An iterative, numeric procedure to obtain pair functions applied to two-electron systems

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Abstract
A general, non-variational method to obtain atomic pair excitations, which are the dominating correction to a HF wavefunction, is described in the framework of diagrammatic many-body perturbation theory. The angular part of the function is treated using the angular momentum graph technique and the radial part of the pair function is obtained as the solution of an inhomogeneous two-dimensional differential equation. The radial equations are solved using the finite difference method, which has been modified to reduce computer time and storage requests. By solving the equations iteratively, pair correlation can be obtained to all orders and expressions are given for the right-hand side of the equation. The method has been applied to some two-electron systems to demonstrate its capability.