J. Phys. Chem. 1996, 100, 8777-8781
8777
An ab Initio Molecular Orbital Study on Hyperpolarizabilities of an Interacting 2-Methyl-4-nitroaniline Molecular Pair: A Molecular Study on the Oriented-Gas Approximation Tomoyuki Hamada* Hitachi Research Laboratory, Hitachi Ltd., 7-1-1, Ohmika, Hitachi, Ibaraki 319-12, Japan ReceiVed: January 2, 1996X
The oriented-gas approximation was examined at the molecular level by using an ab initio molecular orbital method in order to investigate its basic assumption: the additivity of hyperpolarizabilities between molecules. The additivity was examined in an interacting 2-methyl-4-nitroaniline (MNA) pair, the first-neighboring molecular pair in MNA crystal. The first-order hyperpolarizabilities β of the MNA pair were estimated by using the supermolecule technique in coupled perturbed Hartee-Fock calculations, fully taking into account quantum mechanical intermolecular interactions between MNA molecules. The results indicated that hyperpolarizabilities were not additive between the molecules and the intermolecular interactions considerably influenced the hyperpolarizabilities of the MNA pair. The results were analyzed by using the electrical interaction model of Dykstra et al. (J. Mol. Struct.: THEOCHEM 1986, 113, 357), and it was found that electrostatic intermolecular interactions were the predominant influence on the hyperpolarizabilities, similar to the case of urea. The importance of the local field correction in the oriented-gas approximation was discussed from the molecular viewpoint, considering its microscopic basis which corrects the effects of electrostatic interactions between a molecule and the crystal field on hyperpolarizabilities within the framework of mean field theory.
Introduction approximation,1,2
which calculates macroThe oriented-gas scopic nonlinear optical susceptibilities of organic crystals from microscopic hyperpolarizabilities of crystal molecules within the framework of the mean field theory, provides a feasible way to investigate organic nonlinear optical crystals at the molecular level. The oriented-gas approximation uses an assumption of hyperpolarizabilities between molecules being additive to estimate crystal susceptibilities by making a tensor sum of hyperpolarizabilities of crystal molecules and to correct the effects of the crystal field on hyperpolarizabilities by using the local field correction.3 Because of its simpleness and applicability, the oriented-gas approximation has been widely applied to molecular analysis and estimation of crystal susceptibilities, exploiting the direct relationship between crystal susceptibilities and molecular hyperpolarizabilities, though, recently, Mukamel4 pointed out its theoretical defects. For example, Chemla et al.1 analyzed the crystal susceptibilities of benzene derivatives within the framework of the oriented-gas approximation by using the irreducible tensor technique. Zyss and Oudar2 used the orientedgas approximation in order to elucidate the optimal molecular orientations of 2-methyl-4-nitroaniline (MNA), methyl (2,4dinitrophenyl)aminopropanoate, and 3-methyl-4-nitropyridine1-oxide within their unit cells to maximize their crystal susceptibilities. Further, the oriented-gas approximation also has a practical use in molecular designing of organic nonlinear optical crystals, by taking the advantage of its molecular view of crystal susceptibilities. An estimation scheme of crystal susceptibilities was proposed by combining the oriented-gas approximation and the molecular orbital (MO) calculations of hyperpolarizabilities.5 Although the oriented-gas approximation has been widely accepted for organic crystals in which molecules are quite X
Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(96)00022-6 CCC: $12.00
independent, the validity of the approximation has not been theoretically confirmed at the molecular level. Some quantum mechanical studies have been devoted to examination of the microscopic validity, by directly evaluating susceptibilities of interacting molecular systems. However, the results seem to contradict the basic assumption of the oriented-gas approximation: the additivity of hyperpolarizabilities between molecules. Previous ab initio MO studies have indicated that hyperpolarizabilities were not additive between molecules in hydrogenbonding systems such as FH dimer6 or urea crystal,7 and these studies found that electrostatic intermolecular interactions were the source of the nonadditivity. Zyss and Bertheir7 studied the susceptibilities of urea crystal by using an ab initio finite field method and concluded that electrostatic interactions caused by intermolecular hydrogen bonding increase the molecular hyperpolarizabilities. Dykstra et al.6 applied their electrical interaction model in order to investigate the hyperpolarizabilities of the interacting FH dimer, while changing intermolecular distance, and they found that the electrostatic interactions can account for the ab initio hyperpolarizabilities of the dimer. Although the previous studies investigated the nonadditivity in hydrogen-bonding systems, it is possible that nonadditivity is also common to their crystalline state, even when hydrogen bonding does not occur, since most organic nonlinear optical molecules have large dipole moments due to intramolecular charge transfer in their π-electron system, which is the source of nonlinearity.2 We studied the additivity of hyperpolarizabilities in a typical organic nonlinear optical material MNA, examining the additivity in the first-neighboring molecular pair in the crystal (MNA pair). The first-order hyperpolarizabilities β of the MNA pair were directly calculated by using the supermolecule technique in ab initio coupled perturbed Hartree-Fock (CPHF) calculations of hyperpolarizabilities,8 taking into account all the types of short range intermolecular interactions except van der Waals interactions; i.e., charge-transfer (CT), exchange (EX), polariza© 1996 American Chemical Society
8778 J. Phys. Chem., Vol. 100, No. 21, 1996
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tion (PO), and electrostatic (ES) intermolecular interactions.9 Further, we investigated effects of electrostatic interactions on hyperpolarizabilities by using the electrical interaction model of Dykstra et al.6 which estimates hyperpolarizabilities of interacting molecules, regarding molecules as polarizable point dipoles which interact each other. Detail of Calculations We used the ab initio CPHF method in order to calculate the static first-order hyperpolarizabilities β(0;0,0,0). The Buckingham type expansion10 was used to calculate β
1 1 E ) E0 + µiFi + RijFiFj + βijkFiFjFk + 2 6 1 γ F F F F + ‚‚‚ (1) 24 ijkl i j k l where E is the energy of a molecule under the electric field F, E0 is the unperturbed energy of a free molecule, Fi is the vector component of the electric field in the i direction, and µi, Rij, βijk, and γijkl are the dipole moment, linear polarizability, firstorder hyperpolarizability, and second-order hyperpolarizability, respectively. Here, each subscript of i, j, k, and l denotes the indices of the Cartesian axes x, y, z, and a repeated subscript means a summation over the Cartesian indices x, y, and z. The first-order hyperpolarizabilities β were calculated as the thirdorder derivative of E with respect to F. Prior to the calculation of the MNA pair, we examined the basis set dependence of β in MNA to find a suitable basis set by which reliable β values can be obtained within a feasible computational size. We calculated β of MNA, the geometry of which was optimized by the Hartree-Fock energy gradient method, by using several types of basis sets in the CPHF calculations; i.e., a minimal basis set (STO-3G11), split-valence basis sets (4-31G,12 6-31G13), and an extended basis set (631G* 14). Further, in order to reduce the computational size in the supermolecule calculation of the MNA pair, we examined the use of effective core potential (ECP) in β calculations by using a coreless basis set, the LP-31G.15 The LP-31G is a splitvalence type basis set with the ECP which replaces inner-core 1s electrons of the first-row elements. The results of the above basis sets calculations were examined by making a direct comparison with experimental β. We studied the additivity of first-order hyperpolarizabilities between molecules in the MNA pair, the first-neighboring molecular pair in the MNA crystal. The supermolecule technique was used in the hyperpolarizability calculations, fully taking into account all the types of intermolecular interactions except van der Waals interactions because of the Hartree-Fock wave function;16 i.e., CT, PO, EX, and ES intermolecular interactions.9 The structure of the MNA pair is shown in Figure 1. As shown by X-ray experiment,17 the unit cell of MNA crystal contains four MNA molecules (Z ) 4), and they are grouped into two molecular pairs (the MNA pair). Here, the z axis is the crystallographic c axis, and two MNA molecules are related to each other by the 2-fold glide operation along the c axis, due to the space group symmetry of MNA crystal. In the MNA pair, the molecular planes of two MNA molecules are almost parallel to each other (Figure 1b) and no hydrogen bond exists between them. We examined the validity of the oriented-gas approximation by making a comparison between the results of the supermolecule calculations and the oriented-gas approximation. The results of the oriented-gas approximation were obtained by making the tensor sum of molecular hyperpolarizabilities
Figure 1. Structure of the MNA pair, the first-neighboring molecular pair in MNA crystal (ref 17), and the coordinate system used in the hyperpolarizability calculations. Only the atomic position of the firstrow elements is shown. Here, the z axis corresponds to the crystallographic c axis (the glide axis) of MNA crystal. (a) Projection on the yz plane. (b) Projection on the xz plane.
between the two MNA molecules, the hyperpolarizabilities of which were calculated by the CPHF method. The comparison was also made considering the basis set superposition error (BSSE) in the MNA pair, by using the method of Boys and Bernardi.18 We used the ab initio MO program HONDO (7.0) developed by Dupuis et al.19 in the geometry and the CPHF calculations. The SCF convergence criterion of the density matrix was set at 10-5 au in all the electronic structure calculations. The CPHF iterations were continued until no element of the U matrix changed more than 10-4 au between iterations. The molecular geometry optimization was performed by setting the convergence criterion of the energy gradient at 0.0005 au. In order to clarify the effects of intermolecular interactions on hyperpolarizabilities in the MNA pair, we estimated its hyperpolarizabilities by using the electrical interaction model of Dykstra et al.,6 only considering the electrostatic dipoledipole interactions within it. Since details of the electrical interaction model were already described in ref 6, we show only the framework here. The electrical interaction model regards molecules as polarizable point dipoles which have molecular dipole moments µ, linear polarizabilities R, first-order hyperpolarizabilities β, and second-order hyperpolarizabilities γ, etc., and it evaluates the dipole-dipole interaction field in an SCF way, taking into account induced polarization on each dipole due to the interaction field. In the electrical interaction model, hyperpolarizabilities of interacting molecular systems are estimated by making the tensor sum of β + βind over the dipoles. Here, βind is the induced hyperpolarizability of the interacting dipole, due to the interaction field. Since the electrical interaction model does not consider intermolecular polarizations,
Oriented-Gas Approximation Molecular Study
J. Phys. Chem., Vol. 100, No. 21, 1996 8779 TABLE 1: Basis Set Dependence of MNA Hyperpolarizabilities β.a Experimentally Observed βz (EFISH Value) Is Showna STO-3G
4-31G
6-31G
6-31G*
LP-31Gb
exptlc
βxxx -18.472 -22.107 -19.580 -18.669 -22.237 βxxy 0.000 0.000 0.000 0.000 0.000 βxxz -56.263 -170.632 -176.546 -160.486 -160.650 βxyy 1.691 13.207 12.246 11.182 14.199 βxyz 0.000 0.000 0.000 0.000 0.000 βxzz -2.056 -2.179 -1.966 -2.426 -1.088 βyyy 0.000 0.000 0.000 0.000 0.000 βyyz -5.685 -28.670 -27.387 -22.388 -27.225 βyzz 0.000 0.000 0.000 0.000 0.000 βzzz 461.700 1129.966 1152.512 994.661 1036.458 Figure 2. Selected bond length (nm) and bond angle (deg) in the MNA molecule. (a) Optimized structure (planar) (RHF STO-3G). (b) Crystal molecular structure (not planar) (ref 17). The coordinate system used in the hyperpolarizability calculations is also shown (see text).
only intramolecular ones, the CT interaction cannot be considered in this model.20 We estimated β of the MNA pair by using the electrical interaction model, regarding two MNA molecules in the pair as point dipoles with the µ, R, β, and γ (MNA dipoles), the values of which were calculated by the CPHF scheme. The hyperpolarizabilities βijk of the MNA pair were estimated as follows
βijk )
βmijk ∑ m)1,2
(2)
where, βmijk is the first-order hyperpolarizability of the mth MNA dipole (m ) 1, 2) under the dipole-dipole interaction which is calculated as
βmijk ) βm(0)ijk + Fmlγm(0)ijkl
(3)
Here, βm(0)ijk and γm(0)ijkl are respectively the first-order hyperpolarizability and the second-order second hyperpolarizability of the mth MNA dipole, and Fml is the lth vector component of the interaction field experienced by the mth MNA dipole (l ) x, y, z). The second term on the right hand corresponds to the induced hyperpolarizability βind on the mth MNA dipole. In the present study, the SCF calculation of the interaction field was continued until no dipole changed its strength more than 10-20 au between iterations. All the calculations were executed on the HITAC M682 mainframe computer in the computer center of Hitachi Research Laboratory, Hitachi Ltd. The CPU time was about 10 h for the supermolecule calculation when the LP-31G basis set was used. The convergence of the SCF calculation of the electrical interaction model was fairly good. Only about 10 iterations were needed to achieve the convergence. Results and Discussion A. Basis Set Dependence of MNA Hyperpolarizabilities. The molecular geometry of the MNA molecule was optimized in Cs symmetry by using the Hartree-Fock energy gradient method with the STO-3G basis set (RHF STO-3G). The optimized molecular geometry is shown in Figure 2a along with the crystal molecular structure (Figure 2b17). The optimized molecular structure is planar because of its Cs symmetry, being symmetric with respect to the xz plane, while the crystal molecular structure is not completely planar because of the crystal field. The calculation reproduced fairly well the crystal molecular structure, especially its bond length.
βz
399.752 a
10-32
930.644
948.249
811.787
b
839.583
950
c
Unit is esu. Coreless basis set with ECP (ref 15). EFISH value (λ ) 1.907 µm) (ref 21).
The basis set dependence of first-order hyperpolarizabilities was examined for the MNA geometry which was optimized (Figure 2a), by using the STO-3G, 4-31G, 6-31G, and 6-31G* basis sets and the coreless basis set LP-31G. The coordinate system used is shown in Figure 2; i.e., the molecular plane laid in the xz plane and z axis was chosen so as to coincide with the axis of the intramolecular charge transfer, i.e., the dipole moment vector. The results are summarized in Table 1 along with the experimental EFISH βz value.21 Since the CPHF method gives static hyperpolarizabilities with no frequency dispersion, we included an experimental βz observed in an off-resonance frequency region (λ ) 1.907 µm), in which the effect of frequency dispersion is small. βz was calculated by using the Kleinman symmetry relation as25
βz ) βxxz + βyyz + βzzz
(4)
As shown in Table 1, the hyperpolarizabilities of the MNA molecule are very anisotropic. The largest component is βzzz, the hyperpolarizability parallel to the charge-transfer axis. βxxy, βxyz, βyyy, and βyzz are zero, reflecting the molecular symmetry with respect to the xz plane (Figure 2), due to its Cs point group symmetry. There is good agreement between the theoretical and experimental βz values when the split-valence basis sets (4-31G, 6-31G) or the extended basis set (6-31G*) was used, while the agreement is unsatisfactory when the minimal basis set (STO-3G) was used. βz of the 6-31G* basis set calculation was slightly smaller than that of the split-valence basis sets, the 4-31G and 6-31G. βz of the LP-31G calculation is somewhat smaller than that of the 4-31G calculation. As for the other hyperpolarizabilities, the 4-31G, 6-31G, and LP-31G calculations give similar results, whereas the 6-31G* calculation gives a somewhat smaller absolute value for the hyperpolarizabilities than do the split-valence type basis set calculations. From this basis set dependence, we can say that at least the split-valence type basis sets are required to get reasonable MNA hyperpolarizabilities by the CPHF method. The effects of the d type polarization functions in the 6-31G* basis set on the hyperpolarizabilities are not so clear in the present MNA case as they were in the FH case22 in which the functions are essential to get reasonable hyperpolarizabilities. This is an interesting aspect of MNA hyperpolarizabilities, and it seems to contradict the conventional idea which says that a large extended basis set is required to get reasonable hyperpolarizabilities. The difference between MNA and FH molecules can be understood by considering the d function amplitude in molecular orbitals near the HOMO-LUMO gap, from which hyperpolarizabilities arise. If the amplitude is large in the orbital, the d functions can influence hyperpolarizabilities, remarkably. In the case of
8780 J. Phys. Chem., Vol. 100, No. 21, 1996
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TABLE 2: Dipole Moments µ and Hyperpolarizabilities β of the MNA Pair Obtained by Several Methods: (A) Oriented-Gas Approximation; (B) Oriented-Gas Approximation with BSSE Correction; (C) Supermolecule Calculation; (D) Electrical Interaction Model. All Values Are in Atomic Units STO-3G A µx µy µz βxxx βxxy βxxz βxyy βxyz βxzz βyyy βyyz βyzz βzzz
B
LP-31G C
D
A
B
C
D
0.000 0.000 -4.708
-0.003 0.000 -4.705
-0.033 0.005 -4.514
-0.188 0.000 -4.263
0.042 0.000 -6.378
0.046 0.000 -6.362
-0.097 0.045 -5.186
-0.463 0.000 -5.586
-1.902 0.000 9.566 7.592 0.000 22.758 0.000 -35.498 0.000 -786.202
-2.778 -0.148 10.645 7.345 -0.178 23.000 -0.057 -35.467 -0.100 -785.279
-1.209 0.406 10.287 5.914 1.694 12.438 -2.037 -25.142 1.267 -616.380
-1.744 -0.149 10.648 5.405 -1.514 17.817 -3.177 -22.267 45.025 -679.213
-12.988 0.000 58.412 14.370 0.000 58.354 0.000 -4.568 0.000 -1829.040
-12.588 -3.324 73.455 13.720 -1.820 72.018 -0.941 -3.021 -3.032 -1809.707
-7.983 3.076 67.257 10.999 9.150 26.133 -4.797 11.382 16.374 -1298.689
-15.967 -0.714 61.559 9.159 -3.915 42.744 -15.359 139.538 34.063 -1493.920
MNA, the orbitals are π-type and the amplitude of d functions is small in the 6-31G* calculation, whereas a supplemental 6-31G* calculation of FH shows a conspicuous amplitude in the σ* unoccupied orbitals. Thus, it is reasonable that the present results show the less significant effects of the d functions on MNA hyperpolarizabilities, contrary to the FH case. The results of the LP-31G calculation show another interesting aspect of MNA hyperpolarizabilities. Since the LP-31G calculation replaced the inner-core 1s electrons of the first-row elements by ECP, the calculation gave hyperpolarizabilities which have their origin in the valence electrons only. Table 1 shows that the results of the LP-31G calculation are similar to those of the 4-31G and 6-31G calculations, indicating that that valence electrons are the predominant source of MNA hyperpolarizabilities. As is well-known, semiempirical MO calculations such as CNDO/S neglect inner-core 1s electrons in the hyperpolarizability calculations by using semiempirical Fock operators. Our present result can be regarded as providing some theoretical basis for the semiempirical MO calculations. From a computational viewpoint, the LP-31G basis set is also attractive in the supermolecule calculations, since the ECP can reduce the computational size. As mentioned above, the LP31G basis set can provide reasonable hyperpolarizability values, similar to the corresponding all-electron type basis sets, i.e., the 4-31G and 6-31G. Thus, we used both the STO-3G and LP-31G basis sets in the following supermolecule calculations, in order to get the qualitative and quantitative results, respectively. B. Hyperpolarizabilities of the MNA Pair. The hyperpolarizabilities of the MNA pair were calculated by using the supermolecule technique in the CPHF scheme, and the results were compared with those of the oriented-gas approximation. In addition, the effects of electrostatic intermolecular interactions were investigated by using the electrical interaction model. As mentioned in the previous section, we used both the STO-3G and LP-31G basis sets in the supermolecule calculations, in order to get the qualitative and quantitative results, respectively. All the results are shown in Table 2. We included the dipole moment results in order to clarify the degree of charge transfer in the MNA pair. The important point here is that there is a conspicuous difference between the results of the supermolecule calculations (columns C) and those of the oriented-gas approximation (columns A, B). The oriented-gas approximation gives larger βzzz values than do the supermolecule calculations for both the STO-3G and LP-31G basis sets. Namely, the oriented-gas approximation overestimates βzzz. The overestimation occurs even when the BSSE correction was considered (columns B).
The degree of the overestimation is 28% in the STO-3G calculation and 41% in the LP-31G calculation when the BSSE correction was not considered (columns A). Thus, βzzz is not additive between molecules, and it is reduced by the intermolecular interactions in the MNA pair. The reduction of βzzz accords with the reduction of charge transfer along the z axis under the intermolecular interactions. As shown in Table 2, the dipole moment µz of the MNA pair is slightly smaller in the supermolecule calculations (columns C) than in the orientedgas approximation (columns A, B), indicating that the intermolecular interaction reduces the charge transfer along the z axis. Since the charge transfer is the source of MNA hyperpolarizabilities,23 it is reasonable that both µz and βzzz were simultaneously reduced in the MNA pair. The results of the oriented-gas approximation also differ from those of the supermolecule calculations in the other components. βxxy, βxyz, βyyy, and βyzz, which are relevant to the y vector component of β, are zero in the oriented-gas approximation with no BSSE correction (columns A), whereas they are nonzero in the supermolecule calculation (columns C) as well as in the oriented-gas approximation with BSSE correction (columns B). As previously explained, the molecules in the MNA pair are related to each other by the 2-fold glide operation along the z axis (Figure 1). Since one MNA molecule is rotated by 180° around the z axis during the glide operation, βxxy, βxyz, βyyy, and βyzz of one MNA molecule in the pair are obtained by changing the sign of the components of the other MNA molecule owing to the vector character, if the molecules are independent of each other. The oriented-gas approximation with no BSSE correction (columns A) is this case, and consequently the components are cancelled, becoming zero between the two molecules. On the other hand, the molecules are not independent in the supermolecule calculations (columns C) and in the oriented-gas approximation with BSSE correction (columns B), because of the intermolecular interactions and the BSSE correction, respectively. Thus, βxxy, βxyz, βyyy, and βyzz are not zero in these cases. In order to examine the effects on electrostatic intermolecular interactions, we estimated the hyperpolarizabilities of the MNA pair by using the electric interaction model of Dykstra et al.6 (columns D) both for the STO-3G and LP-31G. βzzz of the electrical interaction model (columns D) has an intermediate value between the oriented-gas approximation (columns A) and the supermolecule calculations (columns C); i.e., this is a smaller overestimation compared with the oriented-gas case. The overestimation is 10% in the STO-3G calculation and 15% in the LP-31G calculation. Thus, the electrical interaction model can account for the reduction of βzzz in the supermolecule
Oriented-Gas Approximation Molecular Study calculations, indicating that the electrostatic intermolecular interaction is a predominant source of the reduction. Further, the electrical interaction model also reproduces the reduction of µz in the MNA pair, a feature of the supermolecule calculations. Thus, the reduction of βzzz in the supermolecule calculations can be understood, considering the electrostatic interactions in the MNA pair which cause the reduction of the charge transfer along the z axis, i.e., the source of βzzz. As previously mentioned, the electrical interaction model cannot treat the intermolecular CT interaction. However, the dipole moment µx, which may be relevant to the CT, is very small in the supermolecule calculations indicating smaller CT interactions in the MNA pair. Thus, we can say that the effects of the CT interaction are trivial in this case, and the electrical interaction model can account for most features of the MNA pair hyperpolarizabilities, indicating that the electrostatic interactions reduce βzzz by decreasing the intramolecular charge transfer in the two MNA molecules, which is the source of hyperpolarizabilities of the MNA pair. C. Conclusions: A Warning for the Additivity Approach. Our results indicate the additivity of hyperpolarizabilities, which is the fundamental assumption of the oriented-gas approximation, is not valid at the molecular level in the first-neighboring MNA molecules in the crystal state. As in the case of the urea crystal,7 the electrostatic intermolecular interactions are found to be the cause of the nonadditivity, though the interactions reduce the hyperpolarizabilities unlike in the urea case in which they enhance them. Namely, in the present MNA pair, the electrostatic intermolecular interactions can reduce βzzz by decreasing the degree of intramolecular charge transfer in the two MNA molecules, from which hyperpolarizabilities arise. The results of the MNA pair suggest that inclusion of the electrostatic interactions is needed in the susceptibility calculations of organic nonlinear optical crystals, even if no hydrogen bonds occur between molecules. Hence, the simple additivity approach is questionable in most nonlinear optical molecules which have large dipole moments due to the intramolecular charge transfer,24 since they provide the source of electrostatic intermolecular interactions in the crystal states. In the oriented-gas approximation, the influence of electrostatic interactions can be effectively included in the local field factor,3 which corrects the effective electrostatic interactions between the molecule and the surrounding crystal field, i.e., a mean field approach. Although we cannot consider the validity of the local field correction here, it seems that the oriented-gas approximation may be meaningless if it is used without the local field correction, since the significant effects of the electrostatic interactions are neglected. Our findings should serve as a warning for the conventional molecular designing of organic nonlinear optical crystals which, for convenience, uses the oriented-gas approximation with no the local field correction. The oriented-gas approximation should be used with the local field correction for the proper designing, though exact crystal refractive indices are needed for the correction. Hence, the conventional designing scheme
J. Phys. Chem., Vol. 100, No. 21, 1996 8781 may be useless when it is applied to design a new nonlinear optical crystal, its crystal refractive indices being required, which can only be determined after much experiment. We think the application of the electrical interaction model to molecular crystals may be another way to carry out the molecular designing of organic nonlinear optical crystals, considering electrostatic intermolecular interactions in the crystals at the molecular level. This way is more advantageous than the conventional one, since it can estimate crystal susceptibilities from molecular hyperpolarizabilities directly, without requiring crystal refractive indices. Acknowledgment. This work was performed by Hitachi Ltd. under the management of the Japan High Polymer Center as a part of the International Science and Technology Frontier Program supported by the New Energy and Industrial Technology Development Organization. References and Notes (1) Chemla, D. S.; Oudar, J. L.; Jerphagnon, J. Phys. ReV. B 1975, 15, 4534. (2) Zyss, J.; Oudar, J. L. Phys. ReV. A 1982, 26, 2028. (3) Bloembergen, N. Nonlinear Optics; W. A. Benjamin, Inc.: New York, 1965. (4) Mukamel, S. In Molecular Nonlinear Optics; Zyss, J., Ed.; Academic Press: Boston, MA, 1994; p 2. (5) Itoh, Y.; Oono, K.; Isogai, M.; Kakuta, A. Mol. Cryst. Liq. Cryst. 1989, 170, 259. (6) Dykstra, C. E.; Liu, S.-I.; Malik, D. J. J. Mol. Struct.: THEOCHEM 1986, 135, 357. (7) Zyss, J.; Berthier, G. J. Chem. Phys. 1982, 77, 3635. (8) Hurst, G. J. B.; Dupuis, M.; Clementi, E. J. Chem. Phys. 1988, 89, 385. (9) Yamabe, S.; Morokuma, K. J. Am. Chem. Soc. 1975, 97, 4458. (10) Buckingham, A. D. AdV. Chem. Phys. 1967, 12, 107. (11) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657. (12) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (13) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (14) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; Defrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (15) Topiol, S.; Moskowitz, J. W. J. Chem. Phys. 1979, 70, 3008. (16) Bachrach, S. M.; Chiles, R. A.; Dykstra, C. E. J. Chem. Phys. 1981, 75, 2270. (17) Lipscomb, G. F.; Garito, A. F.; Narang, R. S. J. Chem. Phys. 1981, 75, 1509. (18) Boys, S. F.; Bernardi, G. J. Mol. Phys. 1970, 19, 553. (19) Dupuis, M.; Watts, J. D.; Villar, H. O.; Hurst, G. J. B. HONDO (7.0); QCPE, Indiana University: Bloomington, IN, 1987. (20) Kato, S.; Fujimoto, H.; Yamabe, S.; Fukui, K. J. Am. Chem. Soc. 1975, 97, 4458. (21) Teng, C. C.; Garito, A. F. Phys. ReV. A 1983, 26, 6766. (22) Sekino, H.; Bartlett, R. J. J. Chem. Phys. 1986, 84, 2726. (23) Lalama, S. J.; Garito, A. F. Phys. ReV. A 1979, 20, 1179. (24) Nicoud, J. F.; Twieg, R. J. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic Press: Orlando, FL, 1987; Vol. 2, p 221. (25) Zyss, J.; Chemla, D. S. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic Press: Orlando, FL, 1987; Vol. 2, p 23.
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