Where does tight binding go from here?

Abstract

Density functional tight binding (TB) has been successfully applied to a wide range of materials and problems. Here is asked the question: What is the next step for TB theory? One suggestion for a way forward is proposed that makes extensive use of gaussian expansions to ensure all integrals are analytic.1 Introduction In this special edition we celebrate the many contributions Thomas Frauenheim has made to the simulation of materials. Here I want to pick up on his huge contribution to the application of tight binding (TB); he has used it to study a wide spectrum of materials, ranging from carbon [1] to lanthanides [2], using methods for open boundaries [3] and excited states [4] as well as standard total energy calculations. A key contributor to this success was the innovative approach he took (together with Seifert and coworkers) to building TB models, namely density functional based TB (DFTB) [5]. The use of density functional theory (DFT) to build many of the integrals removed at a stroke much of the problem of fitting parameters, and speed was maintained by keeping a minimal basis set, throwing away a number of integrals, and using look-up tables for the remaining integrals. Accuracy is restored by adding a pair potential fitted to binding energy curves. DFT also provided the theoretical framework within which to derive the corrections from spin polarization and charge transfer [5]. Given the success of DFTB, a natural question to ask is: is this the final word in TB, or are new developments called for? The purpose of this paper is to argue that there are situations in which it is desirable to extend DFTB, and one particular way forward is described.To put the project in context it is useful to remind ourselves of the characteristics of TB. The key one is that molecular orbitals are expanded in atomic type orbitals (usually minimal in number), which allows the single particle Hamiltonian to be written as a matrix. The matrix

Modeling warm dense matter formation within tight binding approximation

“…However, we must keep in mind that the TB parameters are not fitted to reproduce high-lying states within CB, and their quality there diminishes. It is also possible to create TB parameterizations based not on LCAO orbitals, but on other kinds of localized basis functions, such as Gaussian functions 48 . That would also allow for a systematic extension of the basis sets.…”

“…It is also possible to create TB parameterizations based not on LCAO orbitals, but on other kinds of localized basis functions, such as Gaussian functions 48 . That would also allow for a systematic extension of the basis sets.…”

Efficient simulations with electronic open boundaries

“…We can now define the Hamiltonian and overlap matrices by H αα = α Ĥ α and S αα = α | α , respectively. Note that the Hamiltonian includes all the terms associated with self-consistent charge redistribution [8,19]. We partition these orbitals between the system (|β ) and the probes (|pγ p ), where p is the index of the probe and γ p indexes an orbital in probe p.…”

Systematic development of ab initio tight-binding models for hexagonal metals

“…Tight-binding (TB) models lie on the boundary between DFT and empirical potentials. They include an explicit representation of electronic structure, and therefore bond formation, but are calculated in a more approximate (and therefore faster) way than in DFT [9][10][11][12][13][14][15][16][17]. The use of a minimal basis set of atomic orbitals means TB models are not an obvious choice for free-electron-like metals.…”