J. Phys. Chem. 1994,98, 9133-9136
9133
Excited State Dipole Moments from an Efficient Analysis of Solvatochromic Stokes Shift Data? M. Ravi, A. Samanta,' and T. P. Radhakrishnan' School of Chemistry, University of Hyderabad, Hyderabad 500 134, India Received: January 26, 1994; In Final Form: June 6, 1994'3
It is shown that the solvatochromism of Stokes shifts has superior correlation with the solvent polarity function ET^, and the theoretical basis for this is analyzed. The estimation of reliable excited state dipole moments from this correlation as well as the practical advantage of the method in terms of the possibility of employing mixed solvents is demonstrated.
Introduction The knowledge of excited state charge distributions and dipole moments is important in understanding photochemical processes. A prior knowledge of the excited state dipole moment helps to assess the efficacies of quantum chemical derivations of wave functions as well as electron correlation treatments. Lately, there has been a renewed interest in understanding excited state dipole moments, in connection with the design of organic molecules having large hyperpolarizabilities to fabricate efficient nonlinear optical materials.' The growing interest in the phenomenon of twisted internal charge transfer (TICT)Z processes also has brought to focus the relevance of the excited state characteristics. Even though the more equipment-intensive methods like fluorescence polarization,3 electric d i c h r o i ~ mStark , ~ splitting of rotational levels,5 and microwave conductivity6 are considered to be more accurate, the popular method for the experimental determination of excited state dipole moments is based on the analysis of the solvatochromism of absorption and/or fluorescence maxima. In the latter procedure, based on the early experiments of Lippert' and Mataga,8 one normally follows the variations of absorption maxima, fluorescence maxima, or Stokes shift with solvent polarity. Innumerable formulations of this linear relation are known; the review of Koutekg has an exhaustive compilation. Only some of these formulations show good correlation between experimental and theoretical solvatochromicdata, and when they do, it is only under optimal conditions in terms of the number and the choice of solvents. We note that all these models utilize bulk solvent properties like dielectric constant and refractive index to represent the solvent polarity functions. Though the choice of the correct Onsager cavity radius is admittedly a serious problem, the former may further impair the efficacy of the solvatochromism method for the evaluation of excited state dipole moments. During the course of our investigation of the TICT systems and molecules of interest in the design of nonlinear optical materials, we have observed that the Stokes shift data of several molecules showed excellent correlation with the solvent polarity measure, ET^ (or, equivalently, E ~ ( 3 0 )proposed ) by Reichardt.10
Though such correlations have been noted previously,11no detailed analysis has been reported. In this paper we first delineate the theoretical basis for the correlation of solvatochromic Stokes shift data with the ETN parameter. The expressions derived facilitate the direct determination of the excited state dipole moments. f
Dedicated to Prof. C. N. R. Rao on his 60th birthday. published in Advance ACS Abstracts, August 1, 1994.
a Abstract
0022-3654/94/2098-9133%04.50/0
Subsequently, we present an appraisal of thequality of the excited state dipole moments derived from these correlations. Finally, the relevance of this approach from an experimental point of view in terms of the use of mixed solvents is demonstrated.
Theoretical Section Following the formulation of K ~ u t e k the , ~ linear relation between the Stokes shift of a molecule (m) in solvent (s) represented by Y(m,s) and the solvent polarity function X ( s ) is given by Y(m,s) = B(m) X(s) + W m , g ) -
(1)
-
We take Y(m,s) as v, - vf ( j , = wavenumber of absorption, if= wavenumber of fluorescence; one of these may be solvent independent in some cases) and P ( m , g ) is a constant independent of the solvent, sometimes related to the compound in the gas phase. B(m), the regression coefficient, and a commonly used X ( s ) are given by
where A p = pe - pg (pg and pe are the ground and excited state dipole moments), h is the Planck's constant, c is the velocity of light, D and n are the dielectric constant and refractive index of the solvent, respectively, and a is the Onsager radius of the solute molecule. If now we consider X ( s ) = ET^, the B(m) can be obtained as follows. Consider the application of eq 1 to the solvatochromic absorption data of the pyridinium N-phenoxide betaine dye proposed originally by Reichardt et al.15 as a measure of the solvent polarity and which has now become the basis of the ET(30) scale. The dye is not at all fluorescent, and hence one can only follow the shift of absorption maximum with change in solvent polarity. Since the pe (=6 D) of the dye is considerably smaller than pg (=15 D), we can make the safe assumption that the solvatochromic shift of the fluorescence peak, if any, will be negligible -compared to the shift of the absorption peak. Hence, Y(m,s) = v, - constant. Therefore, we can rewrite eq 1 for the Stokes shifts of the dye using the common formulation9 of B(m) (eq 2), but without specifying the nature of X ( s ) , as
where A ~ =D9 D, the change in dipole moment on excitation of the dye, and UD is its Onsager radius. Y(m,g) is a modified 0 1994 American Chemical Society
9134
Ravi et al.
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994
TABLE 1: Correlation Coefficients for the Fit of the Stokes Shifts with the Solvent Polarity Functions EP, Fz(D,n), and F,(D,n) for Different Compounds compound ET^ Fz(D,n)“ F,(D,n)” Nb ref 4-(dimethylamino)-4’-nitrostilbene 0.984 0.843 0.852 13 12 hexamethylbenzene-tetrachloro0.925 0.784 0.790 8 12 phthalicanhydride(CT complex) 4-amino-4’-nitrostilbene 0.968 0.921 0.919 14 13 0.904 0.815 0.774 8 14 1-dicyanovinylnaphthalene 0.861 0.746 0.705 8 14 9-dicyanovinylphenanthrene 0.674 0.703 0.696 8 14 9-dicyanovinylanthracene 0.935 0.863 0.818 8 14 1-dicyanovinylpyrene 6-propionyl(dimethylamino) 0.965 0.943 0.933 8 c naphthalene 0.826 11 c 4-(dimethylamino)phthalimide 0.895 0.840 0.977 0.970 0.962 8 c 4-aminophthalimide This follows the nomenclature of K ~ u t e k for ; ~ Fz(D,n),see text; F,(D,n) is the function used in the respective references. The number of data points in the correlation analysis. Soujanya, T.; Samanta, A. Unpublished results. constant. Using the definition of E ~ ( 3 0 in ) terms of ia,eq 4 can be transformed to
x(S)= 349{hCU~~/2(Ap~)~jE,(30) + y’(m,g)
(5)
To avoid dimensionality problems, the normalized value of ET(30), namely ET^, is employed, so that
+
X ( s ) = 11307.6{h~u,~/2(Ap~)~)E~~ Y”(m,g)
(6)
This treatment of solvatochromism of the dye has thus led to an expression for X ( s ) which may be substituted back into eq 1, so that we arrive at the following working expression: Y(m,s) = 11307.6{(Ap/ApD)2(aD/a)3)ETN
+ P(m,g)
(7)
Equation 7 clearly illustrates that Stokes shift data will have a linear dependence on ET^ values of the solvent. It also shows that A p of the molecules of interest can be extracted from the slopes if standard values for A ~ and D a D are available and an estimate of a is known. It is also significant to note that since a ratio of U / U D is involved, errors involved in the estimation of Onsager radius may be obviated to some extent.
Experimental Section The absorption and fluorescence maxima of various compounds were measured on a Perkin Elmer spectrophotometer (Model Lambda 3B) and a Hitachi spectrofluorimeter (Model 3010), respectively. Spectroscopic grade solvents (Aldrich) were used. They were freshly distilled from P205 and collected over 4A molecular sieves. Betaine dye, received from Prof. Reichardt, was used without any further purification. p-(N,N-Dimethylamin0)benzonitrile (DMABN) was purified by vacuum sublimation followed by recrystallization from hexane.
Results and Discussion We have analyzed the solvatochromic changes of Stokes shifts of several molecules from reported data and our own experiments in termsof a variety of solvent polarity functions. Table 1 provides the correlation coefficients for several systems for the following solvent functions, X ( s ) : (i) the E T N values, (ii) the function Fz(D,n) ( X ( s ) in eq 3) recommended by Koutekg on the basis of a detailed statistical analysis of 16 different model equations, and (iii) the functions used in the original papers. In the statistical analysis, we have excluded those solvents which may have specific local interactions with the probe molecules. It is seen that the Stokes shift data correlate a lot better with ET^ values of the solvent rather than the other bulk solvent polarity
5v 5
I
V 7 ADect,mate
9 r x 1 0 ’ c”)
5
7 AEostlmato
9 ( X 1 0 3 cni’)
Figure 1. Plots of experimental Stokes shift data of DNS versus the Stokes shifts estimated from the fit of the experimental values against the solvent polarity measures: (a) ET^ and (b) Fz(D,n) (see text for explanation).
functions used by the original authors or the one recommended by Koutek. An example is illustrated graphically in Figure 1, which compares the plots of experimental Stokes shifts of 4-(dimethylamino)-4’-nitrostilbene(DNS) versus those estimated using (a) ET^ values and (b) the Fz(D,n) function. Now we turn to the question of extracting the excited state dipole moments from the slopes obtained in the Stokes shift versus ET’ plots. As eq 7 shows, the quality of A p obtained will depend on the accuracy of the Onsager radius for the molecule and the dye. As is well-known, the choice of the Onsager radius is a difficult problem in any solvatochromic method, and this remains so in our procedure as well. However, as noted earlier, partial amelioration of this problem occurs in our procedure since ratios of two Onsager radii are being used. We compare pe from the present analysis with the previous estimates for several molecules in Table 2. The Onsager radius used for each molecule was taken from the original literature. Thevalue of ao was determined through a least-squares fit analysis of the experimental values of AM of the molecules, presented in Table 2 (electrooptical measurements, where available, and previous solvatochromic data), against that calculated using the slope from eq 7. DMABN was not included in this statistical analysis, and its AM given in Table 2 is the one predicted by our procedure as discussed below. The value obtained, 6.2 8, ( r = 0.977), is intuitively meaningful, since it agrees fairly well with the separation of the centers of maximum charge, namely, the N and 0 atoms in the dye (5.8 8, from a molecular mechanics optimization). We note here that even though the original betaine dye as well as its tert-butylsubstituted derivative has been used to prepare the E ~ ( 3 0scale,*O ) since the strong dipole associated with the pyridinium N-phenoxide group is unaffected by the substitution, we assume a single Onsager radius, and the excellence of the correlation bears out thevalidity of this assumption. Table 2 shows that the comparison of the pc from previous literature and from the present analysis using eq 7 and UD = 6.2 8,is good. Since the spread in pe from different experiments is very large, we suggest that the value we obtained here from the analysis which shows excellent correlation of experimental data should be treated as one of the most reliable. A further test of the above result is provided by an independent study we carried out on the prototypical molecule DMABN. This experiment was designed to test two aspects of the present analysis. First, we wanted to check the ability of this procedure to predict excited state dipole moments, which in turn tests the meaningfulness of the slope of the linear regression as well as the choice of the Onsager radius for the dye. Second, we wanted to explore the practical utility of the method in terms of using mixed solvents. From the experimental point of view, solvatochromism studies often become difficult, if the molecule of interest has acceptable solubility only in a very limited number of solvents. The statistical analysis becomes less reliable when the number of data points are few. When mixed solvents are used, to overcome this problem either traditional solvent polarity functions have to be obtained
Excited State Dipole Moments
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9135
TABLE 2 Comparison of pe Obtained from the Present Analysis with Previously Reported Values (Dl compound
a (4
4-(dimethylamino)-4’-nitrostilbene
8.0
7.6
hexamethylbenzene-tetrachloro-
4.5
3.6
4-amino-4’-nitrostilbene
7.2
6.5
4-aminophthalimide 1-dicyanovinylnaphthalene 9-dicyanovinylphenanthrene 9-dicyanovinylanthracene
3.5 3.7 4.4 4.0
1-dicyanovinylpyrene
4.7
3.5 4.7 4.7 4.3 4.8
4-ldimethy lamino) benzonitrile
5.0
6.6
phthalic anhydride (CT complex)
ILg
(D)
solvatochromic method present work previous work (ref) 23.3 25.0 (12) 32.0 (17) 10.5 9.6 (12) 14.0 (17) 20.0
21.0 (13)
5.8
6.7 (20) 7.9 (14) 9.8 (14)
8.6 10.3 7.4 9.9 12.3 13.0”
other methods (ref) 21.9 (3) 23.0 (4) 10.0 (3)
21.0 (18) 22.0 (19) 9 1 (21)
*
7.0 (14)
10.8 (14)
13 k 2 (22a) 12.5 (22b)
16.1 (9)
13.0 (23) 0
Based on the present analysis of the data in ref 24 using the propionitrile-octane mixed solvent system.
TABLE 3 fiN Values Measured for Benzene-Acetonitrile Mixtures of Different Compositions vol % of acetonitrile ErN vol % of acetonitrile 20 0.286 70 30 40 50 60
0.312
0.349 0.360 0.379
80 90 100
-
ET^
I
0.397
through detailed experiments on each mixture to determine its dielectric constants, refractive index, etc., or these values have to be approximated from empirical rules. Further, for some pairs of solvents these functions may not be very sensitive to small changes in composition. E T N on the other hand is very sensitive to composition changes and can be easily measured experimentally using the absorption of the dye. It may also be noted that extra precautions to purify the solvents can be relaxed, since the solvent polarity function is being experimentally determined and used. Of course, impurities that may cause undesirable specific interactions with the probe molecule should be excluded; also, high percentages of solvents with specific interactions may be undesirable. (We are currently looking into the latter aspect in detail.) We have studied the Stokes shift data of DMABN in benzene: acetonitrile mixtures of several composition^.^^ The ET^ values of these compositions were determined separately and are presented in Table 3. The solvatochromism of the TICT emission of DMABN was studied on these mixed solvents, and the results are plotted against the E r N values in Figure 2. The linearity of the plot is excellent (r = 0.995). The ICT and TICT emissions of DMABN do overlap slightly. However, for the solvent compositions we have used, standard deconvolution procedures indicate that the,,A of the TICT emission is unaffected by the ICT emission band. This confirms that we are following the emission from the pure TICT state. The pe evaluated from the slope of the plot is compared in the last row of Table 2 with the values from other studies. The agreement is again quite good. We are currently extending this analytical method to systems where solubility problems have precluded solvatochromic studies earlier.
Conclusion In conclusion, we have shown that the use of E T N as the solvent polarity function for solvatochromism studies of Stokes shifts can be an efficient procedure to determine the excited state dipole moment of organic molecules. The high degree of correlation obtained points to the efficacy Of E T N to describe the microscopic environment of molecular dipoles in solution. The reformulation of earlier equations which relate absorption and/or fluorescence
E
U
0.410 0.420 0.454
m
0 X I
.-
12.2
L v1 VI 0)
Y 0
+
I/)
0.25
0.30
0.35
0.40
0.45
E: Figure 2. Plot of Stokes shifts of DMABN versus ETN value of the solvent mixtures. The straight line is the least-squares fit.
solvatochromism with solvent polarity function in terms of ET^ values reveals the basis for the good correlation and provides a simple expression for the gradient of A; versus ET^ plots, from which pe can be determined. Finally, the ability of the method to employ mixed solvents for solvatochromism studies is expected to be of considerable practical utility.
Acknowledgment. We gratefully acknowledge generous gifts of the betaine dye from Prof. C. Reichardt. M.R., A S . , and T.P.R. thank the CSIR, New Delhi, for a Junior Research Fellowship and financial support via Grants 01(1264)/93-EMRI1 and 02(0366)/92-EMR-I1. References and Notes (1) Chemla, D. S.; Zyss, J. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: New York, 1987. (2) Rettig, W. Angew. Chem., In!. Ed. Engl. 1986, 25, 971. (3) Czekalla, J. Z . Electrochem. 1960, 64, 1221. (4) Czekalla, J. Chimia 1961, 15, 26. (5) (a) Lombardi, J. R. J . Chem. Phys. 1969,50,3780. (b) Lombardi, J. R.J . Am. Chem. SOC.1970, 92, 1831. (6) Haas, M. P.; Warman, J. M. Chem. Phys. 1982, 73, 35. (7) Lippert, E. 2.Naturforsch. 1955, ZOA, 541. (8) Mataga, N.; Kaifu, Y . ;Koizumi, M. Bull. Chem. SOC.Jpn. 1956,29, 465.
(9) Koutek, B. Collect. Czech. Chem. Commun. 1978, 43, 2368. (10) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry; VCH: Weinheim, 1988.
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(1 1) (a) Cox, G. S.;Hauptman, P. J.; Turro, N. J. Photochem. Photobiol. 1984,39, 597. (b) Nagarajan, V.; Brearly, A. M.; Kang, T.;Barbara, P.F. J. Chem. Phys. 1987,86, 3183. (12) Bilot, v. L.; Kawaski, A. Z . Naturforsch. 1962, 17A, 621. (13) Bartoszewicz, B.; Kawaski, A. Bull. Acad. Pol. Sci. Ser. 1971, 19, 249. (14) Katritzky, A. R.; Zhu, D.; Schanze, K. S.J. Phys. Chem. 1991,95, 5737. (15) (a) Dimorth, K.; Reichardt, C.; Siepman, T.;Bohlman, F. Liebigs Ann. Chem. 1963, I , 661. (b) Reichardt, C.; Harbusch-Gornert, E. Liebigs. Ann. Chem. 1983,721. (c) Spange,S.;Lanterboch,M.;Gyra,A. K.;Reichardt, C. Liebigs Ann. Chem. 1991, 323. (16) Reichardt, C. Chem. SOC.Rev. 1992, 147. (17) Lippert, E. Z . Electrochem. 1957, 61, 962.
Ravi et al. (18) Weber, G. J. Chem. Phys. 1965, 43, 521. (19) Labhart, H. Oprische Anergung Organischer Systeme; Verlag Chemie: Gmbh, 1966; S.160. (20) Suppan, P.J. Chem. SOC.,Faraday Trans. 1987, 183, 495. (21) Hagan, T.; Pilloud, D.;Suppan, P. Chem. Phys. Lett. 1987,139,499. (22) (a) Czekalla, J.; Liptay, W.; Meyer, K. 0. Ber. Bunsen-Ges. Phys. Chem. 1963,67, 465. (b) Labhart, H. Adv. Chem. Phys. 1967, 13, 179. (23) Jonker, S.A.; Warman, J. M.Chem. Phys. Lett. 1991, 183, 36. (24) Nag, A.; Kundu, T.;Bhattacharyya, K. Chem. Phys. Lett. 1989,160, 257. (25) Due to specific*-interactions, nonlinearitiesariseat high percentages of benzene. Hence, we have excluded compositions of 510% acetonitrile. We
thank one of the referees for bringing this point to our attention.
