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.