  We use recent theoretical advances to develop a new functional form for
interatomic forces in bulk silicon. The theoretical results underlying the
model include a novel analysis of elastic properties for the diamond and
graphitic structures and inversions of ab initio cohesive energy curves. The
interaction model includes two-body and three-body terms which depend on the
local atomic environment through an effective coordination number. This
formulation is able to capture successfully: (i) the energetics and elastic
properties of the ground state diamond lattice; (ii) the covalent
re-hybridization of undercoordinated atoms; (iii) and a smooth transition to
metallic bonding for overcoordinated atoms. Because the essential features of
chemical bonding in the bulk are built into the functional form, this model
promises to be useful for describing interatomic forces in silicon bulk phases
and defects. Although this functional form is remarkably realistic by usual
standards, it contains a small number of fitting parameters and requires
computational effort comparable to the most efficient existing models. In a
companion paper, a complete parameterization of the model is given, and
excellent performance for condensed phases and bulk defects is demonstrated.
