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
This final version has appeared in a special issue of
the Journal of Computational Electronics: vol. 6 (2007), 349--352, as part
Proceedings of IWCE-11, Vienna, May, 2006, and
it can be viewed in the following format: