A restricted active space (RAS) wave function is introduced, which encompasses many commonly used restricted CI expansions. A highly vectorized algorithm is developed for full CI and other RAS calculations. The algorithm is based on Slater determinants expressed as products of alphastrings and betastrings and lends itself to a matrix indexing C(Iα, Iβ ) of the CI vector. The major features are: (1) The intermediate summation over determinants is replaced by two intermediate summations over strings, the number of which is only the square root of the number of determinants. (2) Intermediate summations over strings outside the RAS CI space is avoided and RAS calculations are therefore almost as efficient as full CI calculations with the same number of determinants. (3) An additional simplification is devised for MS =0 states, halving the number of operations. For a case with all single and double replacements out from 415 206 Slater determinants yielding 1 136 838 Slater determinants each CI iteration takes 161 s on an IBM 3090/150(VF).

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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.

The linear response function for a coupled cluster singles and doubles wave function is used to calculate vertical electronic energies for the closed shell system Be, CH+, CO, and H 2 0. It is shown that excitations of single electron replacement character can be described accurately in such an approach. Improved convergence is obtained using a preconditioned form of the coupled cluster linear response matrix.

The relativistic Dirac Hamiltonian that describes the motion of electrons in a magnetic field contains only paramagnetic terms ͑i.e., terms linear in the vector potential A͒ while the corresponding nonrelativistic Schrödinger Hamiltonian also contains diamagnetic terms ͑i.e., those from an A 2 operator͒. We demonstrate that all diamagnetic terms relativistically arise from second-order perturbation theory and that they correspond to a ''redressing'' of the electrons by the magnetic field. If the nonrelativistic limit is taken with a fixed no-pair Hamiltonian ͑no redressing͒, the diamagnetic term is missing. The Schrödinger equation is normally obtained by taking the nonrelativistic limit of the Dirac one-electron equation, we show why nonrelativistic use of the A 2 operator is also correct in the many-electron case. In nonrelativistic approaches, diamagnetic terms are usually considered in first-order perturbation theory because they can be evaluated as an expectation value over the ground state wave function. The possibility of also using an expectation value expression, instead of a second-order expression, in the relativistic case is investigated. We also introduce and discuss the concept of ''magnetically balanced'' basis sets in relativistic calculations.