Kinetically balanced geometric Gaussian basis sets for relativistic atoms

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We present Dirac–Hartree–Fock (DHF) atomic structure results for many-electron atoms (Z=2–86) using kinetically balanced geometric basis sets of Gaussian functions. There is no ‘‘variational collapse’’ or bound failure if we impose the condition of kinetic balance between the large and the small component spinors along with proper boundary conditions for bound state orbitals. Furthermore, with a finite-size nucleus model, the DHF total energy for atoms converges more rapidly to the numerical Dirac–Fock (DF) limit with a smaller number of basis functions than those calculations where a point nucleus is assumed. By systematically extending the geometric basis sets, we have obtained the DHF total energies for all atoms(up to Z=86) within a few millihartrees of the numerical (DF) limit, with smooth convergence from above.