragmentation mechanisms of 1 and establish the nature of the observed isotope effects on the relative intensities of the OH' and OD' losses from la. We have recently ~ h o w n that * ~ ~semiempirical molecular orbital (MO) calculations can be combined with the statistical RRKM'O theory of the unimolecular reactions to rationalize the data obtained in the mass spectrometric experiments on the fragmentations undergone by radical cations. Here we report the results of ab initio quantum mechanical calculations for the most relevant stationary points on the CZH4O:+ potential energy surface, related to the OH' and HzO losses from 1. The energetic, structural, and vibrational results furnished by this theoretical study are subsequently used to perform R R K M rate constant calculations to predict the relative abundances of the metastable peaks for the losses of OH' and HzO from 1 and the deuterium isotope effects on the relative intensities of the OH' and OD' losses from la. Comparison between these predictions and the available experimental data provides a reliable test of both the accuracy of the calculated relative energies and the fragmentation mechanisms inferred from the computed potential energy surface.

Computational Procedures Standard ab initio M O calculations were carried out by using both a locally modified version" of GAUSSIAN 80 system of programsI2 and MONSTERGAUSS program package.I3 Optimized equilibrium structures and transition structures were obtained with the split-valence 3-21G basis setI4 at the self-consistent field (SCF) (8) Caballol, R.; Poblet, J. M.; Sarasa, J. P. J. Phys. Chem. 1985,89, 5836. (9) Caballol, R.; Poblet, J. M.; Sarasa, J. P. In?. J. Mass Spectiom. Ion Processes 1986, 71, 75. (10) Marcus, R. A.; Rice, 0. K. J . Phys. Colloid Chem. 1951, 55, 894. Rosentcck, H. M.;Wallenstein, A. L.; Washaftig, A. L.; Eyring, H. Proc. Natl. Acad. Sci. U.S.A. 1952, 38, 667. ( 1 1) Solt, A,, unpublished results. (12) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. QCPE 1981, 13, 406. (13) Petersen, M.; Pokier, R. Program MONSTERGAUSS, University of Toronto, Canada, 198 1 .

level of theory using gradient procedures.15 In order to obtain more reliable relative energies, additional single-point calculations were performed with the larger split-valence 6-3 1G basis set,16 with the split-valence plus d-polarization 6-31G*,17 and with incorporation of valence-electron correlation using Mdler-Plesset perturbation theory terminated at second (MP2) and third order (MP3).I8 All calculations at the SCF level were performed within the restricted Hartree-Fock (RHF) formalism" for the closedshell systems and the spin-unrestricted (UHF) approachZofor the open-shell systems. In a first approach, to save computation time, the best relative energies were estimated by assuming additivity of the d-polarization functions and energy correlation effects.z1 That is, the MP2 and MP3 corrections calculated with the 6-31G basis set were added to the SCF/6-31G* energies. Unfortunately, this approach led to a wrong ordering of the relative energies of the transition structures calculated for the rearrangement of 1 to 2 and of 1 to 4. In view of these results, the above additive scheme was abandoned; our best final energies (denoted MP2/ 6-31G* and MP3/6-31G*) were obtained by performing single-point MP2 and MP3 calculations at the SCF/3-21G optimized geometries with the 6-3 lG* basis set. Harmonic vibrational frequencies were calculated at the SCF/3-21G level, by diagonalizing the mass-weighted Cartesian force constant matrix computed numerically by finite differences of analytical gradients,22 both to characterize the stationary points as minima (representing equilibrium structures) or saddle points (representing transition structures) and to evaluate zero-point vibrational energy corrections to the relative energies. The dependences of the rate constants on the internal energies were calculated by employing the standard RRKM theory of unimolecular reactions, which can be formulated aslo

k( E ) = aC* (E-E,) / hN(E)

(1)

where u is the reaction path degeneracy, E, is the critical energy (Le., the potential energy barrier including the zero-point vibrational energy) of the reaction, N ( E ) is the state density in the reactant at the internal energy E , and G*(E-Eo) refers to the integrated states density at the E - Eo energy. N ( E ) and G*(E-E,) were calculated in the rigid-rotor-harmonic-oscillator approach,23using the SCF/3-21G vibrational frequencies.

Results and Discussion C2H4OZ" Potential Energy Surface. The SCF/3-2 1G optimized geometries of the stationary points located on the C2H4O2'+ potential energy surface, which are relevant in relation to the fragmentations of the enolic tautomer of ionized acetic acid, are displayed in Figures 1 and 2. It is worth mentioning that the five optimized structures (a-ac) possess a molecular symmetry plane (i.e., C, point group molecular symmetry) which contains the carbon and oxygen atoms. The harmonic vibrational analysis indicated that the stationary points a, b, and c correspond to equilibrium structures (potential energy minima) of the radical cations 1, 4, and 2, respectively, whereas ab and ac correspond to the transition structures for the rearrangement of 1 to 4 and of 1 to 2, respectively. The total energies obtained at the various levels of theory for these structures and the dissociation products 6 OH' (d), 3 HzO (e), and 5 OH' (f) are shown in Table

+

+

+

(14) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. (15) Schlegel, H. B. J . Comput. Chem. 1982, 3, 214. Murtagh, B. A,; Sargent, R. W. H. Comput. J . 1970, 13, 185. (16) Hehre, W.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 257. (17) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta. 1973, 28, 213. (18) Moller, C.; Plesset, M. Phys. Reu. 1934, 46, 618. Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J. Quantum. Chem., Symp. 1976, 10, 1. (19) Roothaan, C. C. J. Reu. Mod. Phys. 1951, 23, 69. (20) Pople, J. A.; Nesbet, R. K. J. Chem. Phys. 1954, 22, 571. (21) McKee, M. L.; Lipscomb, W. N. J. Am. Chem. SOC.1981,103,4673. Nobes, R. H.; Bouma, W. J.; Radom, L. Chem. Phys. Lett. 1982, 89, 497. (22) Pulay, P. Mol. Phys. 1969, 17, 197. (23) Frost, W. Theory of Unimolecular Reactions; Academic: New York, 1973.

3338 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988

Caballol et al.

TABLE I: Calculated' Total Energies (hartrees) for Stationary Points on the C2H.02" Potential Energy Surface and Several Dissociation Productsb SCFI3-21G SCF/6-3 1G SCF/6-31G* M P 2 /6-3 1G* MP3/6-31G* -227.386 33 -227.495 85 -228.066 11 a -226.225 87 -228.083 17 -228.037 37 b -226.201 68 -221.36263 -227.450 41 -228.020 27 -228.054 1 6 C -226.208 03 -221.365 63 -227.477 95 -228.031 20 ab -226.141 42 -221.290 52 -227.390 14 -227.985 22 -227.995 67 -221.27090 ac -226.1 11 25 -227.39060 -227.919 71 -227.993 22 -228.013 56 d -226.171 53 -221.334 18 -227.439 94 -227.996 61 -228.02091 e -226.155 17 -227.315 1 1 -221.433 55 -228.008 64 -227.939 98 f -226.1 11 84 -221.276 49 -227.365 34 -227.919 39 " A t the SCF/3-21G optimized geometries. * d denotes 6

+ OH', e denotes 3 + H,O, and f denoted 5 + OH'

a ab

b

ac i.lc,c.cl.-

1c2.5

Figure 2. Optimized (SCFf3-21G) transition structures for the rearrangement of 1 to 4 (ab) and of 1 to 2 (ac). All bond lengths are in angstroms and bond angles in degrees. C H 3 C l C i 3 , . - 121.7

Figure 1. Optimized (SCFf3-21G) equilibrium structures for the radical cations 1 (a), 4 (b), and 2 (c). All bond lengths are in angstroms and bond angles in degrees.

I. The relative energies are given in Table 11. At all levels of theory, the enolic structure a is found to be the lower energy tautomer of the keto/enol pair 2/1. This result is in good agreement with previous ab initio calculation^,^^^^^ using comparable computational methods, on other structurally related systems (Le., CH3CRO'+, R = H, OCH3). At the present highest level of theory, namely from the MP3/6-31G* relative energies, the ketonic structure c is predicted to lie 17.8 kcal/mol above the enolic structure a. Inclusion of the zero-point vibrational energy corrections (which are computed to be 40.3 and 40.0 kcal/mol for a and b, respectively) leads to an energy gap of 17.5 kcal/mol. The calculated keto/enol energy difference, therefore, is in fairly good agreement with the approximate value of 22 2 kcal/mol estimated from ionization and appearence energies5 It is worth noting that Apeloig et al.24have calculated that at the same level of theory (MP3/6-3 l G * plus zero-point energy correction) the structurally related ionized acetaldehyde (CH3CHO'+) lies 15.2

*

TABLE 11: Calculated' Relative Energies (kcal/mol) for Stationary Points on the C2H4O2'*Potential Energy Surface and Several Dissociation Productsb

a b C

ab ac d e f

SCF/

SCF/ 3-21G

6-31G

SCF/ 6-31G*

MP2/ 6-31G*

MP3/ 6-31G*

0.0 11.4 11.2 52.8 68.1 34.1 44.3 71.6

0.0 14.9 13.0 60.1 72.4 32.7 38.0 68.9

0.0 28.5 11.2 66.3 66.0 35.1 39.1 81.9

0.0 28.8 21.9 50.8 54.2 43.6 36.1 95.8

0.0 28.1 17.8 54.9 56.4 43.1 39.1 89.9

'At the SCF/3-21G optimized geometries. b d denotes 6 denotes 3 + H 2 0 , and f denotes 5 + OH'.

+ OH',

e

kcal/mol above its enolic tautomer (CH2=CHOH'+), which is in reasonable agreement with the approximate experimental values, ranging from 12.5 to 15 kcal/mol, reported by Holmes et a1.26 In good agreement with an early suggestion by Schwarz et al.,3 the water elimination from 1 involves the radical cation isomer 4 as a discrete intermediate. According to the MP3/6-31G* calculated relative energies (Table 11), this intermediate (b) lies 28.7 kcal/mol above the enolic structure a and 10.4 kcal/mol

(24) Apeloig, Y . ;Karni, M.; Commer, B.; Depke, G.; Frenking, G.; Meyn, S.; Schmidt, J.; Schwarz, H. Int. J . Mass Spectrom. Ion Processes 1984, 59, 21. (25) Heinrich, N.; Schmidt, J.; Schwarz, H.; Apeloig, Y. J . Am. Chem. SOC.1987. 109, 1317.

(26) Holmes, J. L.; Terlouw, J. K.; Lossing, F. P. J . Phys. Chem. 1976, 80,2860. Holmes, J. L.; Lossing, F. P. J . Am. Chem. Soc. 1980, 102, 1591. Holmes, J. L.; Lossing, F. P. J . Am. Chem. SOC.1982, 104, 2646.

Enolic Tautomer of Ionized CH,COOH below the dissociation products e. It is readily seen from Figure 1 that the SCF/3-21G optimized structure b shows a long (1.580 A) C201bond length, suggesting that the water fragment is weakly bonded to the ionized ketene fragment. In a recent high-level ab initio study of the ketene-water radical cation complexes, Postma et aL2’ have reported two local minima (at the SCF/4-31G level) for the [CHzCO-H2O]’+complex showing C202bond lengths of 2.357 and 2.464 A, lying (at the SD-CI/6-31G** level) 19.1 and 18.1 kcal/mol, respectively, below the dissociation products e. We were unable to locate these more stable complexes with the 3-21G basis set. This result is in accord with the conclusion by HeinrichZ8 concerning the need to optimize the structure of such a loosely bound complexes by means of larger basis sets, preferably of at least 6-31G* quality. In this regard, it is to be noted the dramatic influence of the polarization functions on the relative energy of b. Thus, according to Table I, while in the case of a and c inclusion of d-polarization functions in the 6-3 1G basis set leads to an energy lowering of 68.7 and 70.5 kcal/mol, respectively, in the case of b the energy lowering is only 55.1 kcal/mol. Such a different effect of the d-polarization functions can be taken as an indication that the optimum molecular geometry calculated for b with the 3-21G basis set may differ substantially from that optimized with the 6-31G* basis set. This interpretation is supported by the results of ab initio calculations recently reported by Heinrich,28which show the strong influence of the basis set on the molecular geometry of radical cation species such as b. On the basis of the Mulliken population analysis29 and the calculated spin density distribution, it was found that the isomers a and b are best described as r-type radicals (Le., the unpaired electron mainly resides in the out-of-plane 2p-atomic orbital of the C1 carbon atom) while the isomer c is a u-type radical (Le., the unpaired electron resides essentially in a sp2 hybrid atomic orbital, lying on the molecular plane, of the O1 oxygen atom). Hence the ground-state electronic wave functions of a and b belong to the A’’ irreducible representation and that of c to the A‘ one. Consequently, the rearrangement of a to c implies a crossing of the corresponding 2A’’ and 2A’ states. Moreover, since the analogous suprafacial 1,3-hydrogen migration in neutral 1,I-dihydroxyethane (CH,=C(OH),) is a “symmetry forbiddenn30 sigmatropic shift of order [1,3], a high potential energy barrier is expected also for the rearrangement of a to c. However, on the basis of the open-shell nature of the electronic configuration of a, this rearrangement is expected to be more favorable in this radical cation than in the neutral molecule.31 The present calculations indeed reveal a high potential energy barrier (Le., 56.4 kcal/mol at the MP3/6-31G* level) for the 1,3-hydrogen shift in the radical cation a. The same trend has been observed by Apeloig et a].%in the analogous rearrangement of the ionized enol of acetaldehyde to its ketonic tautomer. Thus, the potential energy barrier for the 1,3-hydrogen shift in the radical cation CHz= CHOH’+ (Le., 60.7 kcal/mol at the MP3/6-31G* level) was calculated to be nearly identical with that obtained in the neutral enol CH2=CHOH (Le., 58-67 kcal/mol using comparable computational methods).32 In ab, the transition state for the 1,3-hydrogen migration involved in the rearrangement of a to b, the bonding between the migrating hydrogen and both oxygen atoms is small, as indicated by the relatively large O1H4 and O2H4 distances. Therefore, the rearrangement of a to b involves a relatively high potential energy ~

(27) Postma, R.; Ruttink, P. J. A.; Terlouw, J. K.; Holmes, J. L. J. Chem. SOC.,Chem. Commun. 1986, 683. (28) Heinrich, N. In “Structure/Reactivity and Thermochemistry of Ions”; Proceedings of the NATO Advanced Study Institute on Ions, Les Arcs, France, 1986 Ausloos, P.; Lias, S. G., Eds.; NATO AS1 Series: Serie C, Vol. 193. (29) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833. (30) Woodward, R. B.; Hoffmann, R. The Conservation of the Orbital Symmetry; Verlag Chemie: Weinheim, FRG, 1970. (31) Haselbach, E.; Bally, T.; Lanyiova, Z. H e h . Chim. Acta 1979, 62, 511.

(32) Harding, L. B.; Schlegel, H. B.; Krishnan, R.; Pople, J. A. J . Phys. Chem. 1980,84, 3394. Osamura, Y., Goddard, J. D.; Schaefer, H. F.; Kim, K. S. J . Chem. Phys. 1981, 7 4 , 617.

The Journal of Physical Chemistry, Vol. 92, No. 12, I988 f

3339

l84.l)

-I-

i,

I /

‘il/ a

Cll7.51

10.01

Figure 3. Potential energy levels diagram (kcal/mol) for unimolecular reactions of the ionized enol 1, based on the MP3/6-31G* calculated energies plus zero-point vibrational energy corrections.

barrier at all levels of theory. The energy difference between the transition states ac and ab varies with the level the theory used. However, except at the SCF/6-31G* level, ab is calculated to be lower in energy than ac. At the MP3/6-31G* level, the potential energy barriers for the rearrangement of a to b and of a to c are calculated to be 54.9 and 56.4 kcal/mol, respectively. It is worth mentioning that assuming additivity of the d-polarization functions and correlation energy effects these barriers were estimated to be 58.6 and 55.4 kcal/mol, respectively. The latter results illustrate the danger of using the above additive scheme to evaluate the relative energies of species which are quite close in energy. Regarding the dissociation of b into its components (e), all attempts to locate a transition structure turned out to be unsuccessful. This result is in accord with the conclusion by Postam et aL2’ concerning the lack of any clearly defined reaction coordinate for the fragmentation of the [CH2CO-H20]’+complexes. However, on the grounds of the relatively high potential energy barrier calculated for the rearrangement of a to b, it can be concluded that the latter isomerization is the rate-determining step for the water elimination from 1. As regards the dissociation of c to d, in the present investigation we have not attempted to locate the corresponding transition structure. Owing to the expected extreme nondynamic electron correlation effects involved in the processes implying a homolytic bond breaking, it is likely that a single-configuration S C F wave function does not give a satisfactory description of the transition structure associated to this dissociation. Therefore, a multiconfiguration S C F (MCSCF) approach would be desirable to locate the transition structure for the dissociation of c to d. Because of computation-time limitations, we have not tried to carry out such a saddle point search using an adequate MCSCF wave function. Apeloig et al.24have obtained (at the MP3/6-31G* level) a potential energy barrier of 16.8 kcal/mol for the related dissociation of ionized acetaldehyde to 6 + H’. Moreover, since the OH’ loss from 2 does not have a significant reverse energy,3 it is likely that the transition structure for this decomposition lies close in energy to that of the dissociation products (d). Consequently, the rearrangement of 1 to 2 can be considered the rate-determining step for the OH’ elimination from 1 and, therefore, out best estimate of the ac-a energy gap (Le., 56.4 kcal/mol at the MP3/6-31G* level) is the predicted overall potential energy barrier for the fragmentation of l to give 6 OH’. Analogously, from the aforementioned assumption concerning the rate-limiting step for the water eliminations from 1, it follows that our best estimate of the ab-a energy difference (Le., 54.9 kcal/mol at the approximate MP3/6-3 lG* level) is the predicted overall potential energy barrier for the fragmentation of 1 to give 3 + H 2 0 . Inclusion of the zero-point vibrational energy corrections (which are calculated to be 36.3 and 36.4 kcal/mol for ac and ab, respectively) lead to the predicted activation energies at 0 K of 52.4 and 51.0 kcal/mol for the elimination of OH’ and H 2 0 , respectively, from 1. Indeed, both energy barriers compare satisfactorily with the approximate activation energies of 5 1 and 48 kcal/mol, respectively, reported by Schwarz e t aL3 for these eliminations.

+

3340

The Journal of Physical Chemistry, Vol. 92, No. 12, 1988

TABLE 111: Rate-Constants Ratios for the Rearrangement of 1 to 4 (kab)and of 1 to 2 (kat) Calculated for Different Activation Energies by Using 4 1 activation energies"

E.(ab)

E.(ac)

k,,,/k,,

ion internal energies"

43 46 48 49 50 51 52 54 57 59 43.5 49.5 54.5 59.5 43.3 49.3 54.3 59.3

44 41 49 50 51 52 53 55 58 60 44 50 55 60 44 50 55 60

3.8 3.6 3.6

44 48 51 52 53 54 56 59 62 65 45 52 59 65 45 52 59 65

3.5 3.4 3.4 3.3 3.3 3.2 3.1 2.1 2.2 2.1 2.1 2.7 2.6, 2.55 2.5

TABLE I V Kinetic Deuterium Isotope Effect for the Rearrangement of l a to 2a and Zb, Calculated"for Different Values of the Activation Energy (E,(H), in kcal/mol) Associated to the Rearrangement l a 2b

-

E,(H) kHJkD

47 2.9

49 2.8

50 2.1

51 2.6

52 2.5

54 2.4

57 2.31

59 2.3

"Using eq 3 with E,(D) - E,(H) = 1.0 kcal/mol, at the ion internal energies that generate fragmentations with a rate constant of about lo5 s-' .

to check this hypothesis, the kab/kacratio was computed for different values of the activation energies, E,(ab) and E,(ac), by using the same SCF/3-21G calculated harmonic vibrational frequencies, at the ion internal energies needed to generate fragmentations with a rate constant of lo5 s-l. The results are presented in Table 111. It is readily seen from Table I11 that in order to obtain a kab/k,, value close to the observed relative abundances ratio (Le., ranging from 2.1 to 3.0), it is necessary to assume for the isomerization a b an activation energy slightly lower (by less than 1 kcal/mol) than that assigned to the a c rearrangement. Moreover, it appears that the RRKM-computed rate-constants ratio is extremely sensitive to the error in the calculated relative activation energies. It can be concluded, therefore, that, although relatively high-level ab initio calculations can provide energy barriers which are useful in order to confirm or rule out the postulated mechanisms for competitive fragmentations of a radical cation, they are not accurate enough to reproduce the observed the relative rate constants of these processes. Kinetic Deuterium Isotope Effects. If the losses of OH' and OD' from l a occur via a unique stepwise mechanism which involves the calculated transition structure ac as the rate-determining transition state of the overall fragmentation process, then an intramolecular primary kinetic deuterium isotope effect might be 2a or l a 2b). expected in the rearrangement step (Le., l a Assuming that for a narrow range of internal energies the kinetic isotope effect is independent of the ion internal energy value, then it is possible to calculate within the framework of the RRKM theory the primary kinetic deuterium isotope effect associated with the migration of H or D from oxygen to carbon in the isomerization of l a to 2a or 2b. From eq 1 this can be expressed as

-

In kcalimol.

The calculations reported above allow us to construct the potential energy levels diagram of a portion of the C2H40;+ potential energy surface which is most relevant in relation to the fragmentations of the ionized enol 1. This diagram, based on the relative MP3/6-3 lG* energies including the zero-point vibrational energy corrections, is shown in Figure 3. It is readily seen from Figure 3 that the high dissociation energy (84.1 kcal/mol) calculated for the decomposition of a to f precludes the direct fragmentation mechanism of 1, in agreement with early deuterium-labeling experiments.2 On the other hand, the lack of any concerted reaction path connecting a with d does not lend support to the existence of an alternative higher energy concerted mechanism, such as the postulated by Holmes and L o s ~ i n gfor ,~ the loss of OH' from la. Our calculations thus suggest a unique stepwise mechanism for the fragmentation of 1 to yield 6 OH', involving a rearrangement of 1 to 2 prior to the OH' loss, in agreement with previous conclusions by other author^.?-^,^ Rate Constant Analysis. From the predicted activation energies at 0 K for the rate-determining step of the losses of H 2 0 and OH' from 1 (Le., 51.0 kcal/mol for a b, and 52.4 kcal/mol for a c) and the calculated (SCF/3-21G) harmonic' Nibrational frequencies, a rate-constants ratio of 5.3 was calculated by using eq 1 for these fragmentation processes at the ion energy of 55 kcal/mol. The latter value was determined as the internal energy which is necessary to generate fragmentations with a rate constant of about lo5 s-'. Assuming that to a first approximation the relative abundances of the metastable peaks for two competitive fragmentations of an ion are proportional to the rate constants of these processes,33then it might be expected that

+

-

Caballol et al.

-

where kab,k,, are the rate constants for the rearrangement of a to b and of a to c, and IHIO,Io, the relative abundances of the metastable peaks associated to the losses of H 2 0 and OH' from 1. Three slightly different experimental values have been reported for the ratio of the latter relative abundances: 2.7,2 2.1,3 and 3.0.4 Therefore, the predicted relative abundances ratio of 5.3, estimated from the RRKM calculated rate-constants ratio by using eq 2, is in qualitative agreement with these experimental values. At first sight the above difference between the predicted and the observed relative abundances of the metastable peaks associated with the losses of H 2 0 and OH' from 1 would be ascribed to the expected error in the calculated activation energies. In order (33) Derrick, P. J.; Donchi, K. F. Comprehensive Chemical Kinetics; Elsevier: Amsterdam, 1983; p 83.

-

-

-

-

-

where Eo(H) and Eo(D) are the critical energies for the rear2b and l a 2a. Since the potential energy rangements l a barrier for both processes is the same, the difference between these critical energies can be estimated from the zero-point vibrational energy change of the transition structure ac upon substitution of the migrating hydrogen (Le., H4in Figure 2) by deuterium. Using the SCF/3-21G calculated harmonic vibrational frequencies we obtained Eo(D) - Eo(H) = 1.0 kcal/mol. Table IV shows the kinetic deuterium isotope effect calculated for different values of Eo(H)by using eq 3, at the internal energies needed to generate fragmentations with a rate constant of about lo5 SKI. Assuming again that the relative abundances of the metastable peaks for the losses of OH' and OD' from l a are proportional to the rate constant of the rate-determining step of these processes, then it follows that (4) where ZoD and ZOH are the relative abundances for the losses of OD' and OH' from la. Five different experimental values have been reported for the ratio of the latter relative abundances: 2.63,2 2.44,3 2.38,5 and 3.33.7 From these data an average experimental relative abundances ratio of 2.56 is obtained. It can be seen from Table IV that, if an activation energy of 51 kcal/mol is assumed for the rearrangement of l a to 2b, then the RRKMcalculated kinetic deuterium isotope effect leads to an approximate relative abundances ratio of 2.6, in accordance with the above experimental average value. Therefore, the activation energy derived from the RRKM-calculated kinetic deuterium isotope effect (51 kcal/mol), for the loss of OD' and OH' from la, lends further support to the best value (52.4 kcal/mol) obtained from

J. Phys. Chem. 1988, 92, 3341-3350 the previous ab initio calculations. It is worth noting from Table IV the fact that the RRKMcalculated kinetic deuterium isotope effect is less sensitive to the error in the activation energy used. Consequently, the energy barrier obtained from relatively high-level a b initio calculation appears to be acceptable for performing R R K M kinetic isotope effect computations. The most relevant conclusion emerging from the above kinetic deuterium isotope effect calculations is that, as pointed out by McAdoo et the observed preference of la to lose OD’ rather

3341

than OH’ can be explained assuming the same stepwise mechanism for both fragmentation processes. Acknowledgment. The calculations were carried out by using the IBM 3083 and IBM 4341 computers at the Centre d’Informatics de la Universitat de Barcelona, and the DEC VAX11/750 computer purchased with funds provided by the CAICYT (Grant no. 657/81). Registry No. 1, 68863-94-5; 2, 68890-09-5; 4, 113976-18-4; D2, 7782-39-0.

Anomalously Polarized Emission from Molecules Undergoing Large-Amplitude Motion David J. Tannor Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois 60616 (Received: August 10, 1987; In Final Form: January 8, 1988)

A new formulation of symmetry selection rules and depolarization ratios in resonance Raman scattering (RRS) is presented.

R )coordinate-dependent , transition dipole moment. New and simplified The approach emphasizes the symmetry of P ~ , ~ (the derivations of these symmetry properties are provided by exploiting the global transformation properties of the Born-oppenheimer electronic wave functions. The transition dipole moment enters twice in RRS, once for the incident and once for the scattered photon. Taken in conjunction with a time-dependent approach to RRS, the present formulation predicts anomalous polarization in those cases where there is a “conspiracy” between p,(R),p,(R) and the wavepacket dynamics on the excited ele_ctronic-state surface. Numerical auulication is made to a model two-dimensional double minimum system, suggestive of the C1B2 surface of so,.

1. Introduction Resonance Raman scattering (RRS) has been enjoying a vital resurgence lately. With the availability of new laser frequencies in the UV, R R S spectra of entirely new molecules are being R R S has been shown to give much more detailed information about excited-state structure and dynamics than an electronic absorption spectrum. A molecule with a broad and featureless absorption spectrum will still display sharp lines in its RRS. The intensities of these lines give information about excited-state geometry changes and the dynamics on the excited electronic state potential energy ~ u r f a c e . ~ -RRS ~ is emerging as the ideal tool with which to study short-time photoisomerization and photodissociation p r o c e ~ s e s . ~ ~ ~ Resonance Raman intensities are governed by both the ground and the resonant excited-state potential energy surfaces and the transition dipole moment connecting them. In general, the transition dipole moment has some dependence on nuclear coordinates ( F ( R ) ) .For many purposes it is reasonable to neglect this coordinate dependence (Condon approximation). However, without this coordinate dependence, certain lines which are observed in the R R S spectrum simply could not be populated. In particular, the coordinate dependence of p cannot be ignored in the nontotally symmetric modes of symmetrical molecules, where p ( R ) has certain symmetries. The purpose of this article is severalfold: 1. To provide a new, straightforward derivation for the sym, illustrate these symmetries with a specific metries of P + ~ ( R )and example. Although some authors seem to be aware that global symmetries of p ( R ) exist,6 the standard treatments expand the transition moment in a Taylor series about the equilibrium geZiegler, L. D.; Hudson, B. J . Phys. Chem. 1984, 88, 1 1 10. Friedman, J. M.; Rousseau, D. L.; Ondrias, M. R. Annu. Reu. Phys. 1982, 33, 353. (3) Warshel, A.; Dauber, P. J . Chem. Phys. 1977, 66, 5477. (4) Myers, A. B.; Mathies, R. A. J. Chem. Phys. 1984, 81, 1552. (5) Imre, D.; Kinsey, J.; Field, R.; Katayama, D. J. Phys. Chem. 1982, 86, 2564.

(6) Hale, M. 0.; Galica, G. E.; Glogover, S . G.; Kinsey, J. L. J . Phys.. Chem. 1986, 90, 4997.

0022-3654/88/2092-3341$01.50/0

ometry, and thus exploit the high symmetry of the electronic wave function and its derivatives at the symmetrical equilibrium geometry in the derivation. The present treatment, in the spirit of more modern (and accurate) approaches,’ recognizes the full symmetry of \ke(rJ?)and \kg(r,R) S\k,(r,R) = \ k , ( S 1 r , S I R )= D e ( S ) \ke(r,R)

(1.1)

i.e., as long as one is careful to let the symmetry operation operate on electronic and nuclear coordinates, the Born-Oppenheimer wave functions have the full symmetry of the point group, although they span distorted, nontotally symmetric geometries. Here S is some symmetry operation belonging to the point group of the molecule and De@) is the character of S in the irreducible representation to which \kebelongs. S does not haue the same effect on electrons and nuclei. If S is a reflection operation, for instance, S reflects the electrons through an appropriate reflection plane while it reflects and then permutes back to their original frame the nuclei. This distinction is discussed at length in ref 7 . The symmetry of p ( R ) emerges immediately from the above relationship for the BO wave functions. The symmetries of F ( R )are in direct correspondence with the concepts of electronically allowed and electronically forbidden, vibronically allowed transitions. These concepts become more transparent and are readily applied to systems with large-amplitude motion once the global symmetries of p ( R ) are identified. 2. The time-dependent formulation of RRS has proved valuable both computationally and conceptually in terms of the dynamical processes that come to bear on RRS and the connection between RRS and photochemical Within this formulation, the initial dynamical state is the product of the transition moment, p g ( R ) ,and the initial vibrational state, x , ( R ) . ~ Three J ~ different (7) Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic: Orlando, FL, 1979; Chapter 1 1 . ( 8 ) Lee, S.-Y.; Heller, E. J . J . Chem. Phys. 1979, 71, 4777. (9) Heller, E. J.; Sundberg, R. L.; Tannor, D. J . Phys. Chem. 1982, 86, 1822. (IO) Tannor, D. J.; Heller, E. J. J . Chem. Phys. 1982, 77, 202. ( 1 1) Sundberg, R. L.; Imre, D.; Hale, M. 0.;Kinsey, J . L.; Coalson, R. D.J . Phys. Chem. 1986, 90, 5001.

0 1988 American Chemical Society