Ground-to-excited derivative couplings for the density functional based tight-binding method: Semi-local and long-range corrected formulations

TL;DR

This paper derives efficient and accurate non-adiabatic coupling vectors for the DFTB method, applicable to large systems, and compares them favorably with full DFT calculations, including near conical intersections.

Contribution

It introduces an analytical derivation of non-adiabatic couplings for DFTB, valid for semi-local and long-range corrected formulations, improving computational efficiency and accuracy.

Findings

DFTB couplings are close to DFT results in size and direction.

The method is computationally efficient for large systems.

Good agreement with DFT near conical intersections.

Abstract

A derivation of non-adiabatic coupling vectors for the density functional based tight binding method (DFTB) between ground and excited states is presented. The analytical result is valid both for semi-local and long-range corrected DFTB and includes all required Pulay terms. Electron-translation factors lead to a conceptual simplification of the Slater-Koster scheme for precomputed integrals. Compared to scalar couplings obtained from numerical derivatives, the present approach is computationally more efficient and can be applied to systems with hundreds of atoms. The accuracy of DFTB derivative couplings is assessed by comparison to full density functional theory (DFT) calculations using semi-local and hybrid exchange-correlation functionals with promising results. As exemplified by a case study of furan, DFTB provides non-adiabatic coupling vectors that are close to DFT counterparts in size and direction also in the vicinity of conical intersections.