Least-squares fitting approach using energy, gradient and Hessian data to obtain an accurate quartic force field : Application to H2O and H2CO

Abstract

In this work we present an attractive least-squares fitting procedure to obtain a quartic force field by using energy, gradient and Hessian data arising from electronic wave function calculations on a suitably chosen grid of points. We use the experimental design to select the grid points : a simplex-sum of Box and Behnken grid is used for its efficiency and accuracy. We illustrate the numerical implementation of the method by using energy and gradient data and we test for H2O and H2CO the B3LYP/cc-pVTZ quartic force field performed from 11 and 44 simplex-sum configurations. Results compared to classical 44 and 168 energy calculations, show excellent agreement.