Practical phase-space electronic Hamiltonians for ab initio dynamics

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian H ̂ e l ( X ) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ′) and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, H ̂ P S ( X , P ) . While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator H ̂ e l ( X ) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of H ̂ P S ( X , P ) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.