Spatial distribution of atomic electronic density for elements 1–54 as coming from a Hartree–Fock treatment within the minimum atomic parameters paradigm

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Abstract
The minimum atomic parameters/Moscow–Aachen–Paris (MAP) basis sets—reintroduced in the previous paper—are analyzed with respect to spatial features as orbital shape, possible fits to alternative orbital sets (numerical or quasi‐numerical orbitals, nodeless Slater orbitals), respect of Kato's condition and radial distribution of energy components. For comparing orbital spaces the Frobenius angle between the orbital subspaces they span is introduced as numerical tool. It is shown that the electronic density of the MAP states is depleted around the nucleus with respect to the other orbital sets. Despite this, the similarity between the respective subspaces in all cases (except a unique case of the Pd atom) as measured by the cosine of the Frobenius angle amounts above 0.96 for all atoms. Deviations from the perfect value of Kato's condition amounts systematically to 0.3 and 0.5 for all elements considered. Integrating one‐electron energy contributions from r = ∞ to a finite radius, MAP and Bunge orbitals show about the same values, but for the inner region governed by the polynomial oscillations.

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