Analytic properties of solution of electronic Schrödinger equation

It is shown that for a nondegenerate electronic state of a molecule the energy is an analytic function of the nuclear coordinates everywhere except points at which the nuclei coincide. The proof is based on construction of a parametric substitution of the coordinates and an associated analytic family of operators. It is found that the eigenfunctions of the molecular Hamiltonian do not have a square integrable third derivative with respect to the nuclear coordinates.