19344
J. Phys. Chem. 1996, 100, 19344-19349
Quadratic Nonlinear Optical Susceptibilities of a New SHG Material, 3-Aminoxanthone: A Theoretical Study on Its Molecular and Crystal Susceptibilities Tomoyuki Hamada Hitachi Research Laboratory, Hitachi Ltd., 7-1-1, Ohmika, Hitachi, Ibaraki, Japan ReceiVed: June 25, 1996; In Final Form: September 25, 1996X
Nonlinear optical susceptibilities of a new SHG (second harmonic generation) material, 3-aminoxanthone, were investigated at both molecular and crystalline levels, by using the ab initio CPHF (coupled perturbed Hartree-Fock) method and the oriented-gas approximation. Molecular first hyperpolarizabilities β of 3-aminoxanthone were analyzed in order to investigate the source of β, by using an intramolecular orientedgas approach which assumes the molecular β can be obtained by making a tensor sum of the β of molecular fragments. The analysis revealed the source of β is localized on one aromatic ring, and effective π-conjugation for β is almost completely disconnected between the aromatic rings. The results of the oriented-gas calculations (2) showed the crystal has a phase matching condition of SHG, and its χ(2) 16 is 10.6 times that of the χ14 of urea crystal; these results are in agreement with the results of the SHG powder efficiency measurements. Experimental refractive indices were needed for the local field correction of the oriented-gas approximation in order to estimate the experimental order of magnitude of χ(2). The localized source of β may provide a new way for molecular design of organic nonlinear optical materials.
Introduction (2-methyl-4-nitroaniline),1
Since the discovery of MNA quadratic nonlinearities of organic molecules have been an attractive subject for optical material research because of their potential applicability for SHG (second harmonic generation) devices.2,3 Owing to their larger nonlinearities and higher optical damage threshold as compared with inorganic materials,3 organic materials offer several applicational advantages for these devices. To date, several organic materials have been studied in order to get a suitable organic SHG crystal to be used for a compact blue laser, which satisfies two demands for the SHG laser crystal, i.e., larger nonlinearities for higher SHG efficiency and shorter cutoff wavelength for the good transmittance of blue SHG laser light.2,3 Aromatic compounds with both π-electron-donating and -accepting groups such as MNA, are most typical of organic nonlinear optical materials which have been studied. As shown by Zyss and Chemla3, intramolecular charge transfer caused by π-electron-donating and -accepting groups is the source of their optical nonlinearities. However, such aromatic compounds are impractical for SHG applications in spite of their large optical nonlinearities. Although larger nonlinearities can be obtained by inducing a stronger intramolecular charge transfer, the shorter cutoff wavelength, which is the second demand for SHG laser crystal, cannot be achieved simultaneously in such molecules, since the stronger intramolecular charge transfer generally causes a longer cutoff wavelength.3 Namely, a trade-off relation3 exists between nonlinearities and cutoff wavelength in these types of compounds, and thus they do not satisfy the two demands concurrently. On the other hand, the trade-off relation does not exist for compounds which have disturbed π-electron conjugation. Heteroaromatic compounds such as POM (3-methyl-4-nitopyridine N-oxide)4 or pyridine analogs3 do not show the trade-off relation due to the heteroatom which disturbs the conjugation. Chalcone (benzylideneacetophenone), which has a carbonyl group between its two aromatic rings, also does not show the trade-off relation, X
Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)01892-8 CCC: $12.00
because of the disturbed π-conjugation due to the carbonyl group, as reported by Ohno et al.5 Here, since the longer conjugation length generally causes larger nonlinearities and longer cutoff wavelength simultaneously, the disturbed π-conjugation is assumed to shorten the effective conjugation length for the cutoff wavelength (energy gap) without shortening that for nonlinearities. Because of the shorter cutoff wavelength and larger nonlinearities, molecules which have the disturbed π-conjugation are thought to be promising candidates for SHG laser crystal. Recently, we have developed the aromatic compound 3aminoxanthone (3-aminoxanthen-9-one) as a candidate SHG crystal for a compact blue laser; it shows a large SHG powder efficiency (13 times that of urea) as well as a short cutoff wavelength in the near-UV region (400 nm).6 3-Aminoxanthone has two aromatic rings connected to each other by a carbonyl group and an ether bond (Figure 1). The molecule was designed to achieve the two demands for SHG crystal simultaneously, assuming its disturbed π-conjugation between the two aromatic rings due to the carbonyl group and ether bond. The X-ray crystal structure analysis7 showed the crystal has a noncentrosymmetric structure, and refractive indices measurements6 showed the experimentally grown crystal has the SHG phasematching condition in a wide range of directions when the crystallographic b axis coincides with the optical y axis. Now we have studied the quadratic optical nonlinear susceptibilities of 3-aminoxanthone at both molecular and crystal levels, by using the ab initio CPHF (coupled perturbed HartreeFock) method8 and the oriented-gas approximation.9 The molecular first-order hyperpolarizabilities β were analyzed by using an intramolecular oriented-gas approach, which assumes molecular β can be accounted for by considering β of molecular fragments. From the intramolecular oriented-gas analysis, we found most of the β value can be attributed to the aromatic ring which has the amino group, and the effective conjugation for β of 3-aminoxanthone is almost completely disconnected between the two aromatic rings. The oriented-gas calculation of the crystal nonlinearities showed the material is very promising for SHG device applications, having the crystal © 1996 American Chemical Society
Nonlinear Optical Susceptibilities of 3-Aminoxanthone
J. Phys. Chem., Vol. 100, No. 50, 1996 19345 Crystal Refractive Indices and χ(2) Calculation We calculated refractive indices and quadratic nonlinear susceptibilities χ(2) of 3-aminoxanthone and MNA crystals from the calculated R and β by using the oriented-gas approximation.9 The accuracy of the calculations was examined for MNA crystal by comparing the calculated refractive indices and χ(2) with the experimental values.1 Linear susceptibilities χ(1) were calculated from molecular R in order to get optical axes as well as refractive indices by the oriented-gas approximation with no local field correction as
Figure 1. Molecular structures of 3-aminoxanthone (a), urea (b), and MNA (c). A planar structure is assumed for all the structures. The coordinate system used in the R and β calculations is also shown.
susceptibility χ(2) 16 with the phase matching condition, the value of which corresponds to 10.9 times that of the χ(2) 14 of urea crystal. All calculations were also made for MNA crystal in order to confirm the accuracy of the present approach, by making direct comparisons with the experimental results. Method of Calculation Molecular Polarizabilities and Hyperpolarizabilities Calculation. We calculated static linear polarizabilities and first hyperpolarizabilities of 3-aminoxanthone and MNA (Figure 1) by using the ab initio CPHF method.8 The Buckingham type expansion10 was used in the CPHF calculations:
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, first hyperpolarizability, and second hyperpolarizability, respectively. Each of the subscripts i, j, k, and l denotes the index of the Cartesian axes x, y, z, and a repeated subscript means a summation over the Cartesian indices x, y, and z. Thus, by following eq 1, we calculated R and β as the respective secondand third-order derivatives of E with respect to F. The CPHF calculations were made for molecular geometries of 3-aminoxanthone, urea, and MNA, which were optimized by the Hartree-Fock energy gradient method11 with the STO3G basis set.12 Here, we made the calculations of urea and MNA in order to investigate the basis set dependence of R and β. Both the molecular geometries of 3-aminoxantone and MNA were optimized under the restriction of Cs point group symmetry assuming their planar molecular geometry, and the molecular geometry of urea was optimized under the restriction of C2V point group symmetry. For urea and MNA, we used the 6-31G,13 6-31G*,14 and 6-31G+PD8 basis sets in the CPHF calculations. Here, the 6-31G+PD has auxiliary diffuse pd functions (ζp ) ζd ) 0.05). Because of computational restrictions, we only used the 6-31G basis set in the CPHF calculation of 3-aminoxanthone, considering the basis set dependence of β in MNA. The SCF convergence criterion of the density matrix was set at 10-5 au in all the electronic structure calculations, and the CPHF iterations were continued until no element of the U matrix changed more than 10-4 au between iterations. The molecular geometry calculations was performed by setting the convergence criterion of the energy gradient at 0.0005 au. In the geometry and the CPHF calculations, we used the ab initio MO program HONDO (7.0) developed by Dupuis et al.15
(1) χIJ )
1 V
∑ij ∑s cos(I,i(s)) cos(J,j(s)) Rij(s)
(2)
Here, V is the volume of the crystal unit cell, I and J are indices of orthogonal coordinate axes, i(s) and j(s) denote indices of orthogonal coordinate axes associated with the sth molecule in the unit cell, and R(s) is linear polarizability of the sth molecule. cos(I,i(s)) means the directional cosine between the I and i(s) axes. The summation for i and j is taken over all i(s) and j(s), and the summation for s is taken over all molecules in the unit cell. We defined i(s) and j(s) as the principal axes of inertia of the sth molecule, by using the crystal molecular structure of 3-aminoxanthone7 and MNA.1 We used no local field correction for the χ(1) calculation (f ) 1), avoiding the self-consistent calculation of χ(1) as seen in eq 2, since χ(1) determines itself when the local field correction is considered. Namely, when the local field correction is considered in eq 2, χ(1) depends on the local field factor f which is calculated from refractive indices (eq 6), the values of which are calculated from χ(1) (see eqs 3 and eq 4). The dielectric constant matrix E was calculated from χ(1) as (1) IJ ) 1 + 4πχIJ
(3)
and crystal optical axes were obtained by diagonalizing the E matrix. Namely, optical axes were calculated as the column vectors of the eigenvector matrix of the matrix, and refractive indices were estimated from the components of the diagonalized E matrix (eigenvalue matrix) as
nL ) (LL)-1/2
(4)
Here, the subscript L means the index of the Lth optical axis (given as the Lth column vector of the eigenvector matrix), and it is denoted as X, Y, and Z following the order of the column indices. Quadratic nonlinear optical susceptibilities χ(2) were estimated by the oriented-gas approximation with the local field correction9 as (2) ) χLMN Nd fLfMfL ∑ ∑ cos(L,i(s)) cos(M,j(s)) cos(N,k(s)) βijk(s) Z LMN s (5)
where the subscripts L, M, and N denote the indices of the optical axes X, Y, Z, and Nd means the number of molecules in the unit volume (1 cm3). Z is the crystallographic Z number (number of molecules in the unit cell), and β(s) is hyperpolarizability of the sth molecule. f is the Lorentz type local field factor9 which is calculated from the refractive indices as
fL ) (nL2 + 2)/3
(6)
19346 J. Phys. Chem., Vol. 100, No. 50, 1996
Hamada
TABLE 1: Selected Structural Parameters of 3-Aminoxanthone parameter
calca
expb
parameter
calca
expb
O1-C9 O2-C8B C1-C2 C2-C3 C4-C4A C4B-C9 C5-C8B C7-C8 C8A-C8B
1.227 1.394 1.371 1.410 1.395 1.450 1.410 1.378 1.393
Bond Length (Å) 1.239 O2-C4A 1.362 N-C3 1.352 C1-C4B 1.410 C3-C4 1.376 C4A-C4B 1.442 C5-C6 1.392 C6-C7 1.374 C8-C8A 1.394 C8A-C9
1.393 1.398 1.399 1.390 1.395 1.377 1.396 1.397 1.509
1.366 1.363 1.402 1.391 1.403 1.367 1.380 1.397 1.454
C4A-O2-C8B C1-C2-C3 N-C3-C4 C3-C4-C4A O2-C4A-C4B C1-C4B-C4A C4A-C4B-C9 C5-C6-C7 C7-C8-C8A C8-C8A-C9 O2-C8B-C5 C5-C8B-C8A O1-C9-C8A
117.1 119.8 120.6 120.0 124.5 116.8 120.7 120.4 121.1 121.0 115.2 120.4 122.9
Bond Angle (deg) 119.1 C2-C1-C4B 121.0 N-C3-C2 121.5 C2-C3-C4 119.5 O2-C4A-C4 121.9 C4-C4A-C4B 118.0 C1-C4B-C9 120.5 C6-C5-C8B 121.2 C6-C7-C8 120.8 C8-C8A-C8B 122.0 C8B-C8A-C9 116.2 O2-C8B-C8A 120.7 O1-C9-C4B 121.3 C4B-C9-C8A
121.8 120.1 119.4 114.5 121.1 121.3 118.8 119.6 118.8 120.2 124.5 123.6 113.5
121.7 119.9 118.6 115.6 122.4 122.7 119.3 119.7 118.4 119.6 123.1 122.9 115.8
a
STO-3G SCF results. b X-ray experimental results (ref 7).
βi ) 3/5∑ βijj
Nd was calculated from the weight density D of crystal (D is 1.40 g/cm3 for MNA crystal,1 and D is 1.41 g/cm3 for 3-aminoxanthone crystal7), by using eq 7.
Nd ) NaD/Mr
Although, Hartree-Fock STO-3G calclation of molecular geometries is not so sophisticated, we used the calculated molecular geometry in the following study, considering the reasonable agreement between the experimental and theoretical geometries (see Table 1). As for MNA, we used its geometry optimized by using the Hartree-Fock STO-3G, which was previously calculated.16 Table 2 shows the results of the CPHF calculations, along with the EFISH βz values of urea17 and MNA18 for comparison. In Table 2, the EFISH values have been multiplied by 3, following the reinterpretation of the experimental values.19 In the calculations, we used the coordinate system shown in Figure 1. Here, the x axis was perpendicular to the molecular plane, and the molecular plane laid in the yz plane. In the urea and MNA calculations, the z axis was chosen so as to coincide with the dipole moment vector in order to allow a direct comparison of βz with the EFISH experiment. In the 3-aminoxanthone calculations, the z axis was parallel to the second principal axis of inertia, and it was almost parallel to the C9-O1 bond. We also calculated the vector components of β in order to examine its directional anisotropy, as well as to make a direct comparison with the EFISH experiment for MNA. The vector component for the i direction was calculated by using the Kleinman symmetry relation3,20 as
(7)
Here, Mr denotes the formula weight of the molecules (Mr is 152.15 for MNA, and Mr is 211.11 for 3-aminoxanthone), and Na is Avogadro’s number. We used both the calculated and experimental refractive indices of MNA and 3-aminoxanthone in order to calculate f by eq 6, which was used to calculate χ(2) by eq 5. All calculations were executed on HITAC M682 mainframe computer in the Computer Center of Hitachi Research Laboratory, Hitachi Ltd. Results and Discussion Calculated Molecular Nonlinearities. The calculated molecular geometrical parameters of 3-aminoxanthone (Figure 1) are shown in Table 1, along with the results of the X-ray crystal structure analysis.7 The Hartree-Fock energy gradient method with the STO-3G basis set (STO-3G SCF) reproduced fairly well the crystal molecular structure of 3-aminoxanthone, especially in the bond length, except for the C8A-C9 bond in which the calculated bond length (1.509 Å) differed considerably from the observed value (1.454 Å). For all others, the difference between the calculated and observed bond lengths fell in the range from 0 Å (for the C8-CA bond) to 0.03 Å (for the O2C4A bond). Regarding the bond angles, the agreement between the calculated and observed values was not as good as for the bond lengths. The difference between the calculated and observed angles ranged from 0.1° (for the angle C2-C1-CB) to 2.4° (for the angle O2-CA-CA). Here, the larger difference in bond angles can be understood by considering the distorted crystal molecular structure due to the crystal field. Bond angles may have a greater influence of the crystal field than bond lengths, since bond angles depend on torsion angles which are easily distorted under the crystal field owing to their flexibility.
(8)
i*j
where the subscripts are the Cartesian indices x, y, z. In Table 2, we showed the EFISH βz value of the MNA molecule which was observed at the off-resonance wavelength (λ ) 1.907 µm)18 where the frequency dispersion effects are small, since we calculated the static β by the CPHF method, neglecting the frequency dispersion of β. All the CPHF calculations of urea and MNA underestimated the experimental βz which was obtained by the EFISH method. The 6-31G, 6-31G*, and 6-31G+PD calculations of urea underestimated the EFISH βz by 81, 82, and 79%, respectively, though the calculations reproduced the order of magnitude of the EFISH value. On the other hand, all the calculations of MNA failed to reproduce the order of magnitude of the EFISH βz. The 6-31G, 6-31G*, and 6-31G+PD calculations of MNA underestimated the EFISH βz by 80, 83, and 78%, respectively. This underestimation of βz can be understood, considering the features of the CPHF method. Since the CPHF method neglects the electron correlation21 and the frequency dispersion effects22,23 which enhance β, it is reasonable that the CPHF method underestimates the experimental β. Thus, the present calculations should be regarded as being only qualitative. The β results of urea and MNA indicate the diffuse pd functions of the 6-31G+PD have small effects on β, contrary to the case of γ.8 The difference between the 6-31G and 6-31G+PD calculations was small in both R and β; i.e., the 6-31G+PD calculations of urea and MNA resulted in slightly larger βz than their 6-31G calculations by 8 and 10%, respectively. The degree of the difference accorded with the study of Keshari et al.,23 which showed the neglect of diffuse functions is expected to cause an error of about 10-15% in β calculation. Considering the basis set dependence in urea and MNA, we used the 6-31G for the CPHF calculations of 3-aminoxanthone, exploiting its smaller computational size as compared with the 6-31G* and 6-31G+PD. Table 2 showed 3-aminoxanthone has two strong vector components βy and βz with similar strength. The total strength of the vector components was calculated as the length of the vector and it was 569.508 × 10-32 esu for MNA and 441.068 × 10-32 esu for 3-aminoxanthone (6-31G).
Nonlinear Optical Susceptibilities of 3-Aminoxanthone
J. Phys. Chem., Vol. 100, No. 50, 1996 19347
TABLE 2: Static Polarizabilities and Hyperpolarizabilities of Urea, MNA, and 3-Aminoxanthone Calculated by the CPHF Method and Experimental EFISH Values of Urea and MNA (Only Nonzero Components Are Shown) 6-31G Rxx Ryy Ryz Rzz βxxy βxxz βyyy βyyz βyzz βzzz βy βz βz (exp)
urea 6-31G*
1.382 3.681 0.000 3.071
1.772 3.915 0.000 4.148
0.000 6.855 0.000 -45.673 0.000 66.749 0.000 16.759
0.000 3.283 0.000 -37.984 0.000 61.668 0.000 16.180 87a,c
6-31G+PD 2.898 4.457 0.000 4.929
MNA 6-31G*
6-31G Polarizabilities (Å3) 5.004 15.237 0.612 19.498
6-31G+PD
3-aminoxanthone 6-31G
5.668 15.302 0.632 19.753
8.225 16.706 0.664 21.604
6.142 30.472 -1.574 22.546
Hyperpolarizabilities (10-32 esu) 0.000 -12.246 -11.182 19.928 -27.387 -22.388 0.000 -19.850 -18.669 -59.086 -176.546 -160.486 0.000 -1.966 -2.426 70.303 1152.512 994.660 0.000 -20.275 -19.366 18.145 569.147 487.072 2850b,c
-10.048 -49.789 -22.292 -203.037 0.546 1295.555 -19.076 625.637
-1.287 -8.476 420.009 564.270 138.977 -76.937 557.669 478.957
a EFISH value observed in DMSO (λ ) 1.907 mm) (ref 17). b EFISH value observed in dioxane (λ ) 1.907 mm) (ref 18). c The experimental values have been multiplied by 3, following the reinterpretation of the experimental β (ref 19).
Thus, 3-aminoxanthone was estimated to have the molecular nonlinearity which corresponds to 77% of that of MNA (631G). Intramolecular Oriented-Gas Analysis of β In order to examine the disturbed π-conjugation of 3aminoxanthone, which was assumed in the molecular design, we analyzed the source of β in terms of the molecular fragments by using an intramolecular oriented-gas approach which assumes a localized source of β. Similar to the empirical additivity approach for molecular polarizabilities,24,25 we assumed the molecular β can accounted for by considering β of the molecular fragments. We examined the source of β for 3-aminoxanthone, calculating that of the molecular fragments by the CPHF method. Figure 2 shows the structures of the molecular fragments used in the analysis. The molecular fragments were obtained by omitting some part of 3-aminoxanthone. The omitted part of the molecule is shown by dotted lines. Since the amino (NH2) and carbonyl (CO) groups were respectively thought to be the predominant π-electron-donating and -accepting groups which induce β, we considered the molecular fragments which had both these groups, i.e., the fragments A and B. As seen in Figure 2, fragment A had the aromatic ring with NH2, CO, and hydroxy (OH) groups, and fragment B had the aromatic ring with NH2 and CO groups. Since some chemical bonds of the molecule (3-aminoxanthone) must be broken in order to get the fragments, we terminated these broken bonds by H atoms (asterisked in Figure 2). The positions of the H atoms were determined by the Hartree-Fock energy gradient method with the STO-3G basis set, while fixing the other structural parts of the fragments. Table 3 shows the calculated β of the fragment molecules, as well as that of the whole 3-aminoxanthone molecule. Although there were some differences in β between the fragments and 3-aminoxanthone, the fragments were found to reproduce most features of β of 3-aminoxanthone; i.e., βy and βz of fragment A respectively corresponded to 95 and 82% of those of 3-aminoxanthone. The results indicated that β of 3-aminoxanthone arose from the aromatic ring which has the NH2 group, and the other aromatic ring, omitted in the analysis (Figure 2), did not contribute to β. In particular, fragment A seemed to represent the source of β for 3-aminoxanthone fairly well, providing nearly all the β of 3-aminoxanthone. Thus, the source of β was
Figure 2. Structures of fragment molecules used in the intramolecular oriented-gas analysis (solid line). The dotted lines show the omitted part of 3-aminoxanthone, and these broken bonds are terminated by H* (see text). The fragment molecules are with (a) NH2, CO, and OH groups and (b) NH2 and CO groups.
TABLE 3: Static Hyperpolarizabilities β (10-32 esu) of the Molecular Fragments (see Figure 2) and 3-Aminoxanthone (Only Nonzero Components Are Shown) βxxy βxxz βyyy βyyz βyzz βzzz βy βz
3-aminoxantone
fragment A
fragment B
-1.287 -8.476 420.009 564.270 138.977 -76.937 557.669 478.957
-3.163 -7.965 337.094 403.010 200.771 0.626 534.702 394.418
-3.909 -7.818 382.242 342.151 220.038 4.094 598.371 330.239
localized on the aromatic ring with the NH2 group, and the effective conjugation for β was almost completely disconnected between the two aromatic rings. This confirmed the assumption in the molecular designing, i.e., the π-conjugation between the two aromatic rings was disturbed due to the carbonyl group and ether bond. Further, the results implied that the molecular β could not always be enhanced by the π-conjugation extension, contrary to the conventional idea which assumes a delocalized source for β. Hence, if the molecule has a disturbed π-conjuga-
19348 J. Phys. Chem., Vol. 100, No. 50, 1996
Hamada TABLE 4: Refractive Indices of MNA and 3-Aminoxanthone Crystals Calculated by the Oriented-Gas Approximation MNA nx ny nz
3-aminoxanthone
6-31G
6-31G*
exp
6-31G
exp
1.5 1.4 1.2
1.5 1.4 1.2
2.2a 1.8b 1.6c
1.6 1.3 1.3
1.8d 1.7d 1.6d
a Observed at λ ) 0.532 µm (ref 27). b Observed at λ ) 1.064 µm (ref 27). c Observed at λ ) 0.633 µm (ref 27). d Static value extrapolated from experimental indices (see text).
Figure 3. Optical axes X, Y, Z of MNA (a) and 3-aminoxanthone (b) crystals. Here, the parallelogram shows their crystallographic unit cell projected on the ac plane. The length of the axes corresponds to the relative strength of their refractive indices. The calculated angle θ (θcalc) is shown along with the experimental θ of MNA (θobs) (ref 1).
tion due to heteroatoms, carbonyl groups, etc., like 3-aminoxanthone, it is possible that the molecule has the localized source for β. Previously, we studied the nonlinearity of a fused heteroaromatic compond 8-hydroxyquinoline and found some its derivatives may have the localized source of nonlinearity.26 Due to the N atom in the aromatic system, the derivatives have the disturbed π-conjugation, and their intramolecular charge transfer is assumed to be localized within each of the aromatic rings. Thus, such a localized source of nonlinearity is not unique, and it may be found in other polyaromatic compounds. The intramolecular oriented-gas analysis may be attractive for designing of such compounds, exploiting the concept of the local source of β. Calculated Crystal Nonlinearities Figure 3 shows the calculated optical axes X, Y, Z of MNA (Figure 3a) and 3-aminoxanthone (Figure 3b) crystals, along with the structures of their crystal unit cell projected on the ac plane. Here, the crystallographic b axis is perpendicular to the paper, since the crystals have the monoclinic unit cell. In Figure 3, the length of the optical axes shows the relative magnitude of the calculated refractive indices. In order to fix the orientation of the optical axes, we calculated θ, the angle between the optical X and crystallographic a axes. The experimental θ value (θobs) is also shown for MNA crystal for comparison. The 6-31G and 6-31G* calculations of MNA crystal showed its optical Y axis was parallel to the crystallographic b axis, in agreement with the experiment (Figure 3a). However, the calculated θ value (θcalc) differed considerably from that observed(θcalc),1 indicating the qualitative feature of the present optical axes calculations. The results of 3-aminoxanthone crystal showed the experimentally grown crystal6 satisfied the phase-matching condition, since the calculated optical Y axis was parallel to the crystallographic b axis (Figure 3b). Table 4 shows the calculated refractive indices of MNA and 3-aminoxanthone crystals, along with their experimental values. Since we estimated the refractive indices from the static linear polarizabilities by using the oriented-gas approximation, we showed the experimental refractive indices of MNA crystal observed in the off-resonance wavelength region where the frequency dispersion effects are thought to be small.27 For 3-aminoxanthone, we showed the refractive indices at an infinite wavelength; these were extrapolated from the experimental values6 by using the Sellmeier formula.28 As seen in Table 4, the calculation slightly underestimated all the experimental refractive indices for both MNA and 3-aminoxanthone crystals. For MNA, both the 6-31G and 6-31G* calculations gave the
TABLE 5: χ(2) of MNA and 3-Aminoxanthone Crystals Obtained by the Oriented-Gas Calculation with Two Types of Local Field Corrections, i.e., the Local Field Correction by Calculated Refractive Indices (A) and That by the Experimental Refractive Indices (B) χ
method
6-31G
MNA
χ(2) 11
3-aminoxanthone
d χ(2) 16
A Ba A Bb A Bb A Bb
65.9 115.9 16.3 29.7 8.5 16.2 3.8 7.6
crystal
d χ(2) 14
χ(2) 22
exp 500c
a By refractive indices observed at λ ) 1.064 µm (see Table 4). By refractive indices in infinite wavelength region extrapolated (see text). c Observed at λ ) 1.064 µm (ref 1). d Phase-matching condition is satisfied. b
same refractive indices. The underestimation was largest for nx of MNA (68%), and it was smallest for nx of 3-aminoxanthone (89%). The underestimation could be understood by considering the features of the present calculation, in which the linear susceptibility χ(1) was calculated with no local field correction, neglecting the electron correlation and the frequency dispersion effects on R (see eq 2). Thus, the present refractive indices calculations were qualitative, similar to the optical axes calculations. In order to get quantitative refractive indices, more sophisticated calculations may be needed which consider the electron correlation and frequency dispersion effects. Table 5 shows the quadratic nonlinear optical susceptibilities χ(2) of MNA and 3-aminoxanthone crystals obtained by the oriented-gas approximation (eq 5). The experimental χ(2) 11 of MNA crystal (λ ) 1.064 µm)1 is also noted. Only the predominant components are shown, and the components with the phase-matching condition are asterisked. In the χ(2) calculations, we used the 6-31G results of the refractive indices and β calculations, since the 6-31G* results were not available for 3-aminoxanthone. In the oriented-gas calculations, we used two types of local field correction in (eq 5), methods A and B. Method A used the calculated refractive indices and method B used the observed ones in eq 6 to calculate the local field factor f. Since experimental optical axes were not available for 3-aminoxanthone, we used the calculated optical axes in method A as well as in method B, though the calculated optical axes of MNA crystal differed slightly from the experimental axes (Figure 3a). The table results indicated the oriented-gas calculation could reproduce the experimental order of magnitude 1 of χ(2) 11 of the MNA crystal only when the experimental refractive indices were used for the local field correction (method B). Method B underestimated χ(2) 11 of MNA crystal by 76%, and it seemed to accord with the underestimation of MNA β in the 6-31G calculation (80%). On the other hand, method A was useless to reproduce the experimental order of magnitude of the χ(2) 11 .
Nonlinear Optical Susceptibilities of 3-Aminoxanthone The failure of method A could be understood by considering the underestimated refractive indices and their influence on χ(2). Since χ(2) is very sensitive to refractive indices values, being proportional to the sixth power of the indices values as seen in eqs 5 and 6, a slight underestimation of refractive indices may cause the large underestimation of χ(2). Thus, the failure of the method was thought to be reasonable, since method A used the underestimated refractive indices (Table 4) to calculate the local field factor f. (2) Table 5 shows 3-aminoxanthone crystal had χ(2) 14 and χ16 (2) with phase-matching condition. Following method B, χ16 was 29 estimated to correspond to 10.6 times the χ(2) 14 of urea crystal. This estimation seemed to be in accord with the SHG powder efficiency measurement,7 which showed 3-aminoxanthone powder had 13 times the efficiency of urea powder. Conclusions All the calculated results indicated 3-aminoxanthone has a potential for SHG device applications, owing to its remarkable χ(2) value with the phase-matching condition. Due to the carbonyl group and ether bond, the effective conjugation for β was found to be almost completely disconnected between the two aromatic rings, and most of the β value arose from the aromatic ring with the amino group. Hence, the source of the molecular β was localized in the part of the molecule which contains the aromatic ring, contrary to the conventional idea which assumes a delocalized source. This is an interesting aspect of 3-aminoxanthone. The concept of the localized source of β may provide a new way for molecular designing of organic nonlinear optical materials. In this study, we estimated χ(2) of MNA and 3-aminoxanthone crystals by using the ab initio CPHF method and the orientedgas approximation. Since the calculated refractive indices underestimated the experimental ones, the local field correction by the calculated indices failed to reproduce the experimental order of magnitude of χ(2) of the MNA crystal, and the experimental refractive indices were needed for the accurate χ(2) calculations. Thus, regarding the present calculation method of χ(2), we concluded the present approach is qualitative insofar as the calculated refractive indices were used for the local field correction. In order to make a complete theoretical estimation of χ(2), a more sophisticated calculation method of refractive indices may be needed. References and Notes (1) Lipscomb, G. F.; Garito, A.; Narang, R. S. J. Chem. Phys. 1981, 75, 1509.
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