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

Towards time-dependent, non-equilibrium charge-transfer force fields: Contact electrification and history-dependent dissociation limits