Degree of electron-nuclear entanglement in molecular states

Abstract

The degree of electron-nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground-state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born-Huang potential energy correction evaluated at the minimum. In the case of a double-well potential energy; surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E x epsilon Jahn-Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E x epsilon model demonstrate a nontrivial relation between entanglement and vibronic coupling.