Atomic orbital bases of Bunge and Koga studied by Frobenius products with Moscow-Aachen-Paris (MAP) orbitals
Orbitaliă atomică Bungeniană ac Kogaensiă angulō Frobenianō cum orbitalibus Moscoviae-Aquisgranae-Parisiorum Lutetiae (MAP) dictis investigată
Résumé
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’s 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.
Minimizatio angulōrum Frobenianōrum inter subspatiǎ functionaliǎ prognatǎ copiis differentibus functionum atomicārum est adhibita ad valores exponentium orbitalium ξ determinandos pro basibus minimalium atomicōrum parametrōrum (M oscovia-Aquisgrana-Lutetia Parisiōrum-MAP) quae praebent optimam repraesentationem duābus copiis functionum atomicārum: alterae Bungenianae exsistenti ad elementa H-Xe, alterae Kogaensi porrectae ab H ad Lr (Z = 103). Valores exponentium ita inventi repraesentati ut functiones oneris nuclearis Z regulas lineares sequuntur in segminibus respectivis, praescriptiones regulis Slateri constitutas ergā exponentes Slaterianos simulantes. Exacte tamen regulas Slateri non sequuntur quia valores numeri quantici efficientis n * atque abstectionis incrementa σ ab illis praescriptis differunt. Nihilominus ramos lineares dependetiārum ξā Z juste structuram Tabulae Periodicae Elementōrum sequuntur et proprii sunt ad segmină respondentiă p-, d-(transitionă) et f-(Lanthanoidă ac Actinoidă) elementis.
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