Using the time-dependent Hartree–Fock method two analytical schemes are elaborated for determining the derivatives of frequency-dependent polarizability with respect to atomic Cartesian coordinates. The first scheme is iterative and consists in determining the mixed derivatives of the density matrix with respect to atomic Cartesian coordinates and dynamic electrical fields. The second takes advantage of the 2n+1 rule to express the polarizability derivatives in terms of first-order derivatives. Both schemes are implemented in the GAMESS program. They enable the fully analytical evaluation of the Raman intensities with inclusion of the frequency dispersion. The potential of these methods is illustrated by determining the polarizability derivatives and Raman intensities of small molecules.

The second-order nonlinear optical coefficient of polyphosphazene oligomers of increasing size has been determined by using ab initio methods taking into account electron correlation and frequency dispersion effects. The calculated first hyperpolarizability per unit cell converges rapidly with respect to chain length. It attains an amplitude of about one-third of the one of classical push-pull systems. This amplitude can be strongly increased by replacing the nitrogen of the backbone by silicon. The effects of the side groups (H, CH3, F, Cl, Br, and OH) on the first hyperpolarizability have been investigated as well. The different results have been rationalized in terms of alternations of bond lengths and atomic charges.

Raman and vibrational Raman optical activity (VROA) spectra of helical conformers of polypropylene chains are simulated using ab initio methods to unravel the relationships between the vibrational signatures and the primary and secondary structures of the chains. For a polypropylene chain containing three units, conformational effects are shown to lead to more acute signatures for VROA than for Raman spectra. In addition to regular polypropylene chains, which can display right and left helicities with the same probability, chirality and therefore helicity are enforced by substituting one chain end with a phenyl group. The simulations predict that the threefold helical structures, which correspond to (TG)(N) conformations of the backbone, have a specific VROA backward signature in the form of an intense couplet around 1100 cm(-1). This couplet is associated with collective wagging and twisting motions, while most of its intensity comes from the anisotropic invariants combining normal coordinate derivatives of the electric dipole-electric dipole polarizability and of the electric dipole-magnetic dipole polarizability. A similar signature has already been found in model helical polyethylene chains, whereas it is very weak in forward VROA.

The frequency-dependent vibrational second hyperpolarizability of CH4−nFn molecules with n=0–4 has been computed for the most common nonlinear optical (NLO) processes by adopting the perturbation approach due to Bishop and Kirtman [J. Chem. Phys. 95, 2646 (1991)]. These calculations have been performed by using the Sadlej atomic basis set with the Hartree-Fock technique as well as with the Mo/ller-Plesset second order perturbation theory (MP2) procedure. The inclusion of electron correlation and of the first-order mechanical and electrical anharmonicities turn out to be of quantitative importance for most quantities. In particular, it permits us to improve the agreement with the experimental data for the difference between the anisotropic dc-Kerr and mean electric-field-induced second harmonic generation (ESHG) vibrational second hyperpolarizability of CF4. With the exception of the small ESHG vibrational second hyperpolarizability the infinite optical frequency method turns out to be a satisfactory approximation for evaluating the vibrational NLO responses.

The Raman and hyper-Raman spectra of acetonitrile and its deuterated analog have been investigated by combining experimental analysis and theoretical interpretation. It has been observed that the Raman spectra can easily be reproduced at both the Hartree-Fock and Moller-Plesset second-order levels of approximation and that for these fundamental transitions, inclusion of anharmonicity effects is not essential. On the other hand, the hyper-Raman spectra are more difficult to simulate and interpret. In particular, electron correlation has to be included in order to describe properly the intensity of the CN stretching mode. Then, a pseudo-C(infinity v) symmetry was assumed to better fit the experimental observations. This accounts for the fact that the a1- and e-symmetry modes correspond to time-decoupled vibrations. The e-symmetry modes, associated with nuclear motions perpendicular to the molecular axis are indeed subject to relaxation processes and, except the CCN bending mode, not visible in the hyper-Raman spectra of acetonitrile or of its deuterated analog. This assumption is supported by the gradual decrease of the phenomenon when going from acetonitrile to trichloroacetonitrile, where the presence of the heavier chlorine atoms in the latter reduces the relaxation processes.