Correlation Energy Expressions from the Adiabatic-Connection Fluctuation-Dissipation Theorem Approach

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The random phase approximation (RPA) is a powerful tool for calculating electron correlation energies.
• Understanding and refining RPA methods is crucial for accurate predictions in electronic structure theory.
• Different treatments of exchange interactions lead to distinct RPA correlation energy variants.

Purpose of the Study:

• To explore and compare several random phase approximation (RPA) correlation energy variants.
• To introduce and analyze a novel dRPA-II variant, relating it to existing methods like SOSEX.
• To derive and test spin-adapted forms of RPA variants for closed-shell systems.

Main Methods:

• Utilizing the adiabatic-connection fluctuation-dissipation theorem approach.
• Implementing and comparing different exchange treatment strategies within RPA.
• Deriving spin-adapted formulations for closed-shell systems.
• Performing calculations on atomic and molecular systems, including those with range-separated interactions.

Main Results:

• Clarification of the relationships between various RPA formulations.
• Introduction of the dRPA-II variant, showing its resemblance to the second-order screened exchange (SOSEX) method.
• Successful derivation and testing of spin-adapted RPA variants.
• Evaluation of method performance across different system types and interaction ranges.

Conclusions:

• The study provides a clearer understanding of RPA correlation energy variants and their interconnections.
• The novel dRPA-II variant shows promise and warrants further investigation.
• Spin-adapted RPA methods are effectively derived and validated for practical applications in electronic structure calculations.