Range separated functionals in the density functional based tight binding method: Formalism

TL;DR

This paper extends the density-functional based tight-binding method to include range-separated exchange-correlation functionals using the GKS formalism, enhancing the theoretical framework and implementation details.

Contribution

It introduces a generalized GKS-based DFTB approach with range-separated functionals, expanding the method's applicability and providing detailed derivations and implementation insights.

Findings

Derivation of GKS-TB equations for range-separated functionals

Discussion of integral approximations and implementation issues

Enhanced theoretical framework for DFTB with range-separated exchange

Abstract

A generalization of the density-functional based tight-binding method (DFTB) for the use with range-separated exchange-correlation functionals is presented. It is based on the Generalized Kohn-Sham (GKS) formalism and employs the density matrix as basic variable in the expansion of the energy functional, in contrast to the traditional DFTB scheme. The GKS-TB equations are derived and appropriate integral approximations are discussed in detail. Implementation issues and numerical aspects of the new scheme are also covered.