J. Phys. Chem. B 2001, 105, 2163-2169
2163
Interaction between Monomeric Units of Donor-Acceptor-Functionalized Azobenzene Dendrimers: Effects on Macroscopic Configuration and First Hyperpolarizability Yoshishige Okuno,*,† Shiyoshi Yokoyama,‡ and Shinro Mashiko† Communications Research Laboratory and PRESTO, Japan Science and Technology Corporations (JST), 588-2 Iwaoka Iwaoka-cho, Nishi-ku, Kobe 651-2492, Japan ReceiVed: September 18, 2000; In Final Form: December 18, 2000
To find out why azobenzene dendrimers, which are branched three-dimensional macromolecules with a branch point at each of the donor-acceptor-functionalized azobenzene monomeric units, have large first hyperpolarizabilities, we used theoretical calculations for three types of dimers: (1) two azobenzenes linked covalently head-to-tail; (2) linear dimers where the two azobenzenes are nearly superimposable on the covalently bonded dimers but are not covalently linked; (3) parallel dimers where the two azobenzenes are roughly side by side. We found from ab initio calculations that the optimized geometry is roughly linear for the first type and is nearly parallel and slightly staggered for the third type. We also found that the first hyperpolarizabilities for the linear dimers are larger than those obtained from the sum of the hyperpolarizability tensors for the individual monomers and that those for the parallel dimers are smaller. These findings led us to conclude that the noncentrosymmetric arrangement of the monomeric units forming the azobenzene dendrimers, which causes the large first hyperpolarizabilities, can be partly ascribed to the interaction between the monomeric units and the first hyperpolarizability is increased by the interaction between monomeric units arranged in series. In addition, calculations based on electrical interaction models showed that the changes of the first hyperpolarizability that are due to the interaction between the monomeric units can be qualitatively explained in terms of classical electrostatic interaction, whereas quantum mechanical interactions and/or a more complete electrostatic model need to be considered in accounting for the extent of these changes quantitatively.
I. Introduction Extensive research efforts have been directed toward the design of organic molecular crystals or polymers having large second-order nonlinear optical susceptibility because such crystals or polymers would be useful in optical devices.1-5 There have been experimental attempts1-3 to synthesize these materials, to develop a method for organizing many molecules having large first hyperpolarizabilities into a noncentrosymmetric aggregate, and to evaluate the nonlinear optical properties of materials. Theoreticians,4,5 on the other hand, have tried to calculate the first hyperpolarizabilities of simple molecules and to develop rules regarding prediction of molecules having large first hyperpolarizabilities. Little, however, is known about the interaction between the constituent molecules of these crystals or between the monomeric units of these polymers. To design nonlinear optical materials, one must not only find simple molecules having large first hyperpolarizabilities but must also combine these molecules to form noncentrosymmetric macroscopic structures. This cannot be done without understanding the interactions between those simple monomers. In particular, the electrical interactions between the molecules forming crystals or between the monomeric units forming polymers must be understood comprehensively because these interactions will significantly influence the total second-order nonlinear optical susceptibility of the macroscopic systems. * To whom correspondence should be addressed. E-mail: y_okuno@ crl.go.jp. Tel.: +81-78-969-2285. Fax: +81-78-969-2259. † Communications Research Laboratory. ‡ Communications Research Laboratory and PRESTO, Japan Science and Technology Corporations (JST).
The theoretical studies of Bella et al.6 and of Yasukawa et have provided significant insights into the effects of the intermolecular interaction on the first hyperpolarizabilty values by calculating those values for various orientations of dimers. But the confidence level for the semiempirical calculations made in their studies has not been clear. On the other hand, Hamada8 has found from ab initio calculations that the electrical interaction between two 2-methyl-4-nitroanilines, which contributes to the reduction of the first hyperpolarizability, can be explained well in terms of classical electrostatic interaction. Whether his findings hold generally, however (i.e., for other dimers), is not clear. Yokoyama et al.9-11 recently demonstrated experimentally that azobenzene dendrimers, which are dendritic macromolecules made up of donor-acceptor-functionalized azobenzene monomers (Figure 1), have large first hyperpolarizabilities due to cone-shaped conformations in which all the monomeric units are organized noncentrosymmetrically. This spontaneous macroscopic ordering of the monomeric units is unexpected because monomeric units that have large permanent dipoles would intuitively be expected to tend to pair with their dipoles oriented in opposite directions, resulting in a centrosymmetric macroscopic structure. The first hyperpolarizabilities for the azobenzene dendrimers were also found to be larger than the values estimated from the sum of the first hyperpolarizabilities for the individual monomers. This indicates that the first hyperpolarizabilities are increased by the interaction between the monomeric units. Our previous ab initio study12 indicated that the noncentrosymmetric macroscopic ordering rationalized can be partly attributed to the interaction between the monomeric units al.7
10.1021/jp003353t CCC: $20.00 © 2001 American Chemical Society Published on Web 02/28/2001
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Figure 1. Structure of a four-generation donor-acceptor-functionalized azobenzene dendrimer.
Figure 2. Model species: monomers 4-dimethylamino-4′-carboxyazobenzene M1 and 4-(dimethylamino)-2′-nitro-4′-carboxyazobenzene M2; covalently bonded dimers BD1 and BD2; linear dimers LD1 and LD2; parallel dimers PD1 and PD2.
arranged side by side. However, neither the reasons for the macroscopic ordering of the monomeric units in the azobenzene dendrimers nor the reasons for the increased first hyperpolarizabilities of these dendrimers are comprehensively understood. In the present study, we therefore carried out ab initio molecular orbital calculations for the following model species: the 4-(dimethylamino)-4′-carboxyazobenzene and 4-(dimethylamino)-2′-nitro-4′-carboxyazobenzene monomers; the covalently bonded dimers in which pairs of these donor-acceptorfunctionalized azobenzenes are linked head-to-tail; the linear dimers in which the two azobenzenes are arranged in series; the parallel dimers in which the two azobenzenes are arranged side by side (Figure 2). To clarify the origin of the electrical interactions between the monomeric units, we also analyzed the results calculated for the dimers by using not only electrical
interaction model used in the study of Hamada8 but also two extended models. II. Method of Calculation II.A. Ab Initio Calculations. For the model species M1, BD1, LD1, PD1, M2, BD2, LD2, and PD2 (Figure 2), we carried out ab initio molecular-orbital calculations, using the GAUSSIAN9813 and GAMESS14 program packages. The GAMESS package was used to calculate analytically only some of the second hyperpolarizability tensors. For these calculations, the 6-31G* basis set15 was used at the Hartree-Fock level of theory. To reduce the amount of calculation, we did not use diffuse functions in the basis set. The diffuse functions are not essential to the calculations of the first hyperpolarizabilities for long π-conjugated systems such as the ones we are concerned with
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here because the polarization effects associated with a given center can be adequately described with the help of basis functions positioned at the other centers.16 We did not take into consideration the effects of electron correlation on the first hyperpolarizability. Although these effects must be taken into account when obtaining quantitatively accurate results, even the calculations at the Hartree-Fock level of theory have been shown to be adequate to rationalize qualitatively the order of the hyperpolarizability values for various species.4 To determine the stable structures for the donor-acceptorfunctionalized azobenzene monomer M2, the colvalently bonded dimers BD1 and BD2, and the parallel dimers PD1 and PD2, we first optimized their geometries. (The geometries of the M1 and M2 monomers had been optimized in our previous study,12 but in the present work we found a new optimized geometry for the M2 species. It is more stable, by 0.04 kcal/mol, than the previously optimized one and is thus at the global minimum point. The difference between these geometries, however, and the differences between their calculated properties were found to be small.) Harmonic-vibrational-frequency calculations for these geometries confirmed that the optimized geometries are at minimum points. The geometries for the linear dimers LD1 and LD2 were obtained by an artificial modulation of the geometries optimized for each of the covalently bonded dimers BD1 and BD2; specifically, after we eliminated the carbon labeled “a” in Figure 2 and two hydrogens bonded to this carbon, hydrogen was introduced at each of the two terminal positions left by this elimination. To avoid the unphysical steric hindrance arising from this artificial modulation, we optimized the geometries of the carboxy hydrogen labeled “b” and three hydrogens of the amino methyl group labeled “c” (Figure 2), while the other Cartesian geometries were held fixed and the carboxy hydrogen Hb was restricted to the caroboxy COO plane. For the geometries obtained we calculated the dipole moment, polarizability, static first hyperpolarizability, and second hyperpolarizability tensors µi, Rij, βijk, and γijkl, in which each of the i, j, k, and l denotes either of the x, y, and z axes determined arbitrarily. These tensors are defined as coeffcients of the Buckingham type expansion17 of the total energy with respect to the applied electric field F ) (Fx,Fy,Fz):
E ) E0 -
1
∑i
∑βijkFiFjFk 6 i,j,k
µiFi 1
1
∑ i,j
2
RijFiFj
∑ γijklFiFjFkFl + ...
24i,j,k,l
(1)
Here E is the energy under the existence of the electric field F, E0 is the energy without the electric field, and the summations run over the Cartesian directions x, y, and z. The calculations of all the polarizability tensors Rij, βijk, and γijkl except for the cross terms of the second hyperpolarizability tensors, γiiij and γiijk for i * j, j * k, and i * k, were made by the coupledperturbed Hartree-Fock (CPHF) method.16 The cross terms were calculated by the finite field method from the following equation:
γijkl ≈
3 3 {βijk(Fl) - βijk(-Fl)} {βijk(2Fl) 4Fl 20Fl 1 {βijk(3Fl) - βijk(-3Fl)} (2) βijk(-2Fl)}+ 60Fl
Here βijk(Fl) is the first hyperpolarizability in the presence of the electric field Fl and we used 0.001 au for Fl, because these
terms were not available in the CPHF calculations with the GAMESS program package. The total hyperpolarizability βtot was evaluated by using the following equation:4
βtot ) {
∑i βi2}1/2
(3)
Here
βi )
1
∑j (βijj + βjij + βjji)
3
i ) x, y, z
(4)
The total hyperpolarizability βtot corresponds to the one obtained experimentally when using the hyper-Rayleigh scattering method.18 We also determined the hyperpolarizability tensors βIJK in which each of the I, J, and K denotes either of the X, Y, and Z axes, where the Z axis is parallel to the first hyperpolarizability vector β ≡ (βx,βy,βz), the Y axis is perpendicular to both the Z axis and the dipole moment vector µ ≡ (µx,µy,µz), and the X axis is perpendicular to the YZ plane. II.B. Electrical Interaction Models. To understand the influence of the electrical interaction between the monomers on the first hyperpolarizability in more detail, we evaluated the total first hyperpolarizabilities for the dimers LD1, PD1, LD2, and PD2 by using three models for the electrical interaction between the monomers. In each of these models, it is assumed that the dipole moment and first hyperpolarizability tensors for each monomer are modulated by the influence of the electric field from the neighboring monomer. Then the ith vector component of the dipole moment µidimer for the dimers is given by the sum of the ith vector component of the modulated dipole moment for the individual monomer µip:
µidimer ) µi1 + µi2
(5)
Similarly, the hyperpolarizability tensors for the dimer βijkdimer are given by
βijkdimer ) βijk1 + βijk2
(6)
where βijkp are the modulated hyperpolarizability tensors for the monomer p. The first model, denoted EI-model 1, is the same as the electrical interaction model used in the studies of Dykstra et al.19 and Hamada.8 In this model each of the monomers forming the dimers is regarded as a point at the center of mass. Then for each monomer p, the dipole moment and hyperpolarizability modulated by the influence of the electric field from the neighboring monomer q are assumed to be given by
µip ) µip(0) +
∑j Rijp(0)Fprqj
(7)
∑l γijklp(0)Fprql
(8)
and
βijkp ) βijkp(0) +
where µip(0), Rijp(0), βijkp(0), and γijklp(0) are respectively the permanent dipole moment, polarizability, first hyperpolarizability, and second hyperpolarizability tensors for the monomer p. Here Fprqj is the jth vector component of the electric field-at the center of mass of the monomer p-arising from the neighboring monomer q. The electric field is expressed in terms of multipole expansions at the center of mass by dropping all
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but the first and the second terms in the expansions
Fprq ) l
∑ m
(3(Rlp - Rlq)(Rmp - Rmq) - |Rp - Rq|2δlm)µmq |Rp - Rq|5
(9)
where Rp ) (Rxp,Ryp,Rzp) is the vector from some given origin to the center of mass of the monomer p. The procedure for the evaluation based on the EI-model 1 was as follows. We assumed that the values of µip(0), Rijp(0), βijkp(0), and γijklp(0) calculated for the optimized geometry of each of the monomers and their Cartesian directions with respect to the NdN-C(aniline) plane and line along the NdN bond coincide with those for each of the individual monomers forming the relevant dimer. Then the modulated dipole moment µip and the electric field Fprqj were determined self-consistently using eqs 7 and 9. Using the determined value for Fprql, we calculated the electric-fieldinduced hyperpolarizability tensors βijkp by using eq 8. The second model, denoted EI-model 2, differs from the EImodel 1 in the electric field expression. In the EI-model 2 the electric field is expressed in terms of monopole charges at all the constituent nuclei as follows:
Fprq ) l
(Rlp - rlq(R))qq(R)
∑R
(10) |Rp - rq(R)|3
Here qq(R) is the atomic charge at the Rth nucleus of the monomer q and rq(R) ) (rxq(R),ryq(R),rzq(R)) is the vector from some given origin to the position of the Rth nucleus of the monomer q. Here the summation runs over the number of the atoms forming monomer q. This monopole model not only provides an intuitive way to think about the charge distribution within a molecule but is also expected to give more accurate electric field than that given by the truncated multipole expansion at the center of mass. The reason that the atomic charges are positioned on the nuclei in this model is that the electrostatic potential is reproduced well when these are associated with the centers of the atoms.20 The evaluation procedure was the same as that in the EI-model 1 except for the determination of the electric field. In this model, the electric field was determined by using the atomic charges qq(R) that were given to reproduce the electrostatic potential around the geometry optimized for the relevant monomer by the method of Kollman et al.21 In the third model, denoted EI-model 3, the modulated dipole moment µip and first hyperpolarizability tensors βijkp were determined by carrying out ab initio calculations using a Hamiltonian that includes the Coulomb interaction between the electrons of the monomer p and the atomic charges of the neighboring monomer q. The atomic charges used in this calculation were the same as those used in the EI-model 2. Then the dipole moment and the total first hyperpolarizability tensors for the dimers were calculated using eqs 5 and 6. III. Results and Discussion III.A. Covalently Bonded Dimers. The geometry optimization for the covalently bonded dimers BD1 and BD2 gave roughly linear geometries (Figure 3) rather than folded geometries in which the dipole moment vectors of the two monomeric units are antiparallel. Thus the roughly linear geometries must be more stable than the folded ones, probably because of the steric hindrance caused by the access of the monomeric unit to another monomeric unit and because of the strain caused by bending the linear geometries for the covalently bonded dimers.
Figure 3. (a) Optimized structures of covalently bonded dimers and their total energies (hartree) and (b) partially optimized structures of linear dimers and their total energies (hartree).
TABLE 1: Calculated Hyperpolarizabilities (10-30 esu) and Dipole Moments (D) species
βtot
βZXX
βZYY
βZZZ
|µ|
M1 BD1 LD1 PD1 M2 BD2 LD2 PD2
34.7 75.5 75.1 57.6 44.8 95.0 94.4 72.2
-2.1 12.6 12.8 -1.8 -2.5 15.0 16.1 -0.7
-0.4 -0.2 -0.3 -2.2 -0.4 1.5 0.6 -4.5
37.1 63.1 62.6 61.6 47.8 78.4 77.7 77.5
5.10 8.89 9.16 9.41 5.16 8.45 9.02 8.30
The stability of the roughly linear geometries for the covalently bonded dimers would contribute to the noncentrosymmetric arrangement of the azobenzene dendrimers. We found (Table 1) the βtot value for the covalently bonded dimer having nitro groups (BD2) to be larger than that for the one without the nitro group (BD1). The larger βtot value for BD2 reflects the larger βtot value for the monomer having the nitro group (M2) than for the one without the nitro group (M1). Therefore, the large βtot values not only for M2 but also for BD2 can be ascribed to the general linear relationship5 between the first hyperpolarizabilities and the deformation of π-electron distribution in a π-conjugated system to which is appended substituents such as the nitro group. We also found the order of the values of the dipole moment for the covalently bonded dimers BD1 and BD2 to be the reverse of that for their βtot values (Table 1). This reverse order can be
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J. Phys. Chem. B, Vol. 105, No. 11, 2001 2167
TABLE 2: Orbital Energies (hartree) π(HOMO-1) π(HOMO) π*(LUMO) π*(LUMO+1 )
M1
BD1
LD1
PD1
-0.274 06 0.056 48
-0.275 25 -0.272 20 0.054 46 0.058 93
-0.276 23 -0.270 53 0.052 51 0.059 24
-0.279 27 -0.267 61 0.052 51 0.065 29
Figure 4. Optimized structures of the monomers M1 and M2, vectors of their dipole moment and hyperpolarizability, and their total energies (hartree).
attributed to the significant difference between the conformations of the aromatic rings of the monomeric units forming BD1, which are nearly coplanar, and of those of the monomeric units forming BD2, which are not in the same plane. The distortion of the geometry of monomeric unit from the planar one appears to magnify the difference between the directions of the dipole moment vectors of the individual monomers, whereas such distortion hardly influences the directions of the hyperpolarizability vectors for the two monomers (Figures 3 and 4). The utility of using this kind of nonlinear relation between the first hyperpolarizability and the dipole moment should be recognized, because by taking advantage of the nonlinear relation, one will be able to design molecules with large first hyperpolarizability and small dipole moment; such molecules have bright prospects of forming noncentrosymmetric molecular aggregates with the large second-order nonlinear optical susceptibility.22 Moreover, we found that the βtot value for each of the covalently bonded dimers BD1 and BD2 is more than twice as large as that for the corresponding monomer (Table 1). This indicates that the hyperpolarizability is increased by the interaction between the monomeric units. This increase, which was also observed for the linear dimers, is discussed in detail in the next subsection. The differences in orbital energy between the π and π* for each of the covalently bonded dimers were found to be in good agreement with the difference for the corresponding monomer (Table 2). This agreement shows that the covalent linking of azobenzene monomers does not influence the π∠π* transition energy of the individual monomers. This would be consistent with the results of previous experiments,9-11 in which the absorption maxima of the azobenzene dendrimers due to π∠π* transition was found not to depend strongly on the change of the number of the constituent monomeric units of the azobenzene dendrimers. Therefore, both the results calculated and observed experimentally indicate that the azobenzene dendrimers have the advantages not only of exhibiting the large secondorder nonlinear optical susceptibility but also of suppressing the undesirable bathochromic shift in the optical adsorption maximum. On the other hand, the agreement in the π∠π* orbital-energy gaps between the covalently bonded dimers and the corresponding monomers cannot explain the larger βtot values
M2
BD2
LD2
PD2
-0.281 91 0.040 89
-0.284 33 -0.283 18 0.038 15 0.040 55
-0.284 20 -0.282 81 0.036 07 0.040 99
-0.287 75 -0.284 95 0.036 85 0.044 88
for the covalently bonded dimers compared to those for the monomers on the basis of a two-level model.4 This result differs from the calculated result of Tsunekawa and Yamaguchi,22 where a molecule with smaller βtot values was found to have a larger orbital energy gap. The contribution of the oscillator strength of the optical transition or the difference between excited- and ground-state dipole moments may be large; otherwise, the simple two-level model must be inadequate to rationalize the large βtot values for the covalently bonded dimers. III.B. Linear Dimers. The βtot value for each of the linear dimers LD1 and LD2 was in good agreement with that for the corresponding covalently bonded dimer (Table 1). This agreement indicates that the total first hyperpolarizability is hardly influenced by the covalent linking of two azobenzene monomers. The linear dimers LD1 and LD2 will therefore be regarded as good models of the covalently bonded dimers BD1 and BD2. The βtot value for each of the linear dimers was found to be larger than that obtained from the sum of the first hyperpolarizability tensors for the individual monomers (Tables 1 and 3) as well as to be larger than twice the βtot value for the corresponding monomer (Table 1). This finding, which is the same as that for the covalently bonded dimers, indicates that the total hyperpolarizability for each of the linear dimers is increased significantly by the interaction between the monomers arranged in series. The similar hyperpolarizability increased was found by Bella et al.6 for the head-to-tail arrangements of two p-nitroaniline monomers, where the dipole moment vectors of the two monomers are aligned in parallel as well as the donor substituent of the one monomer is in spatial proximity to the acceptor substituent of another monomer. Therefore, the headto-tail arrangement is expected to exhibit the large first hyperpolarizability generally. From this finding, we are able to conclude that the increased first hyperpolarizability due to an increase in the number of the constituent monomeric units in the azobenzene dendrimers is caused, at least in part, by the interaction between monomeric units arranged in series. It was also found that the ab initio values of the βZZZ for the linear dimers were larger than the βZZZ values obtained from the sum of the hyperpolarizability tensors of the individual monomers, whereas ab initio values of βZXX for the linear dimers nearly coincide with the βZXX values obtained from the sum of the hyperpolarizability tensors of the individual monomers (Tables 1 and 3). This indicates that the enhancement of the first hyperpolarizability by the head-to-tail arrangement of the monomers stem from the enhancement of its ZZZ components. The fact that the βZXX for the linear dimers have some values, in contrast to the βZXX values for the monomers, is due to the difference in orientation between the two monomers. And this fact may result in the insensitivity of the total hyperpolarizability to small bending of the linear dimers, because the increase of βZXX by the bending compensates to some extent for the decrease of βZZZ by the bending. This insensitivity is similar to that demonstrated by Bella et al.,6 where the hyperpolarizability for a cofacial dimer was insensitive to intermolecular tilt and twist distortions. All of the βtot values calculated with the three electrical interaction models for each of the linear dimers were found, like the βtot values obtained from ab initio calculations for the
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TABLE 3: Hyperpolarizabilities (10-30 esu) Calculated by the Simple Tensor Sum and by the Three Modelsa species LD1 PD1 LD2 PD2
βtotSUM
βZXXSU M
βZYYSU M
βZZZSUM
βtotEI-1
βtotEI-2
βtotEI-3
61.2 (9.00) 69.2 (9.67) 79.0 (8.77) 89.4 (8.64)
12.1 -1.1 15.8 -0.8
0.7 -3.4 0.3 -4.5
48.4 73.7 62.8 94.6
62.9 (9.23) 69.3 (9.75) 80.9 (9.03) 90.0 (8.71)
62.2 (9.27) 62.6 (8.76) 81.1 (9.18) 77.1 (6.87)
63.0 (8.98) 64.0 (9.20) 79.9 (9.01) 81.2 (8.18)
a The value obtained from the tensor sum of the first hyperpolarizabilities for the individual monomers is denoted as βtotSUM. The first hyperpolarizabilities calculated on the basis of the EI-models 1, 2, and 3 respectively are denoted as βtotEI-1, βtotEI-2, and βtotEI-3. Values in parentheses are dipole moments in debyes.
Figure 5. Optimized structures of parallel dimers and their total energies (hartree). Distances between atoms are denoted in angstroms.
linear dimers, to be larger than the values obtained from the sum of the hyperpolarizability tensors for the individual monomers (Table 3). Thus the enhancement of the hyperpolarizability by the interaction between monomeric units arranged in series is qualitatively explained in terms of classical electrostatic interaction (i.e., the action of the electric field arising from the neighboring monomer). However, the βtot values calculated with the electrical interaction models were not quantitatively in accordance with those calculated ab initio (Tables 1 and 3). This discordance may be attributed to a quantum mechanical interaction between the two monomers, because these monomers are very close to each other (Figure 3b). But since the present electrostatic treatment is not necessarily complete, the investigation by a more complete electrostatic treatment such as one proposed by Kirtman et al.23 would be required for justifying this attribution. III.C. Parallel Dimers. Carrying out the geometry optimization for the dimers from starting geometries in which the two monomers are arranged side by side, we found that the paralleldimer geometries where the two monomers are parallel and in a slightly staggered conformation were relatively stable (Figure 5). The stabilization energies due to the formation of the parallel dimers PD1 and PD2 from the two corresponding monomers respectively were -2.2 and -2.8 kcal/mol. (The basis-setsuperposition-error-corrected24 interaction energies between the monomers were -0.7 kcal/mol for PD1 and -1.4 kcal/mol for PD2.). This indicates that the interaction between the monomers arranged in rows contributes to the stabilization of the parallel orientation despite the repulsive dipole-dipole interaction (Figure 4). Therefore, the interaction between the monomeric units except for the dipole-dipole interaction is expected to contribute partly to the formation of the cone-shaped configuration of the azobenzene dendrimers. We also found that the βtot value for each of the parallel dimers is larger than that for the corresponding monomer, whereas the βtot value for each of the parallel dimers is smaller
than that obtained from the sum of the hyperpolarizability tensors of the individual monomers (Tables 1 and 3). This finding indicates that the two monomers contribute to the total first hyperpolarizability coherently because of their parallel orientation, but the interaction between the two monomers reduces the first hyperpolarizability for each monomer. Therefore, whereas this parallel orientation is considered to contribute to the noncentrosymmetric arrangement of the azobenzene dendrimers, the enhancement of the β values cannot be ascribed to the interaction between monomeric units arranged in rows. The tendency of the influence of the interaction between the monomers arranged in rows on the first hyperpolarizability is similar to the tendency evident in the findings of Hamada8 and Bella et al.;6 namely, Hamada found that the intermolecular interactions of 2-methyl-4-nitroaniline dimer whose two monomers were roughly side by side reduced the total first hyperpolarizability, and Bella et al. found the first hyperpolarizability decreased as the interplanar distance in a cofacial eclipsed p-nitroaniline dimer approached the van der Waals distance. Therefore, this tendency is expected to hold generally. On one hand, the βtot values calculated with the EI-model 1 for the parallel dimers differed significantly from the ab initio values (Tables 1 and 3), in contrast to the finding of Hamada,8 where the βtot value calculated with the EI-model 1 for the 2-methyl-4-nitroaniline dimer was in good agreement with the corresponding ab initio value. The discrepancy between the results of the present study and the results of Hamada’s study must be due to the donor-acceptor-functionalized azobenzenes being molecules longer than the 2-methyl-4-nitroaniline studied by Hamada. Evidently the electric field around the azobenzene cannot be accurately modeled by the point dipole at the center of mass. On the other hand, the βtot values calculated with both the EI-model 2 and the EI-model 3 were relatively accurate for the parallel dimers (Tables 1 and 3), in contrast to the case of the linear dimers. This indicates that the EI-model 2 as well as the EI-model 3 are good models for reproducing classical electrostatic interaction for the parallel dimers and the electric field around the azobenzene molecules is appropriately reproduced by the atomic charges positioned at all the constituent nuclei. Even so, the intermolecular interaction in the parallel dimers cannot be still explained quantitatively in terms of the classical electrostatic interaction (Tables 1 and 3). Thus, the quantum mechanical interaction and/or a more complete electrostatic model should be also considered to explain the βtot values for the parallel dimers quantitatively. IV. Conclusions Carrying out ab initio calculations for three types of dimers formed by donor-acceptor-functionalized azobenzenes, we have found that the covalently bonded dimers have roughly linear conformations and that the dimers arranged side by side are relatively stable despite the repulsive dipole-dipole interaction. We also found that the hyperpolarizability calculated for each
Functionalized Azobenzene Dendrimers of the covalently bonded dimers and linear dimers is more than twice that calculated for the individual monomer, whereas the hyperpolarizability calculated for each of the parallel dimers is less than twice that calculated for the individual monomer. The calculations based on the electrical interaction models showed that the hyperpolarizability values for the various dimers are explained qualitatively in terms of the classical electrostatic interaction but that the quantum mechanical interaction and/or a more complete electrostatic model must be considered to explain them quantitatively. These findings led us to conclude that the interaction between the monomeric units of azobenzene dendrimers contributes to the noncentrosymmetric arrangement of those dendrimers and that the interaction between monomeric units arranged in series contributes to the increased first hyperpolarizability due to an increase in the number of the constituent monomeric units in the azobenzene dendrimers. References and Notes (1) Williams, D. J. Angew. Chem., Int. Ed. Engl. 1984, 23, 690. (2) Eaton, D. F. Science 1991, 253, 281. (3) Kauranen, M.; Verbiest, T.; Boutton, C.; Teerenstra, M. N.; Clays, K.; Schouten, A. J.; Nolte, R. J. M.; Persoons, A. Science 1995, 270, 966. (4) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. ReV. 1994, 94, 195. (5) Oudar, J. L.; Chemla, D. S. Opt. Commun. 1975, 13, 164. (6) Bella, S. D.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 1992, 114, 5842. (7) Yasukawa, T.; Kimura, T.; Uda, M. Chem. Phys. Lett. 1990, 169, 259. (8) Hamada, T. J. Phys. Chem. 1996, 100, 8777. (9) Yokoyama, S.; Nakahama, T.; Otomo, A.; Mashiko, S. J. Am. Chem. Soc. 2000, 122, 3174. (10) Yokoyama, S.; Mashiko, S. Mater. Res. Soc. Symp. Proc. 1998, 488, 765.
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