Scaled AMO calculations on the hydrogen molecule II. The 1s σ 2p σ 1∑ state

A scaled version of the AMO method is applied to the 1sσ2pσ ¹∑ state of the hydrogen molecule. A method to extend the domain of the mixing parameter λ to the whole complex plane is described and applied in the present calculation. All the parameters introduced have been varied completely. A considerable improvement in the computed energy values is found for large internuclear separations R. The comparison between our potential energy curve and the accurate curve calcualted by Kolos and Wolniewicz is studied and, for example, for R = 12 a.u. the energy difference is only 18% of that for R = 2.43 a.u. The equilibrium separation is found to be 2.140 a.u. in poor agreement with 2.429 a.u. obtained by the previously mentioned authors. In the separated atom limit, the state under consideration does not dissociate into H⁺ + H^?, although the ionic character of the wave function is dominating in the region 3 ≦ R ≦ 8 a.u. The connections with earlier calculations and methods, especially the scaled version of the MO –LCAO approximation, are also pointed out and discussed.