L. Yang et al., FULLY NUMERICAL RELATIVISTIC CALCULATIONS FOR DIATOMIC-MOLECULES USING THE FINITE-ELEMENT METHOD, Physical review. A, 48(4), 1993, pp. 2700-2707
A two-dimensional, fully numerical approach to the four-component Dira
c equation utilizing the finite-element method for diatomic systems is
presented. The convergence properties of the calculations, which are
affected by the singularities of the relativistic wave functions, are
studied and improved. In the Dirac-Fock approximation for H-2, an abso
lute accuracy of about 10(-10) a.u. for the total energy and the 1(j(z
) = 1/2) orbital energy is achieved with only 2116 grid points, where
j(z) is the component of the total angular momentum along the internuc
lear axis. Relativistic total energies, orbital energies, and their re
lativistic corrections were calculated in the Dirac-Fock-Slater approx
imation for some small diatomic systems such as LiH, Li2, BH, and C2.
The accuracies available previously have been improved by several orde
rs of magnitude, yet without presently exceeding 2601 grid points.