Reconstruction of the On-Top Two-Electron Density from Natural Orbitals and Their Occupation Numbers

Spatial derivatives of the natural orbitals (NOs) at their nodal surfaces are shown to encode information about the on-top two-electron density Φ₂(r⃗) in an approximate manner. This encoding, which becomes exact at the limit of an infinite number of nodal surfaces, allows the reconstruction of Φ₂(r⃗) up to a multiplicative constant that can be retrieved from an identity involving the NO in question and its occupation number. This reconstruction provides a new consistency check for electronic structure formalisms, such as the one-electron reduced density matrix theory, that employ NOs as primary quantities.