Double-Perturbation Treatment of the Ground State of the Hydrogen Molecule

The ground state of the hydrogen molecule is treated by a double-perturbation theory through second order. The unperturbed system is defined mathematically by the unperturbed spatial wavefunction, which has the form exp[—s(ra1+rb1+ra2+rb2)] where s is an energy-optimized scale parameter. The perturbations are (a) one-electron terms due to the simple form chosen for the zeroth-order wavefunction, and (b) the two-electron repulsion potential. The first-order wavefunction for (a) is known analytically and that for (b) is obtained approximately from the Hylleraas variational principle using a James—Coolidge type trial function. The energy through second order gives an equilibrium distance within 1% of that obtained by Kol/os and Roothaan and a dissociation energy of 4.988 eV, 5% larger than their value of 4.747 eV. The wavefunction through first order gives expectation values for one-electron operators in good agreement with accurate calculations, but is poor when the electrons are close together.