3525
J. Phys. Chem. 1993,97, 3525-3529
Ab Initio Time-Dependent Coupled Perturbed Hartree-Fock Studies of Optical Nonlinearities of Organic Molecules: Alkyl Derivatives of 4-Amino-@-nitrostyrene Vijaya Keshari, Shashi P. Karna, and Paras N. Prasad' Photonics Research Loboratory, Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 1421 4 Received: October 9. 1992
The dipole moment, p , linear polarizability, a,first hyperpolarizability, @, and second hyperpolarizability, y, of intramolecular charge transfer (ICT) molecules derived from the alkyl substitution of 4-amino-@-nitrostyrene (ANST) have been calculated by a b initio self-consistent-field method using a double-zeta valence Gaussian basis set. The calculated results for a,@, and y show strong dependence on p and the energy difference AE between the lowest unoccupied and highest occupied molecular orbitals. For the (dimethylamino)-@-nitrostyrene and (diethylamino)-@-nitrostyrene, the calculated results for @(-2w;w,w) are in qualitative agreement with the experimental values. The changes in the values of y for various third-order effects among the various alkylsubstituted A N S T are parallel to the corresponding changes in the values of @. The results indicate that the mechanism which leads to the enhancement of @ is also responsible for the enhancement of y values of ICT molecules and that these molecules may provide an alternative to conjugated polymers as a third-order nonlinear optical material.
Introduction
Theory and Computations
Conjugated organic molecules containing donor (D)-acceptor (A) intramolecular charge transfer (ITC) chromophores have been the subject of a number of experimental'-6 and theoretical studies7-lz as second-order nonlinear optical (NLO) materials. Recent experimental studies suggest that not only the secondorder but also the third-order NLO susceptibilities in the case of ICT organic molecules are quite large and comparable to those of the conjugated polymeric system^.'-^*'^-'^ For example, the third-order NLO susceptibility, ~ ( ~ ) ( - 3 w ; o , w , oof ) , (diethylamino)-4'-nitrostilbene (DANS) and 4-(diethylamino)-j3-nitrostyrene (DEANST) has been found from the third harmonic generation (THG) measurements to be as high as lo-'* esuI4. These observations have initiated vigorous efforts to synthesize and characterize the NLO properties of other ICT derivatives of the parent molecule 4-amino-@-nitrostyrene(ANST). In order to complement the experimental efforts and also to understand the influence of substitution of different electron-donating chromophores on the molecular optical nonlinearities of ANST, we have performed ab initio calculations on its alkyl-substituted derivatives. The dipole moment, p , the linear polarizability, a, the first hyperpolarizability,j3,and thesecond hyperpolarizability, y, of ANST and its methyl and ethyl derivatives have been calculated at the Hartree-Fock level of theory using a doublezeta valence (DZV) basis set. The frequency-dependent linear and nonlinear optical properties have been calculated in the framework of the time-dependent coupled perturbed H a r t r e e Fock (TDCPHF) a p p r ~ a c h . ' ~The . ~ ~results, presented in this paper, confirm the recent experimental observations that the ICT molecules are important as both second- and third-order NLO systems. Furthermore, it is noted that the linear and nonlinear optical properties of various alkyl-substituted ANST follow a systematic trend controlled by the electronic charge distribution and excited-state spectra. In order to assess the quality of the basis set employed in the present study, the effect of different basis sets on the calculated values of energy and (hyper)polarizabilities in the case of PNA is first discussed. This is followed by a discussion of the results for the derivatives of ANST and dispersion of a,j3, and y in DEANST.
The polarization p induced in a molecule in the presence of an external electric field E = E(r) can be written as a Taylor series expansion18
0022-3654/93/2091-3525$04.00/0
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p = p + a E + 1 / 2 ! @ E E +1 / 3 ! y E E E + (1) In the above equation, the Einstein convention of summation over repeated indexes is assumed; p is the dipole moment vector, and the expansion coefficients u, 8, and y are the linear polarizability, the first hyperpolarizability, and the second hyperpolarizability tensors of ranks 2 , 3 , and 4, respectively. The experimentally relevant quantities are the mean polarizability (a),the vector quantity Bycc, and the scalar mean second hyperpolarizability (7) defined as
(3) where
The coefficients a,8, and y corresponding to various first-, second-, and third-order processes are denoted as follows: polarizability a(0) for static case, a(o)for dynamic case; first hyperpolarizability, fl(0;O.O) for static case, fl(-w;O,w) for tlectrooptic Pockels effect (EOPE), 8(-2w;w,w) for second harmonic generation (SHG), @(O;o,-w) for optical rectification (OR); second hyperpolarizability y(O;O,O,O) for static case, y(-w;O,O,o) for optical Kerr effect (OKE), y(-u;o,o,-w) for degenerate fourwave mixing (DFWM), y(-2w;O,w,w) for electric-field-induced second harmonic generation (EFISHG), y(-3w;w,w,w) for third harmonic generation (THG), and y(O;O,w,-w) for electric-fieldinduced optical rectification (EFIOR). 0 1993 American Chemical Society
Keshari et al.
3526 The Journal of Physical Chemistry, Vol. 97, No. 14. 1993 TABLE I: Total Energy, Dipole Moment, and (Hyper)polarizabiUtiesof PNA Calculated Using Different
TABLE 11: Calculated Energies and Dipole Moments of PNA and Styrene Derivatives
Basis !%?&ab
DZV
+
2d(0.20,0.05)i
E (a4 w (D) (a(O;O))
8.2 14.3
(a(-w;w))
6"(0;O.O)
4.4
p(-W;O,W)
6"(-20;w,w) ( Y (O;O,O,O)) (Y(-W;o,o,w)) (Y( - w * w , * ) )
(Y(-2w;09w,w)) (Y(-3w;w,w,w))
2.0
+
DZV p(0. I),d(0.2)d -489.127193 7.93 14.0 14.08 4.37 4.52 4.84 1.48 I .53 1.59 1.64 1.84
molecule DZV'' -489.069978 8.40 12.12 12.16 5.01 5.48 (6.819 5.25 1.33 1.38 1.43 (3.84)g 1.48 1.67
The units for a are IO 2J esu. All frequency-dependent quantities calculated at A = 1.907 pm (hw = 0.65 eV). Reference 21. Reference 22. ('This work. 'Calculated at X = 1.064 pm (hw = 1.17 eV). E Calculated at X = 0.602 pm (hw = 2.06 e v ) . The calculations of the elements of a,8, and y for static electric field (hw = 0) and at an optical wavelength A = 1.907 pm ( h w = 0.65 eV) have been performed according to Karna and Dupuis.17 All calculations have been performed using the HONDO molecular electronic structure package.19 A double-zeta (DZ) Cartesian Gaussian basis set was used in the calculation. Experience has shown us that the inclusion of semidiffuse/diffuse functions in the valence basis set is extremely important for a quantitative accuracy in thevalues of and y.20-21 However, the size of the studied molecules and the available computational resources limited our basis set to only a valence set. The lack of auxiliary diffuse functions in the basis set is expected to introduce some numerical error in the calculated values of a,8, and y. In fact, this error in the case of p-nitroaniline molecule is estimated to be within 15% (see the discussion below), and we expect a similar error in the results for other molecules presented here. Geometries of all molecules were optimized a t the HartreeFock level using the same DZV basis set as used for the calculations of the properties. The coordinate system was taken such that the benzene ring lies in the x-y plane with the NO2 group lying in the x-direction (Figure 1). The tensorial components of a,8, and y are given in the inertial frame of the molecules whereby the axes a, b, and c refer to the inertial axes in the decreasing order of the moment of inertia.
Results and Discussion
a. Basis Set Effect in PNA. In order to examine the possible effects of the limited basis set used in this study on the calculated properties, our results for PNA, together with those obtained from more extended basis sets,21.22 are listed in Table I. The first column of the table lists dipole moment, static polarizability, and first and second hyperpolarizabilities calculated by Daniel and Dupuis,21 who used a set of two semidiffuse d(0.2,0.05) functions on the heavy atoms in their basis set. The second column lists the results obtained by Karna et aL22 employing a semidiffuse d(0.2) function on the heavy atoms and a semidiffuse p(O.1) function on hydrogen atoms. The number(s) in the parentheses is(are) the exponent@) of auxilliary functions. It is clear from the table that the dipole moment and the static first hyperpolarizability for PNA are both slightly overestimated by the DZV basis set (this study) by about 2.6% and 995, respectively, with respect to the best results obtained by Daniel and Dupuis2I using a larger basis set. The static linear polarizability, a,and the hyperpolarizability, y, on the other hand, are underestimated by about 14% and 33%, respectively. A similar trend is noted for the frequency-dependent properties when compared with the
PNA ANST MHANST DMANST EHANST EMANST DEANST
total energy (au) -489.069 -565.931 -604.941 -643.948 -643.961 -682.965 -721.982
335 459 194 332 129 277 235
dipole moment (D)
Af( LUMO-HOMO)
8.40 9.94 10.34 10.68 10.66 10.74 10.68
0.3718 0.3316 0.3275 0.3223 0.3264 0.3220 0.3212
(a4
results of Karna et aLzz Assuming that the noted difference in the calculated results for PNA is carried over to the other molecules of this study, we expect an error of about 10-15% in our calculated results for a and 0 and a somewhat larger error in the values of y due to the limited size of the basis set. It would be desirable to extend the basis sets in order to improve the numerical accuracy of the computed results. At the same time, we believe that the generality of the results presented in this paper will not be affected by further basis set improvements. b. Energy, Dipole Moment, and Linear Polarizability. Calculated total energy and dipole moment of the molecules investigated in the present study are listed in Table 11. Also listed in the table is the splitting (At) between the lowest unoccupied (LU) and the highest occupied (HO) molecular orbitals (MO) for each molecule. This quantity (At(LUM0HOMO)) gives a rough indication of the first absorption band for a given class of molecules and provides an important means to relate NLO properties. The ground-state dipole moments of alkyl-substituted ANST arecalculated to be larger than that of the parent molecule ANST which, in turn, is larger than that for PNA. Thecalculated values of the ground-state dipole moment of alkyl-substituted derivatives themselves are very close to each other, indicating only a small overall variation in the totalchargedistribution in these molecules. The alkyl derivatives also share similarities with respect to their At(LUM0-HOMO), which indicates that the first absorption spectra of these compounds are close to each other. As an approximate estimation, the calculated At(LUM0-HOMO) (Table 11) indicates a slight red shift in the absorption peak in going from PNA to DEANST. As discussed in detail in the following sections, the similarities in the calculated values of both the ground-state dipole moment and the energy gap, At(LUMOHOMO), of the alkyl derivatives of the ANST molecule result in very similar values of their (hyper)polarizabilities. Starting with PNA, a large increase of about 40% in the value of a is noted in going to ANST (Table III), whereafter a relatively small but systematic increase is noted upon substitution of amino hydrogens by alkyl groups. The noted trend in the change of a values is consistent with the corresponding changes in the At(LUM0-HOMO) in going from PNA to ANST derivatives (Table 11). Of course, the overall change by a factor of 2 in the value of a in going from PNA to DEANST is dominated by a 41% contribution due to the introduction of a single ethylenic (>C=C EMANST > DMANST > EHANST > MHANST, though the total spread in the value of 8 is within 25%. More importantly, the values of B for DMANST and DEANST, the two experimentally observed molecules, are within 8% of each other. The closeness in the
Optical Nonlinearities of Organic Molecules
TABLE 111: Calculated Values of a (in Units of
The Journal of Physical Chemistry, Vol. 97, No. 14, 1993 3527
esu) for Styrene Derivatives dynamic (A = 1.907 rm)
static molecule PNA ANST MHANST DMANST EHANST EMANST DEANST
ana
ahh
18.12 29.31 32.82 35.30 35.67 38.08 39.49
13.29 15.91 16.86 18.55 18.13 19.69 20.45
TABLE IV: Calculated Values of , @ ,, 10-30 esu) for Styrene Derivatives', molecule PN A ANST MHANST DMANST EHANST EMANST DEANST
a
