  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.
