Bond-order potentials: bridging the electronic to atomistic modelling hierarchies

Novel analytic bond-order potentials (BOPs) may be derived for atomistic simulations by coarse-graining the electronic structure within the orthogonal two-centre tight-binding (TB) representation. We show that these BOPs allow the concept of single, double, triple and conjugate bonds in carbon systems to be quantified, so that they provide the first `classicalʹ interatomic potentials that handle both structural differentiation and radical formation naturally within their remit. Finally, we indicate that this recently developed BOP formalism allows explicit, analytic expressions for the environmental dependence of the TB bond integrals to be derived, thereby providing a systematic methodology for bridging from the electronic to atomistic modelling hierarchies.