Numerical study of the convergence of the linear expansion method for the one-electron Dirac equation

We have carried out relativistic molecular electronic structure calculations using the prescription of ‘strict kinetic balance’ applied to four-component spherical Gaussian spinors centred on the nuclei; the exponents for all atomic symmetries have been chosen according to the ‘even-tempered’ or ‘geometric’ prescription. The upper bound properties and convergence behaviour of the ground states of one-electron molecular ions with two, three and four centres have been investigated. The Dirac energy of the 1σg state of H2+ at an internuclear separation of 2 bohr is computed to an accuracy of better than 1 part in 1010. We calculate the energy of the corresponding level of the highly relativistic Th2179+ system at an internuclear separation of 290 bohr. Studies of models of three- and four-center molecular ions, H32+ and H43+, are reported to demonstrate the applicability of the approach to arbitrary geometries. Our estimates of the relativistic energy converge monotonically from above as the basis sets are enlarged, and nonrelativistic limits obtained by increasing the speed of light used in the computations yield results in excellent agreement with calculations that are nonrelativistic from the outset.