17624
J. Phys. Chem. 1995,99, 17624-17627
Analysis of the Large Hyperpolarizabilities of Push-Pull Quinonoid Molecules M. Ravi and T. P. Radhakrishnan” School of Chemistv, University of Hyderabad, Hyderabad 500 046, India Received: May 2, 1995; In Final Form: August IO, 1 9 9 9
Donor-acceptor substituted quinonoid molecules have been investigated very little in connection with nonlinear optical (NLO)applications. We present a theoretical analysis of the hyperpolarizability, p, of a model pushpull quinonoid molecule as a function of the quinonoid-benzenoid character (QBC). B is found to be quite large at all geometries except the quinonoid extreme; it results from appreciable contributions from a large number of excited states.
Introduction
Synthesis of molecules with large hyperpolarizability, 8, is the primary step in the fabrication of molecular materials for quadratic nonlinear optical (NLO) applications. I Optimal alignment of these molecules in a noncentrosymmetric lattice remains an elusive and difficult problem. However, even in the first step, several nontrivial problems persist. For example, molecules with large /3 often absorb strongly at low energies and therefore are not suitable for visible light applications. Chemical or thermal instability, hygroscopic nature, etc. are also detrimental factors. Push-pull quinonoid molecules have not been extensively investigated for NLO applications. We have recently observed that a family of quinonoid molecules possesses several positive features at the molecular level, like potentially large hyperpolarizability, negligible absorption in the visible region, ease of synthesis, and chemical and thermal stability. While pursuing various strategies to obtain useful bulk material from these molecules, we have also carried out a detailed theoretical analysis of the large hyperpolarizability of these molecular systems and the factors contributing to it. Lalama et a1.* found that 2-(4-dicyanomethylenecyclohexa2,5-dienylidene)imidazolidine has an unexpectedly large /3 and calculations on the model system 7,7’-diamino-8,8’-dicyanoquinodimethane (DADQ) supported this observation. We have chosen the latter as the prototypical system for the large class of amino donor substituted dicyanoquinodimethane molecules we have synthesized recently3 based on an early Du Pont report? Similar to the study of /3 variation in polyenes as a function of bond length altemati~n,~ we present a theoretical analysis of the P ’ s as a function of the quinonoid-benzenoid character (QBC) of this push-pull quinone; as per the definition discussed below, the most quinonoid form of DADQ has a QBC of 0.088 and the most benzenoid form has the value of 0.790. This study provides insight into the effect of substitutions at the donor and acceptor end, on the excitation energy, hyperpolarizability, etc. In view of the relatively small size of the molecules, we find quite large P values, especially for the more benzenoid structures; the /3 is found to peak at a QBC of about 0.592. Since two low-lying excited states with notable oscillator strength (50.6-1.0) are observed in this and similar systems, we decided to have a closer look at their contributions. Our analysis indicates that unlike in most known systems, two-level or three-level approximations are inadequate to explain quantitatively the large p in these quinonoid systems, although qualitative trends can be understood. We indicate briefly where @
Abstract published in Advance ACS Absrructs, November I , 1995.
some of the systems we have experimentally investigated fit into the theoretical picture. Theoretical Methods
We have employed the AM1 semiempirical procedure for all geometry optimizations. The structure of DADQ was optimized under a ~2~ symmetry constraint with different static extemal fields
H*N
NC
vNH*
A
applied along the long axis of the molecule. The latter was done by placing point positive and negative charges along the long axis at equal distances from the center of the ring. We calculate the field produced at the center and assign the sign as positive or negative depending on whether the positive charge is kept at the diamino end or the dicyano end. As the field decreases from the highest positive value (6 x lo7 Vkm) to the lowest negative one (-8 x lo7 Vkm) the structure smoothly varies from the quinonoid extreme to the benzenoid one. Higher applied fields of either sign were seen to affect only negligible further changes and sometimes led to unphysical distortions of the molecule. We define the quinonoid-benzenoid character (QBC) based on the magnitude of the deviations of the ring bonds from a standard value of 1.400 A assumed for benzene. 3
QBC = 1 - 6 x l 1 . 4 0 0 - rJ I
This definition was chosen so that the value of QBC approaches 0 at the quinonoid limit and 1 at the benzenoid limit. Table 1 presents the various applied extemal fields and the corresponding optimized bond lengths, ri, as well as the calculated QBC. It also provides the net charges on the amino end, 4+, and the
0022-365419512099-17624$09.0010 0 1995 American Chemical Society
Hyperpolarizabilities of Push-Pull Quinonoid Molecules TABLE 1: Optimized Bond Lengths rl, r2, and r3 of DADQ Subjected to Different Applied Static Fields (See Text) and the Computed Quinonoid-Benzenoid Character (QBC), and Charges on the Donor (q+) and Acceptor (4-) Moiety for Each of the Structures 6 4 2 1 0 -1 -2 -4 -6 -8
1.450 1.448 1.442 1.439 1.435 1.431 1.426 1.417 1.410 1.405
1.348 1.351 1.354 1.356 1.358 1.362 1.366 1.375 1.381 1.378
1.450 1.450 1.447 1.445 1.442 1.438 1.434 1.426 1.416 1.408
0.088 0.118 0.190 0.232 0.286 0.358 0.436 0.592 0.730 0.790
0.103 0.231 0.374 0.442 0.507 0.570 0.632 0.742 0.827 0.874
0.033 0.106 0.248 0.319 0.360 0.461 0.536 0.684 0.796 0.861
In units of lo7 Vlcm: see text for the sign convention.
cyano end, q-, calculated by adding all the atomic charges on the relevant CX2 (X = N H 2 or CN) group. Transition dipoles, dipole moment changes on excitation, energies of excitation with oscillator strengths, and /? were calculated using the SCAMP routine.6 This program reproduces accurately the experimental p values in a number of test cases7 including the one studied by Lalama et aL8 The sum-overstates (SOS) method is employed for the calculation of /3 and the CI scheme involved 12 molecular orbitals with all single and pair excitations taken into account. To avoid resonance contribution to p, we have calculated the static p (also denoted as p(0) sometimes) throughout. Bv,, is defined in the usual way
i= I
where
p2-1evel (again the projection on
the major dipole axis) is obtained
using the expression9
where i is either of the two low-lying excited states, 1 or 2, which have appreciable oscillator strengths. poi is the transition dipole between the ground and the ith state, Apoi the change in dipole moment on excitation from the ground to the ith excited state, and A&; the energy of this excitation. The P3-1eve1 involving the two states 1 and 2 is easily derived in a similar way, from the usual SOS expression for /3+
[
2 ~ 0 1 ~ 0 2 ~ 1 22
P3-1evel
= 6 AE0,AEO2-t
Poi2Apoi
ZT]
The hyperpolarizability calculations were carried out under three different conditions: in method A, the optimized geometries at different external fields were used, after removing the external point charges; in method B, the gas phase structure (optimized under zero external field) was used with different external fields described above being imposed using the point charges; and in method C, the structures optimized under different extemal fields were used along with the external point charges being present. In the terminology of Gorman and Marder,Io the three methods correspond respectively to non-
J. Phys. Chem., Vol. 99, No. 49, 1995 17625 equilibrium electronic-equilibrium nuclear configurations, nonequilibrium nuclear-equilibrium electronic configurations, and equilibrium electronic-equilibrium nuclear configurations. Results and Discussion Inspection of Table 1 indicates that the variation of rl, 1 2 , and r 3 are as expected. The rI and 13 values change from approximately 1.45- 1.41 A on going from the quinonoid limit to the benzenoid limit. r 2 in the quinonoid limit is close to a normal double bond value of 1.35 8, and approaches 1.38 8, as the benzenoid extreme is reached. The symmetry is close to D 2 h at the two extremes. Verification of these structural features at the benzenoid limit comes from our experimental systems (with ri = r 3 = 1.40 A, r 2 = 1.38 A) noted below. The quinonoid limit could be related to the case of 7,7',8,8'tetracyanoquinodimethane (with rI = 1-3 = 1.45 A, r 2 = 1.35 A).i1 The group charges, q+ and q-, increase as expected with the quinonoid to benzenoid transformation. q- values, in particular, parallel the QBC's. It is noteworthy that the charges do not approach too closely 0 and 1 in the quinonoid and benzenoid forms, respectively. This is likely due to the intramolecular charge transfer from the donor to the acceptor group in the former case and from the ionized acceptor to the ionized donor in the latter in spite of the static external field. The zero applied field structure corresponds to the optimized structure of DADQ. The QBC assigned to this structure is 0.286, and the extent of charge transfer corresponds to 4050%. Methods A and B involve situations with nonequilibrium electronic and nuclear configurations, respectively, and hence the results are of interest only as control cases. The variations of p v e c with QBC in method A and with the applied field, F, in method B are plotted in Figure 1. It is seen that when the electronic configuration is in a nonequilibrium state, the By,, continuously increases with QBC indicating the largest values at the benzenoid limit. On the other hand, if the equilibrium nuclear configuration is ignored, the pveCis found to peak at an external field of about -2 x lo7 Vkm, corresponding to an electronic configuration intermediate between the quinonoid and benzenoid limits. The overall observation is that there is a trend toward larger p values as one goes from the quinonoid end to the benzenoid end whether one considers the related nuclear or electronic configuration changes; however, the imposition of the strong field at either end (in method B) tends to reduce the p values. When the most appropriatei0 procedure considering equilibrium electronic and nuclear configuration is carried out, the following analysis is obtained. Table 2 presents the dipole moment, excitation energy, and hyperpolarizability changes with the quinonoid-benzenoid structure variation, calculated in method C. The ground state dipole moments are very large throughout due to the presence of the external charges. The dipole moment changes associated with the excitation as well as the excitation energies and oscillator strengths (proportional to pol2)are provided for the two excited states, 1 and 2. The Ap are always negative and large, indicating reverse charge transfer on excitation. We have examined the / ? ~ . i ~using ~ ~ l either of the two states and the results are provided in Table 2. We have also listed the /?3-level utilizing both these excited states. Finally, the table also presents the /? value calculated utilizing all the excited states @,,,). The P2-level values for excited states 1 and 2 are strongly influenced by the trends of PO,*and 4values. For the excited state 1, these values go through a maximum near the QBC value of 0.600. The contribution from the excited state 2 is negligible after the QBC value of 0.400 because of the nearly vanishing oscillator strengths.
Ravi and Radhakrishnan
17626 J. Phys. Chem., Vol. 99, No. 49, 1995
0.0
Figure 1. Variation of the static pVe,with QBC calculated using method A ( 0 )and with the applied field, F, calculated using method B (A); see text for details of the method.
TABLE 2: Calculated Ground State Dipole Moment @o), Dipole Moment Change on Excitation (Ma),Excitation and Static /31.level Energy (A&) with Oscillator Strength 0, @) for Excited States 1 and 2, /33.level &), and Bvee for Structures with Different Quinonoid-Benzenoid Character (QBC) Calculated Using Method C QBC
P@
67.6
0.118
86.6
0.190
124.9
0.232
174.9
0.286
14.5
0.358
146.4
0.436
96.0
0.592
56.9
0.730
38.0
0.790
28.3
&ODb
-2.1 -0.9 -5.5 -3.6 -10.6 -5.6 -12.8 -8.0 -14.7 -10.2 -16.6 -12.4 -18.1 -8.9 -20.4 -11.0 -20.7 -12.0 -19.0 -12.8
AEdeV Ob P2(0Pb 8dOy 2.83 (0.006) -0.1 -3.7 -2.7 3.42 (1.130) 2.80(0.044) -1.1 -13.6 3.39 (1.065) -10.1 2.77 (0.195) -9.9 -25.9 3.44 (0.841) -12.7 2.71 (0.264) -17.4 -34.2 3.50 (0.718) -13.9 2.66 (0.326) -26.0 -42.5 3.59 (0.599) -13.6 2.65 (0.390) -35.8 -50.4 3.72 (0.471) -11.6 2.67 (0.457) -44.5 -45.6 -0.6 3.75 (0.032) 2.87 (0.583) -51.4 -52.9 3.71 (0.050) -1.1 3.17 (0.571) -37.9 -37.9 3.75 (0.000) -0.0 3.37 (0.479) -24.4 -24.4 3.78 (0.000) -0.0
0.4
0.6
0.8
'
I
QBC Figure 2. Variation of the static , B z . I (excited ~ ~ ~ ~ state 1) (*),
F / 107V/cm
0,088
0.2
Pvec(0Y
-9.7 -18.5 -35.4 -46.2 -58.6 -75.4 -86.5 -94.0 -67.4 -47.7
esu units. The entries in the first and second All p's are in row are for the excited states 1 and 2, respectively.
Figure 2 analyzes the variation of the full Bye,with the QBC and the contribution of ,&level from the first and the second excited state as well as that of the P3.1evel. The negative sign of the p values is a consequence of the negative Ap. It is seen that the pve,increases steadily from the quinonoid end and peaks at the QBC of 0.592 and then is suppressed to about half the peak value at the benzenoid end. The values except at the quinonoid end are quite large considering the size of these molecules; for comparison, p-nitroaniline has a p(0) value' of 9.1 x esu. The P2-level using the first excited state is negligible at very low QBC values but reproduces about 4050% of pveclater; the P2.1evel from the second excited state contributes about 30% at low QBC and has nearly zero contribution at higher ranges. The P3.1evel is mostly seen to be
/32.ievel
(excited state 2) (V),and j&.level (excited states 1 and 2) (A),and pvec (0) with the QBC in DADQ calculated using method C; see test for details of the method. 1-1 indicates the range of QBC values of our experimental systems.
an additive contribution of the two P2-ievel terms, with the cross term contributing very little. The P3-levelis a fair approximation for pvecat QBC below 0.232, whereas it reproduces only about 50% of pVe,in the more benzenoid structures. The calculations reveal that the traditional pictures based on a single charge transfer excitation are grossly inadequate to describe the pve,, except at low QBC values. At the higher QBC's at least 50% of the Bye,is made up of contributions from the higher excited states. Since individual contributions from these states would be smaller than that from states with lower A E ' s , it is inferred that several of them contribute. The analysis also indicates that the increased polarization of charges on a quinonoid framework substituted with donor-acceptor groups leads to very large p values, though the extreme fields at the benzenoid zwitterionic limit tend to suppress it to some extent. The high /3 values imply that the individual contributions from each of the large number of excited states should be appreciable. The excited states in most cases are associated with decreased net charges at each end and consequently a lower dipole moment. The large and negative Apoi associated with these states enhance their contributions to p. An associated practical problem is the large ground state dipole moment of these molecules which could encourage centrosymmetric crystal lattice formation. This has to be tackled by the several techniques known to induce noncentrosymmetry. Absorption in the UV region (corresponding to the excited state 2 ) is quite strong for QBC values up to 0.358. The absorption in the visible range (excited state 1) picks up oscillator strength after a QBC of 0.190; however, at high QBC values (>0.592), this absorption goes to higher energies, Le., into the W region. Thus the systems toward the benzenoid extreme do not absorb in the visible range and are expected to be useful for device applications involving visible light even though they do not have the maximum p values. Strong donors and acceptors can be utilized to push the QBC to values larger than that found in DADQ. Such substitutions effectively replace the negative external field used in our model study, by appropriate internal fields. In Figure 2 we have indicated the range of QBC values covered by four typical molecules we have synthesized. Average values of the bond
Hyperpolarizabilities of Push-Pull Quinonoid Molecules lengths r ~ r2, , and r3 from single-crystal X-ray structure analysisI2 have been used to assign their QBC values which are found to fall in the range 0.739-0.811. It is interesting to note that experimentally easily accessible systems have approximately 50% of the maximum 8 , value attainable in the full QBC .range. Reducing the donorlacceptor strength may push QBC toward the values corresponding to maximum ,8 values. The experimental (acetonitrile solution) absorption maxima of our molecules fall in the 350-420 nm range in good accord with the calculation above, and the solids are colorless to light yellow. The appreciable transparency of these materials in most of the visible range make them practically interesting. Experimental evaluation of /3 of molecules covering the full QBC range would be interesting in the light of the present theoretical analysis. Acknowledgment. We are very grateful to the referee for several critical comments and Dr. J. Chandrasekhar for providing the SCAMP program. M.R. and T.P.R. thank respectively the Council of Scientific and Industrial Research and the Department of Science and Technology, New Delhi, for financial support. References and Notes (1) (a) Chemla, D. S., Zyss, J., Eds. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: New York, 1987. (b)
J. Phys. Chem., Vol. 99,No. 49, 1995 17627 Prasad, P. N.; Williams, D. J. lnrroduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (2) Lalama, S. J.; Singer, K. D.; Garito, A. F.; Desai, K. N. Appl. Phys. Lett. 1981, 39, 940. (3) Ravi, M.; Rao, D. N.; Cohen, S.; Agranat, I.; Radhakrishnan, T. P. Curr. Sci. (India) 1995, 68, 1119. (4) Hertler, L. R.; Hartzler, H. D.;Acker, D. S.; Benson, R. E. J . Am. Chem. Soc. 1962, 84, 3387. (5) (a) Bourhill, G.; Bredas, J. L.; Cheng, L. T.; Marder, S. R.; Meyers, F.; Perry, J. W.; Tiemann, B. G.J . Am. Chem. SOC.1994, 116, 2619. (b) Meyers; F.; Marder, S. R.; Pierce, B. M.; Bredas, J. L. J . Am. Chem. SOC. 1994, 116, 10703. (6) Jain, M.; Chandrasekhar, J. J. Phys. Chem. 1993, 97, 4044 (7) Clark, T.; Chandrasekhar, J. Isr. J . Chem. 1993, 33B, 435. (8) Experimental valueZof p (ha, = 1.17 eV) is (-245 f 60) x esu and the SCAMP calculated value -243 x esu. (9) Oudar, J. L. J . Chem. Phys. 1977, 67, 446. (10) Goman, C. B.; Marder, S. R. Chem. Mater. 1995, 7, 215. (11) Long, R. E.; Sparks, R. A.; Trueblood, K. N. Acta Crystallogr. 1965, 18, 932. (12) Ravi, M.; Cohen, S.; Agranat, I.; Radhakrishnan, T. P. Struct. Chem., in press. Examples are systems with donor groups, bis(pyrro1idino) (rl = 1.401, 1.391; r2 = 1.363, 1.365; r3 = 1.404, 1.399); bis(piperidin0) (rt = 1.396, 1.394; r2 = 1.372, 1.370; r3 = 1.408, 1.403); bis(morpho1ino) (rl = 1.397, 1.395; 1-2 = 1.372, 1.370; r3 = 1.408, 1.405);and bis(piperazin0) (rt = 1.389, 1.398; rz = 1.377, 1.379; r3 = 1.406, 1.400); the lengths are in A.
JP95 12391
