Spectroscopic constants of MH and M2 (M=Tl, E113, Bi, E115): Direct comparisons of four- and two-component approaches in the framework of relativistic density functional theory

Abstract

The two-component DFT-ZORA (density functional theory, zeroth order regular approximation) method is implemented into the BDF (Beijing four-component density functional) program package so that systematic and direct comparisons between two- and four-component approaches are made possible for the first time. Different implementations of the ZORA method are also compared in this work. The calculated spectroscopic constants (bond lengths, binding energies, and force constants) for MH and M2 (M=Tl, E113, Bi, E115) by the two- and four-component approaches are very similar. The ionization and excitation energies for the metals obtained by these methods also agree very well with each other. Still, minor higher order relativistic effects beyond ZORA can be identified occasionally, but can be “safely” neglected. Therefore, the applicability of transformed (two-component) Hamiltonians to valence properties is well justified. However, the computational efficiency of four-component DFT compares favorably with that of two-component DFT. The problems of symmetry breaking and different treatments of open-shell systems are discussed by taking the Bi atom as an example.