10268
J. Phys. Chem. 1992,96, 10268-10275
(2) Diederich, F.; Whetten, R. L. Acc. Chem. Res. 1992, 25, 119 and references therein. (3) Kikuchi, K.;Nakahara, N.; Wakabayashi. T.; Suzuki, S.;ShuOmaN, H.; Miyake, Y.; Saito, K.; Ikemoto, I.; Kainosho, M.; Achibe, Y. Nature 1992, 357. 142. (4)Li, Q,; Wudl, F.; Thilgen, C.; Whetten, R. L.; Diederich, F. J . Am. Chem. SOC.1992,114,3994. (5) Schmalz, T. G.;Seitz, W. A.; Klein, D. J.;Hite, G.E. Chem. Phys. Lett. 1986,130, 203. Kroto, H.W. Nature 1987, 329, 529. (6) Manolopoulos, D. E. J. Chem. Soc., Faraday Trans. 1991,87,2861. (7) Ettl, R.;Chao, I.; Diederich, F.; Whetten, R.L. Nature 1991,353,149. ( 8 ) Zhang, B. L.; Wang, C. 2.;Ho, K. M. Chem. Phys. Lett. 1992,193,
(10)Scuseria, G.E. Chem. Phys. Lett. 1991. 176. 423. (11) Scuseria, G.E. Chem. Phys. Lett. 1991; 180; 451. (12) Hrdberg, K.;Hedberg, L.; Bcthune, D. S.;Brown, C. A.; Dorn, H. C.; Johnson, R. D.; de Vries, M. Scfence 1991,254,410. (1 3) McKenzie, D. R.;Davis, C. A.; Cockayne. D. J. H.; Muller, D. A.; Vassallo, A. M. Nature 1992, 355, 622. (14) Hehre, W. J.; Radom, L.; von R.Schleyer,P.; Pople, J. A. Ab Idtfo Molecular Orbital Theory; Wiley: New York, 1985. (IS) Almlaf, J.; Fa@, K.,Jr.;Korsell, K.1. Compur. Chem. 1982,3,385. (16) Him,M.; Ahlrichs, R. J . Compur. Chem. 1989, 10, 104. (17)Ahlrichs, R.;Bir, M.; Haser, M.; Horn, H.; Kalmel, C. Chem. Phys. Lett. 1989. 162. 165. (18)van Duijneveldt, F. B. IBM Research Report RJ 945, 1971.
22s.
(9)Saito, S.;Sawada, S.; Hamada, N. Phys. Rev. B, in press.
Ab Initio Molecular Orbital Study of Nitrogen-Containing Polyenes with Donor-Acceptor Substituents: Dipole Moment and Statlc First Hyperpolarizability Tetsuya Tsunekawa* Polymer Research Laboratories, Toray Industries, Inc., 3-2- I Sonoyama Otsu, Shiga 520, Japan
and Kizasbi Yamaguchi Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: June 26, 1992; In Final Form: September 14, 1992)
Ab initio CPHF calculations have been carried out in order to clarify the relationship between dipole moment ( p ) and first hyperpolarizability (8)of nitrogen-containing *-conjugated polyenes with donoracceptor substituentsattached on the end. The systematic calculations on the polyene-like model compounds indicate that nitrogen-atom substitutionsin *-conjugated systems (N substitutions) fluctuate p-values and gradually decrease &values with increasing the number of substituted nitrogen atoms. From the calculated results, several tendencies are recognized for the changes of p- and &values induced by the N substitution. The molecules with nitrogen atom at the even-numbered position counted from an electron-accepting nitro group have larger &value but smaller p-values than those with nitrogen atom at the odd-numbered position, which is the other position of the same double bond. Especially, an introduction of a single nitrogen atom into the even-numbered position of hexatriene analogs decreases the p-value as controlling the reduction of &value. These ab initio mults support our previous conclusions based on semiempirical CNDO/S calculationsof stilbene and benzylideneaniline molecules. The analyses of molecular orbitals and full SCI calculations of the electronic transitions for the model compounds have revealed the intrinsic effects of N substitutions;the decrease of 8-value is mainly attributed to the blue shift of the absorption maxima, and the N substitution at the even-numbed position counted from nitro p u p enhances the indued polarization through the effective variations of the energy levels and shapes of the frontier *-orbitals. It is umcluded that N substitutions at the specifc positions provide us an effective approach in designing molecules with relatively small p-values but large @-values,which are desirable from the view point of crystal engineering of the nonlinear optical materials.
Iatroduction Recently, some organic crystals' comprising donor (D)-dcceptor (A) molecules (DA molecule)2have been intensively studied due to their demonstrated large second-order nonlinear optical susceptibilities which may enable us to realizc optical devioes in future photonic technology such as optical telecommunication and information processing. This characteristic property of organic crystals is attributable to a large intramolecular nonlinearity ( f i t hyperpolarizability, 8) of the DA molecule and a favorable noncentrosymmetric molecular orientation in its crystalline state.' The large @-value originates from strong chargetransfer interaction in the DA molecule which enhances the electronic polarization induced by incident laser light. Therefore, we accomplish large &value through designing an adequate DA molecule. On the other hand, the problem in obtaining a new organic nonlinear optical crystal is a rather difficult task. In light of the present scientific level, molecular orientations and crystal structures are hardly controllable because they are generally determined by the delicate balance among several intermolecular forces such as van der Waals,d i p ~ l d i @ ~and , hydrogen-bonding intetactionS. A Useful working hypothesis for controlling molecular orientation is that smaller p is rather favorable since it suppresses the strong dipoledipole interaction among DA molecule which generally leads to an unfavorable centrosymmetricmolecular packing. Therefore, Oo22-3654/92/2096-10268$03.Oo/O
a promising approach for a new molecular crystal with improved nonlinearity is designing a DA molecule with large but small pvalues as has been already demonstrated e~perimentally.~.~ For the last two decades, detailed studies on B- and 1-values of unsaturated hydrooerbon DA molecules have been camed out both theoretically and experimentally.' It has been already pointed out that &values increase together with the increase of p-values by extending r a n j u g a t a d systems and by introducing a strong D and A pair. Moreover, it is well-known that 8-values compensate for transition energies which limit the wavelength of available laser light for second harmonic generation (SHG).' Concerning DA molecules with heteroatoms involved in *-conjugated systems, systematic investigations on both the 8- and pvalues have not been carried out theoretically even though interesting molecular properties have been found out experimentally.'*5*6For example, DA pyridine molecules skilLfully designed were reported to be effective for improved molecular properties such as smaller ~-valuesS and shorter cutoff wavelengths6 as compared with corresponding hydrocarbon DA molecules. It may be considered that heteroatom substitutions at r-conjugated networb have capabilitiee of providing us a useful guiding principle for new sophisticated organic nonlinear optical crystals. In a previousworl~,~.~ for the purpose of investigating the effects of nitrogen-atom substitutions in *-conjugated systems (N substitutions), we calculated the 1- and &values of DA diphenyl (8
1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10269
Nitrogen-Containing Polyenes compounds as shown in 1, through the semiempirical CNDO/S7
1 X = C H or
A
: electron-accepting group : electron-donating group
D X,Y :CHorN
method combined with timedependent perturbation It was found that the DA bemyliden-niline molecule (la: X = CH, Y = N) has a smaller @-valuethan DA stilbene molecule (lb: X,Y = CH).3 However, our CNDO S results for @-values are not in accord with the results of PPP reported by Dirk et al.," since PPP calculations have predicted that the former has a larger &value than the latter." Although Singer et al.'* reported the experimental @-valuesof DA nitrogen-containing diphenyl compounds determined by measurements of electriefield-induced second harmonic generation (EFISH)," the data to clarify the substituent effects have never been seen. Therefore, the effects of the N substitutions on @-valuesremain unsolved, and the relationships between @- and p-values are not yet clearly explained. In recent years, the computer codes by more reliable ab initio methods as compared with semiempirical methods have been developed. Typical are HONDO and GAUSSIAN program packages which enable us to investigate static @-valuesbased on ab initio coupled-perturbedHartree-Fock (CPHF)14,1sand coupled HartretFock (CHF)16*"formalisms. The static @ are values at zero-frequency and cannot be directly compared to the experimental values by EFISH. In addition, previous studied8concluded that the static hyperpolarizabfitiesby the Hart-Fock methods are generally underestimated as compared with experimental values extrapolated to zero frequency. However, it is considered that these calculationsprovide us useful information for qualitative interpretation of intrinsic effects of N substitutions. For example, the IBM group reportedthat their ab initio CPHF approach works well to reproduce the trends of experimental @-values.18 Now we are systematically investigating the p-values and static @-valuesof various DA molecules with heteroatoms involved in r-conjugation through ab initio CPHF calculations. In a short comm~nication,'~ we have presented briefly the static @-values of DA nitrogen-containing polyenes which include the model compounds of DA diphenyl compounds as shown in 2. In this full paper, the p-values and static @-valuesof these compounds are reported in detail. The organization of the paper is as follows. Firstly, the energy gradient technique is applied to obtain the fully optimized geometries of the nitrogen-containingpolyenes. Secondly, the detailed and extensive analyses of basis set effects on the p- and @-valuesof DA molecules are carried out. Thirdly, the p- and static @-valuesare calculated by the CPHF method, and their mutual relationships are derived. Fourthly, the unsolved effects of N substitutions are explained by analyzing molecular orbitals in the ground state and by investigating the optical properties through full singly-excited configuration interaction (full SCI) calulations. Finally, implications of the ab initio calculated results for the model systems are discussed in relation to significant information on practical large molecular systems.
L
C o m p u t . t i d Method The static polarizability and hyperpolarizabilities based on the CPHF method are defined by the following equation for a molecular energy in the applied static electric field15920 E E(O) - pi - (1 /2h,F,F, - (1 /6)@@IFIF,, ( 1/24)yijk/F,F,FkF/ (
where the subscripts, which indicate the tensor components, are
N, n = 1 - 3
Figure 1. Model compound examined.
summed over the Cartesian axes x , y, and t. E(0) is the unperturbed energy of the ground state, F,is the component of the electric field in the i direction,pI is the permanent molecular dipole moment, a is static polarizability, and @ and y are respectively the first and second hypcrpolarizabilities. These tensors are determined from the analytical derivativa of the energy with respect to the applied electric fields in the case of the CPHF approximation.ls The average @-value(&=) is calculated by the use of the following equation'*
@," =
where
@,is obtained by
(@xz + @y2 + 812)''2
8, = (1/3)C(@ikk + @kik + @kki), k k
(2) x, Y,
(3)
Model compounds in this work are DA nitrogen-containing polyenes with transoid structures shown in Figure 1. All the compounds in Figure 1 are fully optimized without any symmetry constraint, by the use of the restricted Hartree-Fock (RHF) energy gradient method with the 6-3 1G basis set by Helm et al?l The @-tensorcomponents are calculated by using the inertial coordinate system in which one axis nearly corresponds to the direction from the nitro the amino group. Here, we defined this axis as the x axis, a perpendicular axis to the x axis in the molecular plane as they axis, and that perpendicular to the xy plane as the z axis. As mentioned above, ab initio CPHF calculations generally underestimate the & and y-values, as compared with experimental v a l ~ e s . ' ~The J ~ values are more underestimated if the basis set employed is relatively small. It is well-known that additional diffuse p and diffiLpe polarization d functions to split valence basis set on the fiist-row atoms play an important role in improving the underestimated values, especially, the values of y-tensor components representing out-of-plane w-electron polarization. Hurst et al.I5 reported that the 6-31G plus one diffuse p and d function (6-31G+lpld) is a reliable basis set which compromise% quality and size in obtaining a-and y-values of polyene systems. On the other hand, Daniel et d.18pointed out that @- and pvalua of DA compounds could be qualitatively estimated with a relatively small basis set. It was also reported that additional tight p and d functions, which are generally effective in lowering total energy of a molecule, do not improve the hyperpolari~abilities.~~ In comformity with these previous conclusions, we have also investigated the basis set effects for the p- and &values using STO-3G. 6-3 lG, and more extended basis sets including diffuse functionS. Since the complete optimization of the basis set used is impractical and not inevitably necessary for qualitative purposes, we have selected a practical and reliable basis set and have used it in the following calculation. In the prcaent ab initio calculations molecular integrals less than lo4 and orbitals with overlap eigenvalues less than lW5were discarded. We examined the thresholds for SCF iteration, geometry optimization, and CPHF iteration, using l-amino-2nitroethylene as the test compound. The &values by a threshold set adopted by Hurst et alls of lo4 on density matrix, lo-' on the largest energy gradient, and lo-' on U matrices in CPHF iteration were compared with those by the correspondingset of lop5,5 X lo4, and 5 X lo-'. Since the difference between the @-valueswas less than 0.5%, the latter threshold set was used to reduce elapsed times. Full SCI calculations were performed by
10270 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 Set Effectso for w- .ad @-Valuesbof l - ~ ~ n i t r o e t h y ~ STO-3G 6-31G 6-31G+lp 6-31G+ld 8.15 7.98 8.13 5.85 cc 227 225 100 183 Bxxx -45 -43 -37 -18 Bxyy -9 -2 -9 -1 Bx,, -100 Bxxy -36 -9 1 -104 24 16 19 BYYY 5 4 1 1 1 BYZZ 172 179 81 137 8, -73 -74 -84 -30 BY -0.1 0.5 4.1 -0.7 8, 187 156 197 8, 86
TABLE I: BM&
Tsunekawa and Yamaguchi TABLE II: R
6-31G+lpldC 8.12 216 -4 1 -14
-102 23 2 161 -76 0.3 179
r-conjugatd
6-3 lG+lpC
6-31G
8,
molecules D1-1 D1-2 D1-3 D 1-4
system (P)' 424C=N-Ne-N=N-
P
8"ec
P
8.13 7.47 7.97 7.23
2.06 1.53 0.84 0.47
7.98 7.36 7.86 7.12
1.56 1.12 0.71 0.27
D2-1 D2-2 D2-3 D2-4 D2-5 D2-6 D2-7 D2-8 D2-9 D2- 10 D2-11 D2- 12 D2- 1 3 D2- 14 D2- 1 5 D2- 15
C-C--C-CC4--C-NC=C-N=CC=N--C=C-Ne B(D1-3) vs 4D1-2) < p(DI-3), /3(D2-2) > P(D2-3) vs 4D2-2) < p(D2-3), O(D2-7) > B(D2-10) vs p(D2-7) < p(D2-10), and P(D3-4) > B(D3-5) vs r(D3-4) < p(D3-5). The third characteristic is seen among the molecules with the same number of nitrogen atom at the odd or even position. The N substitution at the position closer to the amino group rather drastically decreases the &values; for example, p(D2-2) < 8(D2-4), B(D2-3) < 8(D2-5), b(D2-6) < 8(D2-11), and B(D3-3) < 8(D3-5) < P(D3-7). Dulcic et a1.26pointed out that the 8-values of DA molecules increase approximately in proportion to the square of the length of r-conjugated systems. The results for DA polyenes agree with this suggestion, while those for DA nitrogenantaining polyenes deviate from thii rule to a certain degree as can be seen from the comparison of the D1 and D2 series. The increase of the @-valueswith an extension of r-conjugation is slightly s u p pressed by the effects of N substitution as explained above.
Nitrogen-Containing Polyenes 20
-
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10273 D1-1 D1-2 D1-3 D1-4
D3-6
5.0 0
10
-
0.0
-5.0 7
8
9
10
11
12
13
Dipole mement [ debye ]
Figure 4. Relation between p- and &values by 6-31G basis set: ( 0 )the results of DA polyenes; (0)the results of DA nitrogen-containing polyenes.
Figure 4 shows the relationship between p- and @-valuesof the molecules investigated. It can be seen that N substitution makes the p- and @-valuesdeviate from the relation indicated by values of DA polyenes. This is due to the result that N substitution drastically changes the p- and @-valuesin a different way depending upon nitrogen position, as indicated above. Note here that the @-valuesof DA hexatriene analogs especially deviate from a criterion for DA polyenes and that D3-2, D3-4, and D3-6 molecules have relatively large @-valuesbut small p-values. This may suggest that N substitutions are effective for the even position in relatively long ?r-conjugated systems. D. Energy Levels and Shapes of Molecular Orbitals. In the CPHF approach, the @-valuesare given by analytically calculating the mixings between the occupied and virtual orbitals of a molecule in its ground state.1s*22*27 The degree and direction of orbital transformations induced by the mixings determine the @-value. Therefore, the changes of the @-valuesshould be qualitatively interpreted by investigating the energy levels and shapes of frontier orbitals mainly mixed. As a typical example explaining the changes of the energy levels of frontier ?r-orbitals, the results by 6-31G+lp for the D1 series are shown in Figure 5. In Dl-1, D1-2, and D1-3 molecules, the ?r-orbital with an electron-donating character (rD) is the highest occupied molecular orbital (HOMO) and the ?r-orbital with an electron-accepting character (?rA) is the lowest unoccupied molecular orbital (LUMO). It is anticipated that the mixing between TD- and ?r,,,-orbitals mainly contributes to the @-valuebecause of the small energy gap and their donor and acceptor characters. The N substitution drastically lowers the energy levels of HOMO and bonding r-orbital (rDand r-orbital in Figure 9,and enlarges the energy gaps between occupied and virtual frontier orbitals. This tendency means that the orbital mixings are weakened so that the @-valuedecreases. Note that N substitutions lower the energy level of HOMO so as to make it approach to the energy of a nonbonding ?r-orbital on nitro group (?rNO2). In the D1-4 molecule with a N=N bond, the energy level of the ?rD-orbital becomes lower than that of the ?rN02-orbital. This implies that the ?rD-orbitaldeforms so as to have the electron cloud on the nitro group, and the resultant ?rD-orbitalpartially loses its electrondonating character. The orbital energies of HOMO and LUMO and the gaps for the molecules investigated are summarized in Table IV. The energy levels of HOMO and LUMO in D2 and D3 series behave like those in the D1 series. The energy level of HOMO rather than that of LUMO sinks down, so that the HOMO-LUMO energy gap is enlarged. The energy gaps in Table IV are responsible for changes of @-valuesin Table 11. The molecules with smaller @values have larger energy gaps which weaken the mixing. These results suggest that HOMO and LUMO predominantly contribute to the @-valueas expected. The characteristic orbital transformation relating to the position of the N substitution can be seen in HOMO and LUMO. As
-10.0
-15.0
Figure 5. Changes of energy levels of frontier r-orbitals of the molecules in D1 series. The results by 6-31G+lp (Cp = 0.075) basis set are given. TABLE Iv: Orbital Energies and the Gaps of HOMO and LUMO D1 series D1-1 D1-2 D1-3 D1-4 D2 series D2- 1 D2-2 D2-3 D2-4 D2-5 D2-6 D2-7 D2-8 D2-9 D2- 10 D2-11 D2- 12 D2- 1 3 D2- 14 D2- 15 D2- 16 D3 series D3- 1 D3-2 D3-3 D3-4 D3-5 D3-6 D3-7 D3-8
-10.01 -1 1.02 -1 1.56 -12.32'
1.33 0.91 1.14 0.68
11.34 11.93 12.70 13.00
-8.70 -9.59 -9.57 -8.99 -9.5 1 -10.24 -9.99 -10.34 -10.22 -10.68 -9.79 -1 1.02 -1 1.33 -10.70 -11.12 -1 1.87
1 .oo 0.57 0.88 0.86 0.84 0.4 1 0.37 0.37 0.68 0.69 0.68 0.23 0.18 0.14 0.52 0.002
9.70 10.16 10.45 9.85 10.35 10.65 10.37 10.71 10.90 1 1.37 10.47 11.25 11.51 10.84 1 1.64 1 1.872
-7.82 -8.64 -8.44 -8.15 -8.47 -7.99 -8.33 -8.68
1.07 0.70 0.97 0.80 0.94 0.93 0.82 0.61
8.89 9.35 9.41 8.96 9.4 1 8.92 9.15 9.29
The molecular structures are shown in Figure 2. 'Orbital energy of the next HOMO.
In electronvolts.
typical examples, the HOMO and LUMO of Dl-1, D1-2, and D1-3 molecules are shown in Figure 6, together with their orbital coefficients. As seen from the comparisons of orbital coefficients, the HOMO of the D1-2 molecule more localizes upon the amino group as compared with those of the D1-1 and D1-3 molecules, hence indicating the largest electron-donating character among
10274 The Journal of Physical Chemistry, Vol. 94, No. 25, 1992 0.70
0.64
0.74
n 0
-0.55
-0.62
-0.27
-0.15
-0.21 -0.
-0
-0.
.79
.88
.73 HOMO
HOMO
OzN-CH=CH-NHz
0.66
-0
0 2 N-CH=N-
HOMO NH2
0 2 N-N
=CH-NHr
D1 - 1 D1- 2 D1- 3 Figure 6. Comparisons of HOMO and LUMO among Dl-1, D1-2, and D1-3 molecules. The results by 6-31G+lp (&, = 0.075) are given. The orbital coefficients are summed up for each atomic center.
these molecules. The LUMO of the D1-2 molecule, to some extent, localizes more upon the nitro group than that of the D1-3 molecule. These imply that the induced polarization by the mixing of HOMO and LUMO may be enhanced in the Dl-2 molecule more than that in the Dl-3 molecule, and even more than that in the D1-1 molecule. The similar orbital transformations can be seen in the case of the D2 and D3 series with the nitrogen atom apart from the nitro or the amino group. E. Properties on Electronic Transition. According to the well-known two-level model,28-30the mean @-valuehas the following approximate relation with the properties associated with electronic transition
B
a fApg-e/W3
= fApg-Jma2
(4)
where W is the transition energy and A, is the corresponding absorption maxima, whilef and Ape are respectively the oscillator strength and the difference of dipole moment between ground and excited states. Qualitatively, both f and A,, should be closely related to the degree of the orbital mixings in the CPHF calculation. The Apg+ term corresponds to the polarization induced by the mixings. These optical properties by RHF/SCI calculations and the contribution of the transition from TD- to ?rA-orbitalare summarized in Table V. From Table V it is confmed that ?rD- and ?rA-orbitals (HOMO and LUMO) dominantly contribute to the chargetransfer state throughout all the series. The values of A, and Apg+ are in reasonable accord with the changes of energy levels and shapes of frontier orbitals discussed above. As seen from the results of D1 and D2 series, the N substitution gradually shortens the A, with the increase of the number of nitrogen atoms in ?r-conjugated systems. According to the conventional Dewar's rule31on absorption maxima of heteroatom-containingdyes, a DA molecule with the nitrogen atom at even position should have longer A,, as compared with a DA molecule with ?r-conjugated system comprising of carbon atoms only. The rule is therefore in conflict with our results at the HF-SCF/SCI level. More precise calculations including electron correlation may be necessary for clarification of this point. The calculated Apg+ clarifies the enhancement of induced polarization by the N substitution at the specific position. The DA molecules with the nitrogen atom at the even position have larger Apg* than those with nitrogen atom at the odd position of the same double bond. It should be mentioned here that D2-4, D2-7, and D3-4 molecules have more than 20% larger Apgl as compared with the correspondingDA polyenes in the same series. Thefvalue decreases with N substitution, but the change is not so large except for the D1-4 molecule. Supposing that the more the HOMO and LUMO localize in the ?r-conjugated system the smaller thef values relating to the orbital overlap become, this behavior on f value is reasonably understood. Figure 7 shows the relation between the ,A, and the @-values. Roughly speaking, the relation between the @-valuesand A, of
Tsunekawa and Yamaguchi TABLE V Optical Properties for Charge-Transfer State and the Contribution of HOMSLUMO Transition by RHF/b3lG/fd SCI Calculations transition contributionb molecules" energy (nm) ("/.I f (D) D1-1 207.1 92.7 0.576 4.387 D1-2 189.3 86.0 0.506 4.983 D1-3 72.9 182.0 0.412 3.060 D1-4 177.3 84.2 1.369 0.263 D2- 1 D2-2 D2-3 D2-4 D2-5 D2-6 D2-7 D2-8 D2-9 D2- 10 D2-11 D2-12 D2-13 D2- 14 D2-15 D2- 16
240.8 223.7 223.3 231.0 224.4 216.8 212.6 210.8 205.3 203.3 222.6 197.7 200.6 208.2 196.4 191.5
92.0 89.8 92.1 92.1 91.6 90.7 85.8 88.7 89.1 88.8 92.5 84.0 86.7 89.6 87.1 82.5
1.159 1.1 12 1.062 1.077 1.153 1.073 0.998 1.085 0.919 1.054 1.102 0.934 1.026 1.031 0.921 0.906
5.785 6.030 4.623 7.402 4.729 4.260 7.167 5.880 6.975 3.204 4.962 5.614 3.277 6.466 4.770 4.542
D3- 1 D3-2 D3-3 D3-4 D3-5 D3-6 D3-7 D3-8
268.7 249.8 252.2 259.6 254.0 262.0 261.1 257.8
89.5 87.4 90.6 87.2 88.1 88.2 90.3 88.8
1.744 1.698 1.659 1.629 1.743 1.617 1.726 1.694
6.900 6.298 5.757 8.569 5.346 8.215 5.992 6.005
OThe molecular structures are shown in Figure 2. bThe contribution of a single-electron excitation from HOMO to LUMO (from rD-to ?r,-orbital). The values are calculated by the square of CI coefficients. Oscillator strength. "The difference of molecular dipolar moments between the ground- and charge-transfer states. pvec [ I O -30 esu]
20
J
10
Cb'O
0 1
eoD1-1 180
200
220
240
260
2
kmax [nm]
F i e 7. Relation between A-- and &values calculated by 6-3 1 G basis set. See Tables I1 and V for the values of B and A., ( 0 )The results of DA polyenes. (0)The results of DA nitrogen-containing polyenes.
DA nitrogen-containing polyenes conforms with that observed for DA polyenes. But it appears that the @-valuesof some DA nitrogencontaining polyenes are slightly larger than those expected by the relation in DA polyenes and A, value. N substitutions are effective for shortening the A,, though they do not break down the trade-off between @-valuesand A,., It is considered that the slight deviation from the relation in DA polyenes is attributable to drastic change of A, and in some cases, to enhanced polarization by effective transformations of frontier orbitals explained above. . F. Ab Initio Prediction on a Practical Molecular System. First, we summarized the calculated results of DA diphenyl compounds and the models in Table VI. Ab initio results of model compounds support previous CNSO/S results on the changes in p- and @-
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10275
Nitrogen-Containing Polyenes
TABLE VI: cllleplrtcd 1 rad @ of DA Dipbmyl Compowh rad Model C o m m
. .
DA diDhcnvl comwunds'
-x=y-'* -CH=CH-CH=N-N==CH-N=N-
k2NDOSC @CNDosd
8.64 7.11 9.70 8.42
202.8 135.3 31.8 132.0
fiPPP'
model comwunds*
@PPd
fi&3lG*
@6-310h
10.0 248.0 6.0 371.0 13.3 77.0
11.39 10.35 12.00 11.31
17.78 16.91 12.40 12.90
'DA diphenyl compounds 1 (D = NHz, A = NO2, X,Y = C H or N). bDA hexatricnc analogs 2 (D = NH2, A = N02, X,Y = CH or N). CDipolemoment3g4by CNDO/S, in units of debyes. dFirst hyesu. 'Dipole moperp~larizability~.'by CNDO/S, in units of ment" by PPP,in units of debyes. 'First hypcrpoIarizabdity1' by PPP, in unit of 1WMesu. XDipole moment calculated in this work, in units of debyes. *First hypcrpolarizability calculated in this work, in units of 10-M esu.
values by the N substitutions. The PPP calculations may overestimate the 8-value of DA benzylidene-anilinemolecule l a (X = CH, Y = N). The model compound (X = CH, Y = N) for l a has the smallest p-value among the models and large &value ranked next to that of the DA stilbene molecule l b as expected from the CNDO/S results. Judging from the @-valueonly, l b is attractive due to its largest B-value. However, l a with a small p-value is more advantageous than l b in view of molecular alignment regulation required for an efficient second-order nonlinear optical crystal. Moreover, the calculated results suggest some useful information for designing new nonlinear optical molecular systems. A single or a few N substitutions skillfully selected at a long r-conjugated system could be used for controlling the 1-value with suppression of the decrease of the &value. The even position closer to an electrondonatinggroup is the most effective for that purpose. DA molecules with long *-conjugated systems such as DA phenylbutadiene, reported to have large &value,' are attractive molecular systems to which these suggestions can be applied.
Conclusion In summary, systematic investigations of the p- and &values of DA nitrogen-containing polyenes have been carried out by ab initio CPHF and full SCI calculations. It was found that N substitutions decrease drastically @-valueswith the increase of the number of nitrogen atoms due to the HOMWLUMO energy gap being enlarged, and that the molecules with nitrogen atom at the even position have smaller p-values and larger @-valuesthan the molecules with nitrogen atom at the odd position of the same double bond. Espbcially, the molecules with a single nitrogen atom at the even position of DA hexatriene are promising because of relatively large &values but small p-values. These ab initio results support our previous results by semiempirical CNDO/S calculations on practical DA diphenyl compounds 1. The peculiarity of the even position arises from the increase of induced polahtion
derived by the effective transformation of frontier r-orbitals and the suppression of the enlargment of the energy gap by the N substitution. As mentioned previously, a smaller p-value is morc effective for controlling molecular packing which determines the performance on the second-order optical nonlinearity. It is therefore concluded that the N substitution at the specific position of r-conjugated systems provides us a useful approach for obtaining Promisingmolecules with large &values but small p-values for new organic second-order nonlinear optical crystals.
Acknowledgment. The authors are grateful to Prof. K. Tanaka, Prof. T. Noro, and Prof. F. Sasaki for helpful discussions.
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