Static and dynamic first‐ and second‐order properties by variational wave functions

The problem of the evaluation of first‐ and second‐order energies by the use of arbitrary variational wave functions is examined in detail for time‐independent perturbations as well as for time‐dependent perturbations. By using a compact formalism the general formulae to be used for the case of a fully optimized set of variational parameters are readily obtained and the most prominent features are examined. The generality of the approach is tested by showing how some widely used methods are obtained by using particular types of variational wave functions. The case of incompletely optimized sets of variational parameters is examined examined extensively and several approaches at different levels of approximation are proposed. Emphasis is put upon the importance of considering, in the calculation of higher‐order energies, the variational parameters which may be of negligible importance, and thus often neglected, in the absence of perturbations.