Non-empirical Mixing Coefficient for Hybrid XC Functionals from Analysis of the XC Kernel

Area of Science:

• Quantum Chemistry
• Materials Science
• Computational Physics

Background:

• Hybrid functionals are crucial in electronic structure theory.
• Accurate selection of the mixing coefficient is vital for predictive power.
• Current methods for choosing the mixing coefficient lack non-empirical approaches.

Purpose of the Study:

• To provide a method for the non-empirical determination of the mixing coefficient in hybrid functionals.
• To gain physical insights into the behavior of hybrid exchange-correlation kernels.
• To offer a generalizable approach applicable to various functionals and conditions.

Main Methods:

• Decomposition of hybrid exchange-correlation (XC) kernels into exchange and correlation components.
• Utilizing Hartree-Fock, PBE, and PBE-based functionals for decomposition.
• Integration with exact data for uniform electron gas and Airy gas models.
• Application of a subsystem functional approach.

Main Results:

• A novel tool for non-empirical selection of the mixing coefficient.
• Physical insights into the impact of mixing coefficient variation.
• Demonstration of the approach's applicability under ambient and extreme conditions.
• Validation of the generalizability to screened hybrid functionals.

Conclusions:

• The presented analysis offers a robust framework for selecting hybrid functional parameters.
• This method enhances the accuracy and reliability of electronic structure calculations.
• The approach provides fundamental understanding and practical utility for computational scientists.