The tight-binding bond model

Chemical bonding variations and electron-phonon interactions

A new functional, Psib(Phi), of an electronic state in solids based on the bonding indicator B(tau,tau') in terms of Mulliken's electron partitioning approach has been introduced. Using Psib(Phi), the bonding variations of an electronic state caused by electron-phonon coupling can be studied. With this proposed approach, the differences between the "flat band" states for Hg in coupling to the phonons and the peaklike structure of electron-phonon coupling constants in the q space are well explained.

Analytic environment-dependent tight-binding bond integrals: application to MoSi2

We present the first derivation of explicit analytic expressions for the environmental dependence of the sigma, pi, and delta bond integrals within the orthogonal two-center tight-binding approximation by using the recently developed bond-order potential theory to invert the nonorthogonality matrix. We illustrate the power of this new formalism by showing that it not only captures the transferability of the bond integrals between elemental bcc Mo and Si and binary C11(b) MoSi2 but also predicts the absence of any discontinuity between first and second nearest neighbors for the ddsigma bond integral even though large discontinuities exist for ppsigma, pppi, and ddpi.

Stability of carbon nanotubes: how small can they be?

Experimental evidence has been found for the existence of small single wall carbon nanotubes with diameters of 0.5 and 0.33 nm by high resolution transmission electron microscopy, and their mechanical stability was investigated using tight-binding molecular dynamics simulations. It is shown that, while the carbon tubes with diameters smaller than 0.4 nm are energetically less favorable than a graphene sheet, some of them are indeed mechanically stable at temperatures as high as 1100 degrees C. The 0.33 nm carbon tube observed is likely a (4, 0) tube and is indeed part of a compound nanotube system that forms perhaps the smallest metal-semiconductor-metal tubular junction yet synthesized.

STRUCTURAL DIVERSITY IN SOLID STATE CHEMISTRY:A Story of Squares and Triangles

▪ Abstract  A simple method for calculating the electronic energy of extended solids is discussed in this review. This method is based on the Hückel or tight-binding theory in which an explicit pairwise repulsion is added to the generally attractive forces of the partially filled valence electron bands. An expansion based on the power moments of the electronic density of states is discussed, and the structural energy difference theorem is reviewed. The repulsive energy is found to vary linearly with the second power moment of the electronic density of states. These results are then used to show why there is such a diversity of structure in the solid state. The elemental structures of the main group are rationalized by the above methods. It is the third and fourth power moments (which correspond in part to triangles and squares of bonded atoms) that account for much of the elemental structures of the main group elements of the periodic table. This serves as an introduction to further rationalizations of transition for noble metal alloy, binary and ternary telluride and selenide, and other intermetallic structures.Thus a cohesive picture of both covalent and metallic bonding is presented in this review, illustrating the importance of atomic orbitals and their overlap integrals.