The weakly occupied sigma(u) and pi(g) natural orbitals (NOs) of the ground-state H-2 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 sip patterns at the R = 0 and R -> infinity limits. This mismatch is analogous to that recently uncovered in the harmonium atom. (c) 2006 Elsevier B.V. All rights reserved.