Kinetically balanced geometric Gaussian basis set calculations for relativistic many-electron atoms with finite nuclear size

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We have performed Dirac-Fock atomic structure calculations on many-electron atoms using kinetically balanced, geometric Gaussian basis sets. Our results show that “variational collapse” or bound failure does not occur even at Z=86. Furthermore, with a finite-size nuclear model, we obtain results close to the relativistic Hartree-Fock limit, with a smooth convergence from above. This opens up the possibility of optimisation of exponents in Gaussian basis set calculations within the Dirac-Fock approach for many-electron atoms.