Phase Space Electronic Structure Theory: Diatomic Lambda-Doubling, spin-rotation coupling, and macroscopic Einstein-de Haas

Lambda-doubling of diatomic molecules and spin-rotation coupling are subtle microscopic phenomena that have long attracted the attention of experimental groups, insofar as rotation of molecular nuclei induces small energetic changes in the (degenerate) electronic state.

A direct description of such a phenomenon requires going beyond the Born-Oppenheimer approximation. In this talk, we show that a phase space theory previously developed to capture electronic momentum and model vibrational circular dichroism - and which we have postulated should also describe the Einstein-de Haas effect, a macroscopic manifestation of angular momentum conservation - is also able to recover the lambda-doubling energy splitting and the spin-rotation coupling splitting nearly quantitatively and nonperturbatively (without a sum over states). The key observation is that, by parameterizing the electronic Hamiltonian in terms of both nuclear position (X) and nuclear momentum (P), a phase space method yields potential energy surfaces that explicitly include the electron-rotation coupling and correctly conserve angular momentum. The data presented in this manuscript offer another small glimpse into the rich physics that one can learn from investigating phase space potential energy surfaces as a function of both nuclear position and momentum, all at a computational cost comparable to standard Born-Oppenheimer electronic structure calculations.