Basis Set Requirement for Small Components Besides Kinetic Balance in Relativistic Self-Consistent-Field Calculations of Many Electron Systems

摘要

It is demonstrated by using a highly positive uranium ion as a test case that the exact relation between the small and the large components of a Dirac spinor in relativistic self-consistent-field (RSCF) calculations is not fully satisfied by the kinetic balance condition only even for two electron systems. For a fixed number of large component basis functions, total energies are sensitive to the change of the size of the small component basis sets even after the kinetic balance condition is fully satisfied. However, the kinetic balance condition appears to be a reasonable guideline in generating reliable and practical basis sets for most applications of RSCF calculations. With a complete small component basis set, energies from RSCF calculations exhibit a variational behavior, implying the stability of the present RSCF procedure.