It is the aim of this work to develop analytical force field expressio
ns that can be rapidly evaluated by computers. The new expressions app
roximate the energy hypersurfaces as described by the usual force fiel
ds. The energies and the derivatives of the energy expressions, i.e. t
he forces acting on the atoms, in most cases can be very quickly calcu
lated as functions of one squared distance of two atoms per interactio
n, avoiding slow operations like cosine, square root etc. Formulae and
algorithms are given to calculate the parameters needed from those of
the AMBER force field.