Reworking the Tao-Mo exchange-correlation functional. I. Reconsideration and simplification.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• The revised, regularized Tao-Mo (rregTM) density functional approximation (DFA) addresses limitations of the original Tao-Mo formulation.
• rregTM demonstrates competitive performance against established meta-generalized-gradient-approximation DFAs (e.g., SCAN, r2SCAN) in thermochemistry and solid-state properties.
• A key challenge identified was the intractability of rregTM for de-orbitalization methods.

Purpose of the Study:

• To investigate the cause of non-physical behavior in rregTM related to the regularization of z indicator functions.
• To propose a modified regularization scheme, simplified, regularized Tao-Mo (sregTM), that resolves these issues.
• To determine the optimal correlation functional to pair with sregTM exchange.

Main Methods:

• Analysis of the regularization in rregTM involving the ratio of von-Weizsäcker and Kohn-Sham kinetic energy densities (z).
• Development and calibration of a simplified regularization approach (sregTM).
• Testing sregTM exchange with Perdew-Burke-Ernzerhof correlation.

Main Results:

• Diagnosis of non-physical behavior in rregTM stemming from its regularization of z indicator functions.
• Introduction of sregTM, a simpler regularization that eliminates oddities and reproduces rregTM's error patterns.
• Demonstration that Perdew-Burke-Ernzerhof correlation is sufficient with sregTM exchange, simplifying the functional.

Conclusions:

• The simplified, regularized Tao-Mo (sregTM) functional offers a viable alternative to rregTM, overcoming its de-orbitalization limitations.
• sregTM maintains high performance comparable to leading DFAs while exhibiting improved behavior.
• The development of sregTM paves the way for progress in de-orbitalization techniques within density functional theory.