Non-empirical mixing coefficient for hybrid XC functionals from analysis of the XC kernel

TL;DR

This paper introduces a non-empirical method to determine the optimal mixing coefficient in hybrid exchange-correlation functionals by analyzing the XC kernel through a decomposition approach and model systems, providing physical insights and practical guidance.

Contribution

It offers a novel analysis framework for selecting mixing coefficients in hybrid functionals based on XC kernel decomposition and model system data, enhancing their physical grounding.

Findings

Provides a physical interpretation of the mixing coefficient's effect.

Offers a non-empirical method for choosing the mixing coefficient.

Applicable to various hybrid functional types, including screened hybrids.

Abstract

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0-1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree-Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the nonempirical choice of the mixing coefficient at ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other type of functionals like screened hybrids.