Unoccupied natural orbitals in two-electron Coulombic systems

The weakly occupied σu and πg natural orbitals (NOs) of the ground-state H2 molecule become unoccupied at the internuclear distances R of ca. 4.44 and 5.12 (a.u.), respectively. The appearance of unoccupied NOs at infinitely many values of R is demonstrated in a rigorous manner and traced to the mismatch between the occupancy amplitude sign patterns at the R = 0 and R → ∞ limits. This mismatch is analogous to that recently uncovered in the harmonium atom.