Self-consistent field method for open-shell systems within the density-matrix functional theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Accurate calculation of electron correlation is crucial for predicting molecular properties.
• Existing methods often face computational challenges in scaling with system size.
• Density-matrix functional theory offers a promising alternative for electronic structure calculations.

Purpose of the Study:

• To extend the unrestricted Hartree-Fock method for correlation energy calculations.
• To develop an efficient and accurate computational approach within density-matrix functional theory.
• To investigate the application of an entropic cumulant functional for correlation.

Main Methods:

• Extension of the unrestricted Hartree-Fock method.
• Derivation of an entropic cumulant functional for correlation energy.
• Modification of spin-orbital eigenvalue equations using orbital occupation numbers.
• Application of the Euler equation yielding a Fermi-Dirac distribution for occupation numbers.

Main Results:

• The developed method efficiently calculates correlation energy.
• Orbital occupation numbers are updated efficiently via the Fermi-Dirac distribution.
• The method was successfully demonstrated on the ground state of Oxygen (O$$).

Conclusions:

• The extended Hartree-Fock method within density-matrix functional theory provides an efficient route to correlation energy.
• The Fermi-Dirac distribution offers a computationally advantageous update for occupation numbers.
• This approach holds potential for accurate electronic structure calculations in various chemical systems.