Convergence of Density Functional Iterative Procedures with a Newton-Raphson Algorithm

By: Joseph W. Jerome, Paul R. Sievert, Linhui Ye, In Gee Kim, and Arthur J. Freeman

State of the art first-principles calculations of electronic structures aim at finding the ground state electronic density distribution. The performance of such methodologies is determined by the effectiveness of the iterative solution of the nonlinear density functional Kohn-Sham equations. We first outline a solution strategy based on the Newton-Raphson method. A form of the algorithm is then applied to the simplest and earliest density functional model, i. e., the atomic Thomas-Fermi model. For the neutral atom, we demonstrate the effectiveness of a charge conserving Newton-Raphson iterative method for the computation, which is independent of the starting guess; it converges rapidly, even for a randomly selected normalized starting density.
This final version has appeared in a special issue of the Journal of Computational Electronics: vol. 6 (2007), 349--352, as part of the Proceedings of IWCE-11, Vienna, May, 2006, and it can be viewed in the following format: