Exact Solutions to the Coupled Hartree-Fock Perturbation Equations

Abstract

A new method is presented for obtaining exact solutions to the time‐dependent coupled Hartree‐Fock perturbationequations. We choose an iterative approach, relying on the Aitken δ2 transformation to insure and accelerate convergence. At each iteration the resulting uncoupled inhomogeneous differential equations are solved using the technique previously presented by Alexander and Gordon, based on piecewise polynomial approximation of both the potential and the inhomogeneity. As a numerical application we calculate the frequency‐dependent dipole polarizability of the helium atom within the coupled Hartree‐Fock approximation. Comparison is made with the results of previous variational and numerical calculations. The method can be extended to the solution of integro‐differential equations arising in other areas of chemical physics.