J. Phys. Chem. 1989, 93, 5079-5087
5079
Excited-State Geometry and Dynamics of trans-Hexatriene: A Resonance Raman Intensity Study Anne B. Myers* and Krisanto S. Pranatat Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received: October 20, 1988; In Final Form: January 3, 1989)
UV resonance and preresonance Raman spectra of tram-l,3,5-hexatrienevapor have been obtained with 10 excitation wavelengths between 280 and 234 nm. Absolute resonance Raman cross sections have also been measured with excitation at the peak of the zero-zero band (2512 A). The rigorous resonance spectra exhibit intensity in overtones and combination bands of a, symmetry torsional modes, as well as fundamentals, overtones, and combination bands of the totally symmetric in-plane modes. The spectra are interpreted quantitatively by parameterizing a model for the excited-state potential surface to fit the absorption and resonance Raman spectra. Duschinsky rotation and thermal population of the lower frequency torsional modes are incorporated by time-dependent wave-packet propagation techniques. We find significant reductions in the force constants for both central and terminal double-bond twisting between the ground and lB,+ excited states, but the local equilibrium geometry of the IB,' state is planar. The absolute Raman cross sections and depolarization ratios indicate a homogeneous line width for the isolated molecule of -65 cm-', and the absence of any significant redistributed fluorescence implies that this width is due to population decay of the IBu+ state on a time scale of -40 fs.
Introduction The photochemistry and spectroscopy of the linear polyenes have been the subject of many experimental and theoretical investigations over the past two Interest in this class of molecules stems on the one hand from the importance of linear polyenes and their close relatives in photobiology (e.g., the retinal chromophore in the visual pigments and the triene chromophores in vitamin D). The polyenes have also been studied extensively by physical organic chemists and chemical physicists attempting to understand how their photochemistry and photophysics are influenced by ground-state conformational effects and by the nature and ordering of the excited electronic states. It has often been noted that the shortest members of the trans linear polyene series, butadiene and hexatriene, exhibit spectroscopic and photophysical properties that are qualitatively different from those of the other members of the family. The linear polyenes and most of their alkyl-substituted derivatives with four or more double bonds, as well as all of the trans-a,w-diphenylpolyenes, fluoresce with reasonable quantum yields and exhibit vibronically well-resolved absorption spectra under favorable conditions.'8 While most of these molecules are known to undergo trans-cis photoisomerization, the isomerizqtion evidently is not fast enough to quench the fluorescence. Butadiene and hexatriene, in contrast, are practically nonfluorescent and do not exhibit sharp vibronic bands in absorption under any conditions that have yet been reported, including supersonic jet expansion.12,18 At least two explanations, not mutually exclusive, have been proposed to explain the near absence of fluorescence and the breadth of the spectra even in the ultracold isolated molecule. One possibility is that the initially excited dipole-allowed lBU+state undergoes extremely rapid internal conversion, either to the nearby forbidden lA; excited state or directly to the ground state, broadening the spectrum by a simple lifetime The other is that the initially excited IBu+state twists rapidly about either double or single bonds, causing unresolved Franck-Condon activity in low-frequency torsional coordinates to broaden the s p e c t r ~ m . ' ~ * ' ~ The two effects may be complementary, with a rapid geometry change in the IBu+state enhancing the rate of internal conversion. Gas-phase photolysis studies have shown that trans-hexatriene does photochemically isomerize to cis followed by ring closure to form cyclic dienes.28 These results were attributed to thermal reactions of the hot ground-state molecules formed by rapid internal conversion, but the data do not preclude the possibility that significant isomerization occurs on the excited-state potential 'Present address: Department of Chemistry, University of Washington, Seattle, WA 98195.
surface as well. The reported trans-cis quantum yield in solution is only 0.016.34 The extent of photoisomerization about the (1) Hemley, R. J.; Lasaga, A. C.; Vaida, V.; Karplus, M. J. Phys. Chem. 1988, 92, 945. (2) Cave, R. J.; Davidson, E. R. J . Phys. Chem. 1988,92,614. Cave, R. J.; Davidson, E. R. Chem. Phys. Lett. 1988, 148, 190.
(3) Zerbetto, F.; Zgierski, M. Z.; Negri, F.; Orlandi, G. J . Chem. Phys. 1988, 89, 3681. (4) Trulson, M. 0.;Dollinger, G. D.; Mathies, R. A. J . Am. Chem. SOC. 1987, 109, 586. Trulson, M. 0.; Dollinger, G. D.; Mathies, R. A. J . Chem. Phys. 1989, 90, 4274. (5) Sension, R. J.; Mayne, L.; Hudson, B. J. Am. Chem. SOC.1987,109, 5036. Sension, R. J.; Hudson, B. J. Chem. Phys. 1989, 90, 1377. (6) Dormans, G. J. M.; Groenenboom, G. C.; Buck, H. M.J. Chem. Phys. 1987, 86, 4895. (7) Hemley, R. J.; Brooks, B. R.; Karplus, M. J . Chem. Phys. 1986.85, 6550. (8) Trulson, M. 0.; Mathies, R. A. In Proceedings of the Tenth Interna-
tional Conference on Raman Spectroscopy; Peticolas, W. L., Hudson, B., Eds.; University of Oregon: Eugene, OR, 1986; p 14.36. Trulson, M. 0.; Mathies, R. A., to be submitted for publication. (9) McDiarmid, R.; SabljiE, A.; Doering, J. P. J . Am. Chem. SOC.1985, 107, 826.
(10) Aoyagi, M.; Osamura, Y.; Iwata, S. J . Chem. Phys. 1985,83, 1140. (11) Chadwick, R. R.; Gerrity, D. P.; Hudson, B. S.Chem. Phys. Leu.
1985. .. ~115.~-24. . , (12) Leopold, D. G.; Pendley, R. D.; Roebber, J. L.; Hemley, R. J.; Vaida, V. J. Chem. Phys. 1984, 81, 4218. (13) Leopold, D. G.;Vaida, V.; Granville, M. F. J . Chem. Phys. 1984,81, 4210. (14) Dinur, U.; Hemley, R. J.; Karplus, M. J. Phys. Chem. 1983.87.924. (15) Hemley, R. J.; Dawson, J. I.; Vaida, V. J. Chem. Phys. 1983, 78, 2915. (16) McDiarmid, R. J . Chem. Phys. 1983, 79, 9. (17) Myers, A. B.; Mathies, R. A.; Tannor, D. J.; Heller, E. J. J. Chem. Phys. 1982, 77, 3857. (18) Hudson, B. S.; Kohler, B. E.; Schulten, K. In ExcitedStates; Lim, E. C., Ed.; Academic: New York, 1982; Vol 6, p 1. (19) Granville, M. F.; Kohler, B. E.; Snow, J. B. J. Chem. Phys. 1981, 75, 3765. (20) Heimbrook, L. A.; Kenny, J. E.; Kohler, B. E.; Scott, G. W. J . Chem. Phys. 1981, 75, 4338. (21) Lasaga, A. C.; Aerni, R. J.; Karplus, M. J . Chem. Phys. 1980, 73, 5230. (22) Doering, J. P.; McDiarmid, R. J. Chem. Phys. 1980, 73, 3617. (23) Granville, M. F.; Holtom, G. R.; Kohler, B. E. J . Chem. Phys. 1980, 72, 4671. (24) Tavan, P.; Schulten, K. J . Chem. Phys. 1979, 70, 5407. (25) Nascimento, M. A. C.; Goddard, W. A. 111 Chem. Phys. 1979,36, 147. (26) Gavin, R. M., Jr.; Weisman, C.; McVey, J. K.; Rice, S. A. J . Chem. Phys. 1978, 68, 522. (27) Schulten, K.; Ohmine, I.; Karplus, M. J . Chem. Phys. 1976,64, 4422. (28) Orchard, S. W.; Thrush, B. A. Proc. R . Soc. London 1974, A337,243. (29) Gavin, R. M., Jr.; Risemberg, S.; Rice, S. A. J. Chem. Phys. 1973, 58, 3 160. (30) Hudson, B. S.; Kohler, B. E. Chem. Phys. Lett. 1972, 14, 299. ~
0022-365418912093-5079$01.50/0 0 1989 American Chemical Society
5080 The Journal of Physical Chemistry, Vol. 93, No. 13, 1989
Myers and Pranata
terminal double bonds is unknown, as the products of such an isomerization are indistinguishable from the reactants. Resonance Raman scattering is an ideal approach for evaluating the importance of these spectral broadening mechanisms. Resonance Raman intensities are sensitive to both the underlying vibronic structure of a diffuse absorption band and the dephasing time for the resonant electronic ~ t a t e . ~ ~The - ~ *ground-state vibrations that are most enhanced in resonance Raman scattering are those vibrations along which there is the greatest change in either equilibrium geometry or force constant upon electronic excitation-that is, those vibrations that have the greatest Franck-Condon activity in absorption. Although the electronic spectral bandwidth may be so large that little or no vibronic structure is evident in the absorption spectrum, the ground-state vibrational transitions, which mirror the Franck-Condon structure of the electronic transition, usually are clearly resolvable. In particular, if the electronic spectrum is broadened by extensive vibronic activity in low-frequency torsional modes, even overtones of those torsions should be prominent in the resonance Raman spectrum (odd overtones being symmetry forbidden for a planar ground-state geometry). The absolute resonance Raman cross sections are additionally sensitive to the dephasing time for the resonant electronic state, which, in a collision-free vapor, must be due to relaxation from the initially excited levels to isoenergetic "dark" states. The infrared and nonresonant Raman spectra of trans- and cis-hexatriene have already been studied in considerable detail for the purpose of making ground-state vibrational assignm e n t ~ . ~ "Ultraviolet ~~ resonance Raman spectra of several other polyenes and related molecules have been obtained and analyzed qualitatively and/or q u a n t i t a t i ~ e l y , ~ ~ ~but ~ ~ although . ' ~ ~ ~ . ~the ~~~~ resonance Raman spectra of the hexatriene triplet states have been studied in some detaiP and a preresonance spectrum of the trans isomer has been p u b l i ~ h e d , 'rigorous ~ resonance spectra of the hexatriene ground states have evidently not been reported at all. In this paper, we present resonance Raman spectra of transhexatriene in the vapor phase at low pressure using a variety of excitation wavelengths within the lowest allowed absorption band. Accurate relative intensities are obtained at each excitation wavelength, and absolute intensities for excitation at the 0-0 peak are determined relative to methane as an intensity standard. The
data are analyzed by the time-dependent wave-packet theory of resonance Raman s ~ a t t e r i n g , 'which ~ ~ ~ *simplifies ~~ the treatment of multidimensional potential surfaces that may be either bound or unbound with respect to torsional motion. From this analysis, we can quantitate the contributions to the electronic spectral breadth from both torsional motion and excited-state population decay.
(31) Schulten, K.; Karplus, M. Chem. Phys. Lett. 1972, 14, 305. (32) Warshel, A.; Karplus, M. J . A m . Chem. SOC.1972, 94, 5612. (33) Warshel, A,; Karplus, M. Chem. Phys. Lett. 1972, 17, 7. (34) Jacobs, H. J . C.; Havinga, E. Ado. Photochem. 1979, I I , 305. (35) Myers, A. B.; Li, B.; Ci, X. J . Chem. Phys. 1988,89, 1876. (36) Myers, A. B.; Mathies, R. A . In Biological Applications ofRaman Spectroscopy; Spiro, T. G . , Ed.; Wiley: New York, 1987; Vol 2, p 1. (37) Yan, Y . J.; Mukamel, S. J . Chem. Phys. 1987, 86, 6085. (38) Ziegler, L. D. J . Chem. Phys. 1987, 86, 1703. (39) Sension, R. J.; Kobayashi, T.; Strauss, H. L. J . Chem. Phys. 1987, 87, 6233. (40) Myers, A. B.; Trulson, M. 0.;Pardoen, J. A,; Heeremans, C.; Lugtenburg, J.; Mathies, R. A. J . Chem. Phys. 1986, 84, 633. (41) Jean, J . M.; Friesner, R. A . J . Chem. Phys. 1986,85, 2353. (42) Stallard, B. R.; Callis, P. R.; Champion, P. M.; Albrecht, A. C. J . Chem. Phys. 1984, 80, 70. (43) Brafman, 0.;Chan, C. K.; Khodadoost, B.; Page, J . B.; Walker, C. T. J . Chem. Phys. 1984.80, 5406. (44) Imre, D.;Kinsey, J . L.; Sinha, A,; Krenos, J. J . Phys. Chem. 1984, 88. 3956. (45) Champion, P. M.; Albrecht, A. C. Annu. Reu. Phys. Chem. 1982,33, 353.
(46) Heller, E. J.; Sundberg, R. L.; Tannor, D. J . Phys. Chem. 1982, 86, 1822. (47) Siebrand, W.; Zgierski, M. Z. J . Raman Spectrosc. 1982, 13, 78. (48) Ziegler, L. D.; Albrecht, A . C. J . Raman Spectrosc. 1979, 8, 73. (49) Langkilde, F. W.; Wilbrandt, R.; Nielsen, 0. F.; Christensen, D. H.; Nicolaisen, F. M. Spectrochim. Acta 1987, 43A, 1209. (50) McDiarmid, R.; SabljiC, A . J . Phys. Chem. 1987, 91, 276. (51) Lippincott, E. R.; White, C. E.; Sibilia, J. P. J . Am. Chem. SOC.1958, 80, 2926. (52) Lippincott, E. R.; Kenney, T. E. J . A m . Chem. SOC.1962, 84, 3641. (53) Myers, A . B.; Trulson, M. 0.;Mathies, R. A . J . Chem. Phys. 1985, 83, 5000. (54) Myers, A. B.; Mathies, R. A. J . Chem. Phys. 1984, 81, 1552. (55) Langkilde, F.W.; Jensen, N.-H.;Wilbrandt, R. J . Phys. Chem. 1987, 91, 1040.
Experimental Methods 1,3,5-Hexatrienewas purchased from Aldrich as a mixture of the cis and trans isomers, which were separated by preparative gas chromatography on a 20 ft X in. column of 30% PJ'oxydipropionitrile on Chromosorb W/AW, 30-60 mesh. The carrier gas was helium, and the column temperature was 60 OC. Purified samples were stored in dry ice for up to 3 weeks before use. The samples were dehydrated over CaH2, subjected to repeated freeze-pump-thaw cycles on a vacuum line and then expanded into a 500" glass bulb attached to a fused-silica fluorescence cuvette for the Raman and absorption experiments. Hexatriene pressures ranged from 40 mTorr on-resonance to 1.2 Torr off-resonance, depending on reabsorption considerations (see text below). Pressures were measured by capacitance manometers (MKS Instruments). The resonance Raman experiments were carried out with the excitation and detection system described p r e v i ~ u s l y .Excitation ~~ wavelengths from 280 to 234 nm were obtained by frequency doubling a YAG-pumped dye laser (Rhodamine 590, 610, or 640 dyes) and anti-Stokes Raman shifting in hydrogen gas by 1 or 2 quanta. For the relative intensity measurements, the Ramanshifted excitation was attenuated to 10-20 pJ/pulse and focused into the sample with a 50-cm focal length lens. Under these conditions, the concentration of hexatriene in the bulb was found by absorption spectroscopy to decrease by up to 10% over the course of an experiment (-20-min irradiation time) and some ground-state depletion occurred during each pulse, but the relative intensities were independent of laser power (see Results) and showed little or no contamination from photochemical products. In particular, the strong cis-hexatriene Raman lines at 394 and 1249 cm-' are absent or exceedingly weak in our spectra. A standard 90' scattering geometry was employed. The hexatriene pressures were kept sufficiently low that the calculated corrections to the relative intensities due to reabsorption of the scattered light did not exceed 15% at worst and were considerably smaller in most cases. Where the reabsorption corrections exceed 5%, the tabulated relative intensities (though not the displayed spectra) have been corrected on the basis of the known absorption spectrum and an estimated average scattering path length. All spectra have been corrected for the wavelength dependence of the detection efficiency. For the absolute cross-section measurements it is important to ensure that ground-state depletion is not significant. The fraction of illuminated molecules absorbing a photon during each pulse can in principle be calculated from the absorption cross-section and laser pulse characteristic^.^^ However, the intensity profile of the focused laser beam is often difficult to known accurately. Therefore, the degree of saturation was determined empirically by recording the hexatriene intensities as a function of incident laser power from approximately 6 to 0.2 pJ/pulse. The apparent Raman cross sections varied by about 35% over this range. The true hexatriene/methane intensity ratio was then obtained by extrapolation to zero incident power under the assumption that the decrease in the ground-state population follows simple firstorder kinetics, with no relaxation of excited molecules back to the ground state during the pulse. This is justified because at our pressures the average time between collisions is much longer than the pulse width. Absolute cross sections were measured relative to the 2917-cm-' line of methane as an external standard. The spectra of methane at approximately 1 atm were recorded at higher (56) Lee, S.-Y.;Heller, E. J. J . Chem. Phys. 1979, 71, 4777. (57) Mathies, R. In Chemical and Biochemical Applications of Lasers; Moore, C. 8.. Ed.; Academic: New York, 1979; Vol 4; p 55
Excited-State Geometry and Dynamics of trans-Hexatriene energies of -6-1 50 kJ/pulse to obtain a good signal-to-noise ratio for the nonresonant standard. We were not able to use an internal standard because the nonresonant Raman scattering from methane, which has the highest cross section of the gas-phase standards yet reported,58was too weak to be measured accurately at the low pulse energies needed to record an unsaturated hexatriene spectrum. Depolarization ratios were measured by the method described p r e v i o ~ s l y . The ~ ~ aperture of the collecting lens was masked down to f/2.2 to minimize the solid angle correction. Absorption spectra were recorded on a Cary 118 spectrophotometer at a spectral resolution of approximately 1 A. The relative Raman intensities were determined by nonlinear least-squares fits of regions of the spectra to sums of peaks plus a linear background. The theoretical band shape should be a convolution of the vibration-rotation band contour with the instrument function; however, the nonlinear least-squares algorithm, in order to run efficiently, needs a fairly simple functional form to fit. We chose hyperbolic secant peak shapes, which have no theoretical basis but generally gave a better fit to the data than Gaussian or Lorentzian peaks. The relative intensities of weak bands overlapping stronger ones, such as the 1581-cm-’ line, are fairly sensitive to the functional form assumed for the peak shape, leading to rather large uncertainties in the intensities of such lines.
-
Theoretical Methods The excited-state potential surface parameters were extracted by modeling the absorption spectrum, relative Raman intensities, and absolute Raman cross sections. The calculations were carried out with Heller’s time-dependent formulation, which has been Briefly, the resonance Raman discussed in detail elsewhere. cross section at excitation energy E L and scattered photon energy E, is given by 17,46956
while the corresponding absorption cross section is
~ A ( E L=) 4re2i@EL 6h2c
E P i J m d t ( i J i ( t ) ) exp[i(EL + c i ) t / h - r l r l / h ] 1
-m
Here, M is theelectronic transition length, Pi is the Boltzmann population of state li), ci and cJare the energies of vibrational states li) and #, r is the electronic homogeneous line width, and li(t)) = exp[-iHt/h]li) where H is the excited-state vibrational Hamiltonian. The absorption cross section involves a full Fourier transform of the overlap between li(t)), the initial ground-state wave function propagated on the excited-state potential surface, and itself at time zero. The Raman cross section involves the modulus squared of a half-Fourier transform of the overlap between this same moving wave packet and the final state in the Raman process. Equations 1 and 2 are formally identical with the standard frequency-domain Kramers-Heisenberg-Dirac and golden rule expressions for Raman and absorption, respectively, but the time-domain approach often has significant computational advantages for large molecules, particularly when the ground- and excited-state normal modes are not parallel (the Duschinsky effect) or when the excited-state potential surface is unbound along one or more coordinates. Hexatriene has several low-frequency modes that have significant thermal population at room temperature. Since different molecules do not interfere in spontaneous Raman scattering, thermal effects can be treated in a “brute force” way by simply evaluating the cross section for each initially populated state and (58) Bischel, W. K.; Black, G. In Excimer Lasers 1983; Rhodes, C. K., Egger, H., Pummer, H., Eds.; American Institute of Physics: New York, 1983; p 181. (59) Li, B.; Myers, A. B. J . Chem. Phys. 1988,89, 6658.
The Journal of Physical Chemistry, Vol. 93, No. 13, 1989 5081 weighting by its Boltzmann factor as indicated in eq 1. However, evaluation of eq 1 is complicated by the fact that li(t)) is simple to calculate only if li) is Gaussian, which is the case only for the harmonic oscillator ground state. Higher oscillator eigenstates may be expressed as linear combinations of complex Gaussians as discussed by Heller.60*61 The specific form we employ is q n ( q )=
,+/2nn
Nj=1 exp[-(q Sj)
- qj)2/2
+ ipj(q -
+ iPJqj/2 + 2 r i n j / n l
(3)
where qj = (2r1)’/~cos ( 2 r j / N )
(4a)
p.J = -(2t1)’/~sin ( 2 r j / N )
(4b)
Ten basis states ( N = 10) give an excellent fit to the oscillator eigenstates up to n = 3. li(t)) and the appropriate overlaps are then calculated from the algorithms derived in ref 62, noting that since the Schriidinger equation is linear, thermally excited initial states may be handled by propagating each component Gaussian separately and then summing the overlaps.63 Thermal effects are important only in modes that are Franck-Condon active due to changes in either equilibrium position or vibrational frequency upon excitation. Of the four low-frequency modes of hexatriene (below 300 only the a,, single-bond torsion (vI9) at 93 cm-’ and the a, central double-bond torsion (v18) at 246 cm-’ clearly exhibit vibronic activity, so these were the only thermally excited modes considered. Furthermore, while Duschinsky rotation may occur to some degree in other modes as well, there is experimental evidence for it in only two pairs of vibrations: the a, symmetry single-bond torsion 9 ~ 1 7 and , the ag double-bond and methylene twisting modes, ~ 1 and and single-bond stretches, v5 and vIo. Thus, for the hexatriene case, the multidimensional overlaps (ili(t)) and U i ( t ) ) can be factored into a product of one-dimensional overlaps in the nonrotated modes and two two-dimensional overlaps in the rotated pairs of modes. For the final calculations, the time integrals in eq 1 and 2 were evaluated numerically from a simple sum (rectangle rule integration) with 1000 time steps and an increment of 0.5 fs/step. A Boltzmann average was taken over eight initial states (through n = 3 in uI9 and n = 1 in VIS). The homogeneous line width was also determined independently from the total resonant scattering quantum yield as discussed in ref 35 (5)
where A. is proportional to the oscillator strength:
This expression has the advantage of determining r independent of any assumptions about the form of the ground- or excited-state potential surfaces.
Results Absorption Spectrum. Figure 1 shows the absorption spectrum of trans-hexatriene vapor and indicates nine of the ten excitation wavelengths used for the Raman studies. The shape and position of the spectrum agree well with that published by Gavin et aLZ9 Our extinction coefficients are within 5 1 0 % of those given by Orchard and Thrush at 2531 and 2288 AZabut are about 4 times (60) Heller, E. J. J . Chem. Phys. 1975, 62, 1544. (61) Davis, M. J.; Heller, E. J. J . Chem. Phys. 1979, 71, 3383. (62) Tannor, D. J.; Heller, E. J. J . Chem. Phys. 1982, 77, 202. (63) Analytic formulas for ( i l i ( t ) )at nonzero temperatures have also been derived: Yan, Y. J.; Mukamel, S. J . Chem. Phys. 1986, 85, 5908.
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The Journal of Physical Chemistry, Vol. 93, No. 13, 1989
Myers and Pranata
Raman S h i f t (an-’) Figure 3. Low-frequency region of the Raman spectrum at excitation
frequencies spanning the zero-zero band. All spectra are plotted with the 1635-cm-I band scaled to approximately the same relative intensity. Other conditions are as in Figure 2.
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