J. Phys. Chem. 1990, 94, 227-231 only one cluster structure is observed with a (calculated) binding a significant displacement energy of 937 cm-I. In fl~orene(H,O)~, along the vdW coordinates occurs upon SI So excitation. Studies of fluorene(NH,), and fluorene(ND,), suggest that at least two stable configurations of vdW clusters are possible in fluorene(NH,),; one has a structure in which ammonia coordinates to the fluorene ring and the other has a structure in which ammonia is coordinates to the aliphatic hydrogens and is displaced from the fluorene ring. On the basis of both calculations and interpretation of the fluorene/ammonia, water, and piperidine cluster spectra, one expects that the solvent molecules can coordinate to the aliphatic
-
227
hydrogens of fluorene molecule in at least some cluster configurations. Nonetheless, no evidence (e.g., broad, red-shifted fluorenyl anion emission) which substantiates an excited-state intermolecular proton-transfer reaction can be found in these systems. The absence of any observed anion emission suggests that the proton-transfer reaction at the carbon center occurs at too slow a rate to be observed given the excited-state lifetime of ca. 10 ns. Acknowledgment. This work was supported by Office of Naval Research and the National Science Foundation. Registry No. Fluorene, 86-73-7; ammonia, 7664-41-7; water, 773218-5; piperidine, 110-89-4.
-
Vibrational Structure and Temperature Dependence of the Electronic Absorption (1'6, llA,) of all-trans-&Carotene Hajime Tori and Mitsuo Tasumi* Department of Chemistry. Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan (Received: June 12, 1989)
-
The vibrational structure of the absorption spectrum (l'B,, l l A ) of all-trans-@-carotene has been analyzed by the second-derivative method and spectral simulation. Estimates of the following quantities have been obtained: the vibrational frequencies and vibrational relaxation rate of the strongly Franck-Condon active modes in the 1'B, state, parameters representing the displacement of potential minimum along these modes on going from l'A, to l'B,, and the magnitude of modulation of the 0-0 wavenumber due to intermolecular interactions. Against the primitive inference based on the weakening of bond alternation in the l'B, state, the frequency of the C=C stretch in the l'B, state is higher (though not greatly) than that of the corresponding mode in the l'A, state. On the other hand, the frequency of the C-C stretch in the llB, state is higher by about 90 cm-l than that in the llA, state, in agreement with the primitive inference. The vibrational relaxation time in the l'B, state is estimated to be of the order of 50 fs. Analysis of the temperature dependence of the absorption spectrum indicates that it is not accompanied by a change in the structure of all-trans-@-carotene.
Introduction all-trans-8-Carotene, a representative polyene having a relatively long chain, is an interesting molecule from spectroscopic and biophysical viewpoints. It has been particularly useful in the studies of second-order optical processes.'-'' In those studies the Raman excitation profile resonant with the electronic transition 1 'B, 1 'Aq has been analyzed. However, it is surprising to find how scarce IS the definite knowledge of the excited state l'B,. For instance, the vibrational frequencies of the C==C and C-C stretches in the I'B, state are not well determined, although these modes are thought to be strongly Franck-Condon active. By primitive inference, the C=C stretching frequency is expected to become lower to the same extent as the C-C stretching frequency becomes higher on excitation l'B, l'Ag, because of the weakening of bond alternation. On the other hand, in most of the analyses of the Raman excitation profile'-9 and the absorption sp.ectrum12of this molecule, it has been assumed that the frequencies of the two modes in l'B, are the same as those
-
-
( I ) lnagaki, F.; Tasumi, M.; Miyazawa, T. J . Mol. Spectrosc. 1974, 50, 286. (2) Penner, A. P.; Siebrand, W. Chem. Phys. Lett. 1976, 39, 11. (3) Warshel, A.; Dauber, P. J . Chem. Phys. 1977, 66, 5477. (4) Sufra, S.;Dellepiane, G.; Masetti, G.;Zerbi, G . J . Roman Spectrosc. 1977, 6, 267. (5) Lukashin, A. V.; Frank-Kamenetskii, M. D. Chem. Phys. 1978, 35, 469. (6) Siebrand, W.; Zgierski, M. 2.J . Chem. Phys. 1979, 71, 3561. (7) Tonks, D. L.; Page, J. B. Chem. Phys. Lett. 1979.66, 449. (8) Hoskins, L. C. J . Chem. Phys. 1980, 72,4487. (9) Ho, Z. 2.;Hanson, R. C.; Lin, S.H. J . Chem. Phys. 1982, 77, 3414. (10) Watanabe, J.; Kinoshita, S.;Kushida, T. J . Chem. Phys. 1987, 87, 4471. ( 1 1 ) Sue, J.; Mukamel, S. J . Opt. SOC.Am. 1988, B5, 1462. (12) Kjaer, A. M.; Kjaer, N. J.; Ulstrup, J.; Zakaraya, M. G. Chem. Phys. Lett. 1989, 157, 447.
in the ground state 1lAk. On this assumption, however, one fails to reproduce the absorption spectrum in the visible region, as shown below (see also Figure 2 of ref 13). This implies that the frequencies become higher (at least on the average) on excitation. For shorter polyenes, this kind of frequency upshift had long been proposed from the absorption or fluorescence excitation spectra at low temperatures,'"'* and it was clearly observed in the absorption spectra of jet-cooled hexatriene and o ~ t a t e t r a e n e ; 'the ~.~~ frequencies of both the C=C and C-C stretches are higher in llB, than those in 1lA,. Furthermore, the parameters used in the analysis of the absorption spectrum and the Raman excitation profile of tetradesmethyl-B-carotene2' have also indicated the higher frequency shifts. It is therefore expected that all-trans@-carotene (hereafter simply called @-carotene) would be in a similar situation. Vibrational frequencies of relatively large molecules in excited electronic states are most directly determined by the transient Raman method or the method of fluorescence excitation of jet(13) Okamoto, H.; Saito, S.;Hamaguchi, H.; Tasumi, M.; Eugster, C. H. J . Raman Spectrosc. 1984, 15, 331. (14) Gavin, Jr. R. M.; Risemberg, S.;Rice, S.A. J . Chem. Phys. 1973, 58, 3160. (15) Granville, M. F.; Kohler, B. E.; Snow, J. B. J . Chem. Phys. 1981, 75, 3765. (16) Heimbrook, L. A.; Kenny, J. E.;Kohler, B. E.; Scott, G.W. J . Chem. Phys. 1981, 75, 4338. (17) Hemley, R. J.; Dawson, J. I.; Vaida, V. J . Chem. Phys. 1983, 78, 2915. (18) Kohler, B. E.; Spiglanin, T. A.; Hemley, R. J.; Karplus, M. J . Chem. Phys. 1984, 80, 23. (19) Leopold, D. G.; Vaida, V.;Granville, M. F. J . Chem. Phys. 1984,81, 4210. (20) Leopold, D. G.;Pendley, R. D.; Roebber, J. L.; Hemley, R. J.; Vaida, V. J . Chem. Phys. 1984,81,4218. (21) Sue, J.; Mukamel, S.; Okamoto, H.; Hamaguchi, H.; Tasumi, M. Chem. Phys. Lett. 1987,134,87. Sue, J.; Mukamel, S. J . Chem. Phys. 1988, 88, 651.
0022-3654/90/2094-0227%02.50/0 0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
Torii and Tasumi
cooled molecules. In fact, the lowest excited triplet (Ti) state of 0-carotene has been observed by the former method,**sZ3and the frequencies of 1496 cm-' (C=C stretch) and 1125 cm-' (C-C stretch) have been obtained. However, Dallinger et al.24have noticed that the I 'B, state of this molecule is not observable by the transient Raman method. Although Haley and KoningsteinZ5 have reported the Raman spectrum in the lIB, state, the broadened Raman bands observed by them have been assigned by Carroll and Brus26to nonlinear resonance Raman scattering of the molecule in the ground electronic state. The frequencies obtained in ref 25 are the same as those in the 1 ]A, state and do not reproduce the absorption spectrum. The method of fluorescence excitation is not applicable to 0-carotene, because the quantum yield of fluorescence is extremely low. As a consequence, the 1 'B, state of 0-carotene can only be studied by the absorption in the visible region. We have first applied the second-derivative method to the visible absorption bands of @-carotenein solution to extract information on the vibrational frequencies in the I'B, state. The reliability of this method for this purpose has been discussed e l s e ~ h e r e . ~ ' We have also performed simulation of the absorption spectrum to supplement the results obtained by the second-derivative method. From the simulation, we have obtained information on the vibrational relaxation rate and the displacement of the potential minimum of the 1 'B, state relative to the 1IA, state, in addition to the vibrational frequencies in the llB, state. In the determination of the vibrational relaxation rate from the simulation, the information obtained by the second-derivativemethod has been found to be essential. If the vibrational frequencies are to be determined only by performing spectral simulation, information on the vibrational relaxation rate is necessary. Although Sue and Mukamelll have proposed the vibrational frequencies in the 1 'B, state from the simulation of the absorption spectrum and the Raman excitation profile, their estimates of the vibrational frequencies are different from ours, since the ways of taking the vibrational relaxation into account are different between the two groups. The absorption spectrum of @carotene is known to be strongly dependent on temperature. As the temperature is lowered, the peak height of the 0-0 band grows faster than the one usually called the 1-0 band (vide post), together with sharpening of the bands.28 Since the ratio of the intensities of these two bands is related to the magnitude of the displacement parameters, it is interesting to clarify whether the temperature dependence is related to a change in the structure of 0-carotene. Therefore, we have studied this point by using the parameters we have obtained. Since the width of the 0-0 band is strongly dependent on the magnitude of modulation of the 0-0 frequency due to intermolecular interactions, the temperature dependence of this modulation has also been estimated from the spectral simulation.
to use a solvent of a single component to simplify the situation. We employed isopentane in this case. All the solvents were purchased from WAKO and used as received. all-trans-@-Carotene (synthetic) was purchased from Merck and purified from benzene-methanol solution.29 Concentrations of the solutions were determined spectroscopically. All operations were performed under red light.
228
Experimental Section Spectral measurements were performed with a JASCO Ubest-50 spectrophotometer. An Oxford DN 704 cryostat with a DTC-2 temperature controller was used for measurements at low temperatures. To obtain meaningful second derivatives of the absorption spectra, sample solutions were cooled to 77 K to decrease the bandwidth. We employed for this purpose two kinds of mixed solvents which are known to become glassy at 77 K; methylcyclohexane-isopentane (2: 1 v/v, MCH-IP) and diethyl etherisopentane-ethanol ( 5 : 5 : 2 v/v, EPA). For the analysis of the temperature dependence of the absorption spectrum, it was better (22) Jensen, N.-H.; Wilbrandt, R.; Pagsberg, P. B.; Sillesen. A. H.; Hansen, K. B. J . Am. Chem. SOC.1980, 102, 7441. (23) Dallinger, R. F.; Farquharson, S.;Woodruff, W. H.; Rodgers, M. A. J. J. A m . Chem. Soc. 1981, 103, 7433. (24) Dallinger, R. F.; Woodruff, W. H.; Rodgers, M. A . J. Appl. Spectrosc. 1979, 33, 522; Photochem. Photobiol. 1981, 33, 275. (25) Haley, L. V.; Koningstein, J. A. Chem. Phys. 1983, 77, I . (26) Carroll, P. J.; Brus, L. E.J . Chem. Phys. 1987, 86, 6584. (27) Torii, H.:Tasumi, M. Spectrochim. Acta, Part A , in press. (28) Loeb, J . N . ;Brown, P. K.; Wald, G. Nature 1959, 184, 617.
Calculation of the Second Derivative and Simulation Procedure The method of calculating the second derivative of an absorption spectrum described in a separate paper2' has been used in the present study. Simulation of the absorption spectra has been performed by using the time-domain formula derived by Mukamel and cow o r k e r ~ .In~ their ~ ~ ~formulation, the absorbance u(wL) is given by a Fourier transform of a function of time t expressed as u(wJ =
C q Re X - d t exp( i(wL - wo)t -
where
[
J,(t) = exp --(exp(-At)
-1
+ .kt1
is the band-shape function, and ui(t) is the absorption kernel of the ith mode (explained below). The absorption kernel of a multimode system can be expressed as a product of those of single-mode systems when the Duschinsky rotation is neglected. The notations in eq 1 and 2 are as follows: oLis the wavenumber of the incident light, wo is the average of the fluctuating 0-0 wavenumber, A and A are respectively the magnitude and the rate of this fluctuation, y is the total relaxation rate determined by the radiative (yr),nonradiative (-ynr), and vibrational (y,,) relaxation processes, N is the number of the vibrational modes, and C is a constant. As seen in eq 2, the modulation of the 0-0 wavenumber due to solvent-solute interactions is taken into account in this formula by employing the stochastic mode1,33-35in which the parameters used in the band-shape function have clear physical significance as indicated above. The explicit form of the absorption kernel ui(t) at temperature T is30-32
1 (wj"C+jA-i 4wj'wj"
+ ~j'C-jA+j)(w,lC+jA++ wj"C-jA+j)
(4)
(5) where Cki = 1 f exp(-iw/t)
A+, = (Ei
In these equations,
+ 1) f E i exp(iw/'r)
g)
(6) (7)
tii
= {exp(
w/
and will denote respectively the ith vibra-
- 1)'
(29) Saito, S.; Tasumi, M.; Eugster, C. H. J . Raman Spectrosc. 1983, 14, 299. (30) Mukamel, S.; Abe, S.; Yan, Y.J.; Islampour, R. J. Phys. Chem. 1985, 89, 201. (31) Yan, Y. J.; Mukamel, S.J . Chem. Phys. 1986, 85, 5908. (32) Mukamel, S.Adu. Chem. Phys. 1988, 70, Part I, 165. (33) Kubo, R. Ado. Chem. Phys. 1969, 15, 101. (34) Takagahara, T.; Hanamura, E.; Kubo, R. J . Phys. SOC.Jpn. 1977, 43, 802, 811. (35) Mukamel, S. J . Chem. Phys. 1985.82, 5398.
Electronic Absorption of all-trans-&Carotene N
5
y
z
10
3.0
‘0
;2.0
r I-
$ E
1.0
w
;
0.0
2 0
-1.0 v)
Lu
0
z a
m
1.0
a
%m 4 0.0
24 22 20 18 WAVENUMBER i 103 cm-1
Figure 1. Absorption spectrum of all-trans-0-carotenein MCH-IP at 77 K,and its sign-inverted second derivative. The wavenumbers indicated are the shifts from the 0-0 peak. The concentration of the sample is about 5 X IOd M. The slit width is 0.5 nm (20 cm-’ at 500 nm) and the sampling interval in the calculation is 2.0 nm.
tionai frequencies in the excited and ground states, and Di is the dimensionless displacement between the equilibrium configurations of the two electronic states along the ith mode. Evaluation of ui(t) is based on the Born-Oppenheimer and Condon approximations, a tweelectronic-state approximation, and the vibrational potentials in the harmonic approximation. Absorption spectra with many Franck-Condon active modes at a nonzero temperature can be calculated by performing the Fourier transformation indicated in eq I . We have adopted in this study a three-mode approximation ( N = 3). As seen in the resonance Raman s p e ~ t r a , ’ .only ~ , ~ three = 1525 cm-I, C=C stretch; w2/1 = 1155 vibrational modes (q’’ = 1005 cm-I, CI3-methyl in-plane cm-I, C-C stretch; and are strongly Franck-Condon active in the transition l’B, 1 ‘A,. This assumption was adopted in all the previous analyses of the Raman excitation profilel+’Ji and the absorption spectrum12 of 0-carotene, except for ref IO, in which the analysis has been performed only for the case where the low-frequency side of the 0-0 band is excited. Calculations have been performed using an M-680/682H computer system at the Computer Center of the University of Tokyo. The FFT program listed in Brigham’s book37 has been used for Fourier-transform computations (4096 points with the resolution of 5 cm-I).
-
Results and Discussion A. Estimation ofq’. The absorption spectrum in MCH-IP at 77 K and its second derivative are shown in Figure I . Since, as discussed previously,27 the function whose second derivative is to be calculated should be without the prefactor wL in the right-hand side of eq I , we have normalized (with respect to this prefactor) the absorbance by taking the value at 500 nm as a reference. It should also be noted that the sign of the second derivative in Figure 1 is inverted, in order to make a positive peak correspond to an absorption. In EPA at 77 K, similar results are obtained. The second derivative of the absorption spectrum observed in each solvent has three peaks aside from the 0-0 peak. The peak wavenumbers (the shifts from the 0-0 peak) are 1175 f 8, 1544 f 14, and 2735 f I O cm-’ in MCH-IP, and 11\57 f 23, 1542 f 17, and 2747 f 20 cm-I in EPA. The experimental errors are estimated from the results of several measurements. The estimated errors are a little larger in EPA solution probably because the (36) Saito, S.; Tasumi, M. J . Raman Spectrosc. 1983, 14, 310. (37) Brigham, E. 0. The Fast Fourier Transform; Prentice Hall: Englewood Cliffs, NJ, 1974.
The Journal of Physical Chemistry, Vol. 94, No. I, I990 229 bands are slightly broader in this solution. Since the wavenumber of the third peak at 2735 cm-l is too high to be assigned to a fundamental, it is concluded that we have only two fundamental peaks. On the other hand, since the three modes w1 w 3 are known to be strongly Franck-Condon active from the resonance Raman s p e ~ t r a ,the ~ ~absorption ~.~ spectrum should mainly consist of these three modes. As previously ment i ~ n e d , ~if ’two or more bands exist within a limited wavenumber region and one of them is considerably more intense, it is difficult to resolve the weaker bands by the second-derivative method, and the peak of the unresolved band is shifted to a certain extent from the peak of the stronger band. In the case of @-carotene,the w 3 mode gives rise to the least strong Raman band. Therefore, we conclude that the peak at 1175 (1 157) cm-l in MCH-IP (EPA) arises from an unresolved composite of w i and w3’, and the peak at 1544 (1 542) cm-’ can be assigned to wl’. The shoulder in the second derivative, marked with asterisk in Figure 1, can be assigned to 2wl’, though its wavenumber cannot be determined precisely. Since the observed six peaks (three in each solution) are considered to arise from two components (one is wI’and the other is a composite of w i and w3’), we have determined the wavenumbers of the two components to be 1555 and 1175 cm-’, which fit the observed six wavenumbers most evenly. We adopt 1555 cm-I for wl’ in the following, but it should be remembered that wl’thus determined has an uncertainty of the order of 10 cm-I. Since w i appears unresolved with wj’ in the second derivative, its wavenumber should be determined by performing spectral simulation, as described below. B . Estimation of w i and the Vibrational Relaxation Rate. In the simulation, we use the absorption spectrum measured at 120 K (several degrees above the melting point of isopentane). The 0-0 band of the absorption spectrum at 77 K in MCH-IP is slightly asymmetric (the blue side is slightly broader than the red side, as shown in Figure l), and the tail of the 0-0 band is not well reproduced by the simulation that employs eq 2 as a band-shape function. Although some low-frequency modes having small Franck-Condon factors may exist, we will simulate the absorption spectrum with the three strongly active modes without introducing rather arbitrarily the low-frequency modes. Some of the parameters in eq 1 and 2 can be predetermined as follows. The ratio (not the magnitude) of D,’s can be determined from the ratio of the Raman intensities9 under the 0-0 excitation (at 496.5 nm), since the Raman intensities are shown3’ W;’)-~D? Y (1/2)D; in this to be proportional to 2wjlwjll(w; case. The ratio obtained in this way is D,2:D22:D32= 1.00:0.73:0.31. Although Myers et al.38have used the preresonance Raman intensities in determining D,’s of trans- 1,3,5-hexatriene and isoprene, we do not employ this procedure, because the estimated D,’s are large in our case, in contradiction to the approximation used in ref 38. The vibrational relaxation rate is assumed to be constant over all the vibronic bands. We neglect the contribution of yr + ynr,since the bands are almost Gaussian in shape and they seem to be inhomogeneously broadened. The value of A is fixed to 100 cm-I, a value corresponding to the frequency-modulation rate of 53 fs. This estimate is not unreasonable, compared with the absorption recovery of the order of 100 fs observed for triphenylmethane dyes in ethylene With this value of A, we can get good fits between the observed and simulated spectra by adjusting A to some appropriate values. The resulting values of K ( = A / A ) fall between 0.1 and 0.3, including those used in the analysis of the temperature dependence of the absorption spectrum (see subsection D). They are in good agreement with the results of the previous works.10~2i Finally, since the transition l’B, 1 ’A, is mostly related to the r-electrons in the polyene chain, we have assumed w3/ to be 1005 cm-I, which is the same as 03”.
-
+
-
(38) Myers, A. B.; Mathies, R. A,; Tannor, D. J.; Heller, E. J. J . Chem. Phys. 1982, 77, 3857. (39) Brito Cruz, C. H.; Fork, R. L.; Knox, W. H.; Shank, C. V. Chem. Phys. Letr. 1986, 132, 341.
Torii and Tasumi
230 The Journal of Physical Chemistry, Vol. 94, No. I , 1990
TABLE I: Vibrational Wavenumbers and Vibrational Bandwidths (in cm-') of aff-trans-@-Carotene electronic state w, w, w2 7. 1 IA; 1525 1155 1005 -I5 2IA,b 1 [B,' TId
1177 -1555 1496
I204 (1243 1282 -1245 1125
(1005) 1009
-
-I00 30
Reference 1.
yv is estimated from Figure 1 of ref 1 and Figure 2 of ref 4. bReference 45. eThis work. w3 is assumed to be the same as in llAg. dReference 22. yv is estimated from Figure 1 of ref 22 and
Figure 4 of ref 23. TABLE 11: Magnitude of Modulation of the 0-0 Wavenumber of all -trans-&Carotene in Isopentane temp, K A, cm-l A 2 T 1 ,IO2 K-I 120 351 1.03 150
180 WAVENUMBER 1 103 cm-1
Figure 2. Absorption spectrum of all-trans-/+carotene in isopentane at 120 K (solid lines) and the calculated spectra (broken lines). The concentration of the sample is about 6 X IO" M. The parameters used in the calculationsare A = 100 cm-l, A = 351 cm-I, w( = 1005 cm-I, and y, + ynr= 0 cm-l in all cases, and (a) wl' = 1525 cm-I, w i = 1155 cm-l, D,= I .090, D2= 0.931, D3 = 0.607, yv = 15 cm-'; (b) wI' = 1555 cm-I, w i = 1245 cm-I, DI= 1.125, D2 = 0.961, D3= 0.626, yv = 100 cm-I; (c) wI' = 1590 cm-I, w i = 1200 cm-', D ,= 1.1 IO, D2 = 0.948, D3 = 0.618, and yv = 15 cm-I.
The results of simulation by using three different sets of parameters are shown in Figure 2, together with the observed absorption spectrum in isopentane at 120 K. If the vibrational frequencies in I1B, are assumed to be equal to those in l'A,, the degree of fit between the observed and simulated spectra is rather poor as shown in Figure 2a. To obtain a better fit shown in Figure 2b, it is necessary to adjust w i , D , D3, and yvas given in the caption of Figure 2, with the value of wl' determined in the previous subsection. In this procedure, w i is raised to a much higher value of 1245 cm-I. The values of D,'s are in good agreement with those obtained in ref 1 1. D , and D2 are nearly equal to I , indicating that the potential minimum of the 1 'B, state is located at the edge, along these two modes, of the classically allowed region of the vibrational ground state in the 1 ,A, state. From the yv value of 100 cm-l, the vibrational relaxation time in the I 'B, state is estimated to be of the order of 50 fs. If the vibrational relaxation rate in the llB, state is assumed to be the same as in the 1 'A, state (Le., yv 15 cm-I, which is estimated from Figure 1 of ref 1 and Figure 2 of ref 4), wI'must be raised to around 1590 cm-l to obtain the good fit shown in Figure 2c. The determination of the vibrational frequencies in 1 'B, by Sue and Mukamel" is based on the simulation performed by using parameters similar to those in Figure 2c. The frequency 1590 cm-' used in Figure 2c is out of the range estimated by the second-derivative method. Therefore, the vibrational relaxation is certainly faster in the 1IB, state than in the 1'A, state. It should be noted that the fit in Figure 2b is better than that in Figure 2c of this work and that in Figure 4 of ref 11. C. Comparison with Other States and Other Molecules. The frequencies of the w1 and w2 modes in the 1 IB, state estimated in this work are compared with those in other electronic states in Table I. As for the w , mode, the frequency in the l'B, state is not lower than that in the l ' A , state. This is not consistent with the primitive inference mentioned in Introduction, although the frequency upshift on going from 1 IA, to 1 IB, is small (of the order of a few tens of wavenumbers). On the other hand, w2/ is estimated to be higher than w i ' by as much as about 90 cm-l. The frequency upshifts of these two modes are in good agreement with those observed for shorter polyenes,leZ0 and the parameters used in the analysis of the absorption spectrum and the Raman excitation profile of tetradesmethyl-B-carotene.*' It is interesting
-
-
220 260 292
385 426 476 524 549
0.99 1.01 1.03 1.06 1.03
that the frequencies of these two modes in the triplet (TI) state are, contrary to those in the lIB, state, lower than those in the 1 'A, state. From the recently proposed vibronic coupling theoryw3 of polyenes between the 1!A, and 2IA states via the C=C stretch, the diabatic frequency of the C=C! stretch can be estimated to be in the middle of the frequencies in these two states. If this theory is correct, it is probable that the diabatic frequency is somewhere around 1650 cm-l, an average of the frequencies in 2IA, (1777 cm-')44945and llA, (1525 cm-l),' in the case of @carotene. Compared with this frequency, the frequency of this mode in the llB, state (w,') is lower by about 100 cm-I. Therefore, it may be stated that the bond alternation is weakened in the I'B, state in accord with the primitive inference. It should be noted that the strong Franck-Condon activity of the C=C and C-C stretches would then be reasonably explained by the significant changes in the bond lengths of the C=C and C-C bonds. The bandwidth yvarising from the vibrational relaxation (T2/2 = 50 fs) in the I'B, state is compared with the Raman bandwidths in other states in Table I. It can be seen that the vibrational relaxation is faster in the l'B, state, although the nature of the relaxation (population relaxation or pure dephasing) is not clear. It should be noted that fast vibrational relaxations of the order of 50 fs (or faster) have recently been observed in excited singlet states of several dye molecule^.^"^ D. Temperature Dependence of the Absorption Spectrum. By using the frequencies and the other parameters obtained above, we have analyzed the temperature dependence of the absorption spectrum, to see whether the change in the profile of the absorption spectrum is accompanied by a change in the structure of @-carotene. We have performed simulation of the absorption spectra measured at 120, 180, and 292 K in isopentane. The results are shown in Figure 3. In calculating the spectra in Figure 3, b and c, only A, wo, and Tin eq 1 and 2 are changed from those used for the spectrum in Figure 3a. We have per(40) Orlandi, G.; Zerbetto, F. Chem. Phys. 1986, 108, 187. (41) Zerbetto, F.; Zgierski, M. Z . ; Orlandi, G.; Marconi, G. J . Chem. Phys. 1987,87, 2505. (42) Zerbetto, F.; Zgierski, M. 2.;Orlandi, G. Chem. fhys. Lett. 1987, 141, 138. (43) Simpson, J. H.; McLaughlin, L.; Smith, D. S.; Christensen, R. L. J . Chem. Phys. 1987, 87, 3360. (44) Hashimoto, H.; Koyama, Y . Chem. Phys. Lett. 1989, 154, 321. (45) Noguchi, T.; Kolaczkowski, S.; Arbour, C.; Aramaki, S.; Atkinson, G.H.; Hayashi, H.; Tasumi, M. Photochem. fhotobiof., in press. (46) Taylor, A. J.; Erskine, D. J.; Tang, C. L. Chem. fhys. Lett. 1984,103, 430. (47) Fujiwara, M.; Kuroda, R.; Nakatsuka, H. J . Opt. SOC.Am. 1985, B2, 1634. (48) Angel, G.;Gagel, R.; Laubereau, A. Chem. fhys. 1989, 131, 129.
Electronic Absorption of all-trans-6-Carotene
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 231
0.18
0.20
0.22
bp(l+bp).l
Figure 4. Plots of the 0-0 wavenumbers of all-trans-@-carotenein isopentane vs bp(1 bp)-’ at various temperatures. The temperatures for the six points are 292, 260, 220, 180, 150,and 120 K from left to right.
+
28
24
20
WAVENUMBER / 103 cm- 1 Figure 3. Absorption spectra of all-trans-@-carotenein isopentane at 120, 180, and 292 K (solid lines from (a) to (c)) and the calculated spectra (broken lines). The parameters used in the calculation are w,’ = 1555 cm-I, w2/ = 1245 cm-’, w,’ = 1005 cm-’, D,= 1.125,D2= 0.961,D,= 0.626,A = 100 cm-l, yr ynr= 0 cm-I, yv = 100 cm-I in all cases, and A = 351, 426, and 549 cm-’ in (a) to (c).
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formed simulation of the spectra measured at 150, 220, and 260 K also, and similar degrees of fitting are obtained. It should be emphasized that the same values of D I D3 are used in all the cases. Since the observed and calculated spectra are in good agreement, we conclude that the temperature dependence of the absorption spectrum is not accompanied by a change in the structure of @-carotene;Le., the present result is not in support of the view recently suggested by Kjaer et al.I2 that the displacement parameters slightly depend on temperature. The magnitude A of modulation of the 0-0 wavenumber increases as the temperature rises, as shown in Table 11. This means that the fluctuation of intermolecular interactions varies significantly with temperature. It is also indicated that the value A 2 T ’ is approximately constant over the temperature range studied in this work. This is reasonably explained by the configurationcoordinate which takes into account the effect of the environment by a single external mode with an effective frequency. This confirms our postulate in the simulation that the absorption spectrum of @-caroteneis inhomogeneously broadened for the most part. A similar result has been obtained on the temperature dependence of the absorption spectrum of rhodamine 6G in ethanol by Kinoshita and NishL50 Since the temperature dependence of the absorption spectrum is concluded not to be accompanied by a change in the structure of &carotene, it is expected that the temperature dependence is related to the macroscopic properties of solventsolute interactions. From the Onsager cavity mode1,51-54the red shift of an absorption band 6w and the refractive index n of the solvent is related (in the case of a nonpolar solute) by
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(9)
due to the reaction field of the solvent, where M is the transition moment of the solute and a is the radius of the cavity. The refractive index n is related in turn to the density p of the solvent by the Lorentz-Lorenz relation
where b is a constant. We examine whether these macroscopic formulas can explain the shift of the 0-0 band shown in Figure 3. Experimental data of the density of isopentane in the temperature range of -51.1 to 26.7 OC is given in ref 55. These data can be expressed by a polynomial second order in temperature, which enables us to estimate the densities at other temperatures. The densities thus determined are consistent with the change in the total intensities of the spectra shown in Figure 3. The constant b (=0.3505) in eq 10 is calculated by using n (listed in ref 5 6 ) and p at 20 OC. The 0-0 wavenumbers at six temperatures between 120 and 292 K are plotted against (n2 - 1)/(2n2 1) = bp/(l + b p ) in Figure 4, where a good linear relationship is seen, indicating that the macroscopic formulas satisfactorily explain the experimental results. It should be mentioned that the 0-0 wavenumbers used for the plot in Figure 4 are not the absorption maxima in the observed spectra but are obtained from the simulation; the difference between the “apparent” and “true” 0 4 wavenumbers are about 100 cm-’ near the room temperature. From the gradient of the straight line (-1.9 X lo4 cm-l) and the approximate value em2 cm2, calculated from the oscillator of (2.8 X strengths7f = 2.6), the volume of the cavity (4n/3)a3 is calculated to be 6 X lo2 A3. This value is not far from the volume per molecule in the crystal 858 A3.58
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Conclusion By use of the vibrational frequencies, the vibrational bandwidth, and other parameters estimated in this work, the absorption spectra (1 IB, 1‘A,) of all-trans-6-carotene can be well reproduced by calculation. Concerning the estimated quantities, the following two points should be noted. (1) The vibrational frequency of the C=C stretch in the l’B, state is estimated to be higher by a few tens of wavenumbers than that in the llA, state. This can be explained by the vibronic coupling theory without inconsistency with the strong Franck-Condon activity of this mode. (2) The vibrational relaxation time in the l’B, state is estimated to be of the order of 50 fs, comparable to those in the excited singlet states of several dye molecules. The temperature dependence of the absorption spectra in isopentane is explained by the configuration-coordinate model and the Onsager cavity model. Therefore, this is one of the cases where a large change (concerning the 0-0 wavenumber and the shape) in the absorption spectrum is not accompanied by a structural change in the solute molecule.
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Acknowledgment. We thank Dr. Hiro-o Hamaguchi for stimulating discussions. We are also grateful to Japan Spectroscopic Co. Ltd. for the use of a Ubest-50 spectrophotometer. Registry No. all-trans-P-Carotene, 7235-40-7.
(49) Markham, J. J. Rev. Mod. Phys. 1959, 31, 956. (50) Kinoshita, S.;Nishi, N. J. Chem. Phys. 1988, 89, 6612. (51) Onsager, L. J . Am. Chem. SOC.1936, 58, 1486. (52) Bayliss, N.S . J . Chem. Phys. 1950, 18, 292. (53) Ooshika, Y.J. Phys. SOC.Jpn. 1954, 9, 594. (54) McRae, E. G.J . Phys. Chem. 1957, 61, 562.
(55) Rossini, F. D.;Pitzer, K. S.;Arnett, R. L.; Braun, R. M.; Pimentel, G. C. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds; Carnegie Press: Pittsburgh, 1953. (56)Beilstein Handbuch der Organischen Chemie, Vierte Auflage; Springer-Verlag: Berlin, 1958. (57) Klevens, H.B.; Platt, J. R. J. Chem. Phys. 1949, 17, 470. (58)Sterling, C.Acta Crystallogr. 1964, 17, 1224.
