J. Phys. Chem. 1989, 93, 2341-2341 states are effectively "squeezed" out of existence. However, these extra bands should also then be present in the emission spectrum from the SI vibrationless level if their source is vibronic coupling. The spectrum of Figure 4 shows no splittings or additional bands over those found in the matrix fluorescence spectrum. The hypothesis of coupling to Rydberg states requires that the mechanism be specific to the anthraquinones, also, since there is generally good agreement between the gas-phase and condensed-phase spectra of benzene, naphthalene, anthracene, etc. An alternative interpretation is that the molecules undergo large-amplitude motions in the gas phase and that these modes are dampened out in the matrix environment. A puckering motion of the six-membered pseudoring containing the intramolecular hydrogen bond is a good candidate for such a mode. Furthermore, it seems reasonable that such a mode would couple fairly strongly to other vibrations more or less localized in the pseudoring. On the other hand, there is no evident activity of modes highly localized in the hydrogen bond, i.e., the N-H stretch or in- and out-of-plane bends. The change in the origin isotope shift from 49 cm-I in condensed phase to 8 1 cm-I in the gas phase is curious. Many authors have ascribed the shift entirely to the A-H stretching mode of the A-H-B hydrogen bond arrangement, although a good demonstration the procedure is justified is conspicuously lacking. It is easy to show that the origin shift is 0.146Aw in this approximation, where A w is the reduction of the A-H stretching frequency in the excited-state over the ground-state value. The additional shift of 32 cm-' represents an environmental contribution of almost
2341
220 cm-' to Aw, which is an enormous amount for what must be largely still a localized intramolecular mode. A more detailed investigation into this point is hampered by low signal to noise in the spectra. We attempted to measure the fluorescence lifetime of l-NH,-AQ in the gas phase but could not discern any deviation of the emission from the temporal profile of the laser. This places the lifetime at under 1-2 ns. In solution the lifetime (and fluorescence quantum yield) is solvent dependent,I0 but the longest lifetime of 1.75 ns in benzene only corresponds to a fluorescence quantum yield of 0.058. Efforts are under way to improve the collection efficiency of the optics and to convert to a pulsed nozzle for greater emission signal. Then a better study of the emission from the low-frequency excitation features and their dependence on isotopic substitution can be carried out. We also note that we have not been able to find any genuine fluorescence of 2-aminoanthraquinone, which might have been expected to shed some light on the question of the differences in matrix vs gas-phase spectra and the role of the intramolecular hydrogen bond. Acknowledgment. This work was supported by a grant from the National Science Foundation, and we gratefully acknowledge their support. Registry No. 1-Aminoanthraquinone, 82-45-1; deuterium, 7782-39-0. (10) Inoue, H.; Hida, M.; Nakashima, N.; Yoshihara, K. J. Phys. Chem. 1982, 86, 3184.
Ab Initio Force Constants and the Reassignment of the Vibrational Spectra of all-fransand a//-cis - 1,3,5,7- Oct at et raene Tracy P. Hamilton**+ and Peter Pulay* Department of Chemistry, University of Arkansas, Fayetteville. Arkansas 72701 (Received: August 9, 1988)
Complete scaled ab initio force fields and frequencies have been calculated for the all-trans and all-cis isomers of 1,3,5,7octatetraene. Several peaks in the infrared and Raman spectra have been reassigned, and a medium intensity IR peak at 1580 cm-' is predicted. The agreement between the experimental and theoretical C-C stretching frequencies is very good. We believe that the force constants are superior to previous theoretical ones. A detailed comparison with the results from an extended Pariser-Parr-Pople configuration interaction theory is made. The effect of cis-trans isomerization is discussed. The perdeuterated frequencies are also presented in anticipation of future experimental measurements.
Introduction The vibrational spectra of small linear polyenes has been much studied because many larger molecules, such as carotenoids, visual pigments, and polyacetylene polymers contain linear conjugated chains. Doped polyacetylenel may become an important material in the future; it can be twice as conductive as copper on a weight basis.* The study of the structure and force field of smaller polyenes is essential for understanding the more complex systems. An example of the importance of the vibrational spectroscopy of these molecules is the estimation of the defect density in polya ~ e t y l e n e . ~This is based on the fact that the frequency of the strongest Raman band in linear polyenes decreases smoothly with increasing chain length.4 Both all-cis- and all-trans-polyacetylene are known; their electrical properties are remarkably different. Most carotenoids either are all-trans or contain a single cis-C=C bond. In this Present address: Center for Computational Quantum Chemistry, School of Chemical Sciences, The University of Georgia, Athens, GA 30602.
0022-365418912093-2341$01.50/0
paper, we consider only the all-trans and all-cis forms of octatetraene. Theoretical calculations are essential to the understanding of the vibrational force fields of polyenes because of the long-range coupling caused by the conjugated x system. The latter precludes models with force constants transferred from simple compounds. Obtaining full harmonic force fields from experimental data becomes progressively more difficult as the molecular size increases. For a molecule of the size of octatetraene, it is practically impossible to obtain an experimental force field without the help of a theoretical model. The latter is also important to correct the experimental misassignments that are almost inevitable for a molecule this large. We would like to emphasize the importance (1) Shirakawa, H.; Louis, E. J.; MacDiarmid, A. B.; Chiang, C. K.; Heeger, A. J. J. Chem. SOC.,Chem. Commun. 1977, 578. (2) Naarman, H.; Theophilou, N. Synth. Met. 1987, 22, 1. (3) Kuzmany, H. Pure Appl. Chem. 1985, 2, 235. (4) Rimai, L.; Heyde, M. E.; Gill, D. J. Am. Chem. SOC.1973, 95, 4493.
0 1989 American Chemical Society
2342
The Journal of Physical Chemistry, Vol. 93, No. 6,1989
Hamilton and Pulay
i”
of obtaining force fields, as compared with the frequencies only. An excellent overview on polyene vibrational spectroscopy and force fields has been recently published by Hudson, Kohler, and S ~ h u l t e n .This ~ paper summarizes much of the earlier theoretical
C,
\ H,,
Theoretical calculations of force constants do not have the disadvantages mentioned above but are not without problems. We will briefly discuss three classes of methods: semiempirical, high-quality ab initio, and scaled ab initio methods. One semiempirical approach that contributed decisively to the clarification of polyene vibrational spectroscopy is the quantum mechanical consistent force field (QCFF) m ~ d e l . ~ The J~ u skeleton of the unsaturated system is treated with an empirical force field parametrized to reproduce potential surfaces. The HI, *-electron system is described quantum mechanically by using Figure 1. Geometry and atom numbering of trans,trans-1,3,5,7-octatea modified PPP Hamiltonian, including configuration interaction. traene. This method has been employed to predict properties of the ground and excited states of conjugated m o l e c ~ l e s , ~ ~including ’ l - ~ ~ the We used the scaled quantum mechanical (SQM) method;22this ground-state vibrations of all-cis and all-trans polyenes up to is based on the observation that the transferability of scale factors octatetraene.” As we see it, the greatest shortcoming of this is better than the transferability of force constants themselves. method is the large number of empirical parameters. This makes The SQM procedure also gives a prescription for the reference the conclusive identification of misassignments difficult. Scaled geometry because the frequencies are very sensitive to it. SurC N D 0 / 2 force fields’* contain fewer empirical parameters, but prisingly good results can be obtained from a single-configuration the strong scaling needed to reproduce the experimental freself-consistent field (SCF) wave function, but correlation effects quencies makes these methods less desirable than their ab initio must be accounted for in some systems, such as in benzene.25 analogues. The second molecular orbital (MO) approach to calculation Calculations of force fields is the use of ab initio results with no scaling of the The procedure used in determining the geometries and vibraresults. This requires the use of large basis sets and sophisticated tional spectra of the octatetraenes was the scaled quantum meelectron correlation methods to obtain reasonably accurate chanical (SQM) force field method.22 The reference geometry quadratic force constants. These methods are currently applicable was obtained by optimization using a 4-21G basis set26and then only to smaller systems, even when analytical derivative methodsI9 applying a small systematic correction to the bond lengths to obtain are used. It is easy to understand why the lack of flexibility in an approximate re geometry, as suggested by Blom et aLz3 We the wave function will usually lead to overestimation of the dihave used the geometry corrections in ref 22: the CH bonds are agonal force constants and the frequencies. In some cases, notably lengthened by 0.005 8, and the CC bonds are changed by R = if correlation methods are used without polarization functions, 0.16(1.45 A - Rth). a cancellation of errors occurs: the overestimation of the bond The force constants were calculated by finite differences of lengths decreases the force constants,20and this cancels part of analytic gradients at the corrected (approximate re) geometries. the basis set and correlation error. As pointed out by Yamaguchi The dipole moment derivatives were also evaluated numerically, and Schaefer,21such methods yield, by fortuitous cancellation, including the corrections from the Eckart condition^.^^*^^ Due fairly good vibrational frequencies. to the large number of degrees of freedom, small one-sided disThe third class of theoretical MO force fields are those derived placements of 0.001 A, 0.002 rad, and 0.05 rad were used for bond from scaling ab initio results. This has been found to be quite stretching, bending, and torsions, respectively. useful because of the systematic errors in ab initio force constants. Following the SQM prescription, the force constants were scaled The scale factors are obtained from experimental frequencies, and by factors taken from the simultaneous scaling of several small thus the resulting force field can no longer be referred to as strictly molecules: butadiene, ethylene, formaldehyde, glyoxal, and ab initio, yet it is not nearly as dependent on experimental data acrolein.22 In the SQM method, the scale factor for an off-dias an empirical force field is. The scale factors are usually obtained agonal force constant Fii is the geometric mean of the scale factors from related reference molecules, so the predicted spectra is a for F,, and Fli. The fundamental frequencies were calculated by priori. There are several scaling procedures in the l i t e r a t ~ r e . ~ ~ - ~the ~ standard Wilson G F matrix method. The normal modes were approximately characterized by the total energy distribution (5)Hudson, B. S.;Kohler, B. E.; Schulten, K. In Excited States; Lim, E. (TED) Due to the large number of modes, some were C., Ed.; Academic: New York, 1982;Vol. 6,pp 1-95. made up of many small contributions. (6)Popov, E. M.; Kogan, G. A. Opt. Spectrosk. 1964, 17, 670 [Opt. The unmodified SQM method gave good frequencies except Spectrosc. 1964,17, 3621. for the highest a8 CC stretching, which was 40 cm-’ too high. This (7)Tric, C . J . Chem. Phys. 1969,5 1 , 4778. (8) Gavin, R. M.; Rice, S. A. J . Chem. Phys. 1971,55, 2675. is obviously a correlation effect. The analogous frequency is too (9)Warshel, A,; Karplus, M. J . Am. Chem. SOC.1972,94, 5612. high in the SQM force field of butadiene22and 1,3,5-he~atriene.~’ (10) Inagaki, F.;Tasumi, M.; Miyazawa, T. J . Raman Spectrosc. 1975, In the latter study, it was noted that a simple scaling of the 3, 335. coupling constants between CC stretchings is sufficient to fit this (11)Lasaga, A. C.;Aerni, A. C.; Karplus, M. J . Chem. Phys. 1980,73, important frequency. Extra scale factors for couplings between 5230. (12)Dinur, U.;Hemley, R. J.; Karplus, M. J . Phys. Chem. 1983,87, 924. (13)Kohler, B. E.;Spiglanin, T. S.; Hemley, R. J.; Karplus, M. J Chem. Phys. 1984,80, 23. (14)Hemley, R.J.; Dinur, U.; Vaida, V.; Karplus, M. J . Am. Chem. Soc. 1985,107,836. (15)Hemley, R.J.; Leopold, D. G.; Vaida, V.; Karplus, M. J . Chem. Phys. 1985,82, 5379. (16)Warshel, A. In Modern Theoretical Chemistry; Segal, G. A., Ed.; Plenum: New York, 1977;Vol. 7. (17)Hemley, R. J.; Brooks, B. R.; Karplus, M. J . Chem. Phys. 1986.85, 6550.
(18)Panchenko, Yu. N.; Pulay, P.; Torok, F. J . Mol. Struct. 1976,34,283. (19)For a review see: Pulay, P. Ado. Chem. Phys. 1987,69, 241. (20) Pulay, P.; Lee, J.-G.; Boggs, J. E. J . Chem. Phys. 1983,79, 3382. (21)Yamaguchi, Y.; Schaefer, H. F., 111 J . Chem. Phys. 1980,73,2310.
(22)Pulay, P.; Fogarasi, G.;Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. SOC.1983,105, 7037. (23)(a) Blom, C.E.; Altona, C. Mol. Phys. 1976,31, 1377. (b) Blom, C.E.;Slingerland, P. J.; Altona, C. Ibid. 1976,31, 1359. (24)(a) Botschwina, P. Chem. Phys. Lett. 1974,29, 98. (b) Ibid. 1974, 580. (25)Pulay, P.;Fogarasi, G.; Boggs, J. E. J . Chem. Phys. 1981,74,3999. (26)Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. SOC. 1979,101, 2550. (27)Eckart, C.Phys. Rev. 1935,45,552. (28)Pulay, P.; Torok, F. Acta Chim. Sci. Hung. 1965,47,273. (29)Fogarasi, G.; Szalay, P. G.; Liescheski, P. P.; Boggs, J. E.; Pulay, P. J . Mol. Struct. 1987,151, 341. 29,
all-trans- and all-cis- 1,3,5,7-0ctatetraene
The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2343
TABLE I: Geometry of trans,trrms-l,3,5,7-0ctatetraene (See Figure 1)'
exptlb CIC2 c2c3 c3c4 c4c5
ClH9 ClHIO C2H1, C3H12 C4H I3
LHgCIHlo fC2CIH10 LCICZH11 LC4C3H12 LC3C4H13
LCICZC3 LC2C3C4 LC3C4CS
1.336 (4) 1.451 (3) 1.327 (4) 1.451 (5) 0.97 (3) 1.17 (4) 0.93 (3) 1.02 (3) 1.00(3) 118 (2) 121 (2) 119 (2) 119 (1) 120 (1) 124.7 (3) 125.1 (3) 125.3 (4)
TABLE I1 Geometry of cis,cis-1,3,5,7-0ctatetraene (See Figure 2)'
theoretical Hemley et al.' 4-21G correctedC
theoretical 4-21G correctedc Lasaga et al." 1.3406 (1.3199) 1.4621 (1.4644) 1.3465 (1.3268) 1.4582 (1.4598) 1.0769 (1.0719) 1.0788(1.0738) 1.0806 (1.0756) 1.0810 (1.0760) 1.0812 (1.0762) 116.28 121.86 119.78 119.75 119.56 124.13 123.90 124.07
1.348 1.461 1.363 1.457 1.085 1.085 1.083 1.086 1.085 118.3 120.3 119.3 118.1 117.4 121.5 124.8 124.4
1.347 1.461 1.361 1.457
120.0 120.4 120.3 122.0 121.6 121.6
'Bond lengths are in angstroms; bond angles are in degrees. bX-ray diffraction data from ref 31. CSee the text for the correction of the bond lengths. The original values are in parentheses. "Reference 11. The C-H bond lengths were not given but were probably 1.085 A.
1.3410 (1.3199) 1.4642(1.4644) 1.3489(1.3268) 1.4611 (1.4598) 1.0789 (1.0739) 1.0770 (1.0720) 1.0777 (1.0727) 1.0803 (1.0753) 1.0775 (1.0725) 116.24 121.87 119.16 117.99 117.26 123.04 127.27 126.25
'Bond lengths are in angstroms; bond angles are in degrees. bThe data are from Table V in ref 17. CSeethe text for the correction of the bond lengths. The original values are in parentheses.
d
i
1 1
I
Figure 2. Geometry and atom numbering of cis,cis-1,3,5,7-octatetraene.
C C stretches had to be introduced also in benzene.25 Recently, a correlated force field was published for h e ~ a t r i e n eallowing ,~~ us to more accurately estimate the correlation effects on the force fields. A comparison of the S C F and correlated force fields of Szalay et al.30 shows that electron correlation increases the C C coupling force constants relative to the diagonal C C stretchings, in agreement with the conclusions of ref 29. The ratio of the coupling force constant and the geometric mean of the corresponding diagonal ones, Fij/(Fi,Fjj)lI2,was calculated for the butadiene and hexatriene CC stretching force constants of Szalay et aL30 The ratios for the couplings in the correlated force field were found to be uniformly 17% larger than in the SCF field. The only exceptions were the ratios for the nearest-neighbor C=C,C=C couplings, which were approximately 42% larger. On the basis of these calculations, we have introduced an extra scale factor, increasing the nearest-neighbor C=C,C=C couplings by (1 0.42a), and the rest of the CC,CC couplings by (1 0 . 1 7 ~ ~ ) . The factor a was varied to give the best agreement with the experimental spectrum of all-trans-octatetraene. This procedure takes into account that a calculation with a limited basis set and excitation level recovers only a fraction of the correlation effect; also correlation effects may be more severe in the larger molecule. This fairly simple procedure suffices to correct for correlation effects, as most frequencies were very insensitive to the accurate value of the empirical correction factor a, as discussed below.
+
+
Results and Discussion Geometry. The calculated geometries for the all-trans and cis-transoid geometries are given in Tables I and 11, respectively. The numbering of the atoms referred to in these tables is shown in Figures 1 and 2. Many theoretical calculations have been made on the 1,3,5,7-octatetraenes, particularly on the all-trans isomer. In addition, the all-trans geometry has been determined from (30) Szalay, P. G.; Karpfen, A,; Lischka, H. J . Chem. Phys. 1987, 87, 3530.
Figure 3. Dependence of the C=C stretching frequencieson the extra scaling factor CY (see text): (a) CY = 0; (b) CY = 1; (c) CY = 2, (d) experimental spectrum. Note that the wavenumbers increase to the right.
X-ray diffraction by Baughman et ale3' The C-H bond distances are quite short from the X-ray study, but this is to be expected because X-ray diffraction is unable to locate hydrogen nuclei accurately. What is surprising is that the experimental central C=C bond is shorter than the outer C = C bonds, which is counter to all the theoretical results. Baughman et al.31 recognize this difficulty and suggest that a neutron diffraction experiment would resolve the problem. The differences between the two kinds of measurement can be as much as 0.02 A.32*33 The agreement in the bond angles between the X-ray and our S C F optimized structure is quite good, most importantly in the CCC angles. The CCC bond angles of about 124' for the all-trans molecule are seen in ab initio calculations of up to C22H24.34 MNDO optimized geometries for H(HC=CH),H for n = 4 to n = 10 also show little change.3s This is evidence that the structural parameters for polyacetylene may be well approximated by those of octatetraene. There are no experimental structures for the cis-transoid configuration, but the geometries compare well with previous ab initio structure^.^^ The major effect is the skeletal bond angles increasing to 127' due to nonbonded interactions. Because the (31) Baughman, R. H.; Kohler, B. E.; Levy, I. J.; Spangler, C. Synth. Met. 1985, I I , 3 7. (32) Hazell, A. C.; Larsen, F. K.; Lehmann, M. S. Acta Crystallogr. 1972, 828, 2977. (33) Herndon, W. C. J . Am. Chem. SOC.1974, 96, 7605. (34) Villar, H. 0.;Dupuis, M.; Watts, J. D.; Hurst, J. B.; Clementi, E. J . Chem. Phvs. 1988.88. 1003.
(35) Boudreaux: D.'S.; Chance, R. R.; Bredas, J. L.; Silbey, R. Phys. Rev. B 1983, 28, 6927. (36) Kirtman, B.; Nilsson, W. B.; Palke, W. E. Solid State Commun. 1983, 46, 791.
Hamilton and Pulay
2344 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 TABLE 111: C-C Stretching Force Constants from This Work and from Hemley et al.' SQM Hemley et al.
cis f(C,=C,) 8.574 f(C,-C,) 4.977 f(C,=C4) 8.297 f(C4-C5) 4.969 f(CI=C2,C2-C3) 0.528 f(C2-C3,C3=C4) 0.521 ~ ( C ~ = C ~ , C ~ - C S ) 0.581 ~ ( C I = C ~ , C ~ = C ~-0.202 ) ~ ( C Z - C ~ , C ~ - C ~ ) -0.048 f(c3=c4,c5=c6)
-0.229
0.051 f(CI=C2,C4-C5) ~ ( C Z - C ~ , C ~ = C ~ ) 0.049 f(cI=c2,cJ=c6) -0.030 f(C2-C,,C6-C7) -0.016 ~ ( C I = C ~ , C ~ - C ~ ) 0.014 f(Cl=C2,C,=Cg) 0.001
trans
cis
trans
8.577 5.059 8.294 5.115 0.523 0.486 0.536 -0.185 -0.09 1 -0.197 0.075 0.076 -0.030 -0.008 0.017 0.003
8.465 5.634 8.126 5.737 0.749 0.807 0.844 -0.142 0.023 -0.147 0.030 0.028 -0.018
8.494 5.593 8.061 5.658 0.746 0.706 0.741 -0.142 -0.048 -0.146 0.028 0.026 -0.016 -0.006 0.004 -0.002
-0.006 0.004 -0.003
'The data are from Tables IV and VI in ref 17 QCFF force fields will be compared with the SQM ones in detail, the QCFF structural information from ref 11 and 17 are included in Tables I and 11. Note that the CCC angles are 2-3" smaller in the QCFF structures for both the all-cis and all-trans cases. This and other differences in the reference geometries will cause some of the differences in the force constants and vibrational frequencies. Force Field. In line with the SQM philosophy, most scale factors have been taken from our previous study on small unsaturated compounds.22 The extra correlation scale factor a , described in the calculations section, was determined from a frequency fit. Most frequencies change less than 1 cm-l if a is varied between 0 and 2; only three C=C stretchings around 1600 cm-I show shifts larger than 5 em-'. Figure 3 shows the experimental C=C frequencies and the calculated ones for a = 0, 1 and 2. It is seen that a 2 gives the best fit to the experimental band pattern, indicating that the calculations of Szalay et recover about half of the correlation corrections to the C-C coupling constants. The out-of-plane frequencies, calculated with the original scale factors,22show a slight but systematic deviation from the experimental values. Table 111 compares the values of the C C stretching force constants from the present SQM treatment with the QCFF results of Hemley et aI.l7 The signs of the force constants show the expected sign alternation for all cases except for f(C2-C3,C,-C5) in the all-cis QCFF force field. The magnitude of the couplings decreases with the number of intervening carbon atoms, being insignificant between the two terminal C=C bonds. In general, the two stretching force fields agree remarkably well, the major difference being that the nearest-neighbor interactions are smaller in our force field while the more distant couplings are larger. The diagonal C=C stretching constants agree closely, whereas the SQM diagonal C-C values are 10% below the QCFF ones. On the basis of the previous good performance of the SQM model, we believe that the present results are more reliable than previous ones. The force fields of the trans and cis isomers are similar to each other. The nearest-neighbor interactions in the cis isomer are slightly larger. The primary differences are in the torsional coordinates, since nonbonded interactions in the planar &,cis conformation destabilize it relative to the twisted conformations. This results in the expected decrease in the force constants for torsion about the central C-C and C=C bonds and hence lower frequencies. The force fields in this study are very similar to the SQM force fields for the corresponding butadiene22and hexaexcept for the carbon-carbon stretches, which have been scaled differently.
=
(37) Bock, C. W.; Panchenko, Y. N.; Krasnoshchiokov, S. V.; Pupyshev, V. 1. J . Mol. Srrucr. 1986, 148, 131.
TABLE IV: In-Plane Frequencies and IR Intensities for trans ,trans- 1,3,5,7-0ctatetraene'
approxb character
proposed assgnt
freq
int
cent, term bend CH, rock C-C str C-C str vinyl CH rock trans CH rock cent CH rock CH, scis C=C str C=C str cent, vinyl CH str cent, trans CH str trans CH, CH, str vinyl CH str CH2 str
215 334 528 954 1124 1187 1288 1304 1316 1441 1614 1617 3018 3021 3027 3035 3103
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
cent bend term, cent bend mid bend CH, rock C-C str trans CH rock vinyl CH rock cent CH rock CH2 scis C=C str C=C str trans, vinyl CH str cent, vinyl CH str CH,, cent CH str vinyl, cent CH str CH, str
84 377 559 929 1138 1245 1293 1317 1423 1584 1634 3019 3024 3030 3037 3102
mid, term bend mid bend
a,
exptl deuterated ref freq int
242 353, 340 546 958 1138 1187, 1180 1285, 1284 1304
5 191 5, 42 313 5 457 38 744 38 899 5,42 952 5, 42 1022 38 1029 1161 1432 38 1192 1608. 1607 5, 42 1540 1612 5 1570 3005 br 38 2203 3005 br 38 2225 3005 br 2244 38 3005 br 38 2251 3090 38 2310
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
bu 1.7 -108 5.0 4.1 565 5.6 940 28.2 1138 10.5 1229 39.6 1279 10.8 6.9 1405 7.5 21.8 1631 1.2 2920 6.2 2955 18.1 2988 90.7 3009 41.3 3070
42 38 38 38 38 38 38 38 38 38 38 38 38
16 328 500 741 903 933 1012 1055 1148 1514 1584 2203 2228 2241 2250 2309
1.4 3.0 2.2 11.9 8.7 11.7 12.1 15.1 10.3 10.8 9.3 6.7 30.0 1.5 25.3 20.3
"Frequencies in cm-' and intensities in km mol-'. bTerm, mid, and cent bend refer to skeletal bends of the CCC angles from the outermost to the central ones, respectively. The types of hydrogen atoms from the end to the center are termed CH2, vinyl, trans, and cent, respectively. The complete force field, including the definition of the internal coordinates, is included in the supplementary material (Tables VIII-XI; see paragraph at the end of the paper). In-Plane Modes of the All-Trans Molecule. The calculated in-plane fundamental frequencies for the trans,trans- 1,3,5,7-octatetraene are listed in Table IV alongside the experimental frequencies. Most of the original spectrum was taken from Lippincott et al.38 Some additional Raman peaks were resolved in unpublished spectra by Holtom et al., as given in Table VI1 Note that Hemley et in the review of Hudson et accepted the assignments given by Hudson et aL5 In light of the present results, however, some of this assignment needs correction. The perdeuterated frequencies are also reported in the tables; they are listed only in order of increasing frequency. The predicted pattern of the C-H stretches is significantly different from the results of Hemley et al.,17 no doubt because of the differences in the predicted relative C-H bond lengths. On the basis of the excellent performance of the ab initio method in predicting relative C-H bond lengths and isolated C-H freq u e n c i e ~ we , ~ ~are confident that the ab initio method is more accurate. As usual for C-H stretching vibrations, anharmonicity contributions are very significant but are not expected to affect the relative positions of the bands. The next four fundamentals are C=C stretches. These modes are the ones that the SQM describes rather poorly before the extra (38) Lippincott, E. R.; Feairheller, W. R.; White, C. E. J . Am. Chem. Soc. 1959, 81, 1316. (39) McKean, D. C.; Boggs, J. E.; Schafer, L. J . Mol. Srrucr. 1984, 116, 313.
all-trans- and all-cis- 1,3,5,7-Octatetraene scaling of the coupling constants. The splitting of the two SQM ag modes is in excellent agreement with experiment; as mentioned by Hemley et a1.,I7 this splitting is highly dependent on the interaction constants and is a useful test of the off-diagonal elements of the force constant matrix. The calculations predict two infrared-active b, fundamentals in the 1600-cm-I spectral region, a strong and a medium one, separated by about 50 cm-' (Table IV). Hemley et al.17 predict essentially the same pattern, although they do not calculate the intensities. They identify, however, the lower fundamental (predicted at 1585 cm-' by us) with the observed IR band at 1631 cm-', leaving the higher band (1635 cm-' in Table IV) unassigned. We believe that an error of this magnitude is unlikely. Instead, the observed 1631-cm-I band should correspond to the higher b, C=C fundamental, and there must be a band near 1580 cm-I. Unfortunately, the spectrum shown by Lippincott et al.3s does not cover the spectral range between 1540 and 1600 cm-'. The early spectrum of Woods and Schwartzman" shows a band at about 1575 cm-I. However, this coincides with a CS2 absorption, and it is not clear how reliable this early measurement is; very few experimental details are given in ref 40. A remeasurement of the spectrum would be highly desirable and is planned at the University of Arkansas. We note that a recent remeasurement of the vibrational spectrum of hexatriene by McDiarmid and Sabljic4' has led to a substantial modification of the assignment of the fundamentals. The C H 2 scissor modes at 1405 and 1432 cm-' are in good agreement with our calculated values, which are essentially identical with those of Hemley et a1.I7 The situation is less clear for the IR spectrum in the 1170-1400-cm-' range, where only the three C-H rocking modes are expected to appear. In the spectra of Lippincott et al.38there are five well-defined lines (1 179, 1190, 1229, 1279, and 1373 cm-') and two shoulders (1290 and 1340 cm-l) in this range. Obviously, there is either strong Fermi resonance or possibly contamination. Our assignment given in Table IV for this region is tentative. Neither the broad band, at 1370 cm-I nor the shoulder at 1340 cm-l in the IR spectrum is Considering considered to be a fundamental by Lippincott et that the calculated intensity of the central C-H rocking mode is fair, the 1373-cm-' band is the obvious candidate. It is, however, too high for our calculated frequency (1 3 17 cm-I) and also that of Hemley et aI.l7 (1334 cm-I). A remeasurement of the IR spectrum of both the light and perdeuterated species appears to be necessary to clarify the assignment in this range. The remaining C-H rocking bands can be clearly identified, and we agree with the previous a ~ s i g n m e n t . ~ The 900-1200-cm-' spectral region shows a multitude of overlapping bands. The strong, broad Raman line at 1185 cm-' was thought to contain more than one fundamental by Lippincott et and in the subsequent paper by Hemley et aI.,l7 on the basis of their calculated values of the two ag C-C fundamentals, 1188 and 1181 cm-'. Our calculations predict a much larger splitting of these bands, 1 124 and 1187 cm-I, in good agreement with the two observed Raman lines at 1138 and 1187 cm-l. Hemley et al.17 accept the unpublished assignment of Holtom et al. for the former mode as a CH2 rocking fundamental. The disagreement with the calculated values, both ours and those of Hemley et al.,I7 is, however, unacceptable (calcd 954 or 950 cm-', exptl 1138 cm-I). Our assignment, shown in Table IV, appears more convincing. The weak IR band at 940 cm-' that has been unassigned until now seems to be a fundamental made up primarily of C H 2 rocking. Previous calculated values near 940 cm-' have assigned 1096 cm-' as the corresponding fundamental, a clearly unacceptable discrepancy. The six lowest frequencies for the trans,trans isomer are skeletal bends. We agree with Hemley et al.I7 that these modes have been misassigned. The weak, broad peak at 649 cm-I in the IR spectrum has no frequency near it in the SQM force field, so it is probably not a fundamental. The theoretical frequencies (40) Woods, G.F.; Schwartzman, L. H. J . Am. Chem. SOC.1949, 71, 1396. (41) McDiarmid, R.; Sabljic, A. J . Phys. Chem. 1987, 91, 276. (42) Kohler, B. E.; Snow, J. B. J. Chem. Phys. 1983, 79, 2134.
The Journal of Physical Chemistry, Vol. 93, No. 6,1989 2345 TABLE V Out-of-Plane Frequencies and IR Intensities of trans .trans - 1.3.5.7-Octatetraene" approxb proposed exptl deuterated character freq int assgnt ref freq int
mid C-C tors cent C=C tors CH2 tors cent CH wag CH2 wag trans CH wag vinyl CH wag
146 336 654 892 923 943 1011
b, 0.0 0.0 0.0 0.0 0.0 0.0 0.0
a, 58 0.3 cent C-C tors cent C=C tors 167 0.8 cent, mid C-C tors 239 0.7 CH2 tors 617 10.9 trans CH wag 843 3.9 CH2 wag 926 96.6 vinyl CH wag 976 19.8 cent, vinyl CH wag 1027 114.2
164 353?
5 5
883 905
38 38
627 839 897 954 1007
38 38 38 38 38
131 276 530 697 724 768 813
0.0 0.0
0.0 0.0 0.0 0.0 0.0
53 0.2 134 0.7 208 0.4 471 6.7 697 1.0 712 44.4 747 81.5 798 2.0
"Frequencies in cm-l and intensities in km mol-'. bCent C-C refers to the central C-C single bond, and mid C-C refers to the other two single bonds. The other abbreviations are explained in footnote b of Table IV. calculated previously near 600 cm-l would better fit the 565-cm-' line (the SQM value is 559 cm-I). The assignment of the 627-cm-' peak to calculated values near 400 cm-' is practically impossible. This frequency fits much better as an out-of-plane fundamental. The lowest two in-plane IR modes have evidently not been observed. The three lowest Raman peaks have been correctly assigned by Hudson et aLs The relative values of the SQM Raman frequencies match the experiment very well, but they are systematically too low by 18 cm-'. Out-ofplane Modes of the All-Trans Molecule. The outof-plane frequencies are listed in Table V. The assignment of the four IR-active C-H wagging vibrations is clear and remains the same as previ~usly.~ Note that as demonstrated for butathe reliability of the scaled ab initio method is much better for the out-of-plane modes than the semiempirical method used in ref 17. The QCFF method overestimates these frequencies twice as much as the SQM procedure does. In the theoretical Raman spectrum, our highest b, frequency is 997 cm-', significantly lower than the 1039 cm-' given in ref 17. We believe that our value is too far from the 1080-cm-' line to entertain the possibility that they are the same mode; therefore, the 108O-cm-' line does not appear to be a fundamental. The theoretical 943-cm-' wagging does not have an obvious experimental counterpart, especially considering the tendency of the theoretical frequencies to overestimate the wagging frequencies. In our assignment, the 958-cm-' Raman band corresponds to an in-plane vibration. As a result, we believe that the highest two Raman active wags probably have not been observed. The other two Raman C-H wags have been correctly assigned previously. Of the remaining seven out-of-plane modes, only three can be definitely assigned. The three lowest a, modes have very small calculated intensities; hence they will be very difficult to observe. The 627-cm-' IR band, previously assigned to an in-plane fundamental, fits well the fairly intense a, CH2 torsion. We believe that the 816-cm-' band is not a fundamental. The assignment of the calculated fundamental at 608 cm-' to the 816-cm-' band was already questioned by Hemley et al.17 The highest Raman-active torsion, calculated to be at 654 cm-I, is too far from the previously assigned 722-cm-' line to consider the latter a fundamental. This is also supported by the semiempirical results, which are even lower. The next lower b, fundamental has a SQM frequency of 333 cm-' and is thus nearly degenerate with one of the in-plane Raman frequencies. The assignment of the experimental 353-cm-' line to this one instead of the in-plane fundamental, or to both, is reasonable. The assignment of the 223-cm-l Raman peak to this fundamental can be excluded. The lowest
2346 The Journal of Physical Chemistry, Vol. 93, No. 6,1989
TABLE VII: Out-of-Plane Frequencies and IR Intensities for cis ,cis - 1,3,5,7-0ctatetraenea
TABLE VI: In-Plane Frequencies and IR Intensities for cis ,cis - 1,3,5,7-0ctatetraenea
approxb character
freq
mid bend term bend cent bend CH2 rock C-C str C-C str trans, cent CH rock vinyl CH rock cent CH rock CH2 scis C=C str C=C str cent, vinyl CH str trans, cent CH str CHI, trans CH str vinyl CH str CHI str
200 337 723 875 1014 1182 1283 1307 1397 1465 1602 1614 3023 3028 3052 3069 3103
cent bend term bend mid bend CH, rock C-C str trans, cent CH rock vinyl CH rock cent, trans CH rock CH2 scis C=C str C=C str trans, vinyl CH str cent, vinyl CH str CHI, cent CH str vinyl, cent CH str CH2 str
113 363 562 916 1126 1254 1308 1367 1430 1569 1626 3023 3029 3053 3078 3105
int a8
Hemley et al.c
deuterated freq int
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
244 376 750 90 1 1058 1230 1263 1317 1420 1484 1590 1614 2986 3063 3078 3080 3095
184 299 647 743 816 951 974 1039 1099 1274 1531 1568 2207 2231 2262 2271 2310
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 36.0 4.8 10.6 2.3 1.1 12.1 8.1 5.9 10.6 2.1 12.1 13.7 5.9 28.3 50.5
142 439 614 923 1182 1228 1314 1395 1447 1550 1619 2986 3063 3078 3089 3098
102 315 518 739 862 939 1030 1054 1186 1507 1574 2206 2230 2262 2276 2310
0.0 24.5 7.1 5.6 0.8 0.1 23.9 5.7 6.2 8.9 0.7 4.7 6.3 6.9 18.6 21.3
b"
Hamilton and Pulay
Frequencies in cm-' and intensities in km mol-'. bSee footnote b of Table IV for definition of abbreviations. CTheHemley et al. calculated values are from Table XI11 of ref 17. theoretical Raman-active mode corresponds quite nicely to the observed 164-cm-I peak. All of the torsional modes that can be safely assigned are about 18 cm-l too low in the SQM force field compared to experiment, which is the same trend seen for the skeletal bending motions. Fundamentals of the All-Cis Molecule. Since there are no experimental spectra for the cis,& isomer, comparisons will be made with the trans,trans isomer. The SQM frequencies and intensities are given in Tables VI and VI1 for the in-plane and out-of-plane vibrations, respectively. The C-H stretches increase upon isomerization except for the CH2 group. This is because of the shorter C-H bonds in the crowded all-cis isomer. The C = C stretches decrease by a few wavenumbers, with the splittings between the modes of the same symmetry increasing. The highest two C-C stretching frequencies decrease by a few wavenumbers also, but the lowest C-C stretch drops a dramatic 110 cm-' in going to the all-cis form. The lengthening of the middle C-€ bond because of nonbonded repulsion is responsible for this effect. The central C-H rocking frequencies increase by 50 and 81 cm-', and the C H 2 rocking modes decrease by 13 and 79 cm-'. The most dramatic change is in the central skeletal bend, which increases by 195 cm-I! Again, the increases are seen in modes that increase the nonbonded repulsions, whereas the decreases are due to changes in the equilibrium geometry such as longer C-C bonds and a more acute H-C-H angle on the terminal C H 2 groups. The lowest torsional frequencies in the cis isomer are below those of the trans. The steric strain in the skeletal angles, as seen by the interior angles of 127O, destabilizes the planar conformation relative to the twisted one. This results in a lower torsional barrier and hence lower frequencies. The other out-of-plane modes, the
approxb
character
freq
mid C-C tors cent C=C tors CH2 tors cent CH wag CH2 wag trans, cent CH wag vinyl CH wag
122 397 687 809 928 970 1011
cent C-C tors mid C-C tors cent C=C tors CH2 tors trans CH wag CH, wag vinyl CH wag trans, cent CH wag
40 113 288 606 788 930 987
I010
int b,
Hemley et ale
deuterated freq int
0.0 0.0 0.0 0.0 0.0 0.0 0.0
143 420 635 754 940 953 1044
106 315 550 665 712 781 815
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.1 0.2 0.2 54.1 16.9 133.8 13.0 11.7
53 143 322 617 777 947 987 1031
37 91 253 450 633 711 775 801
0.0 0.1 0.3 33.2 7.3 77.2 1.7 7.6
a"
"Frequencies in cm-I and intensities in km mol-'. bSee footnote b of Table V for the explanation of the abbreviations. CTheHemley et al. calculated values are from Table XI11 of ref 17. C-H wags, are little affected by whether the molecule is cis or trans. The predicted pattern of the C-H stretching frequencies differs in the SQM and the PPP-CI force fields for the di-cis molecule, just as for the all-trans one. The C=C frequencies agree well, but not the single bond C-C stretches: the PPP-CI frequencies are consistently 50 cm-' higher. Even though the two force fields give good frequencies for the experimentally measured trans,tram-octatetraene, the differences in the C-C stretches predicted for cis&-octatetraene indicate that there are significant differences in the relevant force constants. As pointed out earlier, the normal SQM carbon stretching coupling constants are too small and the QCFF ones may be too large for nearest neighbors. The skeletal bending and torsional modes are also consistently higher than the PPP-CI results by an average of 45 and 24 cm-l, respectively. The differences between the SQM wagging frequencies and those from the QCFF force field are not as significant. The only exceptions to these trends were that the QCFF Raman-active CH2 torsion and central C-H wag were lower than the SQM by 52 cm-l. We hope that the vibrational spectra of the cis,cis isomer could be measured to evaluate these differences.
Conclusions We conclude that the following IR frequencies should not be considered fundamentals on the basis of the SQM force field and semiempirical force fields calculated by previous workers: 649, 816, and 1096 cm-'. The Raman peaks that should not be considered as fundamentals are 223, 722, and 1080 cm-'. The IR peak at 940 cm-' should be considered a fundamental, and a medium intensity peak is predicted at 1580 cm-I in the IR spectrum. In addition, the Raman peak at 1187 cm-I is probably not degenerate. Also, the peak at 627 cm-' is most likely an out-of-plane mode, and the 958-cm-' peak is probably an in-plane vibrational mode. Even though the two force fields agree very well on the experimentally known trans,trans carbon stretching frequencie, there is a significant difference in the calculated cis& C-C stretches. Much of the disagreement in the force fields may be related to the choice of reference geometry; this is certainly the case for the discrepancy in the C-H stretching modes. As previously demonstrated for butadiene, the SQM method does a better job of predicting the out-of-plane modes; however, both the SQM and QCFF methods generally overestimate the C-H wagging frequencies. Note Added. While our manuscript was being reviewed, two related papers appeared. Yoshida and Tasumi [J. Chem. Phys. 1988, 89, 28031 remeasured the vibrational spectrum of all-
J . Phys. Chem. 1989, 93, 2347-2358 trans-octatetraene and have reassigned it using ab initio S C F frequencies scaled by our technique. Although they do not correct for electron correlation as we do here, their scaled results are in good agreement with ours. Their proposed final assignment of the light molecule is essentially identical with ours. It is particularly pleasing that our prediction of a medium infrared band near 1580 cm-' has been borne out by the new experiment. Several other weak bands that were predicted by theory have also been found. Another, very recent paper on this subject has been published by Zerbetto et al. [ J . Chem. Phys. 1988, 89, 36811.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American
2347
Chemistry Society, for support of this research. The calculations were performed with a Celerity 1200 minicomputer, purchased with support of the National Science Foundation, under Grant NO. CH-8500487. Registry No.
all-trans-l,3,5,7-0ctatetraene,3725-31-3; all-cis-
1,3,5,7-octatetraene, 1871-50-7.
SuppBementary Material Available: Definition of the in-plane and out-of-plane internal coordinates (Tables VI11 and IX) and the scaled force constant matrices for all-trans- and all-cis-octatetraene (Table X-XIII) (6 pages). Ordering information is given on any current masthead page.
Twisted Internal Charge Transfer Molecules: Already Twisted in the Ground State C. Cazeau-Dubroca,* S. Ait Lyazidi, P. Cambou, A. Peirigua, Centre de Physique MolPculaire Optique et Hertzienne, UA 283, UniuersitP de Bordeaux I , 351 Cours de la LibPration, 33405 Talence. France
Ph. Cazeau, Laboratoire de Chimie Organique de I'Etain et du Silicium, UA 35, UniversitP de Bordeaux I , 351 C o w s de la LibPration, 33405 Talence, France
and M. Pesquer Laboratoire de Physico-chimie ThPorique, UA 503, UniuersitP de Bordeaux I, 351 Cours de la Liberation, 33405 Talence, France (Received: September 4, 1986; In Final Form: April 25, 1988) Starting with the experimental spectroscopicstudy of para-substituted N,N-dialkylanilines in solutions, we show the deforming effect of hydrogen bonds on the conformation of the amine in the ground state, which is planar when the molecule is isolated. The twisted conformation thus acquired causes spectroscopicanomalies: anomalous red shift (ARS) and dual fluorescence. We simulated by intermolecular interaction calculations the twisting influence of water molecules on the amine in the ground state. These simulationsconfirm our hypothesis. The importance of the twisting is seen to increase as more water molecules-up to three-cluster around the amine. We made a correlation between the relative intensity of the anomalous fluorescence and the probability of a twisted conformation of the molecule, as related to the quantity of water contained in the solvent. In general, we conclude that the molecule must have a twisted conformation when still in the ground state to allow the anomalous fluorescence to appear.
Introduction The anomalous dual fluorescence, discovered by Lippert' for p-(dimethy1amino)benzonitrile (DMABN) in solution, has provoked studies of the spectroscopy of stationary s t a t e ~ ' - ~as* well as of time-resolved s p e c t r o ~ c o p y . ' ~Several -~~ models have been proposed (successively) to account for the anomaly. Lippert et al.' suggested an inversion of states SI and S2due to the solvent; Mc Glynn et proposed the formation of an excimer, Kosower et ale3thought that a proton was transferred in the excited state, Chandross et aL4proposed a complexation with the solvent, Visser et suggested formation of exciplexes with free electron pairs of the solvent, and Rotkiewicz and Grabowski worked out the so-called twisted internal charge transfer (TICT) mode1.6T21 This model shows clearly that the abnormal fluorescence Fa, of greatest ~
~~~
~~
~
(1) Lippert, E.; Luder, W.; Boos, H. In Aduances in Molecular Spectroscopy; Mangini, A., Ed.; Pergamon: Oxford, 1962; p 443. (2) Khalil, 0.S.; Hofeldt, R. H.; Mc Glynn, S . P. Chem. Phys. Lett. 1972, 19, 479. Khalil, 0.S.;Hofeldt, R. H.; Mc Glynn, S. P.J. Lumin. 1973, 6, 229. Khalil, 0. S.; Meeks, J. L.; Mc Glynn, S. P. Chem. Phys. Lett. 1976, 39, 457. (3) Dodiuk, H.; Kosower, E. M. Chem. Phys. Lett. 1975, 34, 253. Kosower, E. M.; Dodiuk, H. J. Am. Chem. SOC.1976, 98, 924. (4) Chandrass, E. A. Exciplex; Gordon, M., Ware, W. R., Eds.; Academic: New York, 1975; p 187. (5) Rotkiewicz, K.; Grellmann, K. H.; Grabowski, Z . R. Chem. Phys. Lett. 1973, 19, 315. (6) Rotkiewicz, K.; Grabowski, Z . R.; Krowczynski, A,; Kiinnle, W. J. Lumin. 1976, 12/13, 877.
0022-3654/89/2093-2347$01 S O / O
wavelength, is due to a state with a strong charge-transfer character. This character is brought about by a twisted conformation that the molecule acquires in the excited TICT state. The idea of TICT molecules has since been extended to other classes of molecules with anomalous double fluorescence. These molecules have either an aromatic structure with an acceptor and a donor group in para positions21cg22or two identical aromatic (7) Lipinski, J.; Chojnacki, H.; Grabowski, Z. R.; Rotkiewicz, K. Chem. Phvs. Lett. 1978. 58. 379. 18) Kirkow-Kaminska, E.; Rotkiewicz, K.; Grabowska, A. Chem. Phys. Lett. 1978, 58, 379. (9) Rettig, W.; Wermuth, G.; Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1979, 83. 692. (10) Rettig, W.; Bonavicic-Koutecky, V . Chem. Phys. Lett. 1979, 62, 115. Rettie. W.: Zander. M. Chem. Phvs. Lett. 1982. 87. 229. (1:) Nakashima; N.; Inoue, H.IMataga, N.; Yamanaka, C. Bull. Chem. Soc. Jpn. 1973, 46, 2288. (12) Nitsche, K. S.; Suppan, P. Chimia 1982, 36(9), 346. (13) Suman, P.; Guerrv-Buttv, E. J. Lumin. 1985, 33, 335. (14) Nikashima, N.; Mataga,-N.Bull. Chem. SOC.Jpn. 1973.46, 3016. (15) Struve, W. S.; Rentzepis, P. M.; Jortner, J. J . Chem. Phys. 1973, 59,
5014.
(16) Struve, W. S . ; Rentzepis, P. M. J. Mol. Sci. 1978, 47, 273. ( 1 7) (a) Struve, W. S.; Rentzepis, P. M. J. Chem. Phys. 1974,60(4), 1533. (b) Struve, W. S.; Rentzepis, P. M. Chem. Phys. Lett. 1974, 29(1), 23. (c) Huppert, D.; Rand, S. D.; Rentzepis, P. M.; Barbara, P. F.; Struve, W.S.; Grabowski, Z. R. J. Chem. Phys. 1981, 75(12), 5714. (d) Hilinski, E. F.; Rentzepis, P. M. Acc. Chem. Res. 1983, 16, 224.
(18) (a) Wang, Y.; Mc Auliffe, M.; Novak, F.; Eisenthal, K. B. J. Chem. Phys. 1981, 85, 3736. (b) Wang, Y.; Crawford, M. C.; Eisenthal, K. B. J. Am. Chem. SOC.1982, 104, 5874. (c) Wang, Y.; Eisenthal, K. B. J . Chem. Phys. 1982, 77(12), 6076.
0 1989 American Chemical Society
