Local approximation of the correlation energy functional in the density matrix functional theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Density Functional Theory

Background:

• Accurate calculation of correlation energy is crucial in quantum chemistry.
• Existing methods often face challenges with computational cost and accuracy.
• The first-order reduced density matrix (1-RDM) offers an alternative route to electronic structure calculations.

Purpose of the Study:

• To develop a local approximation formula for the correlation energy functional E(c).
• To express E(c) in terms of the 1-RDM and natural occupation numbers.
• To create a computationally efficient and accurate method for calculating correlation energies.

Main Methods:

• Utilizing the contracted Schrödinger equation to determine the dependence of E(c) on natural occupation numbers.
• Employing effective mass theory to formulate E(c) as a functional of local density and a local variable J.
• Defining J using natural spin orbitals and occupation numbers.

Main Results:

• A novel local approximation formula for the correlation energy functional E(c) was derived.
• The formula accurately reproduces about 90% of the correlation energies for atoms and molecules.
• The approximation satisfies the homogeneous coordinate scaling relation and yields exact results for one-electron systems.

Conclusions:

• The presented local approximation offers a promising approach for calculating correlation energies.
• This method demonstrates high accuracy and efficiency, particularly for atoms and molecules.
• The work contributes to the advancement of density functional theory and quantum chemical calculations.