Chapter 17 - Equations of motion methods for computing electron affinities and ionization potentials

Abstract

The abinitio calculation of molecular electron affinities (EA) and ionization potentials (IP) is a difficult task because the energy of interest is a very small fraction of the total electronic energy of the parent neutral. For example, EAs typically lie in the 0.01 – 10 eV range, but the total electronic energy of even a small molecule is usually several orders of magnitude larger. Moreover, because the EA or IP is an intensive quantity but the total energy is an extensive quantity, the difficulty in evaluating EAs and IPs to within a fixed specified (for example, ± 0.1 eV) accuracy becomes more and more difficult as the size and number of electrons in the molecule grow. The situation becomes especially problematic when studying extended systems such as solids, polymers, or surfaces for which the EA or IP is an infinitesimal fraction of the total energy. Equations of motion (EOM) methods and other related approaches offer a route for calculating the intensive EAs and IPs directly as eigen-values of a set of working equations. A history of the development of EOM theories as applied to EAs and IPs, their numerous practical implementations, and their relations to Greens function or propagator theories are given in this contribution. EOM methods based upon Møller–Plesset, multiconfiguration self-consistent field, and coupled-cluster reference wave functions are included in the discussion as is the application of EOM methods to metastable resonance states of anions.