J. Phys. Chem. 1986, 90, 3968-3975
3968
TABLE I V Localization of Excitation Numben for [2.21Metacyclophaae and [2.21(2,6)and . [2.2](3,5)Pyridinophanes" - . . . .
transitions 7r-?r*(II)b
*-**(I)b
compd [2.2lmeta-
cyclophane [2.21(2,6)pyridinophane [2.21(3,5)pyridinophane
n--IcL* e
n--aS* e
ER, % CR, % ER, % CR,% LE, % LE, % 51.0 30.6 73.2 9.4 75.8
2.0
77.0
5.4
87.8
87.6
71.0
7.4
48.6
25.6
84.0
78.6d
'ER, CT, and LE (%) refer respectively to exciton resonance, charge-resonance and local excited types of transitions. bNumber of 7r-r. experimental band of [2.2]metacyclophane to which the corresponding calculated bands of pyridinophanes refer. c L and S denote respectively the long and short wavelength transitions. dConcernsthe o-n*(2'AU) transition. of electron density toward nitrogen atoms in [2.2](3,5)pyridinophane when compared to 3,5-lutidine. For [2.2](2,6)pyridinophane one should also expect two a-r* transitions. Relative changes in the long wavelength transition are the same as for the other metapyridinophane; however, it is not so for the short wavelength AT* transition: the latter shows a hypsochromic shift because it originates from the short wavelength p a * transition (p band) of 2,6-lutidine, with regard to which it is shifted a little toward the red. All this proves to be a negligible influence for the transannular effect on both a-a* transitions in [2.2](2,6)pyridinophane. Weakening of the interaction between the a-electron systems is caused by the characteristic mutual location of nitrogen atoms in both pyridine moieties. They are located as close as possible and therefore the interacting lone electron pairs effectively isolate the a-electrons of the aromatic rings. Thus, in the ground state of molecule, the strong interaction
between the lone pairs on N atoms and a-electron systems of rings becomes effective. This is visible on the diagram of frontier orbitals, Figure 3. As far as the n-r* transitions are concerned, they appear in the form of two transitions in [2.2](2,6)pyridinophane, but only one transition in [2.2](3,5)pyridinophane. In the case of the former compound the transitions are entirely localized on pyridine rings and originate from the allowed long wavelength transition of 2,dlutidine and the forbidden short wavelength transition. Neglect of mutual interaction between the nitrogen lone pairs in [2.2](3,5)pyridinophane is responsible for only one n-a* transition, originating from the less intense long wavelength transition in 3,5-lutidine. This factor also influences the appearance of the u-a* transition in [2,2](3,5)pyridinophane, which, as in [2.2]metacyclophane, is localized behind the short wavelength AT* band. Both n-a* and 6-a* transitions are localized on pyridine rings. The a-a* transition in [2.2](3,5)pyridinophane can be classified as intermediate between the u-a* transition in [2.2]metacyclophane and the short wavelength n-a* transition in [ 2.21 (2,6)pyridinophane. Good simulation of the UV spectrum of [2.2]metacyclophane (as a reference carbocyclic phane) and of the spectra of isomeric lutidines and good reproduction of the 274-nm absorption band of [2.2] (2,6)pyridinophane shows the usefulness of the theoretical investigation of the nature of electronic transitions by the transition density matrix D method. This is also supported by the authors' results concerning parapyridin~phanes,~ for which experimental spectral data are available. Acknowledgment. We are grateful to Prof. Virgil Boekelheide of University of Oregon for stimulating our interest in the UVspectroscopy problems of pyridinophanes. Registry No. 1, 2319-97-3; 2, 6574-83-0; 3, 17507-09-4;pyridine, 110-86-1;3,5-lutidine,591-22-0; 2,6-lutidine, 108-48-5.
Resonance Raman, Electron Spin Resonance, and Molecular Orbital Studies of m -Benrosemfqulnone Radical Anion' G. N. R. Tripathi,* Daniel M. Chipman, C. A. Miderski, H. Floyd Davis, Richard W. Fessenden, and Robert H. Schuler Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: February 10, 1986) The resonance Raman spectrum of m-benzosemiquinone radical anion, examined by pulse radiolysis methods, shows this radical to have a CO stretching frequency of 1519 cm-I that is similar to that of phenoxy1 radicals and only 4 cm-' lower than that for 3-hydroxyphenoxylradical. A strong Raman band at 1093 cm-l is assigned to a second CO stretching frequency. Theoretical molecular orbital studies suggest that the lowest electronic state is one of C, symmetry, with one CO bond 0.04 A longer than the other. These findings are in accord with the relatively high reactivity of this radical, which indicates that it has substantial phenoxyl-like character, in contrast to the unreactive nature of its para isomer, which is strongly stabilized by resonance, making the CO bonds equivalent. Although the proton hyperfine constants are of the magnitude expected for phenoxyl-like radicals, the protons at C4 and C,, which are expected to have hyperfine constants differing by -2 G, are not experimentally distinguishable in ESR even down to -85 OC. The ESR spectrum indicates either that the radical has C, symmetry or that there is rapid exchange of unpaired spin between the two oxygen atoms in a structure of lower symmetry. From line width studies it is shown that the barrier to any such exchange must be less than -4 kcal/mol. Comparison of the resonance Raman spectrum of this radical to that of phenoxy radicals shows that even though the two CO bonds appear to be nonequivalent they are closely coupled. The energy difference between the C, structure and that of the lowest electronic state of C, symmetry is calculated to be -2 kcal/mol, suggesting that this latter state may be involved in the interconversion of two equivalent mirror image C, structures.
introduction The ESR spectrum of the m-benzosemiquinone radical anion (which we will subsequently refer to simply as m-semiquinone) (1) The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2800 from the Notre Dame Radiation Laboratory.
observed in aqueous solution at room temperature shows that, on the time scale defined by the possible difference in their hyperfine interactions (lo-' the Protons at the c4 and c6 Positions are equivalent. While this radical appears from its ESR spectrum to have C7u. point group it is also possible that rapid (2) Stone, T. J.; Waters, W. A. J . Chem. SOC.1964, 4302.
0022-3654/86/2090-3968$01.50/0 0 1986 American Chemical Society
m-Benzosemiquinone Radical Anion
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 3969
Experimental Section Pulse Radiolytic Studies. The time-resolved optical and resonance Raman methods used in this laboratory have been described in detail in previous paper^.^.'-'^ Raman spectra were taken within 1 ps after the electron pulse with data from -9600 experiments being accumulated to give a signal-to-noise ratio (S/N) sufficient to examine spectral details. 3-Fluorophenoxyl was excited at 407 nm by using Lambda Physik LC 4090 as the laser dye, 3-hydroxyphenoxy at 428 nm using Lambda Physik LC 4250 as the dye, and m-semiquinone at 445 nm using Lambda Physik LC 4400 as the dye. Data were collected at the rate of 7.5 experiments/s and signal averaged on-line with an optical multichannel analyzer (PAR O M A 11). Further averaging and processing was done off-line with a VAX 11/780 computer. The peak positions of the Raman bands of radicals were measured by reference to known lines of ethanol and in general are accurate to f 1 cm-I. Radicals were prepared by oxidation of resorcinol or 3-
fluorophenol with N,'. p!oduced by pulse irradiating a N,O-saturated solution containing 0.1 M NaN3.l1 The substrate was present at 5 m M in the Raman experiments and 1 mM in the optical experiments. At these concentrations the substrate is oxidized with half-periods of 30 and 150 ns, respectively. The p H of the solutions was adjusted with KOH or HC104 and determined with an Orion 811 pH meter calibrated with Fisher buffers. A flow system was used in both the Raman and absorption studies to replenish the sample between pulses. ESR Experiments. ESR measurements were made with a version of the in-situ photolysis apparatus previously described12 that has been improved by addition of a Varian V-7200 nine inch magnet, V-7OOO power supply, and field controller using a Fieldial Mk I1 Hall effect probe to measure the magnetic field. The microwave frequency was monitored by a Hewlett-Packard 5245L frequency counter with 5255A frequency converter. Magnetic field measurements were corrected for drifts in microwave frequency so that individual line positions could be determined to f0.02 G. Measurements of the g factor were made by comparison with the single line of SO3- a t g = 2.003 0613 produced photolytically in the same sample cell and are accurate to -0.00002. The sample flowed through a 0.4-mm flat cell that was inside a Dewar tube in the cavity. Cold nitrogen flowed through the Dewar tube to cool the sample. The temperature was measured by a thermocouple inside the ESR cell at the exit of the flat portion. Typical sample flow rates were 5 mL/min, but the sample did not fully reach the temperature of the gas stream by the time it exited from the flat portion. To reduce error in temperature measurement to no more than a few degrees, the sample was precooled by flowing through a glass helix in a dry ice-acetone bath immediately before entering the cell. Photolysis was with a 1-kW Xe-Hg Hanovia 977B-1 lamp in a housing with an elliptical mirror that collected about 50% of the total light output.I4 The light passed through a cell containing a NiS04-CoSO, solution to remove IR and visible radiations. Resorcinol (98%) was obtained from Aldrich and the acetone used was Fisher ACS Spectra analyzed grade. Acetonitrile (Gold Label), 3-methoxyphenol, potassium tert-butoxide, 18-crown-6, and tetrabutylammonium hydroxide in methanol were from Aldrich. Theoretical Methods. Several programs were used to obtain the computational results reported here. Initial exploratory calculations were made with the GAMESS'' package running on a VAX 11/780 and with the similar H O N D O ~package ~ running on a CRAY X-MP computer. The final geometry and frequency calculations were made with the GAUSSIAN 8217program running on a VAX 11/780 computer. The standard 3-21G1*split valence basis set was utilized to obtain unrestricted HartreeFock energies for the anion. This procedure, commonly abbreviated UHF/321G, has previously been shown to give a very good description of p - s e m i q u i n ~ n e . ~With ? ~ the GAUSSIAN 82 program, the equilibrium geometry was located by a search procedure based on energy and analytic energy derivative calculations. The molecular force constants were then obtained at the computed equilibrium geometry by analytic evaluation of energy second derivatives. This produced a full harmonic force field that was then used in conjunction with the nuclear masses to calculate normal modes. A recent comprehensive study19 of numerous representative
(3) Madden, K. P.; McManus, H. J.; and Schuler, R. H. J . Phys. Chem. 1982, 86, 2926. (4) Schuler, R. H. Radiaf. Res. 1977, 69, 417. (5) Schuler, R. H.; Tripathi, G. N. R.; Prebcnda, M. F.; Chipman, D. M. J. Phys. Chem. 1983,87,5357. Also see: Tripathi, G. N. R. J. Chem. Phys. 1981, 74, 6044. Tripathi, G. N. R.; Schuler, R. H. J . Chem. Phys. 1982, 78, 2139. (6) Chipman, D. M.; Prebenda, M. F. J. Phys. Chem., in press. (7) Tripathi, G. N. R.; Schuler, R. H. J. Chem. Phys. 1984, 81, 113. (8) Tripathi, G. N . R.; Schuler, R. H. J. Phys. Chem. 1984, 88, 1706. Tripathi, G. N . R. In Multichannel Image Detectors; II; Talmi, Y . , Ed.; American Chemical Society: Washington, DC, 1983; ACS Symp. Ser. No. 236, p 171. (9) Patterson, L. K.; Lilie, J. Int. J . Radiaf. Phys. Chem. 1974, 6 , 1929. (10) Schuler, R. H. Chem. Educ., in press. Available from the author as Report NDRL-2687.
(11) Alfassi, 2.B.; Schuler, R. H. J. Phys. Chem. 1985, 89, 3359. (12) Madden, K. P.; Fessenden, R. W. J. Am. Chem. Soc. 1982,104,2578. (13) (a) Behar, D.; Fessenden, R. W. J . Phys. Chem. 1972, 76, 1706. (b) Chawla, 0. P.; Fessenden, R. W. J . Phys. Chem. 1973, 77, 772. (14) Diitsch, H.-R.; Fischer, H. Inf. J . Chem. Kinef. 1981, 13, 527. (1 5 ) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCC Software Catalog, Prog. No. QGO1, GAMESS, 1980, Vol 1. (16) Dupuis, M.; private communication, 1984. (;7).Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University: Pittsburgh, 1983. (18) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. SOC.1980, 102, 939. (19) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrtes, D. J.; Binkley, J. S.; Frisch, M. J.; Whitcside, R. A.; Hout, R. F., Hehre, W. J. Int J. Quantum Chem. 1981, S15, 269.
interchange between equivalent C, structures with different spin densities on the two oxygen atoms averages the individual hyperfine constants. Chemical experiments4 show that this radical is considerably more reactive than its isomers, the p - and obenzosemiquinone radical anions, and has redox properties that more resemble those of phenoxyl radicals than those of the other semiquinones. It is noted that the p - and o-semiquinones are stabilized by quinoid structures that readily allow the odd electron to be equally distributed between the two oxygen atoms. Ab initio calculations and resonance Raman experiments show that the two oxygen atoms of psemiquinone are indeed eq~ivalent.~.~ However, a similar description does not necessarily apply to m-semiquinone, where quinoid structures cannot participate in the delocalization of the unpaired electron over the oxygen systems. This aspect then raises a question as to the point group symmetry of this radical, i.e., whether the two CO bonds are, in fact, equivalent in the proper description of its lowest energy state. If the two CO bonds are not equivalent, then this radical is best thought of as a substituted phenoxyl radical and not as a semiquinone. We report here time-resolved optical and resonance Raman studies together with relevant low-temperature ESR and theoretical studies that attempt to answer the above question. These spectroscopic approaches allow one to probe the structure of this radical on a time scale considerably shorter than ESR. The Raman and theoretical studies indicate that in its lowest energy state the two oxygen atoms of this radical are nonequivalent, Le., that it manifests C, point group symmetry. The Raman spectrum is, however, substantially different from that of 3-fluorophenoxyl or 3-hydroxyphenoxyl radicals, showing that the second oxygen atom influences the vibrational structure considerably. Lowtemperature ESR studies are consistent with either a C, structure or with equivalent C, structures that interconvert rapidly on a time scale faster than lo-* s. The ESR studies indicate an upper limit to the barrier for interconversion of -4 kcal/mol, in accord with the a b initio calculations which give a barrier of less than about 2 kcal/mol for interconversion between two equivalent C, structures. This system provides a particularly important example where quinoid structures cannot participate in delocalization of unpaired spin.
-
3970 The Journal of Physical Chemistry, Vol. 90, No. 17, 1986
Tripathi et al.
WAVELEMTH - "rn
Figure 1. Absorption spectra of 3-fluorophenoxyl (A),3-hydroxyphen-
oxy1 (e),and m-semiquinone (0) radicals observed 2 ws after the electron
pulse (see text). molecules calculated at this level of theory has led to a recommendation that the calculated frequencies be multiplied by the empirical factor 0.89 to correct approximately for the combined errors due to neglect of electron correlation and anharmonicity, both of which generally tend to lower the frequencies. This factor was also found to be near optimal in a recent study of the ps e m i q ~ i n o n e . ~To , ~facilitate comparison with experiment, this factor is applied to all the computed frequencies reported in this work.
Results and Discussion Absorption Spectra of the Radicals. The absorption spectrum of m-semiquinone, determined pulse radiolytically, is reported in Figure 1 along with comparative spectra of the 3-fluorophenoxy and 3-hydroxyphenoxyl radicals. A similar spectrum of the semiquinone has previously been reported by Stenken and Neta.20 In each case oxidation of the substrate was with N3' prepared in 0.1 M NaN, so that the observed spectra are free of interference from H atom addition products or, in the case of 3-fluorophenol, from the semiquinone expected to be produced by OH attack at the fluorine position." Oxidation of these substrates by N3*is rapid ( k > lo9M-' s-I)l1 so that at millimolar concentrations the radicals could be readily prepared at submicrosecond times. The spectrum of 3-fluorophenoxyl radical observed in the pulse radiolysis of 3-fluorophenol at pH 11 has the vibrational structure characteristic of most simple phenoxyl radicals and in particular is very similar to that of phenoxy radical with its most intense band at 407 nm. Three bands separated by 1200 cm-' are apparent. These bands are interpreted as the 0 0, 1 0 and 2 0 vibronic transitions between 2A'relectronic states. It is particularly noted that, as with phenoxyl, the 0 0 transition is very narrow (width -6 nm). This transition is lower in energy than the corresponding one in phenoxyl by -500 cm-I, whereas in the para isomer4 it is shifted to higher energies by -500 cm-I. This change in sign qualitatively follows the unpaired spin population a t the point of substitution, but the magnitude of the shift in the meta isomer is considerably greater than might be expected We conclude that from the low negative spin population at C3.3 the optical spectrum is affected more by interactions of the fluorine atom with the charge distribution than with the unpaired spin distribution. The extinction coefficients and oscillator strength of this electronic transition are comparable to that of phenoxyl. The 3-hydroxyphenoxyl radical, i.e., the conjugate acid of m-semiquinone, was produced by oxidizing resorcinol at pH 4.6. ESR studies definitively show that under these conditions the radical is present in its protonated form.22 This radical exhibits a spectrum similar to 3-fluorophenoxyl though the vibronic bands are appreciably broader. In this case the 0 0 band is observed a t 428 nm, Le., shifted to the red from phenoxyl by 1600 cm-I,
-- -
-
-
+
-
( 2 0 ) Steenken, S.; Neta, P. J. Phys. Chem. 1982, 86, 3661. (21) Schuler, R.H.; Buzzard, G. In?. J. Radial. Phys. Chem. 1976,8, 563. (22) Jinot, C.; Madden, K. P.; Schuler, R. H. J . Phys. Chem., in press.
I
1
I
1400 RAMAN
1
I
.
600
lo00 FREQUENCY -em"
Figure 2. Resonance Raman spectra of (A) 3-fluorophenoxylexcited at 407 nm, (B) 3-hydroxyphenoxyi excited at 428 nm, and (C) m-semiquinone excited at 445 nm. Each spectrum is an average of approximately 9600 recordings.
so there is clearly substantial interaction between the OH group and electronic system. The oscillator strength of this electronic transition is -30% greater than in phenoxyl. The pK, of this radical is 6.422so that above pH 9 it is present as m-semiquinone. It is seen in Figure 1 that the absorption spectrum of this radical is shifted quite far to the red with what appears to be the 0 0 transition a t 447 nm, Le., -2500 cm-' lower in energy than for phenoxyl. The vibrational profile in the 410-450-nm region is much more complex than that for the protonated radical and has contributions from excited-state vi1000, and 1300 cm-'. The brational frequencies of -500, oscillator strength of this electronic transition is about the same as for 3-hydroxyphenoxyl. Resonance Raman Spectra. It is important to point out that, in the ground electronic state, effects of substitution will be small since there is no change in the orbital occupancy. The ring vibrational frequencies in m-semiquinone are, therefore, expected to be comparable to those in phenoxyl radicals unless the symmetry is changed as the result of the two CO bonds in the radical anion being identical. However, comparable modes in different molecules might have quite different intensities because the electronic structure of the excited state involves a change in orbital occupancy. We will examine the resonance Raman spectra of the three radicals of concern here with these aspects particularly in mind. 3-Fluoro- and 3-Hydroxyphenoxyl Radicals. Raman spectra, excited in the 0 0 absorption bands of each of the radicals of interest, are illustrated in Figure 2. These radicals were produced
-
-
+
-
m-Benzosemiquinone Radical Anion
TABLE I: Comparison of the Vibrational Frequencies (cm-I) in Phenoxyl, fFluorophenoxyl,3-HydroxyphenoxyI,and m -Semiquinone Radicals' approx 3-fluOrO- 3-hydroxy- m-semidescripn phenoxylb phenoxyl phenoxyl quinone CC stretch d 1606dvw 162Sdw 157OCvw CO stretch 1505 s 1512s 523 s 1519 s 147Y w CC stretch 1462 w 1398 vw CC stretch 1389 w CC stretch 1331 vw 1329 w 313vw 1314w CX stretch 240 w 1178 w 1093 s 1157vw 1178(w 246w 1227w CH bend CH bend 990m 1078 w 088zvw 1070* w 840vw 984vw 978 vw 970 vw CCC planar distortion 920 vw 931 vw f 528 m 527 w 532vw 533 m CCC planar distortion 'Relative Raman band intensities abbreviated as s, strong; m, medium; w, weak; vw, very weak. bSee ref 7. c A moderately intense band is observed at 1625 cm-I that is likely the combination of the strong 1093- and 533-cm-I fundamental (= 1626 cm-'). In view of the theoretical calculations (Table 111), assignment of the 1570-cm-' frequency as a fundamental is uncertain. dThe CC stretching vibration (Wilson 8a) is observed in the region 1550-1610 cm-l in a number of para-substituted phenoxyl radicals. Observed with excitation at 388 nm. /Assignment uncertain. ZAlso observed at 1088 cm-l on deuteration of the OH group. "The shoulder observed at 1070 cm-l is likely the first overtone of the 533-cm-I vibration. under chemical conditions similar to those used in the absorption studies. In the cases of 3-fluorophenoxyl and 3-hydroxyphenoxyl radicals, phenoxyl-like spectra were observed to be superimposed on a broad fluorescence background. The observed frequencies are given in Table I and compared to those previously reported for phenoxyl. The spectrum of 3-hydroxyphenoxyl is particularly weak, partially because of the low efficiency of the dye use in its excitation, but sufficient features are apparent to make it clear that its vibrational structure is similar to that of phenoxyl. The principal Raman emissions at 1512 cm-' for 3-fluorophenoxyl and 1523 cm-I for 3-hydroxyphenoxyl dominate these spectra and are assigned to a predominantly CO stretching mode similar to that observed at 1505 cm-' in phenoxyl.' The 990-cm-' phenoxyl C-H bending vibration, which involves considerable C O stretching motion, is expected to be shifted toward a higher frequency on meta substitutionz3so that the bands at 1078 and 1088 cm-I in the fluoro- and hydroxyphenoxyl radicals, respectively, are suggested as likely candidates for this type of vibration. Such an assignment for the 3-hydroxyphenoxyl radical is substantiated by studies in D20, which show that there is no significant shift in this band on deuterium substitution. The weak band at 1178 cm-I in 3-fluorophenoxyl is tentatively assigned to the C-F stretching vibration, which is observed at -1200 cm-' in 3fluorophenol and similar systems.23 Since the C-0 stretching vibrations in phenol and resorcinol are very broad and observed at -1200 cm-1,23924the wide band at 1240 cm-I for 3-hydroxyphenoxyl is assigned to a mode of this type. The low-frequency bands a t -530 cm-I are unequivocably assignable to the ringbending vibration which is observed at 528 cm-I in phenoxyl. Because of the substituent, the symmetry of the radical is reduced from C2, to C,so that the number of totally symmetric (a') vibrations increases from 11 in phenoxyl to 21 in the meta substituted radicals. While several new bands appear in the latter, most of these modes are not sufficiently enhanced to be observed at the available S/N. For 3-fluorophenoxyl the 1475-cm-' vibration is not apparent in Figure 1 but becomes distinctly visible with excitation at 388 nm, where the fluorescence does not overlap with the Raman emission. The Raman spectrum of 3-hydroxy(23) Varsanyi, G. Vibrational Spectra of Benzene Derivatives; Academic: New York, 1969. The symmetric C-X stretching vibration frequently correlated with the Wilson mode 7a in literature has been designated as mode 13 in this reference. (24) Tripathi, G. N. R. J . Chem. Phys. 1979, 71, 4025; 1981, 74, 250.
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 3971 phenoxyl radical was far too weak for similar bands, if present, to be observed in that case. m-Semiquinone. The Raman spectrum of m-semiquinone given in Figure 2 was obtained 0.5 ps after pulse irradiating 5 mM resorcinol at pH 11.O. Unlike the phenoxyl radicals there is little fluorescence background in this case. It is seen in Figure 2 that the main Raman features are rather different from those of phenoxyl radicals, showing that the second oxygen atom has a major influence on the observed intensities. In addition to the principal band at 1519 cm-' strong bands are observed at 1093 and 533 crn-'. The three 1 0 vibrational contributions noted above in the discussion of the optical spectrum correlate very well with these three bands, indicating that the lowest electronically excited state has a similar vibrational structure. The vibrational assignments for m-semiquinone are made here by comparison with the assignments previously given for the phenoxy17and p-semiquinone5 radicals, after careful consideration of the modes expected to be resonance enhanced under different point group symmetries. If the oxygen atoms are equivalent (C, symmetry) at most only eight of the eleven totally symmetric a l modes can be expected to be observable since the three CH stretching modes will not have sufficient contributions from CC or CO motions to be enhanced. In phenoxyl radical, which also ~ the has C2, symmetry, only six a i modes are a ~ p a r e n t .While b2 modes can be enhanced as a result of vibronic coupling with the higher excited electronic state these modes are expected to be relatively weak.25 In phenoxyl radical only two vibrations of the ten b2 modes are observable, at 1398 and 1331 cm-I, and these are only -2% as intense as the 7a vibration7 We will not consider the out-of-plane a2 and bl vibrations since the electronic transition moment in the radicals under study lies in the phenyl plane, making it unlikely that these vibrations will be observable. We particularly note here that if m-semiquinone has C2, symmetry only the a l mode associated with the in-phase CO stretching motion is expected to be strongly resonance enhanced.25 The large number of lines observed in the fundamental region of m-semiquinone suggests that this radical must have symmetry lower than C,. In C,point group symmetry, the eleven b2 modes acquire totally symmetric character (a'). Of these six are likely candidates for resonance enhancement, including the out-of-phase stretching vibration involving the CO groups. Because of its intensity the Raman band at 1519 cm-l can be assigned with reasonable certainty to a CO stretching vibration similar to that observed at 1505 cm-' in phen~xyl.~ This frequency is comparable to that observed for the phenoxyl radicals and significantly higher than that found for p-semiquinone (1435 cm-I), where the two oxygen atoms are equivalent and the CO bond order is estimated from the Raman data to be -l.5.5 On protonation of p-semiquinone to form the p-hydroxyphenoxyl radical the observed CO stretching frequency increases by 80 cm-I, to 15 15 cm-l ,26 showing that in this radical the bond order of the C O group is considerably greater than the anion. In contrast the CO stretching frequency of m-semiquinone increases on protonation by only 5 cm-', showing little change in bond order. The high CO frequency in the m-semiquinone, therefore, indicates a bond order similar to that in phenoxyl. The similarity of the C O stretching frequency observed here to that in bona fide phenoxyl radicals strongly suggests that in its lowest energy state the electronic structure of m-semiquinone is essentially that of a substituted phenoxyl radical. Assignment of the strong 1093-cm-I band in m-semiquinone poses some difficulty. Although this frequency is very close to a CH bending frequency in the meta-substitued phenoxyls, the resonance enhancement is unusually high. Since the other bands in the 1300-1650-cm-' region (CC stretch region) are very much weaker than the C O stretching vibration at 1519 crn-', it can be assumed that the CO bond is considerably elongated in the excited electronic state of the radical but that the nuclear displacements
-
(25) Clark, R. J. H. In Vibrational Spectroscopy-Modern Trends; Barnes, A. J.; Orville-Thomas, W. J., Eds.; Elsevier: Amsterdam, 1977, p 121. (26) Tripathi, G . N. R.; Schuler, R. H., to be published.
3972 The Journal of Physical Chemistry, Vol. 90, No. 17, 1986
TABLE 111: Comparison of Experimental and Calculated Fundamental Vibrational Frequencies (cm-’) of m-Semiiuinone
TABLE 11: Geometrv of m-Semiauinone“
Bond Distances, A 1.446 1.406 1.426 1.487 1.381 1.386 1.270 1.255 1.071 1.073 1.078 1.076 1.072 1.071
c,-c2,c2-c3 cI-c6, c3-c4 c5-c6$c4-c5
0-C,, 0-C3 H-C,, H-C4 H-C 5 H-C,
Tripathi et al.
Bond Angles, deg 115.6 115.7 119.8 122.0 c4-c5-c6 124.9 119.7 c,-C2-C3 124.4 124.8 O-CI-C2, O-C3-C2 118.8 127.1 H-C&l, H-C4-C3 118.8 116.3 H-C& 117.5 120.1 H-CZ-C 1 117.8 117.6 c2-Cj-c4 C5-C6-CI, C3-CI-CS c6-cI-c2,
a”
a‘
1.408, 1.463, 1.387, 1.271, 1.074, 1.076 1.072
1.408 1.430 1.389 1.308 1.072
113.2, 119.3 123.7, 118.8 120.7 124.4 125.8, 122.5 116.2, 118.8 119.7 118.2
Energy,bkcal/mol 6.9
1.8
0.0
(SZ) 1.015
0.999
1.221
“Calculated UHF/3-21G results. bEnergies are given relative to -303.120995 au, the calculated total energy of the equilibrium *A’‘ form. along the C C bonds are small. The 1093-cm-’ vibration must involve, therefore, a major contribution from a C O bond displacement and only minor contribution from C C stretching or CH bending motion to explain its unusual resonance enhancement. In this situation, the vibrational mode cannot be attributed to a predominantly CH vibration. The most probable assignment for the 1093-cm-I frequency is to a C O stretching vibration. However, as noted above, if the two CO bonds are equivalent in the msemiquinone one will expect only one CO vibration, the in-phase stretching motion of the two C O groups, to be greatly enhanced when resonance is with an allowed electronic transition.25 The out-of-phase stretching motion of the two CO bonds would be a non-totally symmetric b2 mode and as a result should not be intense. The obvious conclusion is that the two oxygen atoms are nonequivalent and, therefore, that this radical anion has C, point group symmetry, in which case the out-of-phase C O stretching vibration acquires totally symmetric character (a’) and is likely to be strongly resonance enhanced. For both of these C O vibrations to be about equally intense the nature of both bonds must change significantly on electronic excitation. The moderately intense band at 533 cm-’ is readily assigned as a CCC ring-bending mode similar to that assigned above to the other two radicals. The pronounced resonance enhancement noted in Figure 2 can be correlated with the high Franck-Condon factor noted for a similar mode in the electronic spectrum and implies a large change in the CCC bond angles on excitation. The nontotally symmetric C C stretching modes at 1331 and 1398 cm-’ in the phenoxy1 Raman spectrum, which are observed with appreciable intensity only on 1 0 excitation, correlate very well with the 1314- and 1389-cm-’ bands found for m-semiquinone. The relatively greater intensity of these bands observed with excitation in the 0 0 transition can be explained to result from the a’ symmetry in this radical. We tentatively assign the 1462-cm-’ band in m-semiquinone to a C C stretching mode. +-
-
Theoretical Studies
Geometry of m-Semiquinone. Under the constraint of C2, symmetry, two low-energy structures were located during the ab initio geometry optimization. Their geometries are reported in Table 11. Both have CO bond distances about halfway between that of a normal single and double bond. The structure corresponding to a wave function of 2Bl symmetry has most C C bonds close to a normal aromatic distance, except that the C,-C2 and C2-C3 bonds are a little longer than the others. The other structure, which is calculated to be 5.1 kcal/mol more stable,
Wilson mode” 0.89 X calcd 9a 322 15 477 6a 490 6b 496 1 675 18b 852 19a 907 12 979 18a 1016 9b 1106 7b 1140 3 1235 14 1281 8b 1351 8a 1406 19b 1416 13 1533 7a 2936 20b 2975 20a 2992 2 2996 a
obsd
533
970
Wilson mode“ 0.89 17a 17b 16b 16a 4 11 1Oa 10b 5
X
calcd
203 220 43 1 629 654 758 85 1 900 960
1093 1227 1314 1389 1462 1519
See ref 23.
corresponds to a wave function of ZA2symmetry. This form has cI-c6 and C3-C4 bonds that are close to normal single bonds, while the other C C bonds are close to normal aromatic distances. It may therefore be regarded as two separate conjugated systems (OCIC2C30and c&&) joined by C C single bonds. If the C, constraint is lifted, the geometry relaxes (with no energy barrier) to a lower symmetry C, structure, also reported in Table 11, with a wave function corresponding to 2A” symmetry. This form is 1.8 kcal/mol more stable than the 2Azform and is the calculated equilibrium structure of m-semiquinone. One of the two C O bond distances lengthens by about 0.04 A relative to the other and to the C, forms. A Mulliken population analysis of the 2Af‘wave function indicates that whereas the charge and spin are not equally distributed between the two oxygen atoms neither are they predominantly localized on one or the other. Most of the C C distances are similar to a normal aromatic bond, with the exception that C1-CL is closer to a normal single bond. One skeleton to be more can therefore consider the oc1c2c~c4c~c6 or less conjugated while the C3-0 and c1-c6 bonds have only slight double bond character. The two C O bonds may easily “communicate” by a direct .R through-bond interaction via C,( 2 4 3 .
It would seem likely that the C, 2A2form is the transition state for interconversion between the two equivalent C, 2A” structures that can be written. If this is the case, then the calculated energy difference of 1.8 kcal/mol represents the energy barrier for interconversion. However, we cannot absolutely rule out the possibility of a still lower energy transition-state structure having C, symmetry, although the calculations gave no indication of such a form. As seen in Table 11, there was some spin contamination in each of the optimum UHF structures, (S’)differing somewhat from the value of 0.750 that would pertain to a pure doublet state. This raises the question of whether part or all of the calculated energy differences are artifacts due to differential spin contamination. To examine this question, we carried out ROHF calculations at the optimum UHF geometries. This led to a noticeable lowering of the highest energy ZB1form to be just 2.6 kcal/mol above the 2A2 form. However, there was little change in the 2Az-2A” separation, it becoming now 1.7 kcal/mol. This gives some additional confidence that the finding of a low-symmetry (i.e., C,) equilibrium structure is not an artifact of the UHF method. Vibrational Structure. The calculated fundamental vibrational frequencies for the 2A’rstructure are reported in Table 111. Wilson mode designations have been assigned to correlate as closely as possible to the conventions of ref 23. The line calculated at 1533
The Journal of Physical Chemistry, Vol. 90, No. 17, 1986 3973
m-Benzosemiquinone Radical Anion 0 A
0
I
H
1533
H+ cml
(a1
1140 c m ‘
(b)
Figure 3. Calculated normal modes having significant CO stretch character.
cm-I corresponds to the CI-O stretch and can, with certainty, be assigned to the strong 1519-cm-’ line observed experimentally. As seen in Figure 3a, this mode is very similar to the Wilson CO stretch in phenoxy1 radical.’ The line calculated a t 1140 cm-’, corresponding to the vibrational description given in Figure 3b, has significant C3-0 stretch character and is likely correlated with the strong line observed a t 1093 cm-’. Figure 3 also shows that both of the CO stretching motions are coupled to the Cl-C2 stretch and, therefore, indirectly to one another. The remaining calculated a’ frequencies show good correlation with lines observed experimentally. In particular, we note that the 11 ~ 1 5 0 0 - c m -region 1 has more than enough lines to account for the experimental spectrum, as opposed to the higher symmetry C, structures, which do not (see below). The line observed at 1070 cm-’ that is assigned as a harmonic of the strong 533-cm-I line could conceivably be a fundamental corresponding to the line calculated a t 1106 cm-I. The absence of of any calculated lines in the 1600-cm-’ region leads to assignment of the observed 1625-cm-’ line as a combination band (1093 533 = 1626 cm-l). The calculations do not predict any mode to correlate with the weak line noted at 1570 cm-’. As pointed out above, the polarization of the electronic excitation is presumably in the plane of the molecule, making observation of the out-of-plane a” modes extremely unlikely in the resonance Raman experiment. The calculated results for these modes must therefore stand as predictions. It’is also of interest to examine the vibrational modes of the two symmetry-constrained C, structures, which are very similar to one another in this respect. The symmetric CO stretch occurs and 1532 (2A2)cm-’. This and several of the other at 1512 (2B1) calculated a l modes would correlate well with the observed spectrum. However, in the 1100-1500-cm-’ range, where four lines are observed experimentally, each of these structures has only two calculated a l modes. They do have additional calculated b2 modes in that range but such are rarely seen with any appreciable intensity in a resonance Raman experiment. The higher energy 2B1structure has an imaginary frequency of 20633 cm-I for the b2 asymmetric CO stretch. It is therefore not a true equilibrium structure. Displacement of the nuclei in this mode lowers the energy and, with geometry optimization, ultimately leads to the 2A’’ structure. The more stable 2A2form has all real positive calculated frequencies, suggesting a true local minimum structure, but the asymmetric CO stretch has an unusual calculated value of 1860 crn-’. Since this structure is energetically close to the optimum 2A” structure, and since the major geometrical difference between them involves the asymmetric CO stretch, it seems likely that this mode is highly anharmonic. Therefore, the unusual (harmonic) calculated value probably has little physical relevance. One would expect this mode to actually lower the energy and relax toward the 2A” structure if the anharmonicity were accounted for. Unfortunately, it was not possible to verify this due to interference from a broken symmetry (C,) U H F solution for the *A2structure. This lowers the energy by just 0.1 kcal/mol at the constrained 2A2 geometry and, with geometry optimization, leads directly to the optimum 2A”
+
-IOG
-
Figure 4. First-derivative ESR spectra taken during photolysis of 3 mM resorcinol and 3 mM tetrabutylammoniumhydroxide in acetone at +27 and -86 OC. Magnetic field increases to the right.
structure. However, the broken symmetry solution should be interpreted as an artifact of the U H F method and not given physical relevance. To summarize the vibrational calculations, it is found that the low-symmetry C, structure provides a satisfactory account of the experimentally observed resonance Raman spectrum, whereas the two C,, structures do not. This finding provides further evidence that the *A” structure is indeed the equilibrium form of this species. The closely lying 2A2form may, however, have a significant influence on the actual dynamics of this system. ESR Experiments. Low-temperature ESR experiments were carried out to determine if evidence for an unsymmetrical structure could be obtained. The signature of such a situation would be an inequivalence of the hyperfine splittings of the protons at the 4 and 6 positions. This inequivalence would appear as different hyperfine splittings for these two protons and the corresponding structure in the ESR spectrum would consist of four equally intense lines instead of the 1:2:1 triplet seen previously near room temperature. If the radical were unsymmetric and rapidly interconverting between two equivalent forms, then lowering the temperature might reduce the rate sufficiently that the central line of the 1:2:1 multiplets would start to broaden before becoming two separate lines. The experiment described here is an attempt to see such an effect. A number of solvent and base combinations were tried in order to produce m-semiquinone at as low a temperature as possible. The solvents included acetone, acetonitrile, ethanol, EPA (ether, isopentane, and ethanol), and methyltetrahydrofuran (MTHF). The bases tetrapropyl- and tetrabutylammonium hydroxides, KOH, and potassium tert-butoxide were used with inclusion of 18-crown-6 in the latter two cases to complex the cation. The best spectra were obtained with acetone and acetonitrile and the best low-temperature behavior was with the tetraalkylammonium hydroxides. All of the solutions containing ethanol lost ESR signals as the temperature was lowered. The spectra to be described here in detail were all taken in acetone with tetrabutylammonium hydroxide as the base. It was also possible to produce the protonated form of the radical (the neutral radical) and 3methoxyphenoxyl by using acetone with no base. Photolysis of resorcinol in the basic solutions discussed above produced the spectrum of m-semiquinone that consists of 12 lines (top portion of Figure 4). The best spectra were obtained with equal concentrations of resorcinol and base. An increase in base concentration decreased the signal amplitudes and introduced extraneous lines from other unidentified radicals. The production mechanism is not clear except for acetone solution where abstraction of an OH hydrogen by acetone triplet is demonstrated by the simultaneous formation of (CH&COH when no base was
3914
The Journal of Physical Chemistry, Vol. 90, No. 1 7 , 1986
Tripathi et al.
TABLE I V ESR Parameters
hyperfine constantb solvent
temp
g
factor"
acetonitriled acetoned acetoned water
26 27 -8 5 16
2.004 18 2.004 18 2.004 04 2.003 83
acetone' waterf
-67 16
2.004 96 2.004 25
acetone8
27
a2
dOH)
Eac
a3
a6
2.53 2.50 2.51 2.43
11.73 11.62 11.56 1 1.44
3-Hydroxyphenoxyl Radical 2.30 4.49 11.10 3.85 11.21 2.26
8.51 8.69
0.32 0.46
21.80 21.49
3-Methoxyphenoxyl Radical 4.34 1 1.06 2.41
8.80
0.38h
21.79
a4
m-Semiquinone 0.55 11.73 0.76 1 1.62 0.70 11.56 0.68 11.44
21.48 21.50 21.31 21.13
'Accurate to fO.OOO 02; p-semiquinone has a g factor of 2.004 55 and o-semiquinone a g factor of 2.004 55.28
Values in Gauss accurate to fO.O1 G . Assignments are made by comparison with the carboxylated derivatives (see ref 3) and are definitive. CSumof hyperfine constants of ring protons taking a(HJ as of sign opposite to the others. These values compare with 19.74 G in phenoxyl. dSolution was 3 mM in resorcinol, 3 mM in tetrabutylammonium hydroxide with 75 mM methanol. eSolution was 3 mM resorcinol. 'From ref 3. Determined by in situ radiolysis-ESR methods. gSolution was 16 mM 3-methoxyphenol. Splitting by CH, protons. TABLE V: ESR Line Widths for rn-Semiquinone
line' 1
2 3 4 5 6
width, G 0.1 1 0.11 0.11 0.1 1 0.27 0.20
ave shift, G 1.4 2.4 1.6 2.2 3.3 1.3
line' 7 8 9 10 11
12
In order of increasing field position. upon forming the neutral species.
width, G 0.24 0.24 0.25 0.19 0.26 0.19
ave shift, G 3.5 1.3 5.2 1.5 5.4 1.7
Average shift in position
present. The spectra are described by the parameters given in Table IV. Values for aqueous solution obtained by in situ radiolysis are included for comparison. Also included are parameters for the 3-hydroxyphenoxyl radical obtained in the absence of base. In this case splitting by the OH proton is observed, demonstrating that the radical is indeed protonated. The main effect of solvent is a considerable increase in the g factor for the nonaqueous solutions. Similar changes in g factor with solvent have been reported for the para isomer.27 Data for acetonitrile solution is included to show the sensitivity of the value of a2 to the solvent; data for 3-methoxyphenoxyl radical is listed for later comparisons. At low temperature, as is shown in Figure 4, there is a deviation from the simple form of the spectrum of the anion. An alternation of line widths (and correspondingly amplitudes) is seen in the four lines a t high field and the four central lines are also broadened. The observed line widths are given in Table V. The broadening of the central lines is what would be expected if there was a dynamic interconversion between equivalent structures. However, the width alternation in the upper line group would not be explained by such a process. The pattern of line widths here cannot be the result of slow tumbling which incompletely averages the anisotropies, since it is the lines separated by the small splitting that differ. A large anisotropy of a2 would be necessary and it is not possible to associate such a value with a small isotropic splitting in this radical. The best model for the broadening appears t o be protonation by some source (probably the half-ionized resorcinol) and rapid loss of that proton so that the predominant form of the radical is still the ion. If the correlation diagram showing the way in which the various lines move in such a process is constructed, the pattern of shifts in position (see Table V) corresponds approximately with the broadening observed although the widths in the central line group are wider than anticipated on this basis. Attempts to affect the broadening by changes in solution composition had little effect. If a model of rapid interconversion between equivalent structures is assumed, then the minimum rate can be determined from the width of the central lines if the difference in the a4 and a6.hyperfine splittings of the discrete structures is known. A prediction can (27) Zandstra, P. J. J. Chem. Phys. 1964, 41, 3655.
be made from a study of the hyperfine constants of a series of meta-substituted phenoxyl radicals. It appears that the sum of the values of a2 and a6 is approximately constant while different meta substituents change the difference between the two. The sums for hydroxy- and methoxyphenoxyl radicals in Table IV are 13.00 and 13.14 G. That for the unsubstituted radical is 13.22 G.28 If 13.10 G is used for the sum in the 0--substituted radical and a2 is taken as 0.70 G (and of the same sign as as), then the value for a6 of the anion should be 12.40 G in the C, form of the radical. This analysis implies that a4 is 10.48 G so that interconversion between structures can give the 1 1.44 G average of a4 and 0 6 observed. The difference between a4 and a6 is therefore expected to be 1.9 G. The difference in width between the narrow lines of 0.1 1-G width and the average of about 0.24 G for the central lines is the maximum that can be associated with the interconversion between forms. If a Lorentzian line shape is assumed this width difference corresponds to 1/T2 = 1.982 X lo6 s-l. In this limit the rate constant for interconversion is given by k = T ~ ( A w ) ' / ~where , Aw is the distance the line moves upon the interchange (here, the difference in splittings) expressed in radians per second. With a difference of 1.9 G then this rate would be greater than 7.2 X lo7 s-I. If a preexponential factor of 5 X 10l2 SKIis assumed, this rate constant corresponds to a maximum activation energy of 4.2 kcal/mol. It would be necessary to go to considerably lower temperature to reduce this limit by a significant factor and it is presently not evident as to how to carry out such an experiment. The ESR hyperfine constants provide some insight into the nature of m-semiquinone. The sums of the hyperfine constants listed in Table IV measure the spin density on the ring carbons. Although there is no hyrogen at positions 1 or 3 to probe the spin at those positions, it can be estimated that the value for position 3 would be low and similar to that at position 5. On this basis, the sum for positions 2-6 is about 19 G. The value for the unsubstituted radical28is 19.74. Thus over 80% of the spin density is on the carbon atoms. The sums of the hyperfine constants in the four unsubstituted positions in the 0- (8.84) and p-semiquinones (9.52) are very much smaller.28 It is unlikely that the spin density at the substituted positions would greatly increase this sum. On this basis, rn-semiquinone is very much like other meta-substituted phenoxyl radicals in terms of the distribution of spin between the ring and the oxygen atoms and not at all like the highly conjugated 0- and p-semiquinones. Summary While the Raman and theoretical studies both indicate that the lowest energy state of rn-semiquinone is phenoxyl-like, the ESR pattern cannot readily distinguish between possible C, and C2, structures. The time scale appropriate to the ESR studies (-lo-* s) is, of course, considerably longer than that involved in the (28) Neta, P.; Fessenden, R. W. J. Phys. Chem. 1974, 78, 523
J. Phys. Chem. 1986, 90, 3975-3983 Raman experiments s). All of the data at hand are consonant with a m-semiquinone structure having C, symmetry with, however, rapid interchange of unpaired spin and charge densities between the two oxygen atoms. The theoretical and ESR results indicate that the barrier for this interchange cannot be greater than a few kilocalories per mole and it seems likely that the transition state is the C, structure, corresponding to a wave function of 2A2symmetry. The resonance Raman data show that, in fact, the two CO groups are strongly coupled. The theoretical work indicates that this coupling is possible by direct .rr through-bond interaction via the C1-C2-C3 system. One concludes, therefore, that while the lowest electronic state very likely has a C, structure, the symmetrical C,, structure may, as commented on above, contribute significantly to the dynamics of the system and play an important role in determining what is manifest experimentally. Since the energy difference between these two structural forms is clearly very low, this system provides a particularly important example with which to test the effects of symmetry on the dynamics. m-Semiquinone provides a very interesting example of a radical with two possible sites for the unpaired electron. Allyl radical
3975
and the p-semiquinone radical ion are examples of cases with strong coupling between two structures such that the proper description is truly symmetric about the midplane. The anion radical derived from l,2-dinitroethane is an opposite extreme with weak interaction so that the electron is localized at one nitro The present example of the m-semiquinone seems to represent an intermediate case where the ESR results show symmetry but the structure indicated by Raman spectroscopy and a b initio calculations displays a degree of asymmetry between the two C-0 bonds. If other examples of this intermediate type of behavior can be found, considerable insight may be obtained into just what factors determined whether symmetry breaking and localization will occur. Acknowledgment. We thank Dr.K. P. Madden for assistance with the ESR experiments. Registry No. 3-HOC6H40H, 108-46-3; 3-FC6H40H, 372-20-3; 3FC6H40, 51460-60-7; 3-HOC6H40, 24856-47-1. (29) Behar, D.; Fessenden, R. W. J . Phys. Chem. 1972, 76, 1710.
LASER CHEMISTRY, MOLECULAR DYNAMICS, AND ENERGY TRANSFER Unimolecular Reactions in Isolated and Collisional Systems: I s the Transition-State Rate an Upper Limit for the Isomerization of Stilbene? Michael W. Balk and Graham R. Fleming*+ Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (Received: October 8, 1985; In Final Form: March 14, 1986)
The effect of few-body (e.g., binary) collisions on photochemical trans-cis-stilbene isomerization was studied by measuring the transient fluorescence decay from isolated-molecule conditions up to 5 atm of methane gas pressure at room temperature. Simple statistical considerations were found to account for the thermal isolated-molecule decay using as a basis the energy-dependent rates k(Ex)measured in supersonicjet experiments. The isomerization rate was found to increase with methane pressure throughout the 0-5-atm range. In statistical theories of barrier crossing the transition-state rate at temperature T, kmT(T), represents an upper limit for the reaction rate and is expected to be equal to k( T), the thermal average of k(Ex). However, contrary to expectation, for pressures greater than about 2 atm the isomerization rate was found to exceed k(n by over a factor of 2 at 5 atrn and by as much as a factor of 10 at pressures up to 100 atm. Relations between the various types of experimentallyobserved rate constants are explored, including a method for the direct measurement of k(T). Possible origins for the nonstatistical behavior of the stilbene-methane collision dynamics are also discussed.
I. Introduction The dependence of chemical reaction dynamics on the surrounding solvent medium is a topic of much current interest.14 As we have discussed in more detail elsewhere' the photochemical isomerization of stilbene and diphenylbutadiene provide excellent model systems for such studies. By combining the techniques of ultrafast spectroscopy with supersonic jet spectroscopy it has been possible to study the isomerization process progressively from isolated molecules prepared with a well-defined initial energy, through thermal but still isolated (on the isomerization time scale) molecules, to collisional gas-phase conditions, and finally into the Camille and Henry Dreyfus Teacher Scholar.
0022-3654/86/2090-3975$01.50/0
liquid phase. The solvent friction is varied over about 6 orders of magnitude in these studies, which therefore can provide stringent (1) Fleming, G.R.;Courtney,S. H.; Balk, M. W. J . Stat. Phys. 1986,42, 83. (2) Courtney, S.H.; Fleming, G. R. J . Chem. Phys. 1985, 83, 215. (3) Schroeder, J.; Troe, J. Chem. Phys. Lett. 1985, 116,453. (4) Troe,J. Chem. Phys. Lett. 1985, 114, 241. (5) Maneke, G.; Schroeder, J.; Troe, J.; Voss, F. Ber. Bunsen-Ges. Phys. Chem. 1985.89, 896. (6) Felker, P. M.; Zewail, A. H. J. Phys. Chem. 1985, 89, 5402. (7) Lee, M.; Holtom, G. R.; Hochstrasser, R. M. Chem. Phys. Lett. 1985, 118, 359. ( 8 ) Rothenberger, G.; Negus, D. K.; Hochstrasser, R. M. J . Chem. Phys. 1983, 79, 5360.
0 1986 American Chemical Society
