Topic

# Tight binding

About: Tight binding is a research topic. Over the lifetime, 5340 publications have been published within this topic receiving 141059 citations. The topic is also known as: Tight-binding〔TB〕approximation.

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TL;DR: In this paper, the structure of the electronic energy bands and Brillouin zones for graphite was developed using the "tight binding" approximation, and it was found that graphite is a semi-conductor with zero activation energy, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled.

Abstract: The structure of the electronic energy bands and Brillouin zones for graphite is developed using the "tight binding" approximation. Graphite is found to be a semi-conductor with zero activation energy, i.e., there are no free electrons at zero temperature, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled. The electrical conductivity is treated with assumptions about the mean free path. It is found to be about 100 times as great parallel to as across crystal planes. A large and anisotropic diamagnetic susceptibility is predicted for the conduction electrons; this is greatest for fields across the layers. The volume optical absorption is accounted for.

4,395 citations

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TL;DR: In this paper, the LCAO interpolation method was used as an interpolation technique in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods.

Abstract: The LCAO, or Bloch, or tight binding, approximation for solids is discussed as an interpolation method, to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants, so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made, and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given, including tables of matrix components of energy for simple cubic, face-centered and body-centered cubic, and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni, and Howarth on Cu, as illustrations of the fcc case. In discussing the bcc case, the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out, as well as a distribution of energy states for the case of no antiferromagnetism. For diamond, comparisons are made with the calculations of Herman, using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed, and it is shown that their properties fit in with the energy band picture.

3,696 citations

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TL;DR: In this paper, an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability is presented. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations.

Abstract: We outline details about an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations. The zeroth order approach is equivalent to a common standard non-self-consistent (TB) scheme, while at second order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual ``band structure'' and short-range repulsive terms the final approximate Kohn-Sham energy additionally includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approximately includes self-interaction contributions of a given atom if the charges are located at one and the same atom. We apply the new SCC scheme to problems where deficiencies within the non-SCC standard TB approach become obvious. We thus considerably improve transferability.

3,448 citations

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TL;DR: In this paper, a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid is presented, which is suitable for use in connection with conventional electronic-structure codes.

Abstract: We discuss a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ''generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread Sigma(n)(r(2))(n) - (r)(n)(2) of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k points, and carries out the minimization in a space of unitary matrices U-mn((k)) describing the rotation among the Bloch bands at each k point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.

3,155 citations

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NEC

^{1}TL;DR: It is predicted that carbon microtubules exhibit striking variations in electronic transport, from metallic to semiconducting with narrow and moderate band gaps, depending on the diameter of the tubule and on the degree of helical arrangement of the carbon hexagons.

Abstract: On the basis of realistic tight-binding band-structure calculations, we predict that carbon microtubules exhibit striking variations in electronic transport, from metallic to semiconducting with narrow and moderate band gaps, depending on the diameter of the tubule and on the degree of helical arrangement of the carbon hexagons. The origin of this drastic variation in the band structure is explained in terms of the two-dimensional band structure of graphite.

2,954 citations