Analytical potential curve from Non-Born-Oppenheimer wave function: Application to hydrogen molecular ion

Abstract

Although the concept of a potential curve is one of the important outgrowths of the Born-Oppenheimer (BO) approximation, we propose a method to obtain an analytical potential curve from the Non-Born-Oppenheimer (Non-BO) wave functions. The present proceeding reviews this method originally published in J. Chem. Phys. 139, 074105 (2013). A numerical examination was performed with hydrogen molecular ion, where the free complement method was employed to solve the Non-BO Schrödinger equation very accurately. Whereas an ordinary potential curve on the BO approximation is obtained as a numeric curve evaluated at many fixed nuclear coordinates and curve fitting is always required, the present method can describe the potential curve as an analytical continuous function. It indicates that a single Non-BO calculation principally draws the whole potential curve at any nuclear coordinates.