Geometric and electronic structure and nonlinear optical properties of push-push and pull-pull conjugated systems

Synthetic Metals, 4P-50 (1992) 181-186

181

Geometric and electronic structure and nonlinear optical properties of push-push and pull-pull conjugated systems F. M e y e r s a n d J. L. Brddas Service de Chimie des Matdriaux Nouveaux, Universitd de Mons-Hainaut, place du Parc 20, B-7000 Mons (Belgium)

Abstract We present ab initio coupled perturbed Hartree-Fock (CPHF) calculations on the firstorder polarizabilities of phenylene and hexatriene conjugated segments end-capped by either two push (electron donor) groups, two pull (electron acceptor) groups, or one push and one pull groups. The push groups are taken to be amine functionalities, the pull groups are nitro or aldehyde functionalities. The results obtained at the split-valence basis set, without and with polarization functions, indicate that while the ~ values differ by only a factor of two, the T values are scattered over two orders of magnitude. The largest values of T are provided by the push-pull compounds.

1. I n t r o d u c t i o n It is well k n o w n that 7r-conjugation c o n s t i t u t e s an essential i n g r e d i e n t in t h e s e c o n d - o r d e r and t h i r d - o r d e r n o n l i n e a r optical r e s p o n s e of o r g a n i c c o m p o u n d s [ 1 - 3 ] . Usually, the quadratic a n d cubic n o n l i n e a r p r o c e s s e s are c o n s i d e r e d to require different t y p e s of m o l e c u l a r structures. This s t e m s f r o m t h e fact t h a t s e c o n d - o r d e r effects are r e s t r i c t e d to n o n c e n t r o s y m m e t r i c s y s t e m s ; a p r o t o t y p i c a l e x a m p l e o f t h e s e b e i n g p a r a - n i t r o a n i l i n e . In the c h a r g e t r a n s f e r e x c i t e d state o f p a r a - n i t r o a n i l i n e , one e l e c t r o n is formally t r a n s f e r r e d f r o m the d o n o r ( a m i n o g r o u p ) to the a c c e p t o r (nitro g r o u p ) t h r o u g h the c o n j u g a t e d s e g m e n t ( p h e n y l ring). Polarization o f the 7r-electronic c l o u d is t h e r e f o r e e a s y in that direction ( d o n o r to a c c e p t o r ) a n d m o r e difficult in the r e v e r s e direction ( a c c e p t o r to d o n o r ) ; this biases the polarization a n d leads to a s e c o n d - o r d e r effect. The t h i r d - o r d e r optical nonlinearity d o e s n o t require s u c h n o n c e n t r o s y m m e t r i c s t r u c t u r e s a n d p r e f e r r e d directions of i n t r a m o l e c u l a r c h a r g e transfer; a c c o r d i n g l y , m o s t o f the m o l e c u l a r materials that have b e e n c o n s i d e r e d in t h a t c o n t e x t do n o t p o s s e s s d o n o r / a c c e p t o r end substituents. However, it w o u l d be o f interest to investigate the influence o f s u b s t i t u t i o n o n the c u b i c n o n l i n e a r optical r e s p o n s e , in o r d e r to p r o v i d e a d e e p e r u n d e r s t a n d i n g o f the s t r u c t u r e / p r o p e r t y relationships. T h e r e f o r e , we h a v e u n d e r t a k e n a t h e o r e t i c a l s t u d y of the t h i r d - o r d e r polarizability in c o n j u g a t e d m o l e c u l e s w h e r e b o t h e n d s are s u b s t i t u t e d either b y d o n o r g r o u p s ( p u s h - p u s h m o l e c u l e s ) o r b y a c c e p t o r g r o u p s ( p u l l - p u l l m o l e c u l e s ) . F u r t h e r m o r e , since it has b e e n

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182 proposed that reduction of symmetry can actually enhance the cubic nonlinear effect [4], we have also investigated push-pull conjugated molecules. The conjugated compounds under study include hexatriene and benzene. The donor is taken to be the amino group, (--NH2); the acceptor, either the nitro group (--NO2) or the aldehyde group ( - C H = O ) . Calculations are carried out at the Hartree-Fock ab initio level, using a split valence 3-21G basis set [5]. The molecular polarizabilities are evaluated via the coupled perturbed Hartree-Fock approach of Dupuis and coworkers [6]. We stress that the CPHF technique is not based on a description of the excited states (which, in the case of hexatriene, is poor at the Hartree-Fock level), but rather evaluates the total energy modification as a function of electric field, i.e., the Stark energy. The polarizability coefficients are obtained by means of an analytical derivative procedure on the Stark energy [6]. We investigate in detail the effects of substitution on: (i) geometry, (ii) electronic properties, and (iii) static first-order (a) and third-order (T) molecular polarizabilities. The efficiency of the centrosymmetrical p u s h - p u s h and pull-pull compounds is compared to that of the unsubstituted and push-pull molecules. The paper is structured as follows. Section 2 contains a description of the molecules under study in terms of their geometric structures. In Section 3, the atomic charge distributions are considered and the dipole moments and first-order hyperpolarizabilities (fl) of the noncentrosymmetric molecules are compared. Section 4 is devoted to the a discussion of the static firstorder (a) and third-order (T) polarizabilities. 2. G e o m e t r i c

structures

For all the molecules presented in Table 1, geometry optimizations are carried out at the ab initio restricted Hartree-Fock (RHF) level, using a split-valence 3-21G basis set. All bond lengths and bond angles are fully optimized assuming coplanar conformations. The structure of para-nitroaniline (pNA) is discussed in detail elsewhere [7]. The weight of those resonance structures involving charge transfer all the way from the donor to the acceptor is calculated to be negligible in the ground state, even if the average degree of bond-length alternation within the phenyl ring (~r) is calculated-to be 0.022 /~. Compared to pNA, the centrosymmetric para-aminoaniline (pAA) molecule has a lesser quinoid character, with ~)r equal to 0.009/~. In para-dinitrobenzene (pNN), this value is again reduced and becomes slightly negative ( S r = - 0.002/~); this indicates that the geometric structure in the phenyl ring acquires some 'anti-quinoid' character: the bond between the ortho positions is 0.002/~ longer than the one between the ortho and p a r a positions. Compared to pNA, the C--N bonds in the two centrosymmetric compounds elongate, the C--NH2 bond remaining shorter (1.388/~ in pAA versus 1.359/~ in pNA) than the C--NO2 bond (1.454 /~ in pNN versus 1.430/~ in pNA). In the systems where the conjugated segment is the hexatriene molecule (ht), the same observation on the evolution of the C--N bonds can be made.

183 TABLE 1 RHF/3-21G optimized bond lengths (in/~)

c a

benzene ~,~~

,

% ~~-~o

c

d

1.385

1.385

1.385

pNA

1.359

1.402

1.370

1.382

1.430

""2

pAA

1.388

1.390

1.381

1.390

1.388

2

pNN

1.454

1.377

1.379

1.377

1.454

~

N"2~

b

Y

a hexatriene "

"

~

~

'

"

2

~

,o2

b

c

d

e

f

1.322

1.462

1.327

1.462

1.322

htNA

1.360

1.338

1.440

1.337

1.440

1.326

1.429

htAA

1.378

1.330

1.458

1.329

1.458

1.330

1.378

htNN

1.442

1.317

1.453

1.328

1.453

1.317

1.442

htCHO

1.468

1.325

1.455

1.328

1.455

1.325

1.468

N. 2

' c

° ,

2

~

,

~

N02

With r e g a r d to the b o n d - l e n g t h alternation in the p o l y e n i c s e g m e n t , two different t e n d e n c i e s are found. In h e x a t r i e n e itself and the b i s - a c c e p t o r s u b s t i t u t e d (htNN a n d htCHO) c o m p o u n d s , t h e b o n d alternation increases w h e n g o i n g f r o m the middle to the end o f the molecule. In hexatriene, the l e n g t h difference b e t w e e n b o n d s d a n d e (see Table 1), br(d-e), is equal to 0 . 1 3 5 A while b r ( e - f ) = 0 . 1 4 0 /~; in htNN, t h e s e v a l u e s are 0 . 1 2 5 a n d 0 . 1 3 6 /~, respectively, a n d in h t C H O t h e y are 0 . 1 2 7 and 0 . 1 3 0 /~. In the

184 a c c e p t o r - e n d of htNA, this t r e n d is p r e s e r v e d (~r(d-e)=O.103 ~ v e r s u s ~ r ( e - J ) = 0 . 1 1 4 / ~ ) . In the case o f the b i s - d o n o r htAA molecule, a small but r e v e r s e t e n d e n c y is observed. A d e c r e a s e o f 0 . 0 0 1 / ~ in bond-length a l t e r n a t i o n takes place f r o m the middle to t h e end o f the molecule; ~ r ( c - d ) = 0 . 1 2 9 /~ and ~ r ( b - c ) = 0 . 1 2 8 /~. It is also the case for the d o n o r - e n d o f htNA, w h e r e these values are 0 . 1 0 3 and 0 . 1 0 2 /~, respectively. It is, however, i m p o r t a n t to n o t e t h a t globally it is the p u s h - p u l l htNA c o m p o u n d that leads to the smallest d e g r e e of b o n d alternation in the middle o f the molecule. This situation is a n a l o g o u s to that of pNA which has the largest quinoid c h a r a c t e r a m o n g the b e n z e n e derivatives.

3. Charge distributions The 7r-charge distributions of the m o l e c u l e s u n d e r study are c o l l e c t e d in Table 2. T h e s e values are e v a l u a t e d b y m e a n s o f a Mulliken p o p u l a t i o n analysis. Accordingly, the t r e n d s are m o r e relevant t h a n the absolute c h a r g e values themselves. First, we c o m p a r e the influence of the c o n j u g a t e d s e g m e n t on the c h a r g e distribution in the p u s h - p u s h and p u l l - p u l l c o m p o u n d s . The 7r-charge transf e r r e d to or f r o m the c o n j u g a t e d s e g m e n t b y the d o n o r or a c c e p t o r g r o u p s are slightly larger in the case o f h e x a t r i e n e c o m p a r e d to b e n z e n e . F o r htAA, the 7r-charge a d d e d in the h e x a t r i e n e s e g m e n t is equal to 0 . 2 8 H , the c o r r e s p o n d i n g value for b e n z e n e in pAA is 0.22 H . In htNN, the ~r-charge p u m p e d by the two a c c e p t o r ends is 0.101e I v e r s u s 0.081e ] in pNN. In the case o f the o t h e r pull-pull c o m p o u n d u n d e r study, htCHO, the 7r-charge, which is p u m p e d b y the a c c e p t o r s , is slightly bigger and a m o u n t s to 0.12]e]. F o r the p u s h - p u l l c o m p o u n d s , the global ~r-charge distributions p e r substituent g r o u p and c o n j u g a t e d s e g m e n t are the same for pNA and htNA. The difference in dipole m o m e n t (7.8 d e b y e s for pNA v e r s u s 10.7 for htNA) primarily originates f r o m the m o r e e l o n g a t e d g e o m e t r i c s t r u c t u r e of the TABLE 2 RHF/3-21G ~r-charges (in electron charge units) per acceptor or donor and conjugated segment (X and Y refer to the substituents as given in Table 1) X Benzene pNA pAA pNN Hexatriene htNA htAA htNN htCHO

1.82 1.89 4.04 1.82 1.86 4.05 2.06

Conjugated segment 6.00 6.10 6.22 5.92 6.00 6.10 6.28 5.90 5.88

Y

4.08 1.89 4.04 4.08 1.86 4.05 2.06

185

hexatriene segment. It is important to realize that in both compounds the 7r-charge transferred from the donor group all the way to the acceptor group is merely equal to some 0.081el, 0.10 H being added to the conjugated segment. We note that the second-order polarizability (fl) is about four times larger in htNA (30.4 × 10 -a° e.s.u.) than in pNA (7.9 × 10 -a° e.s.u.), a result which reflects both the longer spatial extent and the better delocalization provided by hexatriene with respect to benzene. 4. First- and third-order p o l a r i z a b i l i t i e s In Table 3, we present the average first-order ( ( a ) ) and third-order ((T)) polarizabilities for the molecules under study. As mentioned previously, we are using the coupled perturbed Hartree-Fock analytical derivative approach of Dupuis and coworkers with a split-valence 3-21G basis set. We focus our interest on the trends, more than on the absolute values which are known to be calculated consistently too low. (In a few instances, we have carried out calculations with a double-zeta basis set including polarization functions (6 d-type orbitals on C, O, N; 3 p-type orbitals on H); this is found to enhance the average y value merely by some 12%.) Concerning the first-order polarizabilities, a general observation is that for all the compounds, the (a> value is of the same order of magnitude; it differs at most by a factor of two between the benzene molecule (7.1 /~3) and htCHO (15.8/~3). Larger values of
TABLE 3 CPHF/3-21G average first-order polarizability ((a> in /~3 or 10 -24 e.s.u.) and third-order polarizabilities ( in 10 -a~ e.s.u.)

x/Y

<,~>

H/H NH2/N02 NH2/NH2 NO2/NO2 CHO/CHO

7.1 10.5 9.1 10.9

<~,>

10.2 15.7 13.0 15.5 15.8

0.4 5.6 1.3 3.1

4.3 29.8 10.6 21.7 21.7

186 be m a d e : the pNN molecule, in w h i c h the p h e n y l ring has the m o s t i m p o r t a n t 7r-charge deficiency, p r e s e n t s the largest value. Turning to the a v e r a g e t h i r d - o r d e r polarizabilities, the values we calculate are s c a t t e r e d over two o r d e r s of m a g n i t u d e : f r o m 0 . 3 6 × 10 -36 e.s.u, for the b e n z e n e m o l e c u l e up to 2 9 . 8 × 10 -8~ e.s.u, for htNA. The m o s t i m p o r t a n t result of o u r w o r k is that the n o n c e n t r o s y m m e t r i c p u s h - p u l l - t y p e substitutions are f o u n d to provide the largest values a m o n g either the b e n z e n e o r the h e x a t r i e n e c o m p o u n d s . This is in line with the results of Garito e t a l . [4] and stresses that a s y m m e t r y r e d u c t i o n c a n have a significant i m p a c t on b o o s t i n g the T value. J u s t as in the c a s e o f the first-order polarizabflities, the third-order polarizabilities are always f o u n d to be l a r g e r for the hexatriene derivatives, relative to the b e n z e n e s y s t e m s with the s a m e substitutions. The differences r a n g e here b e t w e e n f a c t o r s of five to seven. If we n o w c o m p a r e the relative intensities of the cubic nonlinear optical r e s p o n s e s in the p u s h - p u s h with r e s p e c t to the p u l l - p u l l c o n j u g a t e d systems, we observe, c o n t r a r y to w h a t we w o u l d have originally expected, that the substitution by a c c e p t o r s increases the value to a m u c h g r e a t e r e x t e n t t h a n the substitution by d o n o r s : = 1 . 3 × 10 -36 e.s.u, in pAA and < T > = 3 . 1 x 1 0 -36 e.s.u, in pNN; for htAA a n d htNN, these values are 10.6 and 21.7 × 10 -36 e.s.u., respectively. At first sight, we w o u l d have t h o u g h t that donors, b e i n g susceptible to increase the ~r-electron density within the c o n j u g a t e d segment, should have led to larger T values. T h e s e theoretical results a p p e a r to be c o n s i s t e n t with the preliminary e x p e r i m e n t a l data r e c e n t l y r e p o r t e d by S p a n g l e r e t a l . [8].

Acknowledgements W e t h a n k SPPS ( P r o g r a m m e G o u v e r n e m e n t a l d ' I m p u l s i o n en T e c h n o l o g i e de l'Information, C o n t r a c t IT/SC/22), FNRS a n d IBM-Belgium for the use of the Belgian S u p e r c o m p u t e r Network. This w o r k h a s b e e n partly s u p p o r t e d by the PSle d'Attraction Interuniversitaire: Chimie Supramol~culaire et Catalyse, FRFC, a n d an IBM A c a d e m i c J o i n t Study.

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