Atomic and Molecular Calculations with the Pseudopotential Method. I. The Binding Energy and Equilibrium Internuclear Distance of the Na2 Molecule

The dissociation energy and equilibrium internuclear distance of the Na2 molecule is calculated with the pseudopotential method. It is assumed that the molecule consists of two closed-shell Na+ electron cores which do not participate in the binding plus two valence electrons which are responsible for the binding. The two valence electrons are moving in the potential field of the two Na+ cores. For the interaction potential of the two valence electrons with the two cores an expression is derived, which consists of two parts: (1) of the Hartree—Fock potentials of the cores, (2) of the so-called pseudopotentials. We are using the approximation in which the requirement that the wavefunction of the valence electrons must be orthogonal to the wavefunctions of the electrons in the cores is removed and replaced by the so-called pseudopotential. In the present calculations we use Hellmann's expression for the pseudopotential. The wavefunction of the valence electrons is a Heitler—London-type function plus an ionic term, both built from hydrogenic 1s-type functions. From the energy minimum principle we obtain for the dissociation energy and equilibrium internuclear distance the values D=0.232 eV and R=6.18 a.u. (experimental values: D=0.74 eV and R=5.80 a.u.).