A numerical solution of the pair equation of a model two‐electron diatomic system

It has been well‐documented that about 90% of the total correlation energy of atomic systems can be obtained by solving so‐called pair equations. For atoms, this approach requires solving partial differential equations (PDE) in two variables. In case of a diatomic molecule, we face devising a method for treating PDEs in five variables. This article shows how a well‐established finite difference method used to solve Hartree–Fock equations for diatomic molecules can be extended to solve numerically a model two‐electron Schrödinger equation for such systems. We show that using less than 100 grid points in each variable, it is possible to obtain the total energy of the helium atom and hydrogen molecule with a chemical accuracy and the S energy of the helium atom and hydride ion as accurately as the best results available.