Dipole hyperpolarizabilities / and

We will divide the survey into three parts (3.1) static dipole polarizabilities, (3.2) static dipole hyperpolarizabilities, and (3.3) dynamic dipole polarizabilities and hyperpolarizabilities. Within each part there will be sub-sections dealing with the three isoelectronic series He, Ne, and Ar. For (3.2) and (3.3) the hydrogen atom will also be included. 

Dykstra and Jasien [9] used the general equations given in the preceding to implement an approach for the calculation of derivatives of the Hartree-Fock or SCF energy. Unique to the DHF approach is its open-endedness. The computer program that was written was immediately able to compute a tenth-dipole hyperpolarizability and beyond, if desired. Derivatives involving geometric parameters could be obtained, too, but then there exists the... 

G. Maroulis, Electric dipole hyperpolarizability and quadrupole polarizability of methane from finite-field coupled cluster and fourth-order many-body peituibation theory calculations. Chem. Phys. Lett. 226, 420 (1994)... 

The quadrupole and octopole moments, the dipole polarizability, the first and second dipole hyperpolarizabilities, and the dipole-quadrupole and dipole-dipole-quadrupole polarizabilities were calculated using MPPT(4) theory [8]. 

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

The molecular quantities can be best understood as a Taylor series expansion. For example, the energy of the molecule E would be the sum of the energy without an electric field present, Eq, and corrections for the dipole, polarizability, hyperpolarizability, and the like ... 

The next terms in the series, denoted. .. in equation 17.1 above, are called the dipole hyperpolarizabilities. The first one is and this also is a tensor. It has three indices, and the corresponding formula for the induced dipole, equation 17.3, becomes... 

Thus coefficients with an even total order I + m + n are real and coefficients with an odd total order I m + n are pure imaginary. In the following we consider only dipole hyperpolarizabilities. In this case the four operators A, B, C and D are cartesian components of the dipole operator and the odd dispersion coefficients vanish. 

The CC2 model performes very different for static hyperpolarizabilities and for their dispersion. For methane, CC2 overestimates 70 by a similar amount as it is underestimated by CCS, thus giving no improvement in accuracy relative to the uncorrelated methods CCS and SCF. In contrast to this, the CC2 dispersion coefficients listed in Table 3 are by a factor of 3 - 8 closer to the CCSD values than the respective CCS results. The dispersion coefficients should be sensitive to the lowest dipole-allowed excitation energy, which determines the position of the first pole in the dispersion curve. The substantial improvements in accuracy for the dispersion coefficients are thus consistent with the good performance of CC2 for excitation energies [35,37,50]. 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

The values for the dipoles, polarizabilities, and hyperpolarizabilities of the H2 series were obtained using (a) a 16-term basis with a fourfold symmetry projection for the homonuclear species and (b) a 32-term basis with a twofold symmetry projection for the heteronuclear species. These different expansion lengths were used so that when combined with the symmetry projections the resulting wave functions were of about the same quality, and the properties calculated would be comparable. A crude analysis shows that basis set size for an n particle system must scale as k", where k is a constant. In our previous work [64, 65] we used a 244-term wave function for the five-internal-particle system LiH to obtain experimental quality results. This gives a value of... 

K. L. C. Hunt. Long-range dipoles, quadrupoles, and hyperpolarizabilities of interacting inert-gas atoms. Chem. Phys. Lett., 70 336, 1980. 

This paper summarizes the theoretical analysis of some new molecules with methylsulfonyl group as the electron acceptor group, describes the syntheses of new stilbene and azobenzene systems, and presents the measurements of their optical spectra, ground-state dipole-moments, and molecular hyperpolarizability coefficients, p. We compare theoretical and experimental results and comment on the potential usefulness of these chromophores as components for NLO materials. The incorporation of sulfonyl-containing chromophores into polymers, and the NLO properties of the resulting materials, will be discussed in our forthcoming paper (9). 

Table I. Theoretical Dipole Moments and Second-Order Hyperpolarizabilities for Selected Methylsulfonyl and Nitro Compounds (A = 1907 nm)...

The calculations predict that azobenzene derivatives have nearly identical dipole moments and molecular hyperpolarizabilities as the stilbenes. Selection of compounds for use in specific applications can therefore, be based on linear optical properties (absorption) and photochemical stability requirements without sacrifice of nonlinear optical response. 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

Fig-8. EO coefficient data, as a function of chromophore number density, for FTC (circles) and FTC-2H (diamonds) chromophores in PMMA. Also shown is the theoretical curve computed for FTC. Note that for FTC-2H, the two butyl groups (attached to the thiophene ring) are replaced by protons. The more ellipsoidal FTC-2H exhibits a smaller maximum electrooptic activity and the position of the maximum is shifted to lower number density. Consistent with EFISH, HRS, and other measurements, the dipole moments and molecular first hyperpolarizabilities of these two chromophores are comparable (The values for FTC-2H may be slightly larger)... 

Fig-9. EO coefficient data, as a function of chromophore number density, for CLD-type chromophores with (solid circles) and without (open triangles) isophorone protection of the polyene bridge. The maximum achievable electro-optic activity is smaller for the naked polyene bridge structure and the maximum of the curve is shifted to lower number density. The dipole moment and molecular first hyperpolarizability values are comparable (The unprotected polyene bridge variation may exhibit slightly higher values of p(3)... 

In modifying chromophores by the addition of bulky substituents, it is important to keep in mind that bulky substituents can influence the conformation which the molecule adopts and can in turn influence Tt-orbital overlap and molecular hyperpolarizability and dipole moment. We have found this to be particularly true for chromophores utilizing a polyene bridge structure. Thus, it is dangerous to reason improvements simply from theoretical calculations that do not consider the possibility of a change in chromophore conformation with addition of substituents. 

Consequently, molecules with structures that lead to large transition dipole moments and small transition energies should display large second-order hyperpolarizabilities. Conjugated molecules with delocalized electronic wavefunc-tions enable the electrons to move over considerable distances and therefore show large transition and difference dipole moments. Furthermore, these molecules show low transition energies. 

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