Quasi-linear dependence of one- and two- electron densities in natural bond orbitals

We explore the possibility of formulating an explicit relation between one- and two-electron densities, which result from correlated wave functions. Based on a second quantized formalism, we derive the relationship P2;0(ϕϕ̄;0)=2 P1;0(ϕ;0)−1 (where P1;0 and P2;0 are one- and two-electron densities in ϕ), which holds under the condition that the two-hole probability in ϕ is negligible; this condition is satisfied when ϕ are bonding natural bond orbitals but not atomic orbitals.