Static Perturbation Theory and Derivative Properties

Perturbation theory (PT) is a method by which the energies and wavefunctions of a system of interest are expressed in terms of the known solutions of a presumably simpler reference system. The Rayleigh-Schrodinger expressions for the wavefunctions and energies of exact states are derived up to 3rd and 4th order, respectively. A simple application deals with substitution effects on the absorption color of organic chromophores. The Moller-Plesset correlation energy is derived in 2nd order (MP2). It is then shown how bi-linear perturbations associated with the electric and magnetic field operators of chapter 21 define properties such as polarizability, magnetizability or susceptibility, nuclear magnetic resonance shielding and spin-spin coupling, harmonic nuclear vibrational frequencies, and many other properties. The bi-linear magnetic perturbation energy is derived for paramagnetic systems with low-energy thermally populated degenerate states. The chapter concludes with a description of derivative techniques for approximate quantum chemical methods.