Abstract
ABSTRACT The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare or functionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.
Highlights
Since the demonstration by Hohenberg and Kohn[1] of the theoretical grounding of the Density Functional Theory (DFT)[2–4], stating that the energy of any electronic system is a universal functional of the density ρ and the proposal of the Kohn-Sham scheme[5] to find the density, DFT has proved ubiquitous in the theoretical description of electronic system properties of atoms, molecules and condensed matter[6,7]
Prior to describe the principles of the Density Functional based Tight Binding (DFTB) method in details, we provide in this subsection a brief general framework for Tight Binding theories
Other approaches rely on the exploration of the complex potential energy surface (PES) with either Monte Carlo (MC) or Molecular Dynamics (MD) simulations, which are combined with regular local optimization of the visited geometries as done for ammonium/water clusters [163]
Summary
Since the demonstration by Hohenberg and Kohn[1] of the theoretical grounding of the Density Functional Theory (DFT)[2–4], stating that the energy of any electronic system is a universal functional of the density ρ and the proposal of the Kohn-Sham scheme[5] to find the density, DFT has proved ubiquitous in the theoretical description of electronic system properties of atoms, molecules and condensed matter[6,7]. The main theoretical handicap of DFT is that the exchange-correlation functional remains unknown This brings various drawbacks in many applications of DFT such as the self-interaction error (SIE)[4,9–13], and consequent inherent failures like improper description of the charge localization in extended compounds, ill-behaved dissociation or an incorrect energy derivative with the number of electrons. The second one, more recent and efficient, tends to be theoretically derived in a top-down approximation scheme, from well established mean-field theories, formerly Hartree-Fock and DFT. It is in this last scheme that the Density Functional based Tight Binding (DFTB) formalism[18–20] has been developed over the two-three decades, described in a number of review [20,36,227?
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