2300
J. Phys. Chem. 1980, 84, 2300-2305
water polyshell network is proposed: Awaterpolyshell =
20.79
+ 0.0651t
(6)
where t is given in "C. Acknowledgment. The present work was reglized while the author was in commission at the Secretaria Ejecutiva del Consejo de Estudios de Posgrado.
References and Notes (1) N. K. Adam, "The Physics and Chemistry of Surfaces", Dover Publications, New York, 1968, p 47.
(2) F. J. Garfias, J . Phys. Chem., 83, 3126 (1979). (3) M. Karplus and R. N. Porter, "Atoms and Molecules", W. A. Benjamin, New York, 1970, p 505. (4) A. V. Deo, S. E. Kulkarni, M. K. Ghapurey, and A. E. Biswas, Indian J . Chem., 2, 43 (1964). (5) In eq 6 of ref 2, f , should appear raised to the second power. (6) W. D.Harkins, "Physical Chemistry of Surface Films", Reinhold, New York, 1952, p 143. (7) V. K. Lamer, T. W. Healy, and L. A. G. Aylmore, J. Co//o/dSd.,19, 673 (1964). (8) H. D. Cook and H. E. Ries, Jr., J . Phys. Chem., 60, 1533 (1956). (9) G. J. Gittens, J. Colloid Interface Sei.,30, 406 (1969). (10) J. T. Davies and E. K. Rideal, "Interfacial Phenomena", Academlc Press, London, 1961, p 12. (11) H. Sobol, F. J. Garfias, and J. Keller, J. Phys. Chem., 80, 1941 (1976).
Spectroscopy of Polyenes. 5. Absorption and Emission Spectral Properties of Polyene AcCds/Esters Related to Retinoic Acid/Ester as Homologues' Paritosh K. Das" Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556
and Ralph S. Becker Department of Chemistry, University of Houston, Houston, Texas 77004 (Received: January 7, 1980)
A number of all-trans polyene acids and esters with chain lengths varying over a range including two longer and two shorter homologues of retinoic acid/ester have been studied for their spectral and photophysical properties. The polyene acids form intermolecularly hydrogen-bonded dimers in nonpolar solvents (3methylpentane and carbon tetrachloride). Upon increasing the polyene chain length as well as upon dimer formation (in the cases of the polyene acids), pronounced changes occur in the absorption-emission spectral maxima, infrared absorption frequencies (carbonyl and hydroxyl stretching), and fluorescence lifetimes and quantum yields. The photophysical dynamics is discussed in terms of a fluorescing state that is primarily of lA;- character (dipole forbidden) in the longer polyene systems.
Introduction Polyene systems containing the retinyl moiety have been widely ~ t u d i e d ~ for- ~their spectral and photodynamical properties in recent times. This is primarily because the retinyl systems form the chromophores in visual and photosynthetic pigments and in the intermediates that result following light absorption by them. Three low-lying singlet excited states6-12can be involved in the photodynamics of the retinyl polyenes. These are l(n,a*), lA *(dipole forbidden), and lB,* (strongly dipole allowed). Tbe relative locationg13 of these three states has been shown to be dependent on (1)structural factors such as geometric distortion of the polyene chain, (2) the nature of the heteroatom at the end of the chain, and (3) environmental factors such as the nature of the solvent (polar, nonpolar, or H bonding) as well as the presence of H-bonding agents. Another interesting feature that has been revealed through the recent spectral and photophysical investigation of retinals,14retinols,15and retinoic acids14J6is that they form aggregates (dimers) under certain conditions of solvent, temperature, and concentration. The structure of the dimers and the nature of intermolecular interaction in them appear to be different for the three classes of retinyl polyenes, and, consequently, their excited-state properties are also affected in very different fashions. Understandably, the relative order and location of the three low-lying singlet excited states, and the effect of dimer formation on spectral and photophysical behavior, are all sensitive functions of polyene chain length. Re0022-3654/80/2084-2300$0 1.OO/O
cently, we undertook a detailed study of the excited-state properties of polyenes related to the retinyl systems as homologues and analogues. In the previous p a p e r ~ , l ~we -~l have reported on the absorption-emission spectral properties as well as the triplet-state photophysics of a number of polyene aldehydes, ketones, alcohols, Schiff bases, and protonated Schiff bases. The present work is concerned with the results of similar studies on a number of all-trans polyene acids and esters related to retinoic acid and ester as homologues. We have examined how the formation of linear, tail-to-tail dimers in the cases of the polyene acids affects their absorption-emission spectral maxima and radiative and nonradiative lifetimes as the polyene chain length is varied over a range including two shorter and two longer homologues of retinoic acid. Also, we have carried out an infrared spectral study in order to obtain evidence in support of formation of intermolecularly hydrogenbonded dimers in the cases of the polyene acids. The structure of the polyene acids and esters (ethyl) under examination are shown in Figure 1. Nomenclature of the polyene systems by the numbers of carbon atoms is used and does not include the two carbon atoms of the ethyl group in the cases of the esters.
Experimental Section The polyene esters were synthesized17 from the corresponding lower polyenals or polyenones of known structure by using a Wittig reaction with triethyl phosphonoacetate (in tetrahydrofuran in the presence of sodium amide) or 0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980 2301
Spectroscopy of Polyenes
4
(e)
Figure 1. Structure of polyene acids and esters, R = H and CzH5: (a) C,5; (b) CI7; (c) Cz0 (retinoic acidlester); (d) C22; (e) c24. p:
a
-
32
I
50
42
34
26
18
WAVENUMBER x 10-3,~t~r1
Figure 3. Absorption spectra of polyene esters in 3MP at 298 K (solld line) and 77 K (dotted line): (a) Cj5; (b) CI,; (C) C22.
a’
A, A i”; I
34 26 WAVENUMBER x 10-3, cm-1
18
Figure 2. Absorption spectra of polyene acids in 3MP at 298 K (s( line) and 77 K (dotted line), and in 3MP plus 10% ether at 77 K (broken line): (a) C15; (b) c17; (c:) &.
ethyl (triphenylphosphoranylidene) acetate (in benzene). The acids were prepared by the saponification of the esters with KOH in aqueous methanol. The esters were purified by column chromatography (silica gel, petroleum ether plus 2% diethyl ether) followed by high-performance liquid chromatography (p-Porasil, petroleum ether plus 2 % diethyl ether). The acids were recrystallized several times from acetonitrile. The purification procedures and the sources of the solvents and reagents, as well as the methods of obtaining the spectra and fluorescence lifetimes, have been described in detail el~ewhere.~’-‘~ The IR spectra were obtained in a Perkin-Elmer 421 spectrophotometer.
Results The absorption and emission spectra of the polyene acids and esters are shown in Figures 2-4. The related data are presented in Tables I and I1 ( a ) Absorption Spectra. The absorption spectra of all-trans CI5 acid/ester (Figures 2a and 3a) are characterized by two strong band systems (I and 11) with their maxima separated from one another by 5000-7000 cm-l. While band system I undergoes the usual red shift on cooling from 298 to 77 K (in 2-methylpentane (2MP)), a
:b
c’
,
,
I
I
p:; I
I
24 2 WAVENUMBER x IO-3,cm-1
l
I
l
I
16
Figure 4. Emission spectra of polyene esters (a-d) and acids (a’-d’) at 77 K: (a,a’) C,5; (b,b’) C1,; (c,c‘) CZ2; (d,d’) CZ4. The solvent is 3MP, except In the case of CZ4acid (d’) where the solvent is 3MP plus 10% ether.
slight blue shift is noticed in the case of band system 11. Part of this blue shift comes from the lessening of overlap between the two band systems. On going from 3methylpentane (3MP) to 3MP plus 10% ether, practically no change occurs in the band maxima of C15 ester. On the other hand, for C15 acid, the maxima of both systems I and I1 undergo large blue shifts on changing solvent from 3MP to 3MP plus 10% ether (Tables I and 11). The magnitudes of these blue shifts are particularly large at 77 K (2400-2500 cm-l). As will be discussed in detail in the Discussion section, in hydrocarbon solvents the polyene
2302
The Journal of Physical Chemistry, Vol. 84, No. 18, I980
Das and Becker
TABLE I: Absorption Spectral Data for Polyene Acids and Esters in 3-Methylpentane all-trans band maxima: nm and 10-3(extinctioncoeff,b M-' cm-' 1 polyene acid/ester temp, K I I1 III IV C,, acid 298 303.0 (16.6) 258.0 (12.6) 77 321.0 (19.2) 255.0 (10.7) 77c 298.0 (20.0) 240.0 (14.5) C,, ester 298 294.0 (15.3) 255.5 (13.2) 77 301.0 (16.1) 250.0 (11.3) C,, acid 298 332.5 (29.7) -280 (9.3)d 77 355.0 (31.4) 280 (7.4)d 7 7c 333.0 (30.7) 280 ( 11.4)d C,, ester 298 322.5 (30.7) -280 (11.3Jd 77 333.0 (28.4) -280 (7.75 C,, acid 298 390.5 (52.2) e 77 400.0 (59.6) e 7 7c 390.0 (55.1) e C,, ester 298 374.0 (51.8) e -270 (5.9) 77 397.5 (50.6) e 270 (4.6) C, acidf 298 410.0 e e 77 422.5 e 280-300 225-250 7 7c 414.5 e 280-300 225-250 c,, esterf 298 395 e 280 e 77 417.5 e 280-315 e a +0.5 nm. 110%;extinction coefficients are given in the parentheses. In 3MP plus 10% diethyl ether. Shoulder of band system I; the extinction coefficients are not corrected for contribution from the tailing of band system I. e Bands are not well defined. f Sufficient quantities were not available for accurate measurement of extinction coefficients. Extinction coefficients are estimated at 70000-80000 M-' cm-' for maximum of band system I.
--
-
-
TABLE 11: Emission Spectral Data for Polyene Acids and Esters
polyeneg
solvent
C,, acid
3MP 3MP plus 10% ether 3MP 3MP 3MP plus 10% ether 3MP 3MP plus 10% ether 3MP
C,, ester C,, acid C,, ester C,, acid
3MP plus 10% ether C,, ester
3MP 3MP plus 10% ether EPA
C,, acid
3MP 3MP lslus 10% ether
temp, K
maxima, cm-' x 1 0 - ~
106(rateconstant), S-
absorption
emissiona
quantum yieldb
77 77
31.15 33.56
25.6 27.0
0.0023d 0.0068e
77 77 77
33.22 28.17 30.03
27.0 21.7 22.3
0.0028f 0.29 0.35
1.4 2.3
4.8 6.6
207 152
507 283
77 77
30.03 30.03
22.2 22.9
0.34 0.37
2.2 1.9
6.5 5.1
155 195
300 332
298 77 298
25.61 25.00 26.95
14.5 15.1 14.7
0.0092 0.039 0.0083
1.3 0.9 1.2
141 23 145
7.1 43 6.9
762 1068 826
77 298 77 298
25.64 26.74 25.16 26.74
15.2 14.5 15.3 14.5
0.043 0.0093 0.046 0.0088
2.7 1.7 3.6 1.9
63 183 78 216
15.9 5.5 12.8 4.6
3 54 583 265 522
77 298 77 298 77 298
25.19 26.25 25.09 24.39 23.67 25.32
15.6 14.5 15.1 13.9 14.5 14.5
0.062 0.033 0.073 0,0019 0.0035 0.0013
3.1
50
20
303
2.2
629
1.6
453
3.1
484
2.1
321
3.1
463
2.2
3 20
0.0064 77 24.13 14.5 298 25.32 14.2 0.0023 0.0067 77 23.95 14.5 a 2200 cm", except in the range 650-750 nm where the error is 2500 cm-'. + l o to i 3 0 % in the range T F = 5-1 ns. A,, = 330 nm. e A,, = 310 nm. ester. C, ester
obsd fluorescence intrinsic liferadiative time: lifetime, ns ns
--
acids form tail-to-tail linear dimers with two hydrogen bonds between the component monomeric units. In 3MP plus 10% ether, the dimerization does not take place because of interaction of the COOH groups with ether molecules. The spectra and photophysics of the acids in 3MP plus 10% ether are comparable to those of the esters in 3MP or 3MP plus 10% ether.
radiative
nonradiative
k10 to *50% in the range @ F= 0.5-0.001. f
A,,
= 320 nm.
g
All-trans polyene acid/
On going from C16to C1,, band system I1 loses its intensity to such an extent that it shows up only as a shoulder of band system I in the C1, molecules at 77 K. By contrast, the intensity of band system I is increased by a factor of about 2. Band system I1 is not noticeable in the cases of longer polyene acids and esters (Czz.md C N ) , and the intensity of band system I progressively increases
The Journal of Physical Chemistry, Vol. 84, No. 18, 1980 2303
Spectroscopy of Polyenes
2,5t h
i
20
I55
\\
15.
0,51
in the locations of fluorescence maxima on going from monomer to dimer. While CZ2shows -10% increase in 4F,the increase in 4Fof C24 acid is about twofold on going from 3MP at 77 K (Le., dimer) to 3MP plus 10% ether at 77 K (i-e., monomer, H bonded to ether). c 1 6 acid and ester show a slight dependence of fluorescence quantum yield on excitation wavelengths. As the excitation wavelength is decreased from 350 to 280 nm, 10-15% decrease in $F is bbserved. The esters and acids with longer polyene chain length (C17-C24) exhibit essentially no excitation wavelength dependence of quantum yield. (c) Radiative and Nonradiative Lifetimes. As the polyene chain length is increased from C17 to C24 acid/ ester, the intrinsic radiative lifetime ( 7 ~becomes ~ ) progressively longer. T$ is calculated from the observed fluorescence lifetime (TF) by the relationship TFO = T F / ~ F . Since the oscillator strength of band system I (assigned lA transition) increases with the increase in as l'B, polyene chain fength, the deviation of TFO from the lifetime obtainable from the integrated area of band system I becomes more and more pronounced along the polyene series. The nonradiative rate constant (k,,) calculated from the relationship k,, = (1 - & ) / 7 F appears to be relatively insensitive to the polyene chain length and is in the range 3 X 10a4 X los s-l for the esters and monomeric forms of the acids (H-bonded to ether in 3MP plus 10% ether at 77 K). Dimer formation in the cases of the polyene acids causes significant enhancements in both radiative (k,)and nonradiative (k,,) rate constants, except for k, of C24 acid which undergoes a slight decrease on going from monomer to dimer. The effect of dimer formation on k, and k,, is the highest for Cz2and retinoic acid@ (three- to fourfold increase). ( d ) Infrared Spectra. The infrared spectral study was undertaken to obtain supportive evidence for the formation of intermolecularly hydrogen-bonded dimers in the cases of the polyene acids. The carbonyl stretching region of the IR spectra of the polyene acids in C C 4 (10-3-10-2 M) shows very clearly two bands at 1724-1731 cm-l (sharp and weak, assigned as v,, of monomer) and 1682-1688 cm-l (strong, assigned as v,, of dimer), respectively. The hydroxyl stretching region also shows two bands, viz., 3545-3550 cm-l (sharp and weak) and 3400-2400 cm-I (very broad, with maxima at ~ ' Jcan ~ J ~explain the red shift in the absorption spectral maxima on going from monomer to dimer. The formation of dimers in the cases of the polyene acids is further supported by the infrared spectral data described earlier as well as by the spectral and photophysical data on the polyene esters which show little change in their absorption-emission spectral maxima, fluorescence quantum yields, and lifetimes on going from 3MP to 3MP plus 10% ether. In a previous paper concerning retinoic acid/ester,16 based on a detailed study of the absorption-emission-excitation spectra and fluorescence quantum yields and lifetimes as functions of concentration, we showed that essentially one kind of aggregate (dimer) was formed in hydrocarbon solvents at the concentrations ranging from 1X to 1 X M. The equilibrium constant for association was estimated at 1 X lo4 in 3MP at room temperature.16 Since the enthalpy of formation of the intermolecular hydrogen bands in the dimer is negative (-6 to -10 kcal/m01),~~ the equilibrium constant for dimer formation would be very much greater at 77 K; that is, all of the molecules would exist in dimeric form in 3MP a t 77 K even at low concentrations (e.g., low5M). Conclusions similar to those reached for retinoic acid should also apply in the cases of its homologues. The equilibrium constant for dimer formation is expected to vary slightly as a function of polyene chain length. Nevertheless, in view of the large magnitude of the association constant and the large, negative enthalpy of association, we would expect 100% dimer formation in the cases of all the polyene acids in 3MP a t 77 K over the concentration range studied (10-4-5 X M). The discussion that follows will be based on the tailto-tail linear structure (intermolecularly hydrogen bonded) for the dimers of the polyene acids. One interesting feature of the absorption spectra of the polyene acids that needs to be explained is the sharp decrease in the magnitude of the red shift in the absorption maxima of band system I on dimer formation as the chain length increases (Figure 5). For the linear dimer, for any transition involving the polyene chromophore, the magnitude of the splitting between the upper and lower exciton states is directly proportional to the square of the transition moment (M) of that transition in the monomer and inversely proportional to the cubic power of the distance (r)between the centers of the component polyene chromophore^.^^,^^ A rough calculation based on the data for band system I (due to
-
-
Das and Becker
'B,* 'A, transition) in cases of the polyene acids indicates that, as the polyene chain length is increased, the effect of increase in oscillator strength on magnitude of exciton splitting is nearly compensated by the effect of concomitant increase in interchromophore distance (r). Then the observed decrease in the magnitude of red shift with increase in polyene chain length is to be attributed to some other factor (s). One important factor is the effect of intermolecular hydrogen bonding in the dimer. A study16of the effect of the addition of reagent quantities of acids such as acetic and trichloroacetic on the absorption spectral maxima of retinoic acid has shown that part of the red shift on going from monomer to dimer is a consequence of the intermolecular hydrogen bonds. The decrease in the red shift in absorption spectral maxima with increasing polyene acid chain length can then be the result of a concomitant decrease in the strength of the intermolecular hydrogen bonds. The evidence for the decrease in the strength of the intermolecular hydrogen bonds is obtained from the observed decrease in the magnitude of the shift in the carbonyl stretching frequencies (dimer vs. monomer) with an increase in the polyene acid chain length (Figure 5). The effect of dimer formation on the maxima of band system I1 in the case of CI5 acid merits discussion. It is noted that the magnitude of the red shift of the maximum of band system I1 on going from ether-bonded monomer to dimer at 77 K (Table I) is even greater than that observed for the maximum of band system I. On the basis of a detailed study of this band system in polyenals,17 polyenones,17polyene alcohols,24and Schiff bases,lg we have previously proposed a tentative interpretation for lA,) of band system I1 in terms of absorption (IB,* 6-s-trans conformers present in solution as minor species. An alternative assignment has been in terms of lA,+ lA, transition (cis peak) based on the isomeric dependence of the intensity of band system I1 in r e t i n a l ~ .The ~ direction lA, transition is of the transition moment of lAgi+ perpendicular to the polyene chain. The exciton interaction in the linear tail-to-tail dimer should result in the upper exciton state of IA;+ parentage being allowed and the lower one being forbidden. Furthermore, the effect of H bonding which is directed along the polyene chain lA, is expected to be less pronounced on the lAg'+ transition (in comparison to the lB,* c- lA, transition). The observed, large red shift in band system I1 on going from monomer (ether bonded) to dimer of c16 acid is then more commensurate with an assignment in terms of a lB,* 'AF transition rather than in terms of a lAg*+ A, transition (for band system 11). The ls3(n,r*) states in the polyene acids/esters are located at energies too high for them to be involved in their photodynamical processes. Thus, unlike the polyene system~l'-~~ where the roles of low-lying 113(n,7r*)states are important, the polyene acids/esters (including retinoic acid/ester16) have relatively high fluorescence quantum yields (at 77 K) and very small quantum yields for intersystem crossing (at room temperature).28 As in the cases chain length, the of polyene s y s t e m ~ l of ~ - comparable ~~ large deviation of the observed intrinsic radiative lifetimes of the long-chain polyene acids/esters (C22 and C24) from the lifetimes (1-2 ns) expected from the respective 'B, lA, transitions (band system I) strongly suggests that the states responsible for fluorescence in these system are primarily of lAg*- character (dipole forbidden). With increase in polyene chain length the lA;- state is less and less mixed with the lBU*state. C17acid/ester appears to be a borderline case where the observed intrinsic radiative +-
-
-
-
-
-
+-
Spectroscopy of Polyenes
lifetimes are relatively short (Table 11)and the fluorescing state probably possesses an extensive lB,* character. The changeri in the radiative (k,) and nonradiative (k,,) rate constants of the polyene acids upon dimer formation (at 77 K) are worth noting (Table 11). In general, there are increases in both k, and k , upon going from monomer (ether bonded) to dimer (except in the case of C24 acid where a slight decrease in k, is noticed). This effect is the most pronounced for CZ2and retinsic acid16 where the increase in both k, and k,, is three- to fourfold upon changing solvent from 3MP plus 10% ether to 3MP (both at 77 K). The lifetime data for the polyene esters, where there is no dimer formation, show that the effect of changing solveint from 3MP plus 10% ether to 3MP (both at 77 K) manifests itself in only a slight decrease (20-30%) in k, and practically no change in k , (Table 11). Therefore the large increase in both k , and k,, of the polyene acids on going from :3MP plus 10% ether to 3MP (at 77 K) has to be explained in terrns of interaction among the low-lying singlet excited states and other effects brought about by the excitation resonance and hydrogen bonding in the dimers. One obvious effect of excitation resonance interaction and hydrogen bonding is the perferential lowering of the allowed exciton state of lB,* parentage and its increased mixing with the lower-lying exciton state of lAg*parentage. This woulld result in the increase in the radiative intensity of the fluorescing state (lA,*-) and hence the increase in k , in the dimers. C24acid probably represents the case where the lAgt- state is far below the lB,* state and is relatively unaffected by the lowering of the lB,* state in the dimers. On the other hand, as suggested earlier, for C17 acid the fluorescing state is probably of predominantly lB,* character, and the ratio q0monomer/TFOdimer is close to two (after -30% correction for the solvent effect on going from 3MP plus 10% ether to 3MP, as noticed for the polyene esters). The lB,* character of the fluorescing state in C17and C15acid can also explain the red shifts in their emission spectral maxima on going from monomer (ether bonded) to dimer. The emission spectral maxima of CZ4,CZ2,and retinoic16 acid remain practically unchanged in position under these conditions. The explanations presented in the preceding paragraph are necessarily qualitative. For a quantitative consideration of the changes in TFO on dimer formation it is necessary to take into account the configuration interaction among the vibronically mixed state and the charge-transfer states. An explanation for the increase in k,, in the dimer is even more difficult. The important factors29that appear to contribute to this change include (1)interaction among the two low-lying singlet excited states resulting in the modification of the excitedl-state potential surface, (2) modification of the electronic wave function due to exciton interaction which affects both radiative and nonradiative
The Journal of Physical Chemistry, Vol. 84, No, 18, 1980 2305
processes in a parallel manner, and (3) strong coupling of the vibrations of one of the polyene molecules (actlng as a hydrogen bonder, bonded directly to the chromophore) with the other polyene molecule (acting as a chromophore), resulting in a more effective heat sink for the nonradiative processes (relative to the lattice vibrations of the solvent). While all of these factors are expected to lead to enhancement of nonradiative processes in the dimers, it is not possible to ascertain their relative importance without a detailed theoretical study.
Acknowledgment. This work was supported in part by a grant from the Robert A. Welch foundation. The authors thank Dr. Gordon L. Hug for valuable interpretative discussions.
References and Notes (1) The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is document No. NDRL-2081 from the Notre Dame Radiation Laboratory. (2) R. S. Becker, G. Hug, P. K. Das, A. M. Schaffer, T. Takemura, N. Yamamoto, and W. Waddel, J. Phys. Chem., 80, 2265 (1976), and references therein. (3) B. Honk and T. 0.Ebrey, Annu. Rev. Biophys. Bhng., 3, 151 (1974). (4) E. J. Land, Photochem. Phorobiol., 22, 286 (1975). (5) A. J. Thomson, J. Chem. Phys., 51, 4106 (1969). (6) B. S. Hudson and B. E. Kohler, Chem. Phys. Lett., 14, 299 (1972); B. S. Hudson and 8 . E. Kohler, J. Chem. Phys., 59, 4984 (1973). (7) K. Schulten and M. Karplus, Chem. Phys. Left., 4, 305 (1972); K. Sdwken, I.Ohmine, and M. Karplus, J. Chem. Phys., 64,4422 (1976). (8) T. Takemura, P. K. Das, G. Hug, and R. S. Becker, J. Am. Chem. Soc., 98, 7099 (1976); 100, 2626 (1978). (9) A. M. Schaffer, W. H. Waddell, and R. S. Becker, J. Am. Chem. 1 SOC., 96, 206371974r (10) P. S. Song, Q. Chae, M. Fujita, and H. Baba, J . Am. Chem. SOC., 98, 819 (1976). (11) R. R. Birge and B. M. Pierce, J . Chem. Phys., 70, 165 (1979). (12) R. R. Birge, J. A. Bennett, B. M. Pierce, and T. M. Thomas, J. Am. Chem. Soc., 100, 1533 (1978). (13) R. R. Birge, K. Schulten, and M. Karplus, Chem. Phys. Lett., 31, 451 (1975). (14) T. Takemura, 0.Hug, P. K. Das, and R. S. Becker, J. Am. Chem. SOC.,100, 2631 (1978). (15) K. Chihara, T. Takemura, T. Yamaoka, N. Yamamoto, A. M. Schaffer, and R. S.Becker, Photochem. Photoblol.,29, 1001 (1979). (16) T. Takemura, K. Chihara, R. S. Becker, P. K. Das, and G. L. Hug, J. Am. Chem. Soc., 102, 2604(1980), (17) P. K. Das and R. S. Becker, J. Phys. Chem., 82, 2081 (1978). (18) P. K. Das and R. S. Becker, J. Phys. Chem., 82, 2093 (1978). (19) P. K. Das, 0. Kogan, and R. S. Becker, Photochem. Photobiol., 30, 689 (1979). (20) P. K. Das and R. S. Becker, J. Am. Chem. Soc., 101, 6348 (1979). (21) P. K. Das and R. S. Becker, Photochem. Photobiol., in press. (22) L. J. Bellamy, “The Infra-red Spectra of Complex Molecules”, 3rd ed., Chapman and Hall, London, 1975. (23) H. Hosoya, J. Tanaka, and S. Nagakura, J . Mol. Spectrosc.,8, 257 (1962); J. N. Murrell and J. Tanaka, Mol. Phys., 7, 363 (1964). (24) H. Baba and N. Kitamura, J. Mol. Spectrosc., 41, 302 (1972). (25) G. Allen and E. F. Caidin, Q . Rev., Chem. Soc., 7, 255 (1953). (26) M. Kasha, H. R. Rawls, and M. A. El-Bayoumi, Eur. Congr. Mol. Spectrosc., 8th, 7966, 371-92 (1966). (27) R. S. Becker, “Theory and Interpretation of Fluorescence and Phosphorescence”,Wlley-Interscience, New York, 1969, Chapter 16. (28) P. K. Das, unpublished results. (29) G. L. Hug, private communication.
