J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1853-1855 1853 Non-linear Optical Properties of Organic Molecules Part 14.~-Calculations of the Structure, Electronic Properties and Hyperpolarisabilities of Cyclopentadienylpyridines John 0.Morley Chemistry Department, University College of Swansea, Singleton Park, Swansea, UK SA2 8PP The structures of a series of cyclopentadienylpyridines have been calculated using the AM1 method and reason- able correlations have been found with crystallographic data where available. Subsequent calculations have been carried out on these structures using the CNDOVSB method to obtain dipole moments, transition energies and hyperpolarisabilities. The two methods are found to give widely different values for the ground-state dipole moments.The calculated hyperpolarisabilities suggest that these molecules have considerably superior non-linear optical properties to conventional donor-acceptor aromatics. Poled polymer films containing an active non-linear com-ponent have attracted considerable interest as potential devices for electro-optic modulation (EOM) and second har- monic generation (SHG).'-' These materials are generally prepared by copolymerisation of a suitable monomer, such as methylmethacrylate, with an active organic such as a donor- acceptor aromatic containing an unsaturated linkage at the donor group. The resulting polymer is subjected to a strong electric field near the glass-transition temperature to orientate the active component along the direction of the molecular dipole moment, and then cooled in the presence of the same field to yield an orientated non-linear material.Typical aro- matics include derivatives of N-alkyl-4-nitroaniline and 4- alkoxy-4'-nitroazobenzene containing at least one acrylate group positioned at the end of the alkyl chain.'-3 The degree of orientation achieved in the poling process and the non-linear activity of the resulting polymer, however, are a function of a number of factors which include the strength of the electric field, the size of the active molecule, the magnitude of the molecular dipole moment and the molecular hyperpolarisability. Although existing materials have reasonable dipole moments, for example 6.3 D for 4- nitroaniline and 6.5 D for 4-methoxy-4-nitroazobenzene,4 molecules with larger values would be expected to show enhanced behaviour provided they also possess substantial molecular hyperpolarisabilities. The present studies have been initiated to explore the potential of the highly polar pyridinium cyclopentadienylide I, the related cyclo-pentadienylides 1,Cdihydropyridine I1 and the azolylidene 1,4-dihydropyridines 111 and IV, a class of molecule with large dipole moments but with unknown non-linear proper- ties.43 I M e-I1 t Part 13: ref. 16. \-/ "9 I11 M e-(,,)=(:DN IV Method of Calculation Molecular orbital calculations were carried out on empirical structures for the cyclopentadienylpyridines I-IV using the AM1 method5 with full optimisation of all bond lengths, angles and torsion angles.The derived structures were then used to calculate the molecular hyperpolarisability using the CNDOVSB method,6 a sum-over-states procedure (SOS) which has been specifically parametrised for SHG applica-tions. A similar SOS approach has been reported by several other a~thors.~-'' As in previous work, all 27 components of the tensor are calculated by the CNDOVSB method, though the most appropriate quantity is the vector component, P, theoretically defined as9 P = Pppp + 5 1(Ppii + Biip) ifp where /3 is aligned to lie along the direction of the molecular dipole moment (p). In addition to the frequency-dependent value, a static value is also calculated in the absence of the applied frequency to give the quantity B0, which is a measure of the intrinsic hyperpolarisability of a given molecular system and which has been used to compare the relative em- cacy of polyphenyls us.polyenes and other conjugated systems.' ' Discussion Structure Optimisation Initial calculations at the AM1 level' with full optimisation of all variables on 4-cyclopentadienylidene-1-methyl-1,4-dihy-dropyridine (11) with the numbering system shown below (Scheme 1) gives a planar structure which shows a reasonably J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Calculated geometries, heats of formation and dipole moments obtained for the cyclopentadienylpyridines I-IV using the AM 1 method" x, Y,z ~~ C(l)-X(2) X(2)-C(3)C(3)--C(4) C(4)-Y(5) Y(5)-W C(6)-Z(7) q7)-C(8) C(8)-C(9)C( 1)- X(2)-C( 3) X(2)-C( 3)-C(4) C(3)-C(4)-- Y(5) C(3)-X(2)-C(12) C( 4)- Y (5)-C( 6) C(4)-Y(5)-C(ll)Y(5)-C( 6)- Z(7) C(6)-Z(7)-C(8) q7)-c(8)-C(9) 1.395 1.394 1.386 1.366 1.463 1.380 1.449 120.4 122.0 118.1 121.4 117.2 126.7 107.8 108.9 1.435 1.390 1.365 1.449 1.362 1.471 1.371 1.466 120.8 121.9 121.9 118.2 122.9 114.2 127.1 108.5 108.7 1.487 1.364 1.354 1.428 1.388 1.442 1.364 1.413 121.1 122.2 122.2 117.8 123.3 113.4 127.2 108.2 109.0 1.438 1.386 1.369 1.441 1.383 1.442 1.324 1.492 120.8 122.0 120.9 118.5 122.1 115.7 124.4 104.8 109.6 1.440 1.383 1.373 1.435 1.400 1.429 1.343 1.499 120.7 121.9 120.8 118.5 122.0 116.0 123.5 104.3 109.2 1.478 1.339 1.366 1.387 1.446 1.359 1.384 1.408 119.9 120.8 120.5 120.3 121.4 117.2 122.1 103.3 108.8 heat of formation 104.04 93.96 115.23 142.54 dipole momentd 4.63 (13.3)" 6.37 (10.3)f 6.82 9.37 (9.03)' ~~ ~~ ~~ " Bond lengths are given in A, angles in degrees, heats of formation in kcal mol-' and dipole moments in D.Average data from the crystal structure of the N-(2,6-dichlorobenzyl) derivative (ref. 12). 'Ref. 13. Experimental results are given in parentheses. Ref. 4. Data for the N-benzyl derivative from ref. 4. Scbeme 1 Numbering system adopted for the cyclo-pentadienylpyridines (I-IV) good correlation with available crystallographic data on the closely related 1-(2',6'-dichlorobenzyl) derivative' (Table 1). The calculated results give C(3)-C(4), C(5)-C(6) and C(7)-C(8) bond lengths of 1,3865, 1.362 and 1.371 A, corre-sponding to double bonds, compared with values of 1.354, 1.388 and 1.364 A, found in the related crystal structure12 (Table 2).Furthermore, the nominal single bonds at C(4)-C(5) and C(6)-C(7) have calculated values of 1.449 and 1.471 8, compared with experimental values of 1.428 and 1.442 A. However, the geometric correlation is less satisfac- tory for 4-( benzimidazol-2-y1idene)-1 -methyl- 1,4-dihydropyri- dine (IV), where the central C(5)-C(6) bond is predicted to be shorter at 1.400 A than that found in the crystal structure at 1.446 A,13 although the double bond at C(3)-C(4) is well reproduced. Electronic Properties Previous calculations have shown that the CNDOVSB method gives a good correlation between the calculated and experimental transition energies for most conjugated organic systems6 and the result obtained for the pyridinium cyclo- pentadienylide I at 515 nm (Table 2) compares favourably with the experimental value of 511 nm determined in chloro- form.14 The approximations adopted to achieve a good spec- troscopic fit,6 however, result in an overestimation of the ground-state dipole moment and an underestimation of the excited-state dipole moment.6 In the examples explored here, the ground-state dipole moments are considerably larger than those obtained with the AM1 method (Tables 1 and 2).Table 2 Calculated hyperpolarisabilities and excited-state proper- ties of the cyclopentadienylpyridines I-IV obtained with the CNDOVSB method" I 13.3' 8.19 0.18 515 0.73 -55.8 -188.5 I1 10.3' 11.54 8.03 431 1.19 -23.3 -48.2 I11 9.92 6.22 471 1.17 -32.6 -81.7 IV 9.03d 14.14 6.32 521 1.35 -93.9 -344.5 a peXp,pgand pe are the experimental dipole moment and calculated ground- and excited-state dipole moments, respectively (in D); 1 is the transition energy or absorption maximum (in nm); f is the oscil- lator strength; Po and are the molecular hyperpolarisabilities at applied field strengths of zero and 0.95 eV, respectively [units of cm5 esu-' (3.71 x C-' m3 F2)].Ref. 4. Data for the N-benzyl derivative from ref. 4. Ref. 13. Experimental evidence suggests that both methods underesti- mate the dipole moment of the pyridinium cyclo-pentadienylide I at 13.3 Dt by a substantial margin,4 with the CNDOVSB method providing the best result at 8.19 D us.4.63 D for AM1. Furthermore, the CNDOVSB value for 4-cyclopentadienylidene-1-methyl- 1,4-dihydropyridine (11) at 11.54 D is much closer to the experimental value for the closely related N-benzyl derivative4 at 10.3 D than the AM1 value of 6.37 D. However, the AM1 dipole moment of 9.37 D for 4-(benzimidazol-2-ylidene)-1-methyl- 1,4-dihydropyridine (IV) is a better fit with the experimental value13 of 9.03 D than the CNDOVSB result which is too large (Table 2). The excited-state results (Table 2) show that there is a sub- stantial reduction in the value of the dipole moment in moving from the ground state to the first excited state (which is the major contributor to the value of the hyperpolarisability), particularly for the cyclo-pentadienylpyridines I and IV.This is a reflection of the t 1 D z 3.33564 x 10-30~. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 change of direction of charge transfer which takes place in each molecule upon excitation. In the ground state of the pyridinium cyclopentadienylide I the structure is polarised with electron donation from the left-hand pyridinium ring to the right-hand cyclopentadienylide ring with a strongly posi- tive nitrogen atom and with overall charges of k0.56, respec-tively. Upon excitation, there is a reversal of the direction of charge transfer, C(6) becomes strongly positive and the rings are now broadly neutral with values of k0.031 (Fig.1). Calculated Hyperpolarisabilities All of the molecules explored in the present studies gave hyperpolarisabilities which are considerably larger than expected with the negative values reflecting the reversal of the direction of charge transfer upon excitation. The values obtained for I and IV are much larger than those for I1 and I11 and mirror the large changes of around 8 D in their dipole moments upon excitation. Furthermore, the cyclo- pentadienylides I and IV show a larger frequency-dependent value, than the cyclopentadienylpyridines I1 and 111. This arises because the SHG expression for the hyperpolarisability l5 is partly dependent on the reciprocal of terms such as Qeg -2R, where Re, is the transition energy between ground (g) and excited state (e) and R is the magni- tude of the applied field (in this case 0.95 eV or 1300 nm).The closer the transition energy approaches the second harmonic of 650 nm the greater the expected resonance enhancement in p .022t029 .019 b .020 b .020 Fig. 1 Ground- (top) and excited-state (bottom) charge distribu- tions for pyridinium cyclopentadienylide (I) line with the calculated results. The approximate three-fold resonance enhancement for the pyridinium cyclo-pentadienylide I is matched by that for 4-(benzimidazol-2- y1idene)-l-methyl-l,4-dihydropyridine(IV) as the transition energies of both molecules at 515 and 521 nm, respectively, are very similar (Table 2). The overall values predicted for the cyclo-pentadienylpyridines I-IV are considerably larger than those for donor-acceptor aromatics such as 4-nitroaniline with Do = 7.02 and comparable to those of much larger systems such as 4-dimethylamino-/?-nitrostyrene with Po = 37.2 and 4-amino-4’-nitrostilbene with Po = 25.6.6 Conclusions The AM1 method appears to give a reasonable account of the geometry of the cyclopentadienylpyridines I-IV, but the calculated dipole moments differ from those obtained using the CNDOVSB method.The calculated hyperpolarisabilities are large and negative and considerably superior to those of conventional donor-acceptor aromatics. With appropriate functionalisation, the materials offer considerable potential for exploitation in non-linear devices. References 1 Nonlinear Optical Eflects in Molecules and Polymers, ed.P. N. and D. J. Williams, Wiley, New York, 1991. 2 Nonlinear Optics of Organics and Semiconductors, ed. K. Kobay-ashi, Springer-Verlag, Tokyo, 1989. 3 Nonlinear Optical Properties of Organic Molecules and Crystals, ed. D. S. Chemla and J. Zyss, Academic Press, New York, 1987. 4 A. L. McClellan, Tables of Experimental Dipole Moments, W. H. Freeman, San Francisco, 1963, vol. I; Rahara Enterprises, San Francisco, 1974, vol. 11. 5 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. Stewart, J. Am. Chem. SOC., 1985,107,3902. 6 V. J. Docherty, D. Pugh and J. 0. Morley, J. Chem. SOC., Faraday Trans. 2, 1985,81,1179. 7 J. A. Morrell and A. C. Albrecht, Chem.Phys. Lett., 1979,64,46. 8 S. J. Lalama and A. F. Garito, Phys. Rev. A, 1979,208, 1179. 9 C. W. Dirk, R. J. Tweig and G. Wagniere, J. Am. Chem. SOC., 1986,108,5387. 10 DeQuan Li, M. A. Ratner and T. J. Marks, J. Am. Chem. SOC., 1988,110, 1707. 11 J. 0.Morley, V. J. Docherty and D. Pugh, J. Chem. SOC., Perkin Trans. 2, 1987, 1351; J. 0. Morley, J. Chem. SOC., Faraday Trans. 2, 1991, 87, 3009; J. 0. Morley and D. Pugh,J. Chem. Soc., Faraday Trans. 2, 1991, 87, 3021; J. 0. Morley, J. Am. Chem. SOC., 1988, 110, 7660; J. 0. Morley, Znt. J. Quantum Chem., 1993,46, 19. 12 H. L. Ammon and G. L. Wheeler, J. Am. Chem. SOC., 1975, W, 2326. 13 E. Alcalde, I. Dinares, J. Frigola, J. Rius and C. Miravitlles, J. Chem. SOC.,Chem. Commun., 1989,1086. 14 J. P. Phillips, L. D. Freedman and J. C. Craig, Organic Elec- tronic Spectral Data, Interscience, New York, 1963, vol. I-X. 15 J. Ward, Rev. Mod. Phys., 1965,37, 1. 16 J. 0.Morley, J. Chem. SOC.,Faraday Trans., 1994,90, 1849. Paper 410068 1J ;Received 4th February, 1994