  Force fields uniquely assign interatomic forces for a given set of atomic
coordinates. The underlying assumption is that electrons are in their
quantum-mechanical ground state or in thermal equilibrium. However, there is an
abundance of cases where this is unjustified because the system is only locally
in equilibrium. In particular, the fractional charges of atoms, clusters, or
solids tend to not only depend on atomic positions but also on how the system
reached its state. For example, the charge of an isolated solid -- and thus the
forces between atoms in that solid -- usually depends on the counterbody with
which it has last formed contact. Similarly, the charge of an atom, resulting
from the dissociation of a molecule, can differ for different solvents in which
the dissociation took place. In this paper we demonstrate that such
charge-transfer history effects can be accounted for by assigning discrete
oxidation states to atoms. With our method, an atom can donate an integer
charge to another, nearby atom to change its oxidation state as in a redox
reaction. In addition to integer charges, atoms can exchange "partial charges"
which are determined with the split charge equilibration method.
