Vibrational analysis for the nuclear-electronic orbital method

The methodology to perform a nuclear-electronic orbital (NEO) vibrational analysis is presented and discussed the physical implications of such an analysis. The methodology involves the calculation of a numerical Hessian, the projection of this Hessian to remove the overall translational and rotational motions, and the diagonalization of the projected Hessian to determine the harmonic vibrational frequencies corresponding to the classical nuclei. The analysis of these frequencies allows the characterization of stationary points on the NEO potential energy surface.