Analysis of the vibrational, static and dynamic, second hyperpolarizability of five small molecules

Various approximate methods for the calculation of vibrational second hyperpolarizabilities are assessed on the basis of results for CH₄, NH₃, H₂O, HF, and CO₂. Three specific variations of the perturbation‐theoretic approach are analyzed. These are defined by the types of terms retained in expansions which involve electrical and mechanical anharmonicities. The lowest‐order approximation being the double‐harmonic one and the next higher one the relaxation method. For the dynamic hyperpolarizabilities, the replacement of the optical frequencies (ω) by ω→∞ (the infinite‐frequency approximation) is also explored. On the evidence at hand it is concluded that the relaxation/infinite‐frequency method is a satisfactory approximation for the nonlinear optical vibrational hyperpolarizabilities.