Atomic Orbital Bases of Bunge and Koga Studied by Frobenius Products with Moscow–Aachen–Paris (MAP) Orbitals

Abstract

The minimization of Frobenius angles between functional subspaces spanned by different sets of atomic functions is employed to determine the values of orbital exponents ξ characterizing minimum atomic parameters/Moscow–Aachen–Paris (MAP) basis sets providing the best representation of two Hartree–Fock based atomic basis sets: that of Bunge et al. available for elements H–Xe and that of Koga and Thakkar spanning H to Lr (Z = 103). So-extracted values of exponents follow piecewise linear laws as functions of the nuclear charge Z resembling the prescriptions set by Slater rules for the orbital exponents. In details, however, the rules proposed by Slater are not precisely followed, neither for effective principal quantum numbers n* nor screening increments σ. Nevertheless, the linear pieces of the ξ vs. Z follow the structure of the Periodic Table being specific for the segments corresponding to p-, d- (transition), and f- (Lanthanides and Actinides) elements, respectively.