Solitonic natural orbitals in Coulombic systems

High-accuracy electronic structure calculations on the members of the helium isoelectronic series and the H₂ molecule with a stretched bond reveal that the ground-state wavefunctions of these Coulombic systems give rise to natural orbitals (NO) with unusual properties. These solitonic NOs (SoNOs) possess fewer nodes than expected from their small occupation numbers, exhibit substantial spatial localization, and respond (with approximate retention of their shapes) in a paradoxical manner (e.g., by moving away from nuclei upon an increase in the nuclear charge or decrease in the internuclear distance) to changes in the underlying Hamiltonian. An efficient tool for the identification of the SoNOs is provided by an index constructed from two expectation values pertaining to a given NO and the corresponding occupation number. In the case of the helium-like species, the rapid decay of the occupation numbers of the SoNOs with increasing nuclear charge Z is governed by an asymptotic expression that involves the radial positions and spreads of the orbitals. Three s-type SoNOs (with the occupation numbers amounting to only ∼7.9·10^-67, 6.8·10^-92, and 9.0·10^-113 in the case of the helium atom) are predicted to turn into unoccupied NOs at Z equal to ∼2.673, 2.587, and 2.536, respectively. The persistence of the analogous p-type orbital beyond Z = 2 is consistent with the computed properties of the σ_u-type SoNO of the H₂ molecule with a stretched bond. In particular, the profiles of this SoNO along two perpendicular lines bear great resemblance to the radial profiles of its p-type counterpart.