8024
J. Phys. Chem. 1995,99, 8024-8032
Optical Nonlinearities in Azoarenes I. D. L. Albert,” J. 0. Morley? and D. €’ugh*?? Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow G1 IXL, United Kingdom, and Department of Chemistry, University College of Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom Received: June 22, 1994; In Final Form: March 1, 1995@
Calculations are reported on the structure of donor-acceptor phenylazobenzenes, phenylazonaphthalenes, phenylazoanthracenes, and phenylazoheterocyclics using the AM1 molecular orbital method. The transition energies of these systems have been calculated using a modified CNDO method and a CI treatment of both singly and doubly excited configurations generated from an active space of 10 molecular orbitals. The results obtained show good agreement in many cases with the experimentally reported absorption maximum (A,,) values recorded in cyclohexane. The calculated dipole moment, n-electron charge densities, and bond orders in the ground and lowest dipole allowed excited state have been related to the relative efficacy of the donors and acceptors present. The frequency dependent polarizability, the second harmonic generation (SHG), and the third harmonic generation (THG) coefficients of the azoarenes have been computed using the correction vector method. An analysis of the coefficients shows that the replacement of a phenyl ring of the phenylazobenzenes by naphthalene or anthracene results in a modest increase in the polarizability and hyperpolarizability values, but the values obtained are highly dependent on the position of the donor group and the tautomeric form. Enhanced values are obtained when a heterocyclic ring is incorporated into the azoarene with the largest value obtained for a donor-acceptor naphthylazothiophene. Substantial resonance enhancement effects occur for those derivatives which absorb in the red or infrared region of the spectrum.
1. Introduction Conjugated organic molecules with intrinsically large first and second hyperpolarizabilities have attracted considerable interest over the past decade for applications in nonlinear optics (NLO).lT4 The large first and second hyperpolarizabilities are generally associated with the delocalized nature of their n-electrons. One of the most promising approaches to the development of materials with optimal orientation for second order NLO application is that of polymer poling? where an active nonlinear molecule in a polymer matrix is heated and poled above its glass transition temperature to orientate it in the direction of the applied field and then cooled in the presence of the electric field to lock in its activity. In an alternative scheme, the polymerization is carried out on bifunctionalized monomers under the influence of the applied field to produce a stable crosslinked nonlinear polymer? In contrast to crystalline organic nonlinear materials, polymeric materials have the potential to be relatively inexpensive to produce and to be easily processed. The studies reported here are based on an investigation of the potential of azobenzenes and related azoarenes as materials for poled polymer applications. These systems are of current interest because the azo linkage is generally stable under polymerization conditions, and their relatively large dipole moments assist orientation in the polymer by an applied electric field. Additionally, the bathochromic shift induced by substitution with donor and acceptor groups in these systems facilitates resonance enhancement effects, and they are easily functionalized chemically to incorporate a wide variety of polymerizable groups. In these studies, there are a number of important factors which have been explored theoretically, such as the change in dipole University of Strathclyde. University College of Swansea. @Abstractpublished in Advance ACS Abstracts, April 15, 1995. +
0022-365419512099-8024$09.OO/O
moments, transition energies, and hyperpolarizabilities induced by either (i) increasing the substitution pattem of the azobenzene by using more than one donor and acceptor group, (ii) changing the aromaticity of the system by using naphthalene and anthracene rings in place of benzene to give the corresponding phenylazoarene, or (iii) modifying the nature of the conjugation path between donor and acceptor by using heterocyclic systems such as thiophene to give phenylazothiophenes.
2. Theoretical Model One of the major advantages of working with organic materials is that the macroscopic bulk NLO susceptibility is related to the hypexpolarizability of the individual molecules. In the case of poled polymer films, for a given degree of chromophore reorientation, the calculated molecular hyperpolarizability is also expected to be proportional to the second order susceptibility. A theoretical model which can reproduce electronic properties, such as the optical gap and the corresponding oscillator strength of a few low-lying states, is expected to give a good estimate of the hyperpolarizability, which is directly dependent on these quantities. The CNDOVSB method,’,* which is based in part on the CNDO/S9 and CNDO/w’o methods, generally gives a good description of the dipole moments, transition frequencies, and corresponding oscillator strengths of polar organic molecules. The present study employs CNDOVSB in a singly and doubly excited configuration interaction (SDCI) study. Limited correlations have been introduced by including all singly and doubly excited configurations obtained from an active space formed by six occupied MO’s and four unoccupied MO’s. The difference in the number of the occupied and unoccupied MO’s arises because of the extra electrons donated by the nitrogens in NMe2 and NO2 groups. Systems in which S and 0 are part of a five-membered ring (where the heteroatom donates two electrons to the ring) and those systems with more than one 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 20, 1995 8025
Optical Nonlinearities in Azoarenes donor andor acceptor group contribute a correspondingly larger number of occupied MO’s and fewer unoccupied MO’s to the active space. Our earlier studies” on the donor-acceptor polyenes and polyphenyls have established the adequacy of an active space formed of 10 MO’s in determining the electronic and optical properties of these systems. The linear and nonlinear optical properties reported in this paper are the frequency dependent polarizability, the second harmonic generation (SHG) coefficient @ (2w;w,o)), and the third harmonic generation (THG) coefficient ( y (3w;o,w,w)). The most commonly used method for the calculation of the linear and nonlinear optical properties is the sum-over-states (SOS) approach.8-12-16Explicit expressions for the frequency dependent polarizability, and the first and second hyperpolarizabilities can be found elsewhere.I6 The ijk Cartesian component of the SHG hyperpolarizability tensor /3, for example, is given by
zz
(olk!ile)(elpjl e’)(e’lk!klO)
pijk
(-2w;w,w) =
I ee’
[woe- 20~1[00,(- 0 1
(1)
where (Olpile) is the electronic transition moment between the ground state (0)and the excited state le). The dipole moment operator pi is defined by pi = pi - (OlpiIO). The frequency woe is the energy difference between state e and the ground state; o is the excitation frequency of the incident light. The sum over I implies the inclusion of additional terms in which the matrix elements are permuted over (ijk) with corresponding changes in the denominators. The expression shows that when e = e’ the term (elpile’) is the difference in dipole moments between the state e and the ground state, usually denoted as b e - , in the two-state model.]’ This quantity has been held to be of primary significance as an indicator of possible high values of the first hyperpolarizability. As in previous work all components of the /3 and y tensors have been calculated, but only the most significant quantities are reported. All values are given relative to a coordinate system in which the x and y axes are in the plane of the conjugated rings and the x axis points along the molecular dipole (which in all cases lies in the xy plane). In the case of /3, the x and y components of the vector part of the tensor (see, for example, refs 2 and 4) are given. The component Px is obtained experimentally from electric field induced SHG measurements in solution, where the signal depends on the quantity In the case of y, the major in-plane components yxxxx,ywr, yyru, and yyyyyare shown. In the semiempirical SOS method, parameters are chosen to match experimental properties such as the lowest excitation energy and the corresponding transition moment and hence lead to a more realistic value of the hyperpolarizabilities. The method also provides an understanding of the nature of the evolution of the hyperpolarizabilitiesas a function of the number of states added in the SOS expression, leading to the identification of the essential states contributing to the final value of the hyperpolarizability. However, the method is limited to smaller systems, as a complete diagonalization of the resultant CI matrix and calculation of transition moments between all the excited states is a prerequisite for doing the summation. The summation itself is time consuming and in practice is expected to be successful only if the hyperpolarizability converges as successive excited states are added, which is sometimes not observed in the case of the second hyperpolarizability (y). An altemative method, the correction vector method,I8 to be discussed briefly in the next paragraphs, enables computation of linear and nonlinear optical properties to be made directly in terms of the
configurations themselves without the necessity of obtaining all the states of the CI matrix. In the correction vector approach, the NLO coefficients are obtained by computing the first and second order correction vectors $(I) and fA2) of the perturbed Hamiltonian. These vectors can in principle be expanded in terms of the set of configurations used in the CI calculation, as
and
(3)
where lk) are the Slater determinants describing the singly and doubly excited configurations used in the CI calculation. The expansion coefficients g(l) and g(2)can be obtained by solving the following equations
(H - E,
+ ho,) $Jij(z)(w1,o2)= -pj 4:’)
(0)
(5)
The above equations can be transformed into matrix equations, by substituting the expansions for IC), #(I), and @C2) into the eqs 4 and 5. Since both the correction vectors and IC) are expanded in the same many electron basis, it is possible to match coefficients and obtain linear inhomogeneous equations for g(l) and g(2). This procedure yields the following matrix equations:
H(w) * g i ( 0 ) = Pi
(6)
and
where
The solutions of the linear inhomogeneous equations are easy to obtain if the associated matrix is positive definite, as the Gauss-Seidel iteration procedureIg will readily converge. If the associated matrix is nondefinite, as is the case with negative frequencies, the Gauss-Seidel iteration scheme does not converge, and in this case an altemative algorithm20is required to provide fast convergence. Once and @(2) are known, the NLO coefficients can be easily written down as a sum of the matrix elements of the dipole displacement operator between the functions @(I) and @(2). For example, the SHG hyperpolarizability can be written as
where P is the permutation operator, implying the addition of terms in which the coordinates and frequencies are permuted.
8026 J. Phys. Chem., Vol. 99, No. 20, 1995
Albert et al.
(111) (101
Figure 1. Molecular structure of phenylazobenzenes.
This method is advantageous in that a complete diagonalization of the CI matrix, the computation of the transition moment between the various states, and the summation over all these states are unnecessary. A few low-lying excited states can be obtained by the Davidson's algorithm,2i without performing a complete diagonalization. Provided the same set of configurations, including the ground state, are used, the final value of the polarizability and the hyperpolarizabilities from the SOS method and the correction vector method should be the same. One minor disadvantage of the correction vector method is that it does not converge at zero frequency. Results can, however, be calculated at low frequency, far from resonance, and second order hyperpolarizabilities obtained for excitation at 0.65 eV should be close to the static values. In this paper the correction vector method has been used routinely to calculate the frequency dependent polarizability and the SHG and THG hyperpolarizabilities as it is computationally more efficient than the SOS procedure.
Figure 2. Molecular structure of azo and hydrazo tautomers of phenylazonaphthalenes.
McHN
0
Ova,
(IVb)
Figure 3. Molecular structure of phenylazoanthracenes.
(Va)
MtlN
b
3. Results and Discussion 3.1. Molecular Structures. In previous studies, calculations of the molecular hyperpolarizabilities were carried out on structures which were based on templates derived from crystallographic data. While there are a number of structures available from the Cambridge Structural Databasez4 for the donoracceptor azobenzenes and phenylazo-2-naphthols, which appear to exist solely as the hydrazone form, there are no suitable templates available for structures such as the substituted phenylazonaphthalenes (11), phenylazoanthracenes (IV), and arylazoheterocycles (V-VI); see Figures 1-5. For the sake of consistency, we have optimized the structures of all the molecules reported in this paper using the Ah41 molecular orbital method.25 In the case of the phenylazobenzenes (I), phenylazonaphthalenes (11), phenylazoanthracenes (IV), and azoheterocyclics (V and VI), the trans conformations were selected for calculation because they are generally more stable and, under conditions of electric field poling, are likely to be more useful because they have the largest dipole moments. All bond lengths and angles were fully optimized, but the aromatic rings were contrained to be planar during the optimization procedure. The results, in Table 1, show the expected variation of the N-N bond length (from 1.23 to 1.32 A) in moving from the azo (11) to the hydrazo (111) forms of the naphthalene dye. 3.2. Electronic Properties. Any comparison between the calculated results and experimental data is fraught with difficulty
(VC)
h
(Vd)
Figure 4. Molecular structure of phenylazoheterocyclics
because the transition energies of many polar organic molecules with long wavelength absorptions vary with solvent polarity. For example, the absorption maximum of a representative system such as 4-dimethylamino-4'-nitroazobenzene (Ib) changes from 444 nm in hexane to 475 in ethanol to 480 in phenyl acetate, and, in the presence of acids, an even larger bathochromic shift is o b s e r ~ e d . ~In~ ,addition ~~ to the state and solvent dependent absorptions found in many azoarenes, some molecules also exhibit tautomerism in solution, and the spectrum observed is dependent on whether an azo or hydrazo form predominates. While the individual tautomers would be expected to show different calculated spectra, the effect of the physical state of a given molecule and its possible solvatochromic shift presents difficulties for exploring resonance enhancement within the CNDOVSB method. In the present studies, the calculated transition energies were compared with experimental spectra recorded in cyclohexane.
J. Phys. Chem., Vol. 99, No. 20, I995 8027
Optical Nonlinearities in Azoarenes
C
WIb)
NHMe
MeHN -
b (VII)
Figure 5. Molecular structure of azoheterocyclics and naphthyla-
zothiophene.
In the CNDOVSB method, the predicted spectrum of a given structure depends on (1)the choice of atom and bond parameters, ( 2 ) the values of the monocentric bielectronic repulsion integrals, and (3) the value of the spectroscopic constant, K , which differentiates between the o and R electron^.^ In the earlier studies on donor-acceptor polyenes and polyphenyls, good correlations were obtained between the calculated and experimental spectra using molecular structures derived from crystallographic data and an unique set of values for (1)and (2), with K set at 0.65 and with the two-center bielectronic repulsion integrals evaluated using the Mataga-Nishimoto approximation.26 Calculations with this set of parameters gives a slightly smaller value (399 nm) of the absorption maximum of Ia compared with the experimental value of 429 nm27 and 411 nm for Ib compared with the experimental value of 444 nm.22,23Adjustment of the spectroscopic constant to 0.58 gives values of 429 nm for Ia and 442 nm for Ib (Table 2), which are in very good agreement with the experimental values. All the results reported in this paper (Table 2 ) were carried out using K = 0.58. The results show that there are a number of factors affecting the absorption maximum of the azoarenes. For example, comparing the absorption maximum of Ia and Ib we see that an azo bridge leads to a bathochromic shift in A,, relative to the ethylenic bridge, and a comparison of Ib, IIa, and IVa shows that replacing the benzene ring in phenylazobenzenes by larger fused aromatic rings, such as naphthalene and anthracene, leads to a longer wavelength absorption. A similar effect occurs when the benzene ring in phenylazobenzenes is replaced by a heterocyclic ring such as furan or also increases with the number thiophene. The value of A,, of donor and acceptor groups, with the donors having the larger effect. In addition to producing a bathochromic shift, increasing the number of donor groups in the molecule also leads to the occurrence of appreciable contributions to the hyperpolarizability from more than one significant excited state as can be seen in Id, Ie, IIb, and IVb. The ground state dipole moments of most of the systems from the CNDO calculation are in good agreement with those obtained from the AM1 calculation (Table 2), which indicates the suitability of the chosen parametrization in these systems, as the AM1 dipole moments are known to be close to the experimental values.25 The rather larger discrepancies for the dipole moments of series V and VI are a consequence of the
inclusion of 3d sulfur orbitals in the CNDO method but not in the MOPAC method. The ground state referred to is that derived from the CI calculation, which consists of the HF ground state with small contributions from excited configurations. The replacement of the benzene ring (Ib) by either a naphthalene ring (IIa) or an anthracene ring (IVa) has little effect on the dipole moment, probably because the effective length of the conjugation path beween the donor and the acceptor remains almost unaltered when the donor and acceptor groups are retained in the 4 and 4' positions. However, the position of the donor or acceptor groups in the larger fused rings does seem to affect the resultant dipole moment as the conjugation length is now changed. Similarly, a comparison of Ib and Va shows that a thiophene ring favors charge separation and hence an increased dipole moment, which is enhanced further when both benzene rings are replaced by thiophene rings as in VIa. The furan ring does not have the same effect (Table 2). Comparison of the dipole moments of Ia and Ib shows that the azo linkage serves as a better bridge than the ethylenic linkage for charge separation and hence increases the dipole moment of the latter. In Table 3 and Table 4 we present the CNDO n-charge distributions** in the ground and the lowest dipole allowed excited states of the various azoarenes. The n-electron charge densities given in Table 3 and Table 4 are the difference between the calculated n-electron charge density and the total number of n-electrons associated with each entity. For example, the number of n-electrons associated with a nitro group is 4, and the calculated n-electron charge density of the nitro group in the ground state of Ia is 4.040. Hence the change in the charge density is -0.040. Since the SDCI calculations account for almost 95% of the correlation energy of the ground state, the ground state dipole moment and charge density should be appreciably better than those obtained from the Hartree-Fock wave function. The ground state results presented here were therefore calculated in the same SDCI approximation employed for the excited states. The results show the charge density values per entity, namely, the donor group, acceptor group, the arene rings, and the azo linkage. Since many of the systems investigated in this paper do not have a proper n-symmetry, the active space is not confined to pure n-orbitals. There is therefore some admixture of H-atom orbitals and, since the charge on the H atoms has been omitted from the charge density, the sum of the contributions from the separate entities does not add up to zero. It is evident from Table 3 that there is a substantial deficit in the n-electron charge of the donor group and an excess in the n-electron charge of the acceptor group. The phenyl ring attached to the donor acts as n-acceptor and the phenyl ring attached to the acceptor acts as n-donor in all the cases. However, the n-electron charge of the bridge group is different in the azobenzene (Ib) and the stilbene (Ia) systems. For example, comparison of the charge density of the bridge group of Ia with that of the other molecules shows that, while the n-electron charge of the bridge group in all the molecules is large, the n-electron charge on the bridge of Ia is minimal. This shows that in the case of the azo arenes the effect of the donor and acceptor groups extends to the bridge group with the azo bridge acting as a n-acceptor. The n-electron charge, however, does not extend past the bridge group in either the azoarenes and stilbenes. The charge density of azobenzenes in the excited state shows the same general characteristics found in the ground state. There is larger reduction in the n-charge of the donor and a larger increase in the n-charge of the acceptor. The charge densities of the various entities in the hydrazo tautomer of the phenylazonaphthalene (111) are remarkably different from those
8028 J. Phys. Chem., Vol. 99, No. 20, 1995
Albert et al.
TABLE 1: Selected Bond Lengths, Angles, and Heats of Formation Calculated by the AM1 Method for the Azoarenes (I-VII) bond lengths (A) angles (deg) structure -N=NAr-NMe2 Ar-NO2 -N-C-a -N-Cb NNCa NNCb heats of formation' 1.483 125.1 71.9 Ia 1.346 1.401 1.449 1.450 125.3 118.4 112.1 Ib 1.233 1.386 1.485 1.425 1.440 121.2 122.4 1.485 119.0 IC 1.235 1.384 1.420 1.434 120.0 121.1 114.5 Id 1.239 1.388 1.484 1.411 1.431 120.5 123.2 1.489 118.9 Ie 1.238 1.387 1.410 1.433 121.5 117.9 127.3 IIa 1.234 1.377 1.484 121.5 1.421 1.439 118.0 1.486 1.429 1.440 IIb 1.232 1.383 121.3 121.0 111 1.321 1.299 1.481 1.321 1.406 139.8 123.9 1.486 118.9 IVa 1.235 1.379 1.424 1.437 218.8 120.1 119.2 1.486 151.1 IVb 1.232 1.383 1.431 1.437 120.1 119.3 1.486 123.9 Va 1.237 1.368 1.396 1.435 120.2 95.3 118.8 Vb 1.238 1.366 1.486 1.388 1.436 122.1 118.7 1.459 1.422 1.413 129.0 vc 1.236 1.386 120.5 119.0 1.471 1.414 1.407 Vd 1.240 1.382 138.1 120.0 1.458 141.0 118.8 VIa 1.241 1.366 1.391 1.409 119.7 119.3 VIb 1.241 1.458 1.379 1.409 85.9 1.364 123.0 119.7 1.405 1.399 VI1 1.245 1.370 1.460 120.6 163.0 a Carbon of the ring containing the electron donor. Carbon of the other ring. In kcal mol-'. TABLE 2: Calculated Electronic Properties of Azoarenes (I-VII) structure pc~(AM1)" P ~ ( C N D O ) Ap~(cND0)c ~ ,Id p 10.18 429.45 1.15 Ia 8.74 8.91 12.20 9.42 9.59 Ib 441.66 1.01 12.84 459.88 1.02 Id 9.91 9.59 7.76 477.88 0.88 Idr 9.81 9.90 3.39 327.15 0.26 3.11 11.02 10.68 522.71 0.25 6.68 478.68 0.72 17.88 IIa 9.63 10.14 477.13 0.94 12.71 7.70 8.84 IIb 484.98 0.53 6.18 347.76 0.31 3.52 111 6.56 6.71 480.13 1.20 7.84 10.10 5.11 538.38 0.76 IVa 3.47 379.25 0.13 13.31 552.87 0.4 1 8.31 8.86 IVb 6.41 387.08 0.34 6.53 Vd 9.81 10.99 498.34 0.91 9.29 11.18 7.64 523.04 0.95 vbf 12.16 494.13 0.85 9.57 9.53 Vcf 12.70 543.15 0.87 10.56 8.70 Vdg VIag 10.39 10.96 9.85 540.03 0.86 4.86 562.04 0.98 9.74 11.05 VIbg VIIh 11.27 677.08 0.69 10.06 7.98 10.44 451.36 0.21 a AM1 ground state dipole moment (D). CNDO dipole moment in the ground state (D). Difference between the CNDO dipole moment in the dipole allowed excited state and the CNDO ground state dipole moment (D). Transition energy (nm). e Oscillator strength. f435 singly and doubly excited configurations from 7 occupied and 4 unoccupied MO's were used in the calculation. g 253 configurations from 7 occupied and 3 unoccupied MO's were used in the calculation. 320 configurations from 8 occupied and 3 unoccupied MO's were used in the calculation.
of the corresponding azo tautomer (IIa), as expected. The most important observation is that the bridge acts as a x-donor in the hydrazo tautomer (m)but as an acceptor in the azo tautomer (IIa), which indicates that the N-H of the azo bridge now serves as a donor and the imino group has more of an acceptor nature as a consequence of the positive charge on nitrogen. The phenyl ring attached to the imino nitrogen in the hydrazo tautomer has a donor character as opposed to the acceptor nature of the corresponding phenyl ring of the azo tautomer. Thus there are two opposing donor-acceptor interactions in the hydrazo tautomer and this is manifested by a low value for the ground state dipole moment. A better understanding of the charge transfer pattern can be obtained from the bond order in the ground (Table 5) and lowest
TABLE 3: SDCI n-Charge Densities per Entity in the Ground State of Azoarenes ~______ ~
molecule
Ia Ib IC Id Ie IIa IIb I11 IVa IVb Va Vb vc Vd VIa VIb VI1
Dla
D2b
Al'
0.241 -0.040 0.176 -0.038 0.186 -0.035 0.177 0.190 -0.040 0.184 0.211 -0.036 0.181 -0.039 0.345 -0.158 -0.222 -0.050 0.213 -0.039 0.158 -0.035 0.212 -0.038 0.198 -0.049 0.178 -0.050 0.192 -0.046 0.213 -0.051 0.252 -0.079 0.164 0.204 -0.048
A2d
@le
@i
-0.103 0.012 -0.100 0.041 0.058 -0.086 0.030 -0.227 0.024 0.038 -0.199 0.018 -0.082 0.038 -0.019 0.096 0.186 -0.082 -0.074 0.038 -0.111 0.053 -0.114 0.031 -0.007 0.016 -0.098 0.044 -0.042 -0.074 0.047 -0.108 0.028 0.047 0.097 -0.045 -0.188 0.027
-X=X-g
-0.019 -0.100 -0.105 -0.157 -0.208 -0.114 -0.248 0.143 -0.114 -0.078 -0.131 -0.185 -0.110 -0.111 -0.140 -0.257 -0.156
a Donor group at the 4-position of the benzene ring. Donor group at the 2-position of the benzene ring or at the 8-position of the naphthalene ring or at the 5-position of the anthracene ring. Acceptor at the 4'-position of the benzene ring. Acceptor at the 2-position of the benzene ring. e Aromatic ring attached to the donor. f Aromatic ring attached to the acceptor. g Ethylenic, or azo or hydrazo bridge of the molecule.
dipole allowed excited states (Table 6). One striking difference between the stilbene and azobenzene systems is in the bond orders of the various bonds in the aromatic rings. For example, when the bridge is an ethylenic bridge, the benzene rings attached to both the donor and the acceptor groups have an almost equal amount of quinonoid character, indicating a charge transfer from the donor to the acceptor. In contrast, with an azo bridge the benzene ring attached to the donor group has a larger quinonoid character than the benzene ring attached to the acceptor group. This shows that most of the charge from the donor does not get past the azo bridge in azobenzenes. A comparison of the bond orders of the various bonds in the ground and the dipole allowed excited state shows that, in general, the quinonoid nature of the benzene ring is enhanced in the excited state, indicating a larger charge transfer in the dipole allowed excited state. The bond order, of the hydrazo tautomer of the phenylazonaphthalene (111), in the ground state shows the quinonoid nature of the benzene ring attached to the imino nitrogen. However, the quinonoid nature of the benzene ring attached to the acceptor in 111 is not much different from the quinonoid nature of the corresponding benzene ring in the azo tautomer IIa. This also supports the fact that the transfer
J. Phys. Chem., Vol. 99, No. 20, 1995 8029
Optical Nonlinearities in Azoarenes
TABLE 4: SDCI Ic-Charge Density per Entity in the Lowest Dipole Allowed Excited State of Azoarenes molecule Ia Ib IC
Id Ie IIa IIb 111
IVa IVb Va Vb vc Vd VIa VIb VI1
D1"
D2"
Al'
A2d
0.359 0.886 -0.072 0.388 -0.039 0.050 0.182 0.172 0.158 -0.045 0.029 0.203 0.224 -0.050 0.278 -0.068 -0.177 0.457 -0.065 -0.251 -0.054 0.263 -0.052 0.247 -0.058 0.464 -0.073 0.314 -0.086 0.354 -0.072 -0.084 0.368 -0.090 0.334 -0.131 0.326 0.253 0.231 -0.075 -0.083
@le
@,f
0.044 0.102 -0.346 -0.487 -0.277 0.127 0.182 0.131 0.096 0.130 -0.050 0.184 0.132 0.173 0.117 0.186 0.152
-0.093 -0.230 -0.218 -0.231 -0.071 -0.010 -0.014 -0.031 -0.055 -0.033 -0.100 -0.173 -0.193 -0.184 0.087 -0.258
-X=X-g
-0.367 -0.561 -0.61 1 -0.530 -0.282 -0.441 0.175 -0.256 -0.287 -0.282 -0.352 -0.280 -0.242 -0.245 -0.415 -0.265
Donor group at the 4-position of the benzene ring. Donor group at the 2-position of the benzene ring or at the 8-position of the naphthalene ring or at the 5-position of the anthracene ring. Acceptor at the 4'-position of the benzene ring. Acceptor at the 2-position of the benzene ring. e Aromatic ring attached to the donor. f Aromatic ring attached to the acceptor. g Ethylenic, or azo or hydrazo bridge of the molecule. of n-electron charge from the donor does not get past the bridge in the azoarenes. 3.3. Linear and Nonlinear Optical Properties. The dominant components of the linear polarizability and the SHG hyperpolarizability of the azobenzenes have been calculated at an excitation energy of 0.65 eV and 1.17 eV and the results are presented in Table 7. The extremely large hyperpolarizability of many of the compounds at an excitation frequency of 1.17 eV (1064 nm) is due to the closeness of the absorption maximum to the doubled excitation frequency (532 nm). A comparison of the polarizability and SHG coefficient of Ia and Ib shows that the azo bridge leads to an appreciably larger hyperpolarizability than the ethylenic bridge, although the polarizability is almost equal in the two cases. The greater preresonant enhancement at the doubled frequency in the case of Ib accounts for this behavior. In general, the calculated polarizability and hyperpolarizability of the azobenzenes increase as more donors or acceptors are introduced into the benzene rings. The effect of the addition of a second donor, which leads to a large increase in hyperpolarizability, is much more pronounced than that of a second acceptor. The reduced effect of the second acceptor is a consequence of it being twisted relative to the molecular plane in the calculated structure, so that only part of its effect is realized. For the same reason, the calculated hyperpolarizabilities of 2,4-bis(dimethylamino)azobenzenes are smaller than expected as the NMe2 group in the 2-position is twisted. However, the introduction of the planar NHMe group into the 2-position to give azobenzene (Id) increases the value of the hyperpolarizability compared to Ib. A comparison of the polarizability and hyperpolarizability of Id and Ie shows that adding an acceptor to Id, to give the azobenzene Ie, leads only to a small increase in the hyperpolarizabilityvalue in accordance with earlier arguments. Overall, the enhancements calculated when additional donors and acceptors are introduced are relatively small and disappointing. Indications that this might be the case have been given by experimental work on other donor/acceptor organic molecules.29 For this reason, attempts have been made to boost the hyperpolarizability of the azoarenes by increasing the length of the conjugation path, without loss of overall stability, through replacement of at least one of the benzene rings with a naphthalene, anthracene, or heterocyclic ring.
The effect of replacing one benzene ring of the phenylazobenzene (Ib) by a naphthalene ring, while retaining the NO2 and NMez groups at the 4- and 4'-positions, results in a structure where neither the donor nor the acceptor groups can adopt a planar conformation in the plane of the naphthalene ring, because of steric interactions with the hydrogen at the 8-position. This effect is illustrated by the hypsochromic shift observed experimentally in moving from 1-(4-nitrophenylaz0)-4-naphthylamine to the corresponding N,N-dimethylated derivative where the absorption maximum falls from 531 nm to 478 nm, r e ~ p e c t i v e l y . ~However, ~,~~ the methylamino group, which shows similar, if slightly less electron donating character than the dimethylamino group, is able to adopt a fully planar conformation. The calculated hyperpolarizability of the resulting N-methyl-4-nitrophenylazo-4'-naphthylamine(IIa) at 0.65 eV is only equivalent to the azobenzene (Ib), and resonance enhancement leads to a relatively larger value of the hyperpolarizability of the latter at an excitation energy of 1.17 eV. The polarizability of the NHMe-substituted naphthalene, on the other hand, exceeds that of the azobenzene at both frequencies. Surprisingly, if the NHMe group is moved to the 5-position of the naphthalene ring (IIb), there is a significant reduction in both the predicted polarizability and hyperpolarizability values accompanied by a change in the sign of the hyperpolarizability. The hyperpolarizability of the related phenylazoanthracene (IVa) shows a small increase over the azobenzene (Ib) and a larger increase in the polarizability. However, the isomer with the NHMe group in the 5-position (IVb) shows a decrease in both the polarizability and the hyperpolarizability value accompanied by a change in the sign in the latter. Thus both the naphthalene and anthracene rings are less efficient than the phenyl ring for charge transfer and hence for the hyperpolarizability. The calculated hyperpolarizability of the corresponding hydrazone tautomer (111) of the phenylazonaphthylamine (IIa) is very small. The reduced value can be attributed to the effect, on excitation, of electron transfer from the hydrazone nitrogen (N3) (see Figure 2) mainly to the adjacent nitrogen (N2) and the imine nitrogen (Nl). This change tends to reduce the value of the molecular dipole moment, which, in fact, shows a net decrease in value from 6.71 in the ground state to 3.52 D in the excited state (Table 2). The usual behavior in donor/acceptor systems is for a large increase in dipole moment on excitation in the same sense as the ground state dipole. The smaller change in the hydrazone tautomer probably arises from the partial cancellation of two effects. More typically, in the azo tautomer (IIa), there is increased donation from the nitrogen (Nl) of the NHMe group to both nitrogens of the azo group on excitation, with a concomitant increase in the dipole moment from 10.14 D in the ground state to 17.88 D in the excited state. The charge density and bond order (Tables 3 and 4 and Tables 5 and 6) of the two compounds support this interpretation. Behavior similar to that observed in the larger azoarenes (I1 and IV) is found when one benzene ring of the phenylazobenzene (Ib) is replaced by a heterocyclic ring, while again retaining the NO2 and NMe2 groups at the 4- and 4'-positions. Only a moderate increase in the value of the polarizability and hyperpolarizability results, with the phenylazofuran (Vb) showing a greater value than the phenylazothiophene (Va), probably because the heterocyclic oxygen atom of the former is acting as an additional and more efficient donor than the sulfur atom in the latter. Support for this comes from the charge densities of the heterocyclic ring of the two molecules (Tables 3 and 4). The charge density of the furan ring, which is negative, is found to be substantially less than that of the thiophene'ring, reflecting the donor character of the furan ring relative to the thiophene
8030 J. Phys. Chem., Vol. 99, No. 20, 1995
Albert et al.
TABLE 5: Selected z-Bond Orders of the Azoarenes in the Ground State, Obtained from the SDCI Calculation' mo1ecu 1e Ar-NMe2 c=c c=c N-C" x=x N-Cb c=c c=c Ar-NO2 Ia 0.380 0.602 0.690 0.241 0.692 0.368 0.859 0.365 0.608 Ib 0.440 0.583 0.686 0.238 0.703 0.374 0.335 0.618 0.868 IC 0.448 0.578 0.709 0.388 0.859 0.345 0.616 0.690 0.234 Id 0.446 0.542 0.685 0.240 0.727 0.434 0.833 0.349 0.618 Ie 0.447 0.550 0.724 0.413 0.755 0.336 0.613 0.692 0.234 IIa 0.437 0.648 0.617 0.624 0.387 0.858 0.336 0.679 0.236 111 0.837 0.344 0.860 0.775 0.390 0.370 0.600 0.680 0.240 IVa 0.431 0.677 0.594 0.393 0.857 0.342 0.635 0.688 0.239 IVb 0.413 0.767 0.547 0.358 0.876 0.336 0.687 0.235 0.636 Va 0.45 1 0.650 0.594 0.410 0.846 0.346 0.613 0.686 0.239 Vb 0.466 0.686 0.240 0.663 0.593 0.355 0.613 0.468 0.811 vc 0.440 0.581 0.704 0.380 0.856 0.358 0.699 0.575 0.258 0.715 0.550 0.253 Vd 0.454 0.574 0.841 0.374 0.716 0.404 VIa 0.455 0.648 0.598 0.416 0.834 0.367 0.700 0.576 0.261 VIb 0.424 0.577 0.524 0.241 0.564 0.462 0.702 0.380 0.671 VI1 0.397 0.713 0.552 0.256 0.469 0.626 0.448 0.809 0.658 " Carbon of the ring containing the electron donor. Carbon of the other ring. X=X is the central bridge bond. The four C=C bonds are (from left to right respectively) the bonds identified as a, b, c, and d in the figures. TABLE 6: Selected z-Bond Orders of the Azoarenes in the Lowest Dipole Allowed Excited State, Obtained from the SDCI Calculationc molecule Ar-NMe2 c-c c=c N-C" x=x N-Cb c=c c=c Ar-NO2 Ia 0.438 0.535 0.739 0.524 0.618 0.520 0.510 0.740 0.286 0.453 0.660 0.474 0.535 0.723 0.278 Ib 0.489 0.505 0.742 IC 0.427 0.569 0.719 0.477 0.637 0.453 0.559 0.701 0.238 Id 0.526 0.745 0.510 0.613 0.442 0.569 0.701 0.245 0.417 Ie 0.434 0.526 0.729 0.503 0.579 0.437 0.552 0.715 0.248 IIa 0.466 0.693 0.464 0.708 0.540 0.436 0.563 0.709 0.260 111 0.759 0.409 0.757 0.568 0.416 0.462 0.542 0.707 0.252 VIa 0.439 0.557 0.682 0.457 0.739 0.4 15 0.612 0.705 0.254 VIb 0.487 0.660 0.449 0.752 0.400 0.700 0.252 0.639 0.618 0.550 0.641 0.474 0.697 0.439 0.561 0.713 0.259 Va 0.469 Vb 0.512 0.598 0.594 0.468 0.662 0.463 0.597 0.717 0.270 vc 0.525 0.734 0.450 0.685 0.499 0.513 0.600 0.665 0.294 Vd 0.510 0.521 0.740 0.437 0.703 0.515 0.647 0.616 0.279 VIa 0.493 0.582 0.626 0.463 0.693 0.505 0.606 0.662 0.296 VIb 0.453 0.530 0.565 0.481 0.552 0.499 0.583 0.277 0.608 VI1 0.464 0.592 0.677 0.422 0.722 0.491 0.664 0.603 0.280 Carbon of the ring containing the electron donor. Carbon of the other ring. X=X is the central bridge bond. The four C=C bonds are (from left to right respectively) the bonds identified as a, b, c, and d in the figures.
TABLE 7: Frequency Dependent Polarizability (in au)" and the Vector Components (Bx and By)in Coefficient of Azoarenes ( I - W )
a,,
an structure Ia Ib IC Id Ie IIa IIb 111
IVa IVb Va Vb Vc Vd VIa VIb VI1 a
0.65 409.12 403.57 420.72 445.06 426.95 445.29 373.18 526.73 510.66 437.79 428.90 469.26 415.20 471.09 422.28 495.61 67 1.08
1 au = 1.4818 x
1.17 456.18 451.58 477.44 507.28 499.55 508.44 419.33 608.34 603.99 506.15 501.14 562.27 482.42 519.32 628.18 939.39
0.65 85.12 85.75 88.65 97.86 81.56 180.71 176.43 120.08 277.38 263.71 106.83 92.21 119.64 121.11 81.98 60.81 163.27
esu of the SHG
P,
P x
1.17 89.52 90.03 92.99 103.93 87.03 190.27 185.88 126.29 296.48 282.45 112.99 96.29 127.38 87.87 63.92 174.60
0.65 66.46 75.52 100.02 80.82 117.03 65.85 -33.19 4.32 80.96 -29.83 69.99 89.17 90.30 136.91 124.38 76.14 222.08
1.17 189.91 247.23 399.50 379.51 1603.88 346.65 -236.47 112.51 1913.87 368.17 547.34 3243.76 748.29 -3012.09 -627.27 -423.61
0.65 -6.30 -11.23 -3.85 -4.00 17.35 -10.19 17.41 5.27 -10.21 -48.01 38.13 55.31 3.35 89.30 -76.20 -22.58 -231.09
1.17 -22.28 -40.85 -24.15 -20.04 324.42 -57.37 134.12 34.19 428.53 635.49 296.40 21 11.03 4.72 1759.25 168.11 365.72
esu.
ring. The dinitroazothiophene (Vd), however, shows a substantial increase in the hyperpolarizability over the dinitroazobenzene (IC)at an excitation energy of the 0.65 eV. Because the absorption maximum of the former at 534 nm is very close to the doubled frequency at 1064 nm, the solutions to the linear equations did not converge and hence the NLO coefficients of
Vd at that frequency are not reported. While the ring oxygen atoms assist the dimethylamino group to produce an overall more powerful electron donating effect in the phenylazofuran (Vb), it has the opposite effect in the azobifuran (VIb) where one of the ring electron donating oxygens counteracts the effect of the nitro group. The net result is a fall in the hyperpolar-
J. Phys. Chem., Vol. 99, No. 20, 1995 8031
Optical Nonlinearities in Azoarenes
TABLE 8: Dominant Components of the THG Hyperpolarizabilityin lo) aua of Azoarenes (I-VII)
Y= structure
(I
0.65 . 1.17 Ia 3.437 -14.295 Ib 3.904 -16.193 IC 5.715 -24.271 Id 4.442 - 16.022 Ie 6.799 -67.950 IIa 4.406 -24.096 IIb 1.616 4.643 I11 3.665 -4.275 IVa 7.478 0.179 IVb 5.370 -15.264 Va 3.228 13.428 Vb 3.739 270.433 vc 7.729 -115.737 Vd 10.002 VIa 6.232 - 16.407 VIb 4.642 1.023 VI1 -26.254 4.056 esu. 1 au = 5.0366 x
YWY
0.65 0.008 0.049 -0.057 0.045 0.028 0.240 0.509 0.169 0.571 1.339 0.975 1.618 -0.059 3.662 2.794 -0.255 -14.860
YYYYY
YYYXX
1.17 -0.004 -0.235 0.146 0.150 2.633 -4.982 0.626 -0.739 16.291 3.283 7.347 -126.027 0.937 -11.158 -0.294 9.561
izability to give a value which is smaller than that found in phenylazofuran (Vb). In contrast, the azodithiophene (VIa) shows a substantial increase over the phenylazothiophene (Va). Trends have been observed in other cases where thiophene rings have been substituted for benzene rings,30which are similar to those reported here. Finally, a combination of the electron attracting dinitrothiophene ring with the electron rich diaminonaphthalene ring to give naphthylazothiophene (VII) produces a large bathochromic shift in the absorption, and substantial increases in the polarizability and hyperpolarizability values which are futher increased by resonance enhancement. The value obtained for the hyperpolarizability, which is the largest in the series of the compounds considered in this paper, is around three times larger than the simple azobenzene that was initially considered. For an excitation frequency of 1.17 eV, the hyperpolarizability is negative and large because the absorption maximum, at 677 nm, occurs at a wavelength longer than that of the second harmonic, at 532 nm. The dominant components of the THG hyperpolarizability of the series of compounds considered in this paper have again been calculated at 0.65 and 1.17 eV, and the results are presented in Table 8. The trends shown by the THG hyperpolarizabilities are very similar to that shown by the SHG hyperpolarizability. Most of the THG hyperpolarizability coefficients at an excitation frequency of 1.17 eV are negative owing to the two photon resonance. Again the azo linkage serves as a better bridge and results in a larger second hyperpolarizability than the ethylenic bridge, and addition of donors and acceptors increases the hyperpolarizability. Replacing the benzene ring in phenylazobenzenes by larger fused aromatics results in a small increase in the THG hyperpolarizability, and the presence of the NHh4e group in the 5-position leads to a decrease in px. Replacing the benzene ring in the phenylazobenzene (Ib) by a heterocyclic ring (Va, Vb) results in a decrease in the THG coefficient. The reduction is greater for thiophene than for furan. The THG coefficient of the dinitroazothiophene (Vd) is almost twice that of the corresponding dinitroazobenzene (IC),and the second hyperpolarizability of azobifuran (VIb) is less than that of the azodithiophene (VIa). The large negative value of yu for VI1 at 0.65 eV is due to the fact that the tripled photon energy slightly exceeds the excitation energy to the state at 677 nm. In all other cases, the tripled photon frequency (at 0.65 eV) is less than the lowest transition frequency. The THG coefficients at 1.17 eV are included for the sake of completeness but show
0.65 0.062 0.102 0.005 0.085 0.117 0.232 0.648 0.212 1.029 2.618 0.908 1.330 0.011 3.973 2.410 0.151 -21.302
1.17 -0.379 -0.95 1 -0.491 -0.843 - 19.122 -0.95 1 -8.462 -0.516 -12.327 -13.939 -41.072 111.801 1.816 -65.434 0.849 -6.031
0.65 0.009 0.006 0.024 0.017 0.090 0.095 0.233 0.082 0.403 0.786 0.210 0.552 0.016 1.613 0.870 -0.133 -18.122
1.17 0.072 0.041 0.098 0.106 -2.934 -0.554 2.697 0.780 3.247 3.950 -15.034 -44.876 -0.023 -24.830 -0.001 -13.115
erratic behavior because the tripled frequency lies above the lowest excitation frequency, in a region where there are a number of absorption bands.
4. Conclusions The Ah41 method appears to give a reasonable account of the geometry of the azoarenes discussed here, and the spectroscopic calculations with the CNDOVSB method, using a limited configuration interaction treatment, give transition energies which are in very good agreement with the experimentally reported Amax values. Longer wavelength absorptions are found when the number of donor or acceptor groups are increased or when the benzene ring in the phenylazobenzene is replaced by larger fused aromatics such as naphthalene or anthracenes or by heterocyclics. The results of the calculations on the charge density and bond orders have been used to correlate the extent of charge transfer induced by the donor and acceptor groups in these systems. In the case of the hydrazo tautomer of phenylazonaphthalene, there are two opposing charge transfer interactions leading to a reduction in the dipole moment in relation to the azo tautomer (IIa). Calculation of the frequency dependent polarizability SHG and THG coefficients shows that the azo bridge leads to a larger NLO coefficient than that of the ethylenic bridge. The replacement of a phenyl ring of the phenylazobenzenes by larger fused rings such as naphthalenes and anthracenes does not seem to result in a large increase in the nonlinear properties. The final values of the hyperpolarizability of the larger fused ring systems are found to be highly dependent on the position of the donor and acceptor groups and also on the tautomeric forms. However, replacing a benzene ring in phenylazobenzenes by heterocyclic rings such as furan or thiophene results in an increase in the SHG and THG coefficients, and when both benzene rings of the phenylazobenzene are replaced by two thiophene rings, much larger coefficients are obtained. The largest NLO coefficients are observed when the electron attracting dinitrothiophene is combined with the electron rich diaminonaphthalene ring to give a naphthylazothiophene. The SHG coefficient is found to be about three times that of the normal phenylazobenzene. The closeness of the absorption maximum of many of the compounds studied in this paper to the doubled frequency results in substantial resonance enhancements.
8032 J. Phys. Chem., Vol. 99, No. 20, 1995 References and Notes ( 1) Nonlinear Optical Properties of Organic and Polymeric Materials; Williams, D. J., Ed.; American Chemical Society: Washington, 1983. (2) Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic: New York, 1987. (3) Nonlinear Optics of Organics and Semiconductors; Kobayashi, K., Ed.; Springer-Verlag: Tokyo, 1989. (4) Nonlinear Optical Effects in Molecules and Polymers; Prasad, P. N., Williams, D. J., Eds.; John Wiley: New York, 1991. (5) Willand, C. S.; Feth, S. E.; Scozzafava, M.: Williams, D. J.; Green, G. D.; Weinschenk, J. I., 111 In Nonlinear Optical and Electroactive Polymers; Prasad, P. N., Ulrich, D. R., Eds.; Plenum: New York, 1988. (6) DeMartino, R. N.; Choe, E. W.; Khanarian, G.; Haas, D.; Leslie, T.; Nelson, G.; Stamatoff, J.; Stuetz, D.; Teng, C. C.; Yoon, H. In Nonlinear Optical and Electroactive Polymers; Prasad, P. N., Ulrich, D. R., Eds.; Plenum: New York, 1988. (7) Pugh, D.; Morley, J. 0. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic: New York, 1987. (8) Docherty, V. J.; Pugh, D.; Morley, J. 0. J . Chem. Soc., Faraday Trans. 1985, 81, 1179. (9) Del Bene, J.; Jaffe, H. H. J . Chem. Phys. 1968, 48, 1807. (10) Francois, P.; Carles, P.; Rajzmann, M. J . Chim. Phys. 1977, 74, 606; 1979, 76, 328. (11) Albert, I. D. L.: Morley, J. 0.;Pugh, D. J . Chem. SOC.,Faraday Trans. 1994, 90, 2617. (12) Monell, J. A.; Albrecht, A. C. Chem. Phys. Lett. 1979, 64, 46. (13) Lalama, S. J.; Garito, A. F. Phys. Rev. A. 1979, 20, 1179. (14) Dirk, C. W.; Tweig, R. J.; Wagneire, G. J . Am. Chem. Soc. 1986, 108, 5387.
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