Analytical Calculation of Geometrical Derivatives in Molecular Electronic Structure Theory

Abstract

This chapter reviews the techniques recently available for the analytical calculation of molecular energy and property derivatives. The chapter focuses on the techniques that are simple and general, in particular those which can handle large basis sets and configuration expansions. It presents derivative expressions for most commonly used methods in molecular electronic structure theory, and their computational implementations. It is seldom possible to give expressions that are optimal under all conditions, regardless of the number of electrons, basis functions, and configurations. The analytical calculation of energy derivatives has recently been reviewed by Pulay and Gaw and Handy and the analytical calculation of property derivatives by Amos. The development of and computational implementation of analytical expressions for the derivatives of ab initio electronic energy surfaces and molecular properties have undergone rapid growth in recent years. This growth reflects the central role these derivatives play in understanding chemical reactions and in interpreting many spectroscopic experiments. The approach taken in this chapter constitutes a good basis for developing efficient procedures for calculation of geometrical derivatives under any particular set of circumstances.