Frequency dependent hyperpolarizabilities with application to formaldehyde and methyl fluoride

Abstract

Methods for the determination of the frequency dependent hyperpolarizabilities, β(−2ω;ω,ω), β(−ω;ω,0), and β(0;ω,−ω) at the self-consistent field (SCF) level of theory are discussed and compared. Two efficient alternatives are proposed; one involves determination of appropriate response vectors which arise in first-order perturbation theory at frequency ω, and the other involves solving first-order perturbation theory equations at frequency 0 (static), ω and 2ω. Neither approach involves solution of the second-order perturbation theory equations. The method is illustrated with application to formaldehyde and methyl fluoride using large one-particle basis sets. The basis set requirement for convergence of this property at the SCF level of theory is investigated. Basis sets including up to d functions on first row atoms and p functions on hydrogen incorporating diffuse functions appear to be adequate. The effect of electron correlation on the static hyperpolarizability is estimated using second-order Mo/ller–Plesset theory. Comparison is made with experimental values where available.