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Tight-Binding Theory and Computational Materials Synthesis

Published online by Cambridge University Press:  29 November 2013

A.P. Sutton ,
P.D. Godwin  and
A.P. Horsfield
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Extract

At the heart of any atomistic simulation is a description of the atomic interactions. A whole hierarchy of models of atomic interactions has been developed over the last twenty years or so, ranging from ab initio density-functional techniques, to simple empirical potentials such as the embedded-atom method and Finnis-Sinclair potentials in metals, valence force fields in covalently bonded materials, and the somewhat older shell model in ionic systems. Between the ab initio formulations and empirical potentials lies the tight-binding approximation: It involves the solution of equations that take into account the electronic structure of the system, but at a small fraction of the cost of an ab initio simulation, because those equations contain simplifying approximations and parameters that are usually fitted empirically.

Tight binding may be characterized as the simplest formulation of atomic interactions that incorporates the quantum-mechanical nature of bonding. The particular features that it captures are as follows: (1) the strength of a bond being dependent not only on the interatomic separation but also on the angles it forms with respect to other bonds, which arises fundamentally from the spatially directed characters of p and d atomic orbitals, (2) the filling of bonding (and possibly antibonding) states with electrons, which controls the bond strengths, and (3) changes in the energy distribution of bonding and antibonding states as a result of atomic displacements. These features enable one to obtain considerable improvements in accuracy compared to the simple “glue models” of bonding since use is made of the physics and chemistry of bonding.

Type
Interatomic Potentials for Atomistic Simulations
Information
MRS Bulletin , Volume 21 , Issue 2 , February 1996 , pp. 42 - 48
Copyright
Copyright © Materials Research Society 1996

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