Ab initio determination of the vibrational and electronic

Ab initio determination of the vibrational and electronic Ðrst hyperpolarizabilities of reference compounds for non-linear optical (NLO) applications 3-Methyl 4-nitropyridine 1-oxide (POM) and N-(4-nitrophenyl)-(L)-prolinol (NPP) Beno•ü t Champagne,¤ Eric A. Perpe` te,” Thierry Legrand, Denis Jacquemin° and Jean-Marie Andre L aboratoire de Chimie T he orique Applique , Faculte s Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium

The electronic and vibrational Ðrst hyperpolarizabilities of POM and NPP are determined at the HF/6-311G** level of approximation by using the coupled HartreeÈFock and double harmonic oscillator schemes, respectively. The geometrical parameters, charge distributions, Ðrst hyperpolarizabilities and vibrational normal modes and frequencies of POM and NPP are compared with available experimental and theoretical investigations. The vibrational Ðrst hyperpolarizability is analysed in terms of the most contributing vibrational normal modes. The ratio between the vibrational and electronic Ðrst hyperpolarizabilities is considered as a function of the chemical nature of the p-conjugated system, the NLO process and the response time.

1 Introduction Quantum chemical evaluations of the polarizabilities (a), Ðrst and second hyperpolarizabilities (b and c) and their interpretation in terms of structureÈproperty relationships help in the design of new compounds for NLO applications.1 Recently, particular attention has been given to the vibrational contributions and, since they turn out to be of the same order of magnitude as their electronic counterpart, to their optimization.2 When addressing the e†ects of external electric Ðelds on matter, it is common to resort to the clamped nucleus or canonical (CN) approximation, which assumes that the Ðelds act sequentially on the electron and nuclear motions.3,4 The Ðrst-order non-BornÈOppenheimer correction to this CN approximation, which originates from the simultaneity of the Ðeld-induced distortions on the electron and nuclear motions, has recently been shown to be quite small for prototypes of p-conjugated systems presenting a large electronÈphonon coupling.4 Adopting the CN scheme leads, therefore, to distinction between the electronic (ae, be and ce) including the zero-point vibrational average (ZPVA) and the pure vibrational (av, bv and cv) contributions to the (hyper)polarizabilities. The present study concerns the comparison of the electronic and vibrational Ðrst hyperpolarizabilities of two reference compounds for NLO applications, POM and NPP. Both molecules present large molecular Ðrst hyperpolarizability and large crystalline second-order susceptibility.5 The former is directly related to a dominant charge-transfer excitation from the donor (N-oxide group for POM and amino group for NPP) to the nitro acceptor group. The latter originates from optimal crystalline structures, induced by speciÐc intermolecular interactions. In addition to the phase matching conditions on the refractive indices that require a di†erent crystal ¤ Research Associate of the National Fund for ScientiÐc Research (Belgium). ” ScientiÐc Collaborator of the National Fund for ScientiÐc Research (Belgium). ° Research Assistant of the National Fund for ScientiÐc Research (Belgium).

packing for maximizing each NLO response, the Ðrst nonlinear response of the bulk for non-centrosymmetric molecular constituents can be zero, as a result of a centrosymmetric crystal packing. Indeed, the dipolar interactions dominate in most of these pushÈpull compounds and tend to favour the head-to-tail antiparallel dimerization of molecules. Hence, they lead to a decrease, if not a cancellation, of the bulk optical non-linearity. Thus, the crystalline noncentrosymmetric orthorhombic structure of POM has been ascribed to the quasi-vanishing ground-state dipole moment of the POM molecule, which results from the antiparallel polarity of the N-oxide and nitro groups. On the other hand, for NPP, chirality prevents centrosymmetric packing but, in addition, the dipolar forces are overshot by the intermolecular hydrogen bonds, which ensure an NLO-efficient parallel planar stacking of the NPP molecules. Consequently, although of similar electronic structure to p-nitroaniline (p-NA), NPP crystals exhibit second-order NLO responses, whereas the centrosymmetric packing of p-NA molecules leads to a vanishing second-order susceptibility. Many experimental and theoretical investigations have already been devoted to the characterization of the molecular and crystalline structures and to the NLO properties of POM6h11 and NPP.12h16 The dipole moment of POM has been either inferred from X-ray data8 or determined by more or less elaborate quantum chemical methods.8,11 The latest determination, due to Glaser, provides a dipole moment value of 0.89 DÒ (0.35 au) making a 48.7¡ angle with the nitro/Noxide axis at the MP2/6-311G** level of approximation.11 The force Ðeld of POM and its vibrational IR and Raman spectra have been addressed several times and compared with its sister-molecule, 4-nitropyridine N-oxide (NPO).8,10 Berthier et al.9 have calculated the static b (\b ] b ] b ) z zzz xxz yyz tensor component of POM at the coupled HartreeÈFock level by using a double-f type basis set. For the POM2 geometry, it attains [1074 auA whereas k \ 0.03 au. Similar b values are z Ò 1.0 au of dipole moment \ 8.478 358 ] 10~30 C m \ 2.5415 D. p 1.0 au of Ðrst hyperpolarizability \ 3.2063 ] 10~53 C3 m3 J~2 \ 8.641 ] 10~33 esu.

J. Chem. Soc., Faraday T rans., 1998, 94(11), 1547È1553

1547

obtained for the POM1 geometry, where one hydrogen atom of the methyl group points in the direction of the NO group. 2 Sigelle and Hierle6 have determined the electro-optic coefficients of POM crystal and, from a comparison with the second harmonic generation (SHG) response,7 have deduced that the mean vibrational contribution to the electro-optic dcPockels (dc-P) susceptibility has an opposite sign to the electronic one and is about four times smaller. This comparison is based upon the assumption that the longitudinal b \ b zzz L component is dominant and is mainly governed by a single charge-transfer excitation process. NPP has been extensively studied because of its quasioptimal angle with respect to the quadratic phase-matching conditions, which leads to an SHG signal two orders of magnitude larger than in KTP, the state of the art in inorganic NLO crystals.12 Semi-empirical Ðnite Ðeld (FF)13 and SOS/ CNDOVSB14 methods have been applied to estimate its b tensor components and show that the dominant b elements L amount, in the static limit, to 1991 au and 1793 au, respectively. X-Ray di†raction has been used to determine both its geometrical structure and electronic density distribution, which was then employed to estimate the linear polarizability and Ðrst hyperpolarizability.15,16 In the Ðrst investigation of Fkyerat et al.,15 the agreement between the theoretical estimates for the free molecule13,14 and the X-ray electron density-derived values associated with the molecule in the crystal is rather good. Although adopting the same procedure, relying on the Unsold approximation, their second investigation16 provides X-ray derived quantities which are strangely 1È2 orders of magnitude larger than the theoretical estimates. A few studies have already considered the possible relationships between the electronic and vibrational Ðrst hyperpolarizabilities of pushÈpull p-conjugated compounds.2,17h24 Zerbi and co-workers17h19 have found that, for many second-order NLO conjugated molecules, the calculated static electronic and vibrational hyperpolarizabilities are very similar. Using experimental data, they came to the conclusion that bv/be is close to unity. In the latter case, the vibrational Ðrst hyperpolarizability is evaluated from IR and Raman absorption spectra whereas electric Ðeld-induced SHG (EFISHG) measurements give the electronic counterpart which, to be correct, would have required extrapolation to zero frequency. Then, they argued that such a coincidence is not fortuitous and that bv and be are just two manifestations of the same underlying physical phenomenon. They made the connection with the strong electronÈphonon coupling along the coordinate, which is associated with the variation of the bond length alternation (BLA). A Ðrst quantitative demonstration of their assumption has recently been elaborated by Castiglioni et al.20 However, in addition to its restriction to the two-state approximation for computing be, whereas bv is evaluated at the double harmonic oscillator approximation by neglecting all the modes but the BLA mode, their approach neglects an important contribution.22,23 Their ideal equivalence relation is further questionable on the basis of the results of two recent studies. On the one hand, the bv/be ratio has been shown to depend strongly upon both the chain length and the nature of the linker.2 On the other hand, for a set of mono-substituted benzenes, the variations in be upon substitution are most accounted for by the mesomeric e†ects whereas, for bv, the inductive e†ects are also of importance.24 This is not to mention the dependence upon the NLO process and the frequencies. Indeed, the variations in be can be described by a power expansion in the square of the source frequency whereas, at optical frequencies, bv is rather non-sensitive to the frequency but depends upon the NLO process. The present work aims at characterizing and comparing the electronic and vibrational Ðrst hyperpolarizabilities of POM and NPP. The second section brieÑy summarizes the method1548

J. Chem. Soc., Faraday T rans., 1998, V ol. 94

ological context of our Ðrst hyperpolarizability calculations and also addresses the key computational points. Section 3 presents the b values and their analysis. The vibrational normal mode contributions to bv are displayed and the vibrational motions of the dominant ones are analysed. Comparisons with speciÐc experimental and other theoretical studies are also carried out. In the last section a synopsis is provided.

2 Methodological and computational aspects The time-dependent HartreeÈFock (TDHF) level is employed for computing the electronic Ðrst hyperpolarizability tensor components, which are evaluated as the second order derivatives of the dipole moment with respect to the external Ðelds.25 This procedure includes the Ðeld-induced electron reorganizational e†ects self-consistently in terms of the average Coulomb and Pauli potential. It is equivalent to the random phase approximation (RPA).26 In its static limit, the TDHF procedure is equivalent to the coupled-perturbed HartreeÈFock (CPHF) and the HartreeÈFock Ðnite Ðeld (HFFF) methods. The HONDO 95.3 program27 has been used for computing the frequency-dependent quantities whereas GAUSSIAN9428 has also been adopted for evaluating be(0 ; 0, 0). The 6-311G** basis set has been used throughout this study.29 The static vibrational counterpart is calculated at the RHF/ 6-311G** level within the double harmonic oscillator approximation.30h32 It reads bv ([u ; u , u ) \ [ka]0, 0 fgm p 1 2 (Lke/LQ ) (Lae /LQ ) 1 f a 0 gm a 0 (1) \ ;P ; ~p, 1, 2 (u2 [ u2) 2 a p a where 0, 0 indicates that no electrical or mechanical anharmonicity is included, u \ u ] u , ; P is a summap 1 2 ~p, 1, 2 tion over the six permutations of the pairs ([u , f), (u , g) p 1 and (u , m). Q is the normal coordinate of the vibrational 2 a motion with circular frequency u \ 2pl , and the subscript 0 a a indicates the equilibrium nuclear conÐguration. All the bv calculations have been performed with the GAUSSIAN94 program28 on the RHF/6-311G** optimized structures which have also been used for the be calculations. A tight convergence threshold on the residual forces (1.5 ] 10~5 E a~1 h 0 or E rad~1) has been adopted to meet a satisfactory accuracy h in computing the (LP/LQ ) values. a0 be and bv depend upon the NLO process as well as upon the optical frequencies but in very di†erent ways. Indeed, at rather small optical frequencies, be satisÐes the relation33 be ([u ; u , u ) \ be (0)[1 ] Au2] (2) fgm p 1 2 fgm L where u2 \ u2 ] u2 ] u2 . A is a parameter which depends L p 1 2 upon the molecule but not upon the NLO process. On the other hand, by adopting the enhanced34 or inÐnitefrequency35 approximation, which relies on the fact that the optical frequencies are at least one order of magnitude larger than the vibrational ones, one obtains, for any diagonal tensor component of bv, such as the longitudinal one bv([u ; u, 0) \ bv(0 ; u, [u) \ 1 [ka]0, 0 (3) L u?= L u?= 3 L‰ u/0 bv([2u ; u, u) \0 (4) L u?= In other words, for SHG bv is negligible whereas, for the dc-P L and optical rectiÐcation (OR) processes, it amounts to 1/3 of the static quantity. Similar relations can also be written for isotropically averaged quantities such as b \ (1/3) ; b g f ffg ]b ]b and, therefore, for b \ ; (k b /o k o) and fgf gff vec g g g b \ (b2 ] b2 ] b2)1@2 where k and o k o are the components tot x y z g and norm of the dipole moment. The totally di†erent frequency dependences of the electronic and vibrational pheno-

Table 1 RHF/6-311G** optimized bond lengths (Ó), bond angles and inter-ring torsion angle (¡) of POM and NPP POM

Fig. 1 Cartesian space representation and atom labels for POM and NPP

mena has obviously to be accounted for in optimizing the responses as a function of the NLO process. It is also striking to remember that we have adopted throughout this work the Taylor series convention (denoted bT in ref. 36) for the Ðelddependence of the dipole moment. bT values should therefore be divided by a factor of 2 to match the power series convention (denoted bB in ref. 36). The molecules have been oriented such that the N2 and C7 atoms of POM (C1 and C6 atoms of NPP) belong to the z- or longitudinal axis while the aromatic ring lies in the yz plane (Fig. 1).

O1N2 N2C3 N2C4 C3C5 C4C6 C6C11 C5C7 C6C7 C7N8 N8O9 N8O10 O1N2C3 O1N2C4 C3N2C4 N2C3C5 N2C4C6 C3C5C7 C4C6C7 C4C6C11 C7C6C11 C5C7C6 C5C7N8 C6C7N8 C7N8O9 C7N8O10 O9N8O10

NPP 1.254 1.344 1.342 1.367 1.383 1.511 1.384 1.394 1.462 1.188 1.187 120.3 120.2 119.5 120.5 123.6 120.0 116.1 117.2 126.6 120.3 117.0 122.7 117.3 118.0 124.7

3 Results and Discussion 3.1 Geometry and charge distribution In Fig. 1 are represented the POM and NPP molecules with their atom labels. The optimized RHF/6-311G** geometrical parameters are listed in Table 1 and the atomic charges obtained within the Mulliken population analysis are given in Table 2. The average BLA in the aromatic ring is 0.025 and 0.015 Ó for POM and NPP, respectively. At the same level of investigation, the average BLA is 0.013 Ó for p-NA. The RHF/6-311G** optimized geometrical parameters of POM are in close agreement with the neutron di†raction data due to Baert et al.8 Without considering the parameters involving hydrogen atoms, the rms deviation is 0.021 Ó for the bond lengths and 0.6¡ for the bond angles. Nevertheless, the neutron di†raction structure predicts an NO twist angle of 14.7¡ 2 whereas, in the ab initio-optimized structure, the NO group 2 and the benzene ring are coplanar. In agreement with the study of Berthier et al.,9 the POM2 conformer is determined as the most stable structure, because it minimizes the electrostatic interactions between the methyl and the nitro groups. Indeed, the hydrogen atom (H15) of the methyl group, which is in the same plane as the benene ring, points in the opposite direction to the nitro group (Fig. 1). A similar acceptable agreement is obtained between the optimized RHF/6-311G** structure of NPP and its X-ray and neutron di†raction structures,15 which have conÐrmed the earlier structure proposed by Zyss et al.12 If neglecting the hydrogen atoms, the rms deviation with respect to the X-ray data is 0.018 Ó for the bond length and 1.0¡ for the bond angles whereas, when refering to the neutron di†raction data, the rms deviation decreases to 0.015 Ó and 0.9¡, respectively. The nitro group is nearly coplanar with the benzene ring whereas the amino is not planar. The pyrrolidine group adopts an approximate C2 symmetry (half-chair) with the twofold axis passing through N10 and the centre of the C13wC14 bond. Owing to the absence of hydrogen bonding, the RHF/6-311G** structure of the CH wOH group is oriented di†erently than in the crystal. 2 This di†erence is, however, not expected to have a substantial e†ect upon b because it is not part of the p-conjugated path.

C1C2 C1C3 C2C4 C3C5 C4C6 C5C6 C1N7 N7O8 N7O9 C6N10 N10C11 N10C12 C11C13 C12C14 C13C14 C11C15 C15O16 C2C1C3 C1C2C4 C1C3C5 C2C4C6 C3C5C5 C4C6C5 C3C1N7 C2C1N7 C1N7O8 C1N7O9 O8N7O9 C4C6C10 C5C6C10 C6N10C11 C6N10C12 C11N10C12 C4C6N10C11 C4C6N10C12

1.384 1.384 1.374 1.374 1.409 1.408 1.448 1.190 1.190 1.362 1.462 1.454 1.543 1.524 1.529 1.527 1.401 120.3 119.9 120.0 121.1 121.1 117.5 119.9 119.8 117.8 117.9 124.3 121.5 121.0 124.6 123.3 111.8 340.7 166.9

See Fig. 1 for the labels.

The total charge associated with the atoms of the aromatic ring of POM and NPP (C NH and C H ) is 0.46 and 0.56 e, 5 3 6 4 whereas the corresponding charge for C H in p-NA is 0.50 e. 6 4 This electron deÐciency is mainly counterbalanced by the electron-rich NO species. With the exception of O1 and the 2 methyl group, most of the Mulliken charges of POM are in rather good agreement with the X-ray reÐnement III values due to Baert et al.8 For O1 their value of [0.44 e contrasts with the RHF/6-311G** value of 0.16 e. The opposite di†erence holds for C11 for which the X-ray and ab initio charges Table 2 RHF/6-311G** Mulliken charges (in au ; 1.0 au of charge \ e \ 1.602 177 33 ] 10~19 C) of POM and NPP POM O1 N2 C3 C4 C5 C6 C7 N8 O9 O10 C11

NPP [0.51 0.00 0.34 0.36 0.00 [0.23 0.20 0.35 [0.38 [0.38 0.25

C1 C2 C3 C4 C5 C6 N7 O8 O9 N10 C11 C12 C13 C14 C15 C16

0.02 0.14 0.14 [0.07 [0.08 0.42 0.38 [0.40 [0.40 [0.67 0.09 0.27 0.04 0.02 0.33 [0.23

The hydrogen charges have been summed to the charge of their connected heavy atom. See Fig. 1 for the labels.


1549

are 0.29 and [0.27 e, respectively. On the other hand, for NPP, the charges obtained by Fkyerat et al.15,16 after a multipolar reÐnement of the X-ray data present several di†erences with respect to our values. The aromatic ring charge is much smaller (0.02 e), the N10 charge is positive (0.08 e) and the negative charge of the NO group is smaller ( [ 0.27 e). Such 2 a large di†erence between the X-ray and theoretical charge distributions could certainly account for the much di†erent be estimates15,16 (see Section 3.2). 3.2 Electronic and vibrational Ðrst hyperpolarizabilities Table 3 lists the inequivalent CHF/6-311G** be(0 ; 0, 0) tensor components of POM and NPP. As expected for pushÈpull conjugated systems, be is largely dominated by the b \ b zzz L component where z is along the charge-transfer axis. b is yyz the only other non-negligible component which, for both compounds, is a factor of 5.6 smaller than b . Assuming that L Berthier et al.9 have also adopted the Taylor series convention, their estimates are 38% larger for both the b and b of L z POM whereas they employed a rather small basis set of double-zeta quality. Although the only available experimental data for POM are second-order susceptibilities of the crystalline structure, which have required the use of Lorentz local Ðeld factors to estimate b, it is of interest to make a comparison with our theoretical estimates. By accounting for the fact that Zyss and co-workers37 adopted the power series convention, by assuming that the longitudinal component is dominant and by considering the fact that the vibrational contribution to SHG is negligible, b ([2u ; u, u) \ be ([2u ; L L u, u) \ 1967 ^ 463 au at j \ 1064 nm, whereas the TDHF/6311G** b e([u ; u, u) value is 1355 au. By following Sigelle L and Hierle,6 who employed the two-state approximation to determine be ([u ; u, 0) from b e([2u ; u, u), the electronic L L part of b ([u ; u, 0) is estimated to attain 1849 au whereas L the TDHF/6-311G** be([u ; u, 0) value is 1328 au. The simL pliÐed treatment of the crystal packing e†ects and the lack of electron correlation account, therefore, for the di†erence between theory and experiment. In what concerns NPP, our b estimates are 40% and zzz 20% smaller than the semi-empirical FF and SOS/ CNDOVSB results due to Barzoukas et al.13,14 They are also much smaller than the most recent X-ray electron densityderived b e(0 ; 0, 0) estimates due to Fkyerat et al.16 that range L between 226.6 ] 102 and 969.7 ] 103 au. It is striking to note that, at the same CHF/6-311G** level of approximation, the static b , b and b of NPP is nearly twice as large as in zzz z tot p-NA. This can be attributed to the larger electron-donating e†ect of the pyrrolidine moiety with respect to the amino group. For bv(0 ; 0, 0), b remains the largest component at the zzz RHF/6-311G** level of approximation but, contrary to be(0 ; Table 3 CHF/6-311G** be(0 ; 0, 0) tensor components of POM and NPP electronic b bxxx bxyy bxzz x b bxxy byyy byzz y b bxxz byyz bzzz z b tot

1550

POM

NPP

3 È [3 È

[2 5 32 36

[3 5 11 13

11 40 [4 47

[27 156 [878 [749

[50 [252 1426 1124

749

1126


Table 4 RHF/6-311G** bv(0 ; 0, 0) tensor components of POM and NPP in au vibrational b xxx b bxyy bxzz x b xxy b byyy byzz y b xxz b yyz b bzzz z b tot

POM

NPP

330 [72 [37 221

17 92 840 949

443 [54 [15 374

354 [17 [64 273

659 [49 [1493 [883

561 [9 2157 2709

984

2372

0, 0), other components are far from being negligible (Table 4). b , b and b for POM and b , b and b for NPP xxz xxx xxy xxy xxz xzz are also important. This is further evidence that be and bv are at least partly governed by di†erent physical phenomena. In the static limit, the bv/be ratio is equal to 1.70 and 1.90, L L whereas the bv /be ratio attains 1.31 and 2.11 for POM and tot tot NPP, respectively. At the same level of approximation, the bv /be and bv /be ratios are 2.04 and 2.60 for p-NA. No simple L L tot tot relation has been obtained between the charge deÐciency of the aromatic ring and the bv/be ratio. On the other hand, it is striking to note again that the bv/be ratio increases when the BLA decreases. Similar conclusions have been drawn for the bv/be ratios of a,x-nitro-amino-polyenes and a,x-nitro-aminopolyynes,2 as well as for the cv/ce ratio of various p-conjugated polymers.38h41 Other factors, such as the aromaticity42 and the donor/acceptor strengths24 could also be taken into account to explain the bv/be variations but they deserve investigating with a larger set of compounds. As explained in Section 2, these bv/be ratios are strongly dependent upon the optical process (mainly bv) and the optical frequency (be). If considering the dc-P e†ect, the corresponding ratios decrease by a factor greater than 3, whereas they nearly vanish for SHG. For a wavelength of 632.8 nm, the TDHF/6-311G** scheme provides be([u ; u, 0)/be (0 ; 0, L L 0) \ 1.32 and be ([u ; u, 0)/be (0 ; 0, 0) \ 1.35 for POM. Contot tot sequently, at this wavelength, the bv([u ; u, 0)/be([u ; u, 0) L L and bv ([u ; u, 0)/be ([u ; u, 0) ratios of POM decrease to tot tot 0.43 and 0.32, respectively ; the bv([u ; u, 0) values having been evaluated within the enhanced approximation.34,35 The order of magnitude of the bv([u ; u, 0)/be([u ; u, 0) ratio is in rather good agreement with the work of Sigelle and Hierle,6 but the sign is di†erent. Indeed, they have obtained opposite signs for the electronic and vibrational contributions of POM. Several probable reasons can be advanced : (i) the crystal packing e†ects are ignored in our theoretical study whereas they have been described by ideal local Ðeld factor expressions by Sigelle and Hierle ; (ii) the assumption in ref. 6 that b is zzz the only non-negligible tensor component, which is particularly incorrect for the vibrational part ; (iii) the two-level approximation adopted by Sigelle and Hierle to evaluate be ([u ; u, 0)/be ([2u@ ; u@, u@) ; and (iv) the limitations zzz zzz of the theoretical approach that neglects electron correlation e†ects. 3.3 Characterization of the most important vibrations contributing to bv For most second- and third-order NLO compounds investigated to date, only a few typical vibrational normal modes contribute signiÐcantly to bv and cv.21,38h41 In these pconjugated systems these modes are mainly characterized by a substantial BLA variation component. Such a simple picture

of the bv and cv origin is of importance with respect to the optimization of the vibrational contribution to the NLO properties because, in Ðne, one would be able to tune speciÐcally the geometric and electronic parameters which mostly a†ect the vibrational contributions of these modes. Moreover, the normal mode vibrational frequency is related to the response time : the lower the frequency, the slower the process. Table 5 gives the main vibrational normal mode contributions to b , b , b and b , the dominant bv tensor comxxx xxy xxz zzz ponents in POM. Two modes (30 and 117 cm~1) are responsible for most of the b , b and b contributions. xxx xxy xxz They correspond to out-of-plane displacements with respect to the aromatic ring (Fig. 2). The very small vibrational frequency makes important the contribution to b of the 30 zzz cm~1 mode, which attains 30% of the total b . It originates zzz mainly from rotation motions of the nitro group with respect to the aromatic ring, which modify both the charge transfer and the electronic delocalization along the z-axis. All the other contributing modes to b present important in-plane zzz carbon, nitrogen and oxygen atom motions, leading to symmetric or asymmetric CxC, CwN and NwO stretchings. Fig. 2 displays the Cartesian displacements of these modes. In particular, the 1172 cm~1 mode can partially be described by in-phase CwO and NwO stretchings, whereas the corresponding out-of-phase motion characterizes the 1643 cm~1 mode. Obviously, the in-phase stretchings modify more k and z a than the out-of-phase stretchings, leading therefore to a zz much larger, 16-fold, vibrational b contribution. The 1790 zzz cm~1 mode typically describes the oscillation of POM between a more aromatic-like and a more quinonoid-like structure. Although CwH stretchings and CwCwH bendings are present in these eight modes, the CxC, CwN, and NwO stretching motions are at the origin of most of the bv contriL butions, because they vary both the charge transfer between NO and NO groups, leading to a large (Lk /LQ ) , and the 2 L a0 BLA along the charge-transfer axis, inducing a substantial (La /LQ ) . L a0 Although the HartreeÈFock technique overestimates systematically the normal mode vibrational frequencies by ca. 10%, it is possible to establish a partial correspondence between the RHF/6-311G** calculations and the IR and Raman spectra of POM in its crystalline state recorded by Plaza and co-workers.10 Part of the important discrepancy between the theoretical and experimental values has also to be attributed to the crystal packing e†ects. The measured vibrational normal mode frequencies of 1087, 1342, 1509 and 1602 cm~1 correspond to the calculated values of 1172, 1622, 1728 and 1790 cm~1. This correspondence satisÐes the qualitative features of the IR and Raman spectra, as well as the main characteristics of the POM atom displacements. Further association between the measured and computed spectra is, nevertheless, hampered by the main di†erence between the two set of results : on one hand, the representations of Table 5 RHF/6-311G** bv(0 ; 0, 0) contributions (in au) of the most important vibrational normal modes of POM u/cm~1

b

xxx

b xxy

b xxz

b

30 117 1172 1382 1435 1622 1643 1728 1790 1845

356 [27 1 È È È È È È È

206 244 1 È È È È È È È

210 418 [9 È È [2 È È È È

[447 [1 [417 [149 [104 [194 [26 [19 [120 [6

total

330

443

659

[1493

zzz

Only the non-negligible bv tensor components have been considered.

Fig. 2 Cartesian displacements of the vibrational normal modes of POM that contribute most to bv. The length of the arrows is proportional to the atomic displacements. With the exception of the 30 and 117 cm~1 modes, all the displacements take place in the yz plane.

the normal modes in ref. 10 are very schematic whereas, on the other hand, the theoretical calculations provide vibrational normal modes involving motions of many atoms or groups of atoms. A similar distinction between the low- and high-frequency J. Chem. Soc., Faraday T rans., 1998, V ol. 94

1551

vibrational normal modes occurs for NPP where bv is mainly L due to four modes involving stretchings of the NO wPhwNw moiety (Table 6). The similarity with the 2 most important vibrational normal modes in p-NA is striking : the 1230, 1605 and 1774 cm~1 modes of NPP (RHF/6311G**) correspond to the 1245, 1447 and 1798 cm~1 modes of p-NA (RHF/6-31G).21 Again, they involve aromatic to quinonoid motions of parts or the whole of the NLO-active NPP entity (Fig. 3). The 37 cm~1 mode also presents an Table 6 RHF/6-311G** bv(0 ; 0, 0) contributions (in au) of the most important vibrational normal modes of NPP u/cm~1

b

xzz

b

xxz

b xxy

b

zzz

37 54 75 90 168 225 1230 1528 1605 1774

376 [31 7 [40 167 266 [2 21 [1 6

308 61 92 [6 [18 138 È [4 1 2

[206 464 172 132 [10 [64 È È È È

195 10 [6 È 134 [156 325 307 675 261

total

840

561

354

2157

Only the non-negligible bv tensor components have been considered.

important bv contribution that is linked to the out-of-plane displacements (with respect to the aromatic ring) of the nitro and amino groups. Table 6 lists the contributions of the most important modes for the b , b , b and b tensor comxzz xxz xxy zzz ponents, which exhibit both in-plane and out-of-plane atomic displacements over the entire NPP molecule. In particular, the 54, 75 and 90 cm~1 modes present substantial torsion motions around the two CwN bonds whereas, in the 168 and 225 cm~1 modes, the main displacements occur in the pyrrolidine. Since the vibrational normal modes responsible for bv have L a frequency ranging between 1100 and 1800 cm~1 their corresponding vibrational NLO response time is roughly one order of magnitude larger than the electronic response. On the other hand, the vibrational response is 2È3 orders of magnitude slower in what concerns the normal modes contributing mainly to the transverse and perpendicular bv tensor components.

4 Synopsis The subject of this study was the determination, at the ab initio HartreeÈFock level, of the electronic and vibrational Ðrst hyperpolarizabilites of two reference molecules, POM and NPP, which are the active constituents of two efficient molecular crystals for NLO. We have again demonstrated that the bv/be ratio depends upon the chemical nature of the p-conjugated compound. In particular, the smaller the BLA, the larger the bv/be ratio. At the wavelength of 632.8 nm, the theoretical estimates of the bv([u ; u, 0)/be([u ; u, 0) ratio L L amounts to 0.43 of POM, which is of the same order of magnitude but opposite sign to the estimate of Sigelle and Hierle.6 Several ideas which have been proposed to account for such discrepancy should initiate further experimental and theoretical investigations. For both POM and NPP, the most contributing vibrational normal modes to bv exhibit substantial L CC, CN or NO stretching character, which can be more or less related to the switch between the aromatic and quinonoid forms. These vibrational normal modes have a frequency ranging between 1100 and 1800 cm~1, leading to a response time one order of magnitude slower than the electronic response. Forthcoming studies will address the importance of the crystal packing e†ects : hydrogen bonding, dipolar and quadrupolar interactions, upon these second-order NLO properties. Indeed, on the one hand, crystal packing modiÐes some geometrical parameters of the molecules, mainly the torsion angles, which inÑuence the NLO response but, in addition, it has a direct e†ect upon the NLO response.43 Another direction of improvement of our theoretical estimates will consist of including the electron which has recently been shown to modulate rather di†erently the NLO response of chemically di†erent p-conjugated pushÈpull compounds.44 B.C., E.A.P. and D.J. thank the Belgian National Fund for ScientiÐc Research for their Research Associate, ScientiÐc Collaborator and Research Assistant positions, respectively. It is a pleasure to acknowledge the fruitful discussions with Prof. B. Kirtman. The calculations have been performed on the IBM SP2 of the Namur ScientiÐc Computing Facility (Namur-SCF) for which the authors gratefully acknowledge the Ðnancial support of the FNRS-FRFC, the “ Loterie Nationale Ï for the convention No. 2.4519.97 and the Belgian National Interuniversity Research Program on “ Sciences of Interfacial and Mesoscopic Structures Ï (PAI/IUAP No. P4/10).

Fig. 3 Schematic drawing of the Cartesian displacements of the vibrational normal modes of POM that contribute most to bv. The length of the arrows is proportional to the atomic displacements. For the 37 cm~1 mode, the atomic displacements going outward (inward) from (to) xz plane are represented by wide (dotted) lines.

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References 1

Organic Materials for Nonlinear Optics, ed. D. S. Chemla and J. Zyss, Academic, New York, 1987 ; vol. I and II ; P. Prasad and D. J. Williams, Introduction to Nonlinear Optical E†ects in Mol-

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23

ecules and Polymers, Wiley, New York, 1991 ; R. W. Boyd, Nonlinear Optics, Academic, New York, 1992 ; Int. J. Quantum Chem., 1992, 43(1) ; Molecular Nonlinear Optics, Materials, Physics and Devices, ed. J. Zyss, Academic, New York, 1993 ; Chem. Rev., 1994, 94(1) ; D. M. Bishop, Adv. Quantum Chem., 1994, 25, 1 ; Polymers for Second-Order Nonlinear Optics, ed. G. A. Lindsey and K. D. Singer ACS Symposium Series, New York, 1995, vol. 601 ; T heoretical and Computational Modeling of NL O and Electronic Materials, ed. S. P. Karna and A. T. Yeates, ACS Symposium Series, New York, 1995, vol. 628. B. Kirtman and B. Champagne, Int. Rev. Phys. Chem., 1997, 16, 388. D. M. Bishop, Rev. Mod. Phys., 1990, 62, 343. D. M. Bishop, B. Kirtman and B. Champagne, J. Chem. Phys., 1997, 107, 5780. J. Zyss and D. S. Chemla, in Organic Materials for Nonlinear Optics, ed. D. S. Chemla and J. Zyss, Academic, New York, 1987, vol. 1, p. 23. M. Sigelle and R. Hierle, J. Appl. Phys., 1981, 52, 4199. J. Zyss, D. S. Chemla and J. F. Nicoud, J. Chem. Phys., 1981, 74, 4800. F. Baert, P. Schweiss, G. Heger and M. More, J. Mol. Struct., 1988, 178, 29. G. Berthier, M. Defranceschi, P. Lazzeretti, G. Tsoucaris and R. Zanasi, J. Mol. Struct. (T HEOCHEM), 1992, 254, 205. P. Plaza, F. Le Guiner, M. Joyeux, N. Q. Dao, J. Zyss and R. Hierle, J. Mol. Struct., 1991, 247, 363 ; F. Bri†aut-Le Guiner, N. Q. Dao, M. Jouan and P. Plaza, Spectrochim. Acta A, 1994, 50, 2091. R. Glaiser and G. S. Shen, Chem. Mater., 1997, 9, 28. J. Zyss, J. F. Nicoud and M. Coquillay, J. Chem. Phys., 1984, 81, 4160. M. Barzoukas, D. Josse, P. Fremeaux and J. Zyss, in Nonlinear Optical and Electroactive Polymers, ed. P. N. Prasad and D. R. Ulrich, Plenum, London, 1987, p. 69. M. Barzoukas, D. Josse, P. Fremeaux, J. Zyss, J. F. Nicoud and J. O. Morley, J. Opt. Soc. Am. B, 1987, 4, 977. A. Fkyerat, A. Guelzim, F. Baert, W. Paulus, G. Heger, J. Zyss and A. Perigaud, Acta Crystallogr. B, 1995, 51, 197. A. Fkyerat, A. Guelzim, F. Baert, J. Zyss and A. Perigaud, Phys. Rev. B, 1996, 53, 16236. M. Del Zoppo, C. Castiglioni and G. Zerbi, Nonlinear Optics, 1995, 9, 73. P. Zuliani, M. Del Zoppo, C. Castiglioni, G. Zerbi, S. R. Marder and J. W. Perry, J. Chem. Phys., 1995, 103, 9935. P. Zuliani, M. Del Zoppo, C. Castiglioni, G. Zerbi, C. Andraud, T. Brotin and A. Collet, J. Phys. Chem., 1995, 99, 16242. C. Castiglioni, M. Del Zoppo and G. Zerbi, Phys. Rev. B, 1996, 53, 11319. B. Champagne, Chem. Phys. L ett., 1996, 261, 57. D. M. Bishop and B. Kirtman, Phys. Rev. B, 1997, 56, 2273. C. Castiglioni, M. Del Zoppo and G. Zerbi, Phys. Rev. B, 1997, 56, 2275.

24 B. Champagne, Int. J. Quantum Chem., 1997, 65, 689. 25 C. E. Dykstra and P. G. Jasien, Chem. Phys. L ett., 1984, 109, 388 ; H. Sekino and R. J. Bartlett, J. Chem. Phys., 1986, 85, 976 ; S. P. Karna and M. Dupuis, J. Comput. Chem., 1991, 12, 487 and references therein. 26 J. Linderberg and Y. Ohrn, Propagators in Quantum Chemistry, Academic Press, New York, 1973. 27 M. Dupuis, A. Marquez and E. R. Davidson, HONDO95.3 from CHEM-Station, 1995, IBM Corporation, Neighborhood Road, Kingston, NY. 12401. 28 M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. DeFrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, GAUSSIAN 94, Revision B.1 Carnegie-Mellon University, Pittsburgh, PA, 1995. 29 R. Krishnan, J. S. Binkley, R. Seeger and J. Pople, J. Chem. Phys., 1980, 72, 650 ; A. D. McLean and G. S. Chandler, J. Chem. Phys., 1980, 72, 5639. 30 B. Kirtman and D. M. Bishop, Chem. Phys. L ett., 1990, 175, 601. 31 D. M. Bishop and B. Kirtman, J. Chem. Phys., 1991, 95, 2646. 32 D. M. Bishop and B. Kirtman, J. Chem. Phys., 1992, 97, 5255. 33 D. M. Bishop, J. Chem. Phys., 1991, 95, 5489 ; D. M. Bishop and D. W. De Kee, J. Chem. Phys., 1996, 104, 9876 ; 1996, 105, 8247. 34 D. S. Elliott and J. F. Ward, Mol. Phys., 1984, 51, 45. 35 D. M. Bishop, M. Hasan and B. Kirtman, J. Chem. Phys., 1995, 103, 4157. 36 A. Willetts, J. E. Rice, D. M. Burland and D. P. Shelton, J. Chem. Phys., 1992, 97, 7590. 37 J. Zyss, D. S. Chemla and J. F. Nicoud, Chem. Phys., 1981, 74, 4800 ; J. Zyss and J. L. Oudar, Phys. Rev. A, 1982, 26, 2028. 38 B. Kirtman, B. Champagne and J. M. Andre, J. Chem. Phys., 1996, 104, 4125. 39 E. A. Perpe`te, B. Champagne and B. Kirtman, J. Chem. Phys., 1997, 107, 2463. 40 B. Champagne, E. A. Perpe`te, J. M. Andre and B. Kirtman, Synth. Metal., 1997, 85, 1047. 41 E. A. Perpe`te, B. Champagne, J. M. Andre and B. Kirtman, J. Mol. Struct. (T HEOCHEM), 1998, 425, 115. 42 B. Champagne, unpublished results. 43 T. Yasukawa, T. Kimura and M. Uda, Chem. Phys. L ett., 1990, 169, 259 ; S. Di Bella, M. A. Ratner and T. J. Marks, J. Am. Chem. Soc., 1992, 114, 5842. 44 D. Jacquemin, B. Champagne and J. M. Andre, Int. J. Quantum Chem., 1997, 65, 679.

Paper 8/01229F ; Received 12th February, 1998


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