A new multi-center approach to the exchange-correlation interactions in ab initio tight-binding methods

TL;DR

This paper introduces a new multi-center approach for calculating exchange-correlation interactions in ab initio tight-binding methods, improving accuracy and efficiency for complex systems.

Contribution

It develops a generalized scheme for exchange-correlation matrix elements using a correction approach, enhancing tight-binding molecular dynamics calculations.

Findings

Accurately computed bulk properties of metals and oxides.

Demonstrated flexibility across different material types.

Achieved computational efficiency with good accuracy.

Abstract

A new approximate method to calculate exchange-correlation contributions in the framework of first-principles tight-binding molecular dynamics methods has been developed. In the proposed scheme on-site (off-site) exchange-correlation matrix elements are expressed as a one-center (two-center) term plus a {\it correction} due to the rest of the atoms. The one-center (two-center) term is evaluated directly, while the {\it correction} is calculated using a variation of the Sankey-Niklewski \cite{Sankey89} approach generalized for arbitrary atomic-like basis sets. The proposed scheme for exchange-correlation part permits the accurate and computationally efficient calculation of corresponding tight-binding matrices and atomic forces for complex systems. We calculate bulk properties of selected transition (W,Pd), noble (Au) or simple (Al) metals, a semiconductor (Si) and the transition metal oxide Ti$O_2$ with the new method to demonstrate its flexibility and good accuracy.