H2+, HeH and H2: Approximating potential curves, calculating rovibrational states

Accurate analytical expression for the potential curves of the hydrogen molecule H2 for the states 1Σg+ and 3Σu+ is presented. The ground state 1Σg+ contains 15 vibrational states (ν,0),ν=0-14. In general, this state supports 301 rovibrational states. The potential curve of the state 3Σu+ has a shallow minimum: it does not support any rovibrational state, it is repulsive.