| In most quantum descriptions of chemical reactions, the Born-Oppenheimer (BO) approximation is invoked that separates the motion of light electrons and heavy nuclei, thereby restricting the motion of those nuclei to a single adiabatic electronic state. Intersections between neighboring electronic states are more common in molecular systems of interest to chemistry and biology than in diatomic molecules. The picture is further complicated due to nonadiabatic couplings which can be present in these systems even in the absence of intersections between electronic states. These couplings are solely responsible for all nonadiabatic effects in chemical and biological processes. For understanding these nonadiabatic effects, the BO picture needs to be replaced by the general Born-Huang (BH) description, in which the nuclei can sample an arbitrary number of electronic states.; A general BH treatment is presented for a polyatomic system evolving on n adiabatic electronic states. All nonadiabatic couplings are considered in this adiabatic representation. These couplings can be singular for electronically degenerate nuclear geometries. The presence of these nonadiabatic couplings (even if not singular) can lead to numerical inefficiencies in the solution of the corresponding nuclear motion Schrödinger equation. This problem is circumvented by going to a diabatic representation, in which these couplings are not only never singular but are also minimized over the entire dynamically important nuclear configuration space. This BH description is applied to the benchmark triatomic system H3 by obtaining an optimal diabatic representation of its lowest two adiabatic electronic states. A two-electronic-state quantum dynamics formulation is also presented, which, in addition to providing reaction cross sections over a broad energy range, will also enable a quantitative test of the validity of the BO approximation. |
