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

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Natural Orbitals (NOs) are fundamental in describing electron correlation.
• The on-top two-electron density (Φ₂(r⃗)) provides insights into electron pairing.
• Existing methods for reconstructing electron density from NOs have limitations.

Purpose of the Study:

• To explore the relationship between spatial derivatives of NOs and the two-electron density.
• To develop a novel method for reconstructing the two-electron density from NOs.
• To introduce a new consistency check for electronic structure theories.

Main Methods:

• Calculating spatial derivatives of NOs at their nodal surfaces.
• Utilizing an identity involving NOs and their occupation numbers.
• Reconstructing the two-electron density Φ₂(r⃗).

Main Results:

• Spatial derivatives of NOs approximate the on-top two-electron density.
• This approximation becomes exact with an infinite number of NOs.
• A method to retrieve the multiplicative constant for exact reconstruction was identified.

Conclusions:

• The spatial derivatives of NOs offer a pathway to reconstruct electron density.
• This provides a valuable consistency check for theories like one-electron reduced density matrix theory.
• The findings enhance the utility of NOs in electronic structure calculations.