The Sigma- states of the molecular hydrogen

Abstract

A class of doubly excited electronic states of the hydrogen molecule is reported. The states are of Sigma− symmetry and are located ca. 200000 cm−1 above the ground state and about 75000 cm−1 above the ionization threshold. The electronic wave functions employed to described these states have been expanded in the basis of exponentially correlated Gaussian (ECG) functions with the nonlinear parameters variationally optimized. The lowest triplet-Sigma−g and singlet-Sigma−u states dissociate into hydrogen atoms in the n = 2 state, whereas the lowest triplet-Sigma−u and singlet-Sigma−g states have H(n = 2) and H(n = 3) as the dissociation products. All the four states are attractive and accommodate vibrational levels. The location of the vibrational energy levels has been determined by solving the radial Schrödinger equation within the Born–Oppenheimer approximation.