The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

Abstract

A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and positions of which were determined by invoking the variational principle for the corresponding non-relativistic problem. Using only 27 s -type functions for the large component and a small component basis set constructed according to the kinetic balance prescription a sub- μ Hartree level of accuracy is achieved in the finite basis set solutions when compared with the finite difference study reported by Sundholm et al. Some advantages of the distributed basis set approach in relativistic electronic structure studies are discussed.