Chemical potential equilibration models have proven to be a promising approach for describing charge transfer and polarization in the context of classical force fields. These have generally been justified in an ad hoc manner and are known to behave incorrectly in certain cases, presenting a stumbling block to widespread application. In this paper, we present a new wave function-based derivation of a CPE-like model, shedding some light on the nature of the approximations that are made. The concept of a pairwise hardness arises naturally from this derivation, leading us to suggest a model that employs a pairwise electronegativity. We show that this leads to a CPE-like model that dissociates correctly for a diatomic and furthermore predicts charges in agreement with ab initio methods for a simple diatomic.

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Proton collisions with hydrogen molecules at 30 eV in the laboratory frame is a simple ion-molecule system exhibiting a number of distinct processes such as inelastic scattering, charge transfer, rearrangement, and dissociation. The electron nuclear dynamics (END) theory which allows full electron nuclear coupling and which does not restrict the system from reaching any of the possible product channels, is applied to this sytem to produce transition probabilities, differential, and integral (vibrationally resolved) cross sections. Comparisons with experiment demonstrate that END, even in its simplest implementation, with a single determinantal state for the electrons and with classical nuclei, yields results that are competitive with other theoretical approaches.

Coherent states suitable for the description of molecular rotations are developed and their connection to similar coherent states in the literature are explored. In particular their quasiclassical properties are developed. The use of such coherent states in time-dependent electron nuclear dynamics studies of molecular collision processes is discussed.