Molecular orbitals and optical nonlinearities for symmetrically substituted benzylidene anilines

Synthetic Metals, 51 (1992) 147 151

147

Molecular orbitals and optical nonlinearities for symmetrically substituted benzylidene anilines Yuhei Mori*, Takashi Kurihara, Toshikuni Kaino and Satoru Tomaru N T T Opto-electronics Laboratories, Nippon Telegraph and Telephone Corporation, Shirakata, Tokai, Ibaraki 319 11 (Japan)

Abstract Molecular structure and orbitals are calculated for symmetrically substituted benzylidene anilines. From calculation of the electronic structure, the third harmonic generation is approximately explained by a three-level system in which the A~ excited state plays an important role. The molecular orbitals that contribute to X(3) are clarified. From the calculation relating to the displacement of atoms, it is found that symmetry is broken at the optimum point of the B u excited state. This phenomenon contributes to Z(;~) in situations such as the two-photon resonance region.

1. I n t r o d u c t i o n S e v e r a l t h e o r e t i c a l [1, 2] a n d e x p e r i m e n t a l [3, 4] i n v e s t i g a t i o n s h a v e b e e n c a r r i e d o u t to find a c e n t r o s y m m e t r i c m o l e c u l e t h a t h a s a l a r g e X(3). W e h a v e r e p o r t e d t h e s y m m e t r i c a l m o l e c u l e s S B A a n d S B A C as n e w m a t e r i a l s [4]. T h e s e a r e t e r e p h t h a l - b i s - ( 4 - N , N - d i e t h y l a m i n o a n i l i n e ) a n d 2, 5 - d i c h l o r o - t e r e p h t h a l - b i s - ( 4 - N , N - d i e t h y l a m i n o a n i l i n e ) , s h o w n in Fig. 1. T h e i r Z (3) v a l u e s c o m p a r e w e l l w i t h t h o s e o f c o n j u g a t e d p o l y m e r s , e v e n t h o u g h t h e y a r e s h o r t - c o n j u g a t e d m o l e c u l e s . I t is i m p o r t a n t to e x a m i n e t h e e l e c t r o n i c m e c h a n i s m s of t h e s e m o l e c u l e s . I n t h i s w o r k , t h e e f f e c t i v e m e c h a n i s m s for X(3) e n h a n c e m e n t a r e s t u d i e d . M o l e c u l a r o r b i t a l s a n d t h i r d - o r d e r s u s c e p t i b i l i t y for S B A a n d S B A C a r e c a l c u l a t e d . T h e e f f e c t o f o r b i t a l s h a p e u p o n t h i r d - o r d e r n o n l i n e a r i t y is i n v e s t i g a t e d . T h e S t o k e s s h i f t a n d t h e o p t i m i z e d s t r u c t u r e a r e c a l c u l a t e d for t h e l B , e x c i t e d s t a t e .

- - ~ N~ ~

N

(CI) (CJ)

Fig. 1. Calculated molecules, SBA and SBAC.

*Present address: Davy-Faraday Research Laboratories, The Royal Institution of Great Britain, 21 Albermarle Street, London WlX 4BS, UK.

0379-6779/92/$5.00

1992 Elsevier Sequoia. All rights reserved

148

To check the c a l c u l a t i o n result, the THG Z (3) has been m e a s u r e d by irradiation at the f u n d a m e n t a l w a v e l e n g t h a r o u n d 1 pm.

2. C a l c u l a t i o n o f t h e e l e c t r o n i c s t a t e s

The geometry of the ground state has been optimized by an M N D O program to obtain bond lengths and angles. With the optimized structures, the excitation energies and the transition moments have been obtained by a C N D O / S - S D C I program. Third-order susceptibilities have been c a l c u l a t e d by the Z (3) expression [5-7] derived from time-dependent perturbation. The calculated values of third-order susceptibility at 0.656 eV are: 7(SBAC) = 7.7 × 10 -35 esu, and 7(SBA) = 6.4 × 10 .35 esu. According to the expression of Z (3), one sequence of four non-zero transition moments, which starts and ends at the ground state, c o n t r i b u t e s to the third-order susceptibility. It is found that the term, g - 1 B u - 2 A g 1 B u - g c o n t r i b u t e s to the third-order susceptibility most effectively in this c a l c u l a t i o n for SBA and SBAC. In the sequence g - 1 B u - 2 A g 1Bu - g, the transition g - 1Bu is mainly composed of the H O M O - L U M O transition. As for the intermediate transition 1 B u - 2Ag, three kinds of orbital transition are used, for the 2Ag state is expressed mainly as a linear c o m b i n a t i o n of three configurations according to the results of CI. The three orbital transitions are: H O M O - 1 to HOMO, H O M O to L U M O and L U M O to L U M O + 1, as shown in Fig. 2. Of these, the H O M O - 1 to H O M O is most effective [2]. The LCAO coefficients of the orbitals used for transitions in Fig. 2 are shown in Fig. 3. In this Figure, the horizontal u

V

W

LUMO+I-~

L:o:°oT •-t-t--

_H_I

HOMO-1 = = II

I

I

112Ag 4.06eV /

//p

_l

-H--

/~

~

/ //

/ /

~

s

k 1 Bu 3.56eV

g (i Ag) Fig. 2. The excited states and the orbital states w h i c h c o n t r i b u t e to the third-order susceptibility,

149

.N ~

0.4 0.2

0

I

-0.2

III ~

0.4 0.2

-0.2 -0.4

LUMO+I

II"

-0.4

0

ii,,,

l.i I I lI~ll

It 'II IIII I I I I'!lri I

0.2,,I

~UM0

II IIIl!lt.ll!lmll

o II1

1 I1111 -021blllttllllltll!l Ililllil ,0M0 • l Ill! 0.4

I=111 i-iilll!f

I'1

o2; l i .11 I ILl I, IIII itill.! i.!l,ilillj °li]illi 'i",Jl II .OMO. -211'i L i I,!1 k'l Fig. 3. Molecular orbital LCAO coefficients of SBA. axis represents the positions of the atoms. Comparing the orbitals between H O M O - 1 and H O M O for SBA in Fig. 3, most of the respective LCAO coefficients on the left side of the molecule have opposite signs, while most of those on the right side have the same signs. This is the significant reason for the large transition moments b e t w e e n the Bu and the A~ states c o n t r i b u t i n g to the large third-order susceptibility.

3. O p t i m i z e d s t r u c t u r e in t h e e x c i t e d s t a t e a n d its e f f e c t u p o n Z(3)

The results m e n t i o n e d above are based on the c a l c u l a t i o n of the electronic states only and where lattice distortion associated with the electronic excitation is not t a k e n into account. As for the m e a s u r e d electronic excitation spectra of SBA and SBAC, vibrational coupling occurs [4], and the Z (~) spectra are maximized at the peak with the lowest v i b r a t i o n a l energy [4], which is different from the vertical transition. It is necessary, therefore, to investigate the electronic s t r u c t u r e at the b o t t o m

150

of the potential curve of the Bu excited state. In this work, the molecular structure for the potential minimum point is obtained by optimizing the energy for the Bu excited state by the MNDO method. The results are shown in Fig. 4. Figure 4(a) shows the difference between the optimized bondlength of the Bu excited state and that of the optimized ground state. In this Figure, the distribution of the C-C bond length is distorted. For the right side of the molecule, the structure is almost the same as that of the ground state, while for the left side, the C=N double bond is extended and the single bonds are shortened: the molecular symmetry is broken. This distortion of the molecular structure in the excited state is consistent with the shape of the fluorescence spectrum [8]. Figure 4(b) shows the difference of charge density between the excited state and the ground state. The charge distribution changes mainly on the left side of the molecule. This excited state has a dipole moment. Considering the effect of this phenomenon on the 3~3> expression, one summation term, which includes the dipole moment of this state, contributes to the third susceptibility in addition to the sequences of the four transition moments. The effect of this symmetry distortion increases •(3> in the following case, for example: (i) the molecules are in the condition where polarized states are stabilized;

• o~/ _i_l (a) ~±

I

Ill. ••'-~-I

,I~ jJi

,, J!/

I

I

I I

J I I

it, II

I I

I

I I

+HI

+I

'-C.,,,,, /~

i I I

0.]

-i

0.05

H

It

I t I

~

J

l,

I

I ,,II

f +1 I

t

I

I

~.__(/, I

t r It

J I i / I I I I I

~/-"X~

J I J I

I

I

~

.... II

+ 't!/,'- : o

I

1

/

I .... -I I,.-.

-0.05

Fig. 4. Calculated optimized structure for the B,, excited state• (a) Bond-length difference between excited optimized structure and the ground optimized structure; (b) charge-density difference between the excited state and the ground state.

151 TABLE 1 Measured Z(3) values around the two-photon resonant region I(1.064)/I(1.90) means the THG intensity at 1.064 gm compared with that at 1.90 t~m. SBA

SBAC

1(1.064/~m)/I(1.90 gm) (powder)

7.05

14.6

Z(:~)(1.064 tzm) (deposited film)

4x10 -llesu (thickness 750 A)

5 x 1 0 ~lesu (600 A)

Z(:~)(0.98gm) (deposited film)

5x10 ~esu (750 ,~)

7 x 1 0 ~esu (600 A)

(ii) At the two-photon r e s o n a n c e point for the irradiation of light, the forbidden r e s o n a n c e becomes allowed, and the e n h a n c e m e n t of Z(3) due to r e s o n a n c e occurs. To check the second case, the optical nonlinearities have been measured by irradiation at the f u n d a m e n t a l w a v e l e n g t h a r o u n d 1 gm, which is nearly twice as long as t h a t of the absorption edge of the Bu excited state. The intensity of T H G light at 1.064 #m, is stronger t h a n t h a t at 1.90 pm, as is shown in Table 1. The Z(3) values at 1.069 and 0.98 ~m are s h o w n in Table 1 and these large values are presumed to be due to the two-photon resonance.

4. S u m m a r y and c o n c l u s i o n s The effective mechanism for Z(3) e n h a n c e m e n t in SBA and SBAC have been studied. From the c a l c u l a t i o n of electronic structure, the third harmonic generation is explained approximately by a three-level system w h e r e the A~ excited state plays an i m p o r t a n t role. The effect of the orbital shape upon the third-order nonlinearity is clarified. From the calculations involving the displacement of atoms, it is found t h a t a b r e a k in symmetry occurs at the optimized point of the B u excited state. This distortion of the potential surface is presumed to cause the two-photon resonance.

References 1 M. G. Kuzyk and C. W. Dirk, Phys. Rev. A, 41 (1990) 5098. 2 Y. Mori, T. Kurihara, T. Kaino and S. Tomaru, Jpn. J. Appl. Phys., 31 (1992) 896. 3 L. R. Dalton, J. Thomson and H. S. Nalwa, Polymer, 28 (1987) 543; L. R. Dalton, Nonlinear Optical and Electroaetive Polymers, Plenum, New York, 1988 p. 243. 4 T. Kurihara, N. Oba, Y. Mori, S. Tomaru and T. Kaino, J. Appl. Phys., 70 (1991) 17. 5 R. Loudon, The Quantum Theory of Light, Clarendon Press, Oxford, 1983. 6 J. A. Armstrong, N. Bloembergen, J. Ducuing and P. S. Pershan, Phys. Rev., 127(1962) 1918. 7 B. J. Ward, Mol. Phys., 20 (1971) 513. 8 Y. Mori, T.Kurihara, T. Kaino and S. Tomaru, in preparation.