Nodeless wave functions and spiky potentials

The exact (nonadiabatic) nuclear and electronic factors of a molecular wave function are expanded in the basis of eigenfunctions of the electronic Hamiltonian according to the Rayleigh–Schrödinger perturbation theory of Born and Huang. Thus it is shown that, with rare exceptions, the exact nuclear factor (a marginal amplitude) is a nodeless function. The nodes in vibrationally excited nuclear wave functions within the Born–Oppenheimer approximation become node-avoiding minima in the exact nuclear wave function. Corresponding to each node-avoiding minimum in the nuclear wave function the exact (nonadiabatic) effective potential for the nuclear motion has a spiky barrier superimposed upon the Born–Oppenheimer (adiabatic) eigenenergy of the electronic Hamiltonian. These barriers are the result of nonadiabatic coupling between electronic states, which is strongest in the vicinity of the nodes in the Born–Oppenheimer-approximation nuclear (vibrational) wave function.