Simultaneous equations for calculating the pair density.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The pair density (PD) is crucial for understanding electron-electron interactions in quantum systems.
• The N-representability problem poses a significant challenge in accurately calculating PD from fundamental electronic structure.
• Existing methods often struggle with the computational complexity and accuracy of PD calculations.

Purpose of the Study:

• To develop a practical and accurate scheme for calculating pair density (PD).
• To overcome the N-representability problem inherent in PD calculations.
• To provide a computationally feasible approach within density functional theory (DFT).

Main Methods:

• Implementation of the variational principle applied to PDs derived from single Slater determinants (SSDs).
• Utilizing an approximate kinetic energy functional based on electron-coordinate scaling laws.
• Solving simultaneous equations for the constituent orbitals of the SSD.

Main Results:

• The proposed method successfully yields the best SSD-representable PDs.
• Demonstrates a practical approach to circumventing the N-representability problem.
• Provides accurate PD calculations within the SSD framework.

Conclusions:

• The developed scheme offers a robust solution for calculating pair density.
• This method enhances the applicability of DFT for electronic structure problems.
• It paves the way for more accurate investigations of electron correlation effects.