Screened Exchange Corrections to the Random Phase Approximation from Many-Body Perturbation Theory.

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Many-Body Theory

Background:

• The random phase approximation (RPA) often overestimates correlation energy and underestimates cohesive energies.
• This inaccuracy stems from uncancelled Pauli exclusion principle violating (EPV) contributions, leading to unphysical negative pair densities for spin-parallel electrons.

Purpose of the Study:

• To develop an efficient exchange correction for RPA that addresses the dominant EPV contributions.
• To improve the accuracy of electron correlation energy and pair density calculations, particularly in the uniform electron gas (UEG).

Main Methods:

• Proposes an exchange correction based on many-body perturbation theory by exchanging adjacent particle/hole pairs in RPA diagrams.
• Implements a computationally efficient method with a complexity scaling of O(N^4) or O(N^5) in orbital space and O(N^3) in real space, where N is the system size.

Main Results:

• The proposed correction significantly improves the pair density of spin-parallel electrons near coalescence in the UEG.
• Achieves correlation energy accuracy comparable to existing second-order screened exchange (SOSEX) methods.
• Demonstrates slightly higher accuracy for spin-polarized UEG compared to other SOSEX variants.

Conclusions:

• The developed exchange correction offers a computationally feasible approach to enhance RPA accuracy.
• It effectively mitigates unphysical electron density issues and improves correlation energy calculations.
• The method presents a promising advancement for electronic structure calculations in various physical systems.