Exact Mo̷ller-Plesset Adiabatic Connection Correlation Energy Densities

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Electronic Structure Theory

Background:

• The Mo̷ller-Plesset adiabatic connection (MPAC) is crucial for developing density functional theory (DFT)-like approximations.
• Mapping Hartree-Fock (HF) densities to wave function-based correlation energy leverages both DFT and wave function concepts.
• Correlation energy density is well-studied in DFT but largely unexplored in wave function theory.

Purpose of the Study:

• Introduce a rigorous formulation of wave function-based correlation energy density within MPAC.
• Implement and analyze this quantity for small atomic and diatomic systems.
• Explore its potential for developing new electronic structure approximations.

Main Methods:

• Formulation of wave function-based correlation energy density using a general gauge strategy.
• Implementation via full configuration interaction (FCI) calculations.
• Derivation of the MP2 limit in terms of HF orbitals.

Main Results:

• A rigorous definition and implementation of wave function-based correlation energy density.
• Analysis of its behavior and contributions in small systems.
• Identification of commonalities and differences with DFT correlation energy density.
• Derivation of the MP2 limit.

Conclusions:

• The developed wave function-based correlation energy density offers a new perspective on electronic structure.
• It provides a bridge between DFT and wave function methods.
• These energy densities can serve as targets for new machine learning and traditional electronic structure approximations.