Based on the Ehrenfest theorem, an equation of motion that takes relaxation into account has been presented in wave-function theory, and the resulting response functions are nondivergent in the off-resonant as well as the resonant regions of optical frequencies. The derivation includes single- and multideterminant reference states. When applied to electric dipole properties, the response functions correspond to the phenomenological sum-over-states expressions of Orr and Ward [Mol. Phys. 20, 513 (1971)] for polarizabilities and hyperpolarizabilities of an isolated system. A universal dispersion formula is derived for the complex second-order response function. Response theory calculations are performed on lithium hydride and para-nitroaniline for off-resonant and resonant frequencies in the electro-optical Kerr effect and second-harmonic generation.

The linear response function has been derived and implemented in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations with consideration made for the finite lifetimes of the electronically excited states. Inclusion of damping terms makes the response function convergent at all frequencies including near-resonances and resonances. Applications are the calculations of the electric dipole polarizabilities of hydrogen fluoride, methane, trans-butadiene, and three push–pull systems. The polarizability is complex with a real part related to the refractive index and an imaginary part describing linear absorption. The relevance of linear absorption in nonlinear optics is effectively expressed in terms of figures-of-merit. Such figures-of-merit have been calculated showing that the nonresonant linear absorption must be considered when the nonlinear optical quality of a material is to be assessed.

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Perturbation formulas are derived for calculating the vibrational dynamic polarizability (αv) and hyperpolarizabilities (βv and γv ) of polyatomic molecules. These formulas, based on an initial harmonic oscillator approximation, include corrections for mechanical anharmonicity (cubic) terms in the vibrational potential and electrical anharmonicity (quadratic) terms in the dependence of the electrical field polarization potential on nuclear coordinates. Results are presented for FH and CO2. In the former case, comparison is made to ‘‘exact’’ numerical values. Fully documented computer programs for the perturbation treatment are available.

A simple method is presented for calculating approximate static and dynamic vibrational hyperpolarizabilities. It involves determining electrical properties in the presence of a static field with and without geometry optimization. This method is readily applicable to all tensor components of a general polyatomic molecule.