A Finite Difference NewtonRaphson Solution of the Atomic HartreeFock Problem
Abstract
The SCF iteration is coupled with a finite difference NewtonRaphson algorithm to solve the set of coupled secondorder integrodifferential equations with split boundary conditions which constitutes the atomic HF problem. In the new method the twopoint boundary conditions at r = 0 and r = ∞ as well as the Lagrange multipliers are incorporated into a large system of nonlinear algebraic equations which are solved by means of a generalized NewtonRaphson iteration which converges rapidly and efficiently. The need to estimate initial slopes of the radial functions and values of Lagrange multipliers has been completely eliminated. As an example a calculation of the 1 S^{2}2 S openshell configuration of Li is presented. Through the use of Richardson extrapolation an accuracy of nine significant figures has been achieved. The new method is easier to apply and more versatile than the conventional methods. Although only Li and Be have been attempted so far (each with complete success) the method can certainly handle very large systems.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1974
 DOI:
 10.1016/00219991(74)900709
 Bibcode:
 1974JCoPh..15...81C