Applications of B-Splines to the Local Density Functional Calculations for Atoms from H to Ca

Horng-Tay Jeng ； Chen-Shiung Hsue

《Chinese Journal of Physics》 35卷3期 (1997/06) Pp. 215-242

並列摘要

B-splines is employed to solve the Kohn-Sham equations of the local density functional theory for atoms from H to Ca in a variational self-consistent field procedure. The local-density-approximation (LDA), local-spin-density-approximation (LSD), and self-interaction-correction local-spin-density-approximation (SIC-LSD) schemes have all been considered and comparisons of the results are presented. Both the Gunnarsson-Lundqvist (GL) and Ceperley-Alder (CA) exchange-correlation energies are used. We have tried to achieve high accuracy in the numerical procedure. Comparisons of the energies show that the results of SIC-LSD are more accurate while LDA and LSD are more efficient. The results are in agreement with published results. The expectation values of different powers of r for each orbital which depends on the detailed behavior of the wave functions of the atoms are given. Additional corrections including relativistic effects, the reduced mass effects and the finite nuclear size corrections are also considered. The calculated results including these corrections are presented and compared with experimental data and other theoretical calculations. The comparison illustrates the ability of the B-spline applications to the density functional theory to be an efficient method and yet is capable of arriving at accurate results which can compete with results of sophisticated methods. As an additional test of the method, we have calculated the oscillator strengths of the 3s-3p and 4s-4p transition of the alkali iso-electron atoms: Na, Mg^+ and K, Ca^+. Compared with available experimental results, our results are among the best published theoretical values so far.