Suppressing the gauge problem in local hybrid functionals without a calibration function: The choice of local mixing...

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Local hybrid functionals (LHs) offer advantages over traditional functionals by balancing self-interaction and static-correlation errors.
• A key challenge for LHs has been the gauge problem, stemming from ambiguities in exchange-energy densities.

Purpose of the Study:

• To investigate a method for reducing gauge problem artifacts in LHs without using calibration functions (CFs).
• To develop and evaluate a new functional that minimizes unphysical contributions by tailoring the local mixing function (LMF).

Main Methods:

• Development of exchange-LMFs (x-LMFs) based on the ratio of exact-exchange (EXX) and semi-local exchange-energy densities.
• Spatial tailoring of the EXX admixture to suppress spurious positive energy-density contributions.
• Comparative analysis of integrated and spatially resolved energy densities with existing functionals.

Main Results:

• The proposed x-LMF approach significantly reduces unphysical contributions from the gauge problem without requiring CFs.
• The resulting LH24x functional demonstrates accuracy comparable to established functionals like LH20t on the GMTKN55 test suite.
• Detailed energy density analyses confirm the effectiveness of the tailored LMF in mitigating gauge artifacts.

Conclusions:

• Tailoring the local mixing function (LMF) is an effective strategy to address the gauge problem in local hybrid functionals.
• The LH24x functional offers a promising alternative, achieving high accuracy without the need for calibration functions.
• The inherent cancellation of unphysical artifacts contributes to the robust performance of LHs for chemical energy differences.