Construction of an accurate quartic force field by using generalised least-squares fitting and experimental design

In this work we present an attractive least-squares fitting procedure which allows for the calculation of a quartic force field by jointly using energy, gradient, and Hessian data, obtained 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 was chosen for its efficiency and accuracy. We illustrate the numerical implementations of the method by using the energy and gradient data for H2O and H2CO. The B3LYP/cc-pVTZ quartic force field performed from 11 and 44 simplex-sum configurations shows excellent agreement in comparison to the classical 44 and 168 energy calculations. (C) 2004 Elsevier B.V. All rights reserved.