Response Theory and Calculations of Molecular Hyperpolarizabilities

This chapter reviews the development and application of response theory with respect to a particular molecular property—the hyperpolarizability—and demonstrates the potential of this development with some illustrative examples. It reviews recent progress in ab initio calculations of hyperpolarizabilities that have turned into an important research area of quantum chemistry. It particularly emphasizes on the development of multi-configurational (MCSCF) theory. Hyperpolarizabilities can be expressed in terms of response functions that represent an elegant and efficient way of rationalizing the results of time-dependent perturbation theory. The chapter describes an analytic implementation of the linear and quadratic response functions for an MCSCF state. The implementation is direct in the sense that response matrices are never set up explicitly, only linear transformations of the response matrices on trial vectors and iterative techniques are used to solve the response matrix equations. One of the benefits of these techniques is that large, many-dimensional, and therefore accurate reference wave functions can be employed; calculations with configuration spaces containing several million determinants can, thus, routinely be carried out.