Multiple Solutions to the Hartree–Fock Problem. II. Molecular Wavefunctions in the Limit of Infinite Internuclear Separation

Abstract

The restricted Hartree–Fock equation for a closed‐shell molecule is investigated in the limit of infinite internuclear separation. The conventional molecular equation reduces, in the limit, to a set of modified Hartree–Fock equations for the individual fragments. The modification consists of admitting fractional occupation numbers for occupied orbitals. The individual fragment equations are coupled by conditions on the orbital energies and on the fractional “charges.” The self‐consistent field equation, being nonlinear, admits a variety of mathematically acceptable solutions. For lithium hydride a wavefunction corresponding to ionic fragments Li⁺ and H⁻ is one such limiting solution. Contrary to popular notion, it is not the solution of lowest energy even within the restricted SCF formalism. Limiting solutions are obtained for H₂, LiH, and CH₄. The separated hydrogen molecule is shown to have an SCF energy which is exactly one‐quarter that of the helium atom. The long‐range interaction of two hydrogen atoms is described by an inverse first‐power potential according to Hartree–Fock theory. The $Z$ dependence of correlation energy at infinite separation is analyzed in terms of a charge‐transfer process. It is argued that in passing from the equilibrium separation to infinity the ground‐state SCF wavefunction for a molecule such as lithium hydride becomes at first more and then less ionic.