Application of the Space-Pseudo-Time Method to Density Functional Theory

A numerical solution of the Kohn–Sham (KS) differential equation within the local density approximation is presented. The present method involves solving for the Hartree potential from its differential form which is the Poisson equation. Radial differential equations are derived for closed-shell atoms and are solved as initial value problems. A self-consistent procedure for solving the resulting radial KS equations based on our new algorithm for solving differential equations is also discussed. Numerical tests are done on the Helium atom and comparison with results obtained from spectral exponential and Gaussian type basis functions are shown.