Band Structure from the Reduced Density-Matrix Functional Theory: Application to Si and Diamond

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Materials Science

Background:

• Accurate calculation of electronic band structure is crucial for understanding material properties.
• Traditional density functional theory (DFT) methods face challenges in accurately describing band gaps.
• Reduced density-matrix functional theory offers an alternative approach to electronic structure calculations.

Purpose of the Study:

• To develop and apply a reduced density-matrix functional theory incorporating an entropic functional for correlation.
• To investigate the mathematical structure of the resulting band structure and its relation to the Fermi-Dirac distribution.
• To demonstrate the method's capability in calculating band gaps for semiconductors like silicon and diamond.

Main Methods:

• Utilized reduced density-matrix functional theory with a novel entropic functional for electron correlation.
• Employed the Fermi-Dirac distribution to describe electron occupation numbers in bands.
• Approximated exchange energy using the X_α model for calculations on silicon and diamond.

Main Results:

• The developed theory yields a simple mathematical structure for band structures, directly following the Fermi-Dirac distribution.
• The method successfully accommodates a band gap based on the occupation numbers of the lowest conduction and highest valence bands.
• Calculations for silicon and diamond demonstrate the practical applicability and accuracy of the approach.

Conclusions:

• The reduced density-matrix functional theory with an entropic correlation functional provides a robust framework for electronic band structure calculations.
• The method's adherence to the Fermi-Dirac distribution simplifies the understanding and prediction of band gaps.
• This approach offers a promising avenue for accurate material property predictions in condensed matter physics and chemistry.