Density functional tight binding

Abstract

This paper reviews the basic principles of the density-functional tight-binding (DFTB) method, which is based on density-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of atomic densities and potentials. The Kohn-Sham orbitals are then expanded to a set of localized atom-centred functions, which are obtained for spherical symmetric spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrices contain one-and two-centre contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a selfconsistent representation, where the deviation of the ground-state density from the reference density is represented by charge monopoles only. This leads to a computationally efficient representation in terms of atomic charges (Mulliken), chemical hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no additional adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.

A Comparative Density Functional Theory and Density Functional Tight Binding Study of Phases of Nitrogen Including a High Energy Density Material N8

“…It achieves DFT-like accuracy for systems for which it is well parametrized. Several parameter sets have been benchmarked for DFTB with which DFTB provides ab initio accuracy for several classes of materials, including organic molecules, selected inorganic solids, and interfaces [29][30][31][32][33][34]. While several parameterizations of N-N interactions for DFTB are available, the suitability of these parametrizations for the modeling of nitrogen allotropes has, however, not been established.…”

“…Density Functional Tight Binding (DFTB) is an approximate DFT-based method that is about three orders of magnitude faster compared to DFT. It can be considered as a parametrization/tabulation of the most expensive parts of DFT [26][27][28][29]. It achieves DFT-like accuracy for systems for which it is well parametrized.…”

Kajian Teoritis Kemampuan Capping Katekin, Kateku Tanat Dan Quarsetin Terhadap Nanopartikel Perak Dengan Menggunakan Metoda DFT-B

“…Secara teoritis dalam bidang komputasi, metoda yang cukup sering digunakan untuk mempelajari mekanisme interdifusi adsorbsi adalah metoda DFT-B (Density Functional Tight Binding) [10] . DFT-B adalah metoda semi-empirik yang merupakan penurunan persamaan DFT-GGA, sehingga untuk sistem tertentu metoda ini memiliki akurasi perhitungan yang baik sama halnya dengan metoda DFT itu sendiri [11] . Metoda ini berkembang sangat pesat dan banyak digunakan dalam mempelajari sifat-sifat dari suatu sistem.…”

Interactive Chemical Reactivity Exploration

“…The DFTB method is based on a Taylor expansion of the DFT energy around a reference electronic density [25], which is a superposition of the atomic densities. It neglects second and higher-order terms and its energy reads…”