4710
J. Phys. Chem. 1987, 91, 4710-4714
Excitation and Fluorescence Spectra of Jet-Cooled Coronene-d,, German Bermudezt and I. Y. Chan* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: February 20, 1987)
We report a spectroscopic study of jet-cooled coronene-d12that parallels our previous work on coronene-h12. The results are consistent with vibrational assignments made earlier. Vibronic interactions are enhanced upon deuteriation. The totally symmetric progression-promoting mode ( y o ) is observed. The IVR process is more prevalent, consistent with an increase in the density of states. Spectral observations corroborate our previous interpretation of line-shape features resulting from anharmonic coupling.
Introduction In the first part of this work] (I) we presented excitation and fluorescence spectra of coronene-h12under supersonic expansion conditions. As a summary, many lines of diverse symmetry (including n ~ n - modes) e ~ ~ were observed, Soand SI potential energy surfaces were found to be very similar, and the spectral manifestations of vibrational relaxation (IVR) were demonstrated only on an expanded energy scale. In addition, energy regions showing different extents of vibrational mixing were observed. In this paper we report a parallel study on perdeuteriated coronene. The observations are found to be consistent with the results in coronene-h12and to provide additional information on the vibrational spectroscopy of this large molecule. Several interesting line-shape features of coronene were attributed in I to static or dynamic anharmonic coupling. Additional spectral evidence from the perdeuteriated species fully corroborates the previous picture. As in I, the term IVR is used here to indicate anharmonic coupling, in the sense that temporal evolution may be observed in a properly designed experiment.2 With a nanosecond laser pulse width, our experiments were steady-state in nature and no coherent timeresolved observations were attempted. A review of previous spectroscopic studies of coronene may be found in I. Experimental Section Coronene-d12(isotopic purity 97.9 atom %) was obtained from MSD Isotopes. A mass analysis of the sample was consistent with the rated isotopic composition. No benzoperylene-dlo (BP-dlo) impurity parent peak was observed in the mass spectrum, even though the characteristic features of its S2 band were seen in excitation scans. After vacuum sublimation of this sample at 135 OC (aimed at removing volatile impurities), no significant changes in the excitation spectrum were observed. Triphenylene (Aldrich), the matrix used in the condensed-phase experiments, was recrystallized twice from ethanol-benzene mixtures, sublimed under vacuum at 140 O C , and extensively zone refined. The experimental apparatus and methods have been described before.] The working temperatures were 255 O C for the sample tube and 270 O C for the nozzle. All spectra reported here were taken with 1 psig of argon as the carrier gas. Similar cooling was also achieved with 80 psig of helium. Results and Discussion Excitation Spectrum. Figure 1 shows an overview of the fluorescence excitation spectrum. The figure is truncated at 372.2 nm where the onset of the S, state of the BP-dlois seen. The line intensity of this impurity is reduced IO-fold as compared with the corresponding impurity in the coronene-h12study. Accordingly, benzoperylene is not thought to produce any spurious features in the wavelength range of Figure 1. Table I contains the spectral analysis of SI in coronene-d12. The capital letter designations used in this paper correspond to the lower-case ones in the previous work.] Vibronic line correlations were made by following two guidelines: (1) all vibrational mode energies must be shifted to ‘Present address Sterling Chemistry Laboratory, Yale University, New Haven. CT 065 I 1 .
0022-36541871209 1-47 10$01.50/0
lower values in the deuteriated species and (2) the frequency and intensity distribution patterns are similar for both isotopic modifications. Since correlation of the strongest lines, e.g., A, K, and S (q’= 360.2, v3’ = 910.8, and vq/ = 1294.1 cm-I, respectively) are unequivocal, they provide a framework upon which further correlations among the weaker lines can be made. The frequency v{ is calculated to be (A’ - A in Figure 1) 1367.7 cm-I. The origin was not observable. As in I, its location was estimated by using the ul’ shift of coronene-d12in the triphenylene matrix. Being unavailable in the literature, the solid-state excitation and fluorescence spectra were taken in this laboratory at 2 K with a dopant concentration of 1 X mol ratio. Its spectroscopy is parallel to that of the h,2 a n a l ~ g u e . The ~ results are summarized in Table 11. The estimated origin for the jet spectrum is 23 872 cm-’, 50 cm-’ to the blue of the c ~ r o n e n e - horigin. ,~ Details of the excitation spectrum, as well as the low-temperature triphenylene matrix work, may be found in ref 4. While the excitation spectrum may be correlated with the equivalent spectrum in normal coronene, there is a notable qualitative difference. Namely, vibronic activity is generally more developed here, giving the spectrum a more crowded appearance. Especially, the modes N and J, together with their combination with yo, are nearly as strong as the prominent e2glines A, K, and S. Since the electronic contributions to the transition dipole remain unaffected by isotopic substitution, the changes in the intensity pattern must result from changes in the purely vibrational factors in the Herzberg-Teller scheme. The vibrational factors, to the first order, are of the type (4glQ,14e),where 4g and 4, are the vibrational components in the ground (al,) and excited states, respectively, and Q, is a normal coordinate. Thus, the vibrations J and N are most likely of ezg~ y m m e t r yproducing ,~ a nonvanishing Herzberg-Teller contribution for the vibronic transition moment. J was assigned e2gsymmetry in our previous work. N is likely to be of’this symmetry as well. A second explanation is possible although unlikely. Lines J and N could arise from an isotopic impurity that is responsible for the full observed intensity. Although the isotopic abundance is 97.9%, due to the large number of substitutional sites (12), the actual proportion of coronene-d, impurity in the sample could be up to 28%. This would formally be a distortion from the D6* symmetry of the perdeuteriated species, relaxing the symmetry selection rule. However, no origin signal was observable in our experiments and no other transitions are similarly enhanced. Indeed, genuine isotopic impurity lines were identified for the strongest features in the spectrum as one or two satellites 5 and 10 cm-I red-shifted from the main lines. While most lines in the perhydrocoronene spectrum are correlated in the deuteriated analogue with certainty, line v in I can not be correlated with any confidence. In the region where line ( I ) Bermudez, G.; Chan, I . Y. J . Phys. Chem. 1986, 90, 5029. (2) Freed, K. E.; Nitzan. A. N. In Energy Storage and Redistribution in Molecules; Hinze, J., Ed.; Plenum: New York, 1983; pp 467-491. (3) Ohno, K.; Inokuchi, H. Chem. Phys. L e f t . 1973, 23, 561. (4) Bermudez, G. Ph.D. Thesis, Brandeis University, Feb 1987; available from University Microfilm, Ann Arbor, MI. (5) Names, R.; Lee, E. K. C. J . Chem. Phys. 1986, 84, 5290.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4711
Spectra of Jet-Cooled Coronene-d12 TABLE I: Spectral Analysis of Corooene-d12 index* wavelength, A shift! cm-' A
B? C D E F G H I J
K
L M N
O? O? P
Q
R S T
YO
W
X Y A'
Z B'? C' D' E' F' G'? I' J' K'
L' M' " Of?,P'?
Q
R' S'
T' 2VO
X' Y'
A+2uo Z'
4126.8 4111.3 4102.0 4100.7 4099.5 4088.9 4078.8 4073.5 4063.3 4060.8 4049.8 4047.1 4043.9 4038.5 4035.1 4031.1 4024.9 4018.6 4011.0 4009.6 4005.7 3999.1 3992.4 3990.2 3981.O 3976.2 3973.7 3970.5 3968.6 3963.2 3962.0 3955.5 3951.1 3936.9 3936.0 3933.4 3925.6 3922.4 3906.3 3901.9 3897.9 3892.1 3883.9 3882.8 3875.2 3855.2 3852.9 3850.1 3837.2 3834.7 3826.1 3826.9 3820.3 3815.0 3809.2 3801.5 3797.9 3785.5 3775.1 3770.9 3768.5 3766.1 3764.6 3757.9 3732.8 3722.9 3708.4 3704.4
intensitv'
360.2 45 1.6 506.9 514.4 521.3 585.0 645.2 677.0 739.1 753.8 820.8 837.2 857.0 870.0 910.8 935.6 973.7 1012.5 1059.4 1068.8 1092.9 1134.1 1176.2 1189.7 1247.8 1277.8 1294.1 1314.2 1326.1 1360.3 1368.3 1409.5 1437.6 1529.2 1534.2 1551.7 1602.2 1623.2 1727.9 1756.8 1783.3 1821.1 1875.6 1882.8 1953.4 2067.2 2082.9 2101.6 2189.0 2204.9 2264.7 2279.4 2304.0 2340.9 2380.4 2433.6 2458.4 2445.1 2617.8 2647.4 2663.8 2680.9 269 1.6 2739.2 2917.9 2988.9 3094.1 3123.4
126 4 10 7 2 2 3 14 4 8 34 120 14 45 500 18 34 17 8 14 205 4 4 12 19 52 202 16 14 12 120 17 15 17 17 98 36 171 232 194 17 19 5 15 8 13 10 10 40 68 159 362 12 28 44 39 259
u",d cm-'
dd? ns
364.2
713 (4)
802.6 832.3
695 (5) 680.0 (2.5)
885.0 919.2
700.6 (2.3)
assignment
984.3 707 (8) 1078.4
708.7 (2.7)
1224.5
-
1286.2 1318.1
702.3 (2.8) 691.1 (1.4)
1367.8
679.8 (2.6)
1794
649 (4) 720.6 (3.0) 681 (5)
vo
+B +c vo + D Yo + E Yo + F +G Yo + I UO + J vo Yo
YO
694 (5) 693 (4)
yo
uo
uo YO
I 24 59 280 72 81 81 40 82 64 37
+A
uo PO
666 (6)
Yo
vo
+ Y3
+L +M +N +Q +R
+s
+T
2u0 2u0
+A
OCapital letter labels in this table correspond to the lower-case ones in Table I of ref 1. *Shifts from estimate of unobserved origin at 23 872 cm-'. 'Relative to line K = 500. dCorresponding frequency in So. e 7 = fluorescence lifetime; u = standard deviation.
V is expected, neighboring lines are accounted for, but V is conspicuously absent. Presumably it experiences an unusually large isotope shift away from its neighbors. This mode v (3060 cm-I) was the only fundamental found in the high-energy region of the coronene-h,, excitation spectrum.' The large deuterium
effect corroborates the C-H stretch character of this mode. A pure C-H mode would give a shift that would correspond to any of the new lines around Y and Z, within the uncharacterized 1362-1757-cm-' energy range. These new features also appear as combinations with vo and give the characteristic coronene
4712 The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Bermudez and Chan
K
K'
A "0
J
WAVELENGTH (nm) Figure 1. Fluorescence excitation spectrum-a composite of seven experimental scan ranges. Arrows indicate artificial base-line changes. The spectrum has been normalized for laser output, and the intensities are accurate to within 15%. Nozzle temperature 270 O C ; Po = 1 psig Ar; X / D = 18. Letter indices are those in Table I and correspond to the lower-case indices used to label the coronene-h12spectrum. TABLE 11: Vibrational Frequencies in the Ground and SIExcited States of Coronene-d12in Triphenylene Matrix'.* vibration u", cm-' u', cm-' '4 (4 368 3 60 B? 416 47 1 J 832 K (v3) 915 910 N 1101 1093 s (y4) 1339 1297 "0 1368 1381
'Origin: 4312.0 A, 23 191.1 cm-'. bDopant concentration: 1 X lo-' mol ratio. T = 2 K.
fluorescence spectrum. Thus they cannot be ascribed to impurities. Mode u (ezg) is also difficult to correlate in the deuteriated compound. An examination of the isotopic shift pattern for the observed e2g modes as a function of increasing energy shows a distinct, albeit irregular increase in the deuterium effect: A, 7.9; J, 53.4; K, 72.9; N, 65.6; and S, 144.3 cm-'. Extrapolating according to this trend, line U may be located at about 1500 cm-I. Thus U can be any of the 1410-1529-cm-' lines. The isotopic shift pattern just described for the eZgmodes is not followed by the a l g (vo) mode deduced at 1367 cm-I. Here the deuterium displacement is only 4.4 cm-I, the smallest of all observed shifts. Conceivably, this is a pure C-C skeletal breathing mode. A line of moderate intensity a t 3962 A is most interesting, as it may be assigned as vd at 1368.3 cm-I. There are three observations in favor of this interpretation. (1) The calculated energy difference A - A' is identical, within the uncertainty of the measured energies (1 cm-I), with the observed 1368.3-cm-I line in the jet excitation spectrum. (2) The observed vo in the solid-state excitation spectrum is at 138 1.1 cm-I. The jet line is downshifted from the matrix value by 12 cm-I, while known eZgmodes present matrix-induced shifts of less than 3 cm-I. These values are consistent with similar observations in coronene-h,,: a 10-cm-' downshift was seen for vo in the gas phase, while e g modes showed a matrix shift of about 1 cm-I. That is, alg breathing modes are more susceptible to a matrix shift than e2* modes. (3) More definitive information on the nature of the 1368-cm-' line in the excitation spectrum is provided by the dispersed fluorescence. Such fluorescence spectra are discussed in detail in the next section and in Figure 3A. For the sake of assigning this line, we make the relevant arguments here. Besides the familiar cyig fluorescence pattern, where cy is the mode being pumped and p is one of the prominent eZgmodes, including J and N, the dispersed fluorescence from the 1368 line shows a set of features assignable as X$:, with X = 1368 and (3 = ezg. Analogous features were observed in the fluorescence spectra from combination states containing vo (A', K', and S'). The new pattern is most developed
r . . .
1
400
1
,
1
1
1
1
1
,
,
450
,
,
,
,
,
,
,
,
,
'
I
I
i
500
WAVELENGTH (nm) Figure 2. Fluorescence spectra pumping the four main lines in the excitation spectrum: (a) line A, (b) line K, (c) line S, and (d) line K'. The sharp feature just to the blue of the prominent line ((~13'3in (a) and (b) is the ci;J!, which coalesces with the former in (c) and (d). Slit resolutions below 450 nm are (a) 12, (b) 12, (c) 21, and (d) 41 cm-'. The resolutions at the longer wavelengths are twice these values, but the gain is equal. The spectra are the average of three to five scans. The striped bands correspond to the main bands observed in coronene-h12(ref 1). The dotted bands are their combinations to yo. for the A'dispersed fluorescence (O&lipy),as shown in Figure 3B below. On the basis of this parallel behavior of known yo combinations, we assign the 1368-cm-' feature to the vo vibration. The fact that a totally symmetric mode can be seen in the fluorescence spectrum for deuteriated coronene but not for coronene-h,, suggests a significant change in the Herzberg-Teller factor (#JglQil#Je) = (ezglQilaIg)for mode vo induced by isotopic substitution. Less likely, it could be due to a minute (e.g., isotopic) distortion from the D6>geometry. A third possibility is that this level is a mixed vibrational state having some optically active character. Since a Fermi resonance can only occur between states of the same overall symmetry, the best possible candidate for mixing with vo would be the 1'3, level which, however, does not have any transition strength. Further analysis of the nature of the 1368-cm-' line requires polarization studies or measurement of the rotational band contour. Fluorescence Spectra. Figure 2 presents the dispersed fluorescence spectra obtained by excitation of lines A, K, S, and K' (vI', v3', vq/, and v3' + vd). This is the analogue of Figure 4 in I. The striped bands are those involvin the prominent vi'', u3", and vq/l modes in fluorescence: the C Y $ , 0 type, where a is the mode being pumped and p is one of the main e2gvibrations. Their combinations with u,," are shown as dotted bands. Compared with the fluorescence spectra of coronene-h12,the deuterio analogue has more vibronic activity. Within the a{Py cluster, the J and N modes also appear distinctly. Further, more features were observed at wavelengths closer to the laser excitation. Most prominent is a new progression of the type ah30,, where cy is the mode being pumped, including u0. These progressions are labeled in Figure 2. The line intensity becomes greater as higher vibronic levels are pumped. The 3' and 4' fluorescences are special
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Spectra of Jet-Cooled Coronene-dlz
4713
TABLE 111: Coronene-dI2Fluorescence Exciting Line K' wavelength: 8, shift,bcm-l intensity assignment 4039 1393 2 013i) 4111 41 37 4205 4265 4303 4371 4404 4447 4477 4524 4567 4639 4677 4726 4761 4819 4949 4993 5053
1824 1982 2370 2705 2910 3271 3442 3664 3817 4047 4257 4593 4768 4991 5147 5402 5945 6122 6362
6 12 8 49 20 90 64 82 58 13 4 30 14 19 8 4 8 3 3
013 BY? OA3; 0'314: 0'3;l: Oi3: 0',3I 013iN: 0'314: Oi3: Of3;I: 0'3' 0!3!
I
'
l
400
OdI"?
l
I
'
450
nm
Oi3'4: 0'3: 0 ~ 3 ~ 1 ~ Oi3' 0'3fN; Oj314:
'Slit resolution is 41 cm-I. bRelative energy from Oo of So. Frequency mismatch with the calculated values is due to the low slit resolution employed and to the IVR shifts at 2279 cm-l of vibrational excitation (see text). in the sense that, for a couple of features, a strong optically active mode is shed in favor of the weaker vo vibration not originally excited in SI. Other lines, peculiar to each pumped level, were also observed. The 1' fluorescence produces a feature at 437.5 nm that may be assigned to 1tL:, suggesting L is an ezgvibration. Fluorescence from 3l gives a 3h4: line at 427.0 nm. Generally, IVR-induced red-shifts are greater for coronene-dlz than for coronene-h12 and this must be accounted for when fluorescence bands involving higher vibronic levels are assigned. These shifts may be up to 100 cm-'. The ground-state vibrational frequencies quoted in Table I were extracted from the fluorescence spectra as described for coronene-hlZ,' with the exception that the frequency of a given pumped mode CY was obtained from the ai 1: rather than from the a',3:, which was found to coalesce with nearby emission features (involving J, L, and N modes). This vibrational relaxation effect is already significant at the 4l excitation level (Figure 2C). Table I11 presents the spectral analysis of the O13I (K') fluorescence. To avoid clumsy labeling, the assignments are given assuming no vibrational relaxation. However, quoted shifts in Table I11 show the IVR red shift. Other fluorescence spectra with characteristic features are shown in Figure 3. Upon 0: (vo) and Ohlh (A') excitation unusually strong emission lines, indicative of the dipole activity of vo in coronene-dlz, are seen. For A' fluorescence the full features at longer wavelengths are repeated upon shedding vo (Figure 3B). Line widths are significantly larger for the longer wavelengths, presumably due to vibrational relaxation in the ground manifold. Similar OhB: ( p = e2J transitions occur to a lesser extent for many lines: A', K', S', and, last but not least, v,'. This is shown in Figure 3A, and this fact is used above (see Excitation Spectrum) to help establish the v,,' assignment. Finally, even though no splitting of the excitation line J was seen with the available laser resolution, the fluorescence lines Ji, Ji37, and JiN: (and presumably all others in the fluorescence spectrum) show under high-resolution conditions a distinctive splitting, without any broadening, of 25 cm-I (Figure 3C). Level J may be composed of a Fermi resonance pair or of two closely lying levels, each from a different isotopic species. Vibrational Relaxation. We reported in the Introduction some spectral behavior of coronene concerning intramolecular vibrational relaxation. The main features are briefly summarized here to facilitate further presentation. (1) As one excites vibronic states with successively higher vibration energy, the fluorescence spectra remain relatively simple and well resolved. This is a result of the similarity between the energy surfaces of So and S,. Broadening and red-shift of fluorescence lines due to IVR are relatively small.
I
I 435
I
I nm
I
I
I 440
Figure 3. (a) and (b), fluorescence spectra from levels u,, and A', respectively. The slit resolution is 41 cm-'. The dotted lines correspond to the three prominent peaks in I. (c) A high-resolution portion of fluorescence spectrum from the level J, showing the splitting.
(2) The 4137 fluorescence line exhibits a splitting of -45 cm-'. We have interpreted this bimodal distribution to result from the small number of dark states available in the IVR process for a gateway state with intermediate vibrational energy. The IVR red-shift cannot develop into a Gaussian (or more complicated) spectral profile due to the small statistical basis. (3) The 1!3: fluorescence is a doublet with -20 cm-I splitting. Similar splittings exist in all stronger lifl ( p = e2J lines. the 1; excitation line (a) is also slightly split. We have ascribed these observations to a Fermi resonance of v1 in S1. These plausible interpretations had to be regarded as tentative at the time I was written. An effective way to seek (or deny) corroboration to the above picture is through investigation of analogous spectral lines in the deuteriated species. The IVR process is determined both by the anharmonic coupling strength and the density-of-states at the gateway. Isotopic substitution allows one to change the density-of-states without modifying the force field, thus separating the two contributions. In this section we examine some detailed fluorescence line profiles from this perspective. As we shall see, our results are fully consistent with the picture summarized above. Fluorescence line shapes for four strong excitation lines in coronene-d12 are shown in Figure 4 (lines A, K, L, and S; 360-1294 cm-I above the S, origin). In all cases the line monitored is the 4-1:. Let us first address the issue of the vI' splitting in I. The line width for the lt3: line (pumping line A, 360 cm-') is the same as in the 3; fluorescence in coronene-h12,showing no effects of broadening by vibrational relaxation. The split character of the lines that are li3: in fluorescence and 1; in excitation for coronene-h12is absent in the perdeuterio case. This is consistent with the Fermi resonance assignment given to vl' in coronene-hlz; it is reasonable to expect the two levels involved to have different isotopic shifts so that their mixing is decreased beyond the detection limit of the dark-state emission in our experiment. A reassuring characteristic in Figure 4 is that a similar pattern of red-shifting and broadening is observed for coronene-d12at
J. Phys. Chem. 1987, 91.4714-4723
4714
B
A
Figure 4. Fluorescence line shapes for the 43': transitions. The excited modes are (a) A, (b) K, (c) L,and (d) S. Slit resolutions are (a) 10, (b) 10, (c) 25, and (d) 30 cm-I. The traces have been justified in frequency and the intensities made arbitrarily equal. Sum of four to nine scans.
excitation merges below 1300 cm-l as for coronene-h12below 2300 cm-I. This is of course a consequence of the increased densityof-states in coronene-d12. Thus, the 4i3: emission (Figure 4D) is a broad featureless line, not unlike the k' profile shown in Figure 6d of I. Presumably, a similar, large number of dark levels are
effectively coupled to the e2, mode in coronene-d,, at 1294 cm-' (level S), as in coronene-h,, a t 2356 cm-I (level k' in ref I). This behavior of the v i mode is in stark contrast to that of the h,, equivalent, where a broad doublet with a 45-cm-I separation was observed. We believe this comparison strengthens our previous suggestion for the origin of the splitting: a small number of dark states does not constitute an adequate statistical basis for a normal distribution in the line profile. Going from coronene-h,, to coronene-d12,the same mode u i will couple anharmonically to the same set (symmetrywise) of dark combination states if available. On increasing the density-of-states, however, the number of dark states contributing to the red-shift in the dI2species has increased to the extent that the splitting is conspicuously absent. As a further corroboration, consider the Li3: fluorescence (Figure 4C) from level L, 974 cm-' above the origin. With a slight stretch of the imagination a weaker component to the blue of the main peak may be identified as lining up with Figure 4A,B. While the signal-to-noise ratio is poor, the same feature appears in each separate scan making up the final picture, so the peak is real. This behavior mimics the splitting of the 4i3: line (at 1348 cm-') in coronene-h12, except that the vibrational energy of the gateway state is now 974 cm-'. We believe that the effects of vibrational relaxation to a limited subset of dark states are being observed in both cases. Again, the energy domain for the appearance of this intermediate region is consistent with the increase in the density-of-states in the perdeuterio species. The lifetimes measured for coronene-d,, in a jet were about 200 ns longer than those for the perhydro species. This is consistent with a decrease in the intersystem crossing rate in perdeuteriated coronene. The same general trend of near-constant lifetime, as vibrational energy increases, also prevails in the perdeuteriated species. Such lifetime data are included in Table I.
Conclusion This work complements and completes a jet spectroscopic investigation of coronene started in I. Most of the ez8vibrations (1 1 out of 12) are now identified. Two tentative interpretations of interesting spectral line profiles in I are now established beyond reasonable doubt. Registry No. Coronene-dr2,16083-32-2.
Solvent Reorganization in Optical and Thermal. Electron-Transfer Processes: Solvatochromism and Intramolecular Electron-Transfer Barriers in Spheroidal Molecules Bruce S. Brunscbwig,* Stanton Ehrenson,* and Norman Sutin* Department of Chemistry, Brookhaven National Laboratory, Upton, New York (Received: February 25, 1987; In Final Form: May 4, 1987)
1I973
Expressions for the shift of the absorption and emission band maxima of a solute with changes of the solvent's dielectric properties are presented for solute molecules with shapes and polarizabilitiesthat can be approximated by those of a spherical dielectric-continuum cavity. The derivations use a nonequilibrium thermodynamic approach developed by Marcus. A series of accurate approximations for the solvent shifts are presented. The new expressions are shown to reduce to equations previously derived by McRae, Ooshika, Mataga, and others when point-dipole approximations are made and particular values of the solute polarizability are assigned. The polarizability of the solute can be related to the internal dielectric constant of the cavity, and general expressions for the band shift in the point-dipole limit containing the dielectric constant of the cavity as a parameter are derived.
The interaction of a solute with surrounding solvent is sensitive to the charge distribution and polarizability of the solvent (and solute) molecules. If the solvent interacts with the solute in a specific manner (e.g., by hydrogen bonding or other donor-acceptor interactions), large changes in the energy of the solvated 0022-3654/87/2091-4714$01.50/0
molecule can occur with changes in solvent. Even if the solutesolvent interactions are nonspecific, changes in the energy of the solvated molecule will still occur with changes in solvent, especially for polar solvent molecules or solutes that have high charges or dipole moments. The various solute-solvent interactions lead to 0 1987 American Chemical Society
