On non-adiabatic potential energy surfaces

The concept of a Born–Oppenheimer (BO) potential energy surface (PES) has been extended to non-adiabatic wavefunctions by Hunter and by Wilson. A Hunter non-adiabatic PES corresponding to an excited vibrational state has a set of spikes superimposed on a BO-like PES. It was believed that Wilson PESs were spike-free. We show that it is not the case and that the Wilson PES value at a given nuclear configuration is not the expectation value of a quantum observable but a quotient of such expectation values. Consequently, BO PESs have the quantum interpretation of quotients of approximate expectation values of observables.