Fully numerical relativistic calculations for diatomic molecules using the finite-element method.

Abstract

A two-dimensional, fully numerical approach to the four-component Dirac 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 ${\mathrm{H}}_{2}$, an absolute accuracy of about ${10}^{\mathrm{\ensuremath{-}}10}$ a.u. for the total energy and the 1(${\mathit{j}}_{\mathit{z}}$=1/2) orbital energy is achieved with only 2116 grid points, where ${\mathit{j}}_{\mathit{z}}$ is the component of the total angular momentum along the internuclear axis. Relativistic total energies, orbital energies, and their relativistic corrections were calculated in the Dirac-Fock-Slater approximation for some small diatomic systems such as LiH, ${\mathrm{Li}}_{2}$, BH, and ${\mathrm{C}}_{2}$. The accuracies available previously have been improved by several orders of magnitude, yet without presently exceeding 2601 grid points.