Introduction to response theory

Abstract

This chapter provides a concise introduction to quantum chemical response theory as implemented in a number of widely used electronic structure software packages. While avoiding technical derivations of response functions, the fundamental idea of response theory, namely, the calculation of field-induced molecular properties through changes in expectation values, is explained in a manner equally valid for approximate wave function and density functional theories. Contrasting response theory to textbook treatments of perturbation theory, key computational concepts such as iterative solution of response equations and the identification and calculation of electronic excitation energies are elucidated. The wealth of information that can be extracted from approximate linear, quadratic, and higher-order response functions is discussed on the basis of the corresponding exact response functions. Static response functions and their identification and numerical calculation as energy derivatives are discussed separately. Practical issues related to the lack of gauge and origin invariance in approximate calculations are discussed without going into too much theoretical detail regarding the sources of these problems. Finally, the effects of nuclear motion (molecular vibrations, in particular) and how to include them in computational studies are treated in some detail.