Density‐functional tight binding—an approximate density‐functional theory method

Abstract

In this paper, we review the foundations of the density‐functional tight‐binding (DFTB) method. The method is based on the density‐functional theory as formulated by Hohenberg and Kohn. It introduces several approximations: First, densities and potentials are written as superpositions of atomic densities and potentials. Second, many‐center terms are summarized together with nuclear repulsion energy terms in a way that they can be written as a sum of pairwise repulsive terms. For small distances, the nuclear repulsion dominates, whereas for large distances, these terms vanish. The Kohn–Sham orbitals are expanded in a set of localized atom‐centered functions. They are represented in a minimal basis of optimized atomic orbitals, which are obtained for spherical symmetric spin‐unpolarized neutral atoms self‐consistently. The whole Hamilton and overlap matrices contain one‐ and two‐center contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. In addition, we discuss a self‐consistent charge extension, the treatment of weak interactions, and a linear response scheme in connection with the DFTB method. Finally, some practical aspects are presented. © 2012 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Semiempirical Electronic Structure Methods

Efficient Calculation of Electronic Absorption Spectra by Means of Intensity-Selected Time-Dependent Density Functional Tight Binding

“…As the absorption peaks are scaled with the oscillator strength f I of the excitation, the absorption spectrum is mostly determined by the excitations which have a large oscillator strength. Looking at equation (19) for the transition dipole moment of the excitations, it is easy to see that single orbital transitions with a small transition dipole moment d ia contribute little to the transition dipole moment of the excitation d I , and hence its oscillator strength f I . Consequently it appears to be a reasonable approximation to remove those single orbital transitions from the basis for which the oscillator strength f ia is small.…”

Edge-Corrected Mean-Field Hubbard Model: Principle and Applications in 2D Materials

“…TB method is developing fast in recent decades and widely used in the investigation of large system as reviewed in articles [28][29][30] and books [38,39]. TB method is a parameterized and semi-empirical calculation method which can deal with much larger system with typically two to three orders of magnitude faster than ab initio methods do [29].…”

“…TB method is a parameterized and semi-empirical calculation method which can deal with much larger system with typically two to three orders of magnitude faster than ab initio methods do [29]. TB parameters and codes have been developed by various groups, such as Harrison [40], Papaconstantopoulos with NRL-TB code [28], Bowler with DensEL code [41], and Seifert with DFTB code [30,42]. [41], and Seifert with DFTB code [30,42].…”

“…TB parameters and codes have been developed by various groups, such as Harrison [40], Papaconstantopoulos with NRL-TB code [28], Bowler with DensEL code [41], and Seifert with DFTB code [30,42]. [41], and Seifert with DFTB code [30,42]. The comparison is considered from basis set, applicable system, parameterization of Hamiltonian matrix, electron-electron interaction, and self-consistent charges.…”

“…At the large scale above ∼1,000 atoms, the classical force field of MD is fit for simulations. Tight-binding (TB) approach, although developed earlier than DFT [27], is developing fast in recent decades and widely used in the investigation of system of 100-1,000 atoms as reviewed in articles [28][29][30]. However, under-coordinated modifications at edge, defect and surface sites to conventional TB method are usually neglected in lowdimensional systems or investigated case by case [31,32].…”