Self-Consistent-Field Method for Correlated Many-Electron Systems with an Entropic Cumulant Energy.

Area of Science:

• Quantum Chemistry
• Computational Many-Body Physics
• Density Matrix Functional Theory

Background:

• Correlated many-electron calculations are computationally expensive.
• Existing methods struggle to balance accuracy and computational cost.
• Accurate treatment of both dynamical and non-dynamical electron correlation is crucial.

Purpose of the Study:

• To develop a computationally efficient yet accurate method for correlated many-electron systems.
• To reduce the cost of correlated calculations to that of Hartree-Fock.
• To achieve accuracy comparable to sophisticated configuration interaction methods.

Main Methods:

• A self-consistent field (SCF) method within density matrix functional theory (DMFT).
• Utilizes information entropy and Fermi-Dirac distribution for two-electron cumulant energy.
• Derives an eigenvalue equation connecting orbital energies and occupation numbers.

Main Results:

• Achieves computational cost similar to the Hartree-Fock method.
• Maintains accuracy comparable to advanced configuration interaction techniques.
• Occupation numbers closely match natural orbital occupation numbers.
• Successfully captures both non-dynamical and dynamical electron correlation.

Conclusions:

• The presented SCF method offers a significant breakthrough in computational chemistry.
• Enables large-scale potential energy surface calculations and molecular dynamics simulations.
• Provides a unified and efficient approach for treating electron correlation.