Solving the Schrödinger equation of the hydrogen molecule with the free-complement variational theory: essentially exact potential curves and vibrational levels of the ground and excited states of Π symmetry

Abstract

Following a previous study of the Σ states (Phys. Chem. Chem. Phys., 2019, 21, 6327), we solved the Schrödinger equation (SE) of the hydrogen molecule in the ground and excited Π states using the free complement (FC) variational method. This method is a general method to solve the SE: the energies obtained are highly accurate and the potential energy curves dissociate correctly. The calculated energies are upper bound to the exact energies, and the wave functions at any distance are always orthogonal and Hamiltonian-orthogonal to those in the different states calculated in this study. Using the essentially exact potential energy curves, the vibrational energy levels of each state were calculated by solving the vibrational Schrödinger equation.