  The leading terms in the large-$R$ asymptotics of the functional of the
one-electron reduced density matrix for the ground-state energy of the H$_2$
molecule with the internuclear separation $R$ is derived thanks to the solution
of the phase dilemma at the $R \to \infty$ limit. At this limit, the respective
natural orbitals (NOs) are given by symmetric and antisymmetric combinations of
"half-space" orbitals with the corresponding natural amplitudes of the same
amplitudes but opposite signs. Minimization of the resulting explicit
functional yields the large-$R$ asymptotics for the occupation numbers of the
weakly occupied NOs and the $C_6$ dispersion coefficient. The highly accurate
approximates for the radial components of the $p$-type "half-space" orbitals
and the corresponding occupation numbers (that decay like $R^{-6}$), which are
available for the first time thanks to the development of the present
formalism, have some unexpected properties.
