Non-Born–Oppenheimer electron, nuclear and nuclear–electron second-order density matrices for exactly solvable four-particle model system

Abstract

Properties of the non-Born–Oppenheimer two-matrix are examined for four-particle systems of the Coulomb–Hooke and Moshinsky types. We obtain for both these models explicit closed-form analytic expressions for the electron and nuclear 2-RDM. An explicit expression is also obtained for the electron–nuclear 2-RDM in the Moshinsky case, which shows coupling between the electron and nuclear coordinates.