Classical models for electronic degrees of freedom: The second-quantized many-electron Hamiltonian

A classical Hamiltonian is constructed which corresponds to the general second-quantized Hamiltonian operator for a many-electron system. This classical electronic Hamiltonian properly accounts for the fermion character of electrons (i.e., the anticommutivity of the electron creation and annihilation operators). By having a classical description of the electronic degrees of freedom one is able to incorporate electronically nonadiabatic effects into a classical trajectory simulation of nuclear motion in a dynamically consistent way. Several applications are described which illustrate the nature of the model. It can be viewed, for example, as a generalization of an earlier classical valence bond model (based on a Heisenberg–Van Vleck spin Hamiltonian), the generalization being to include the effects of ionic as well as covalent configurations in the description. The present model, therefore, is able to describe charge transfer aspects of the electronic degrees of freedom.