Lecture notes on TightBinding Molecular Dynamics,.pdf

Lecture notes on Tight-Binding Molecular Dynamics, and Tight-Binding justification of classical potentials Furio Ercolessi Dipartimento di Fisica, Universit`a di Udine email: furio.ercolessi@fisica.uniud.it 7 February 2005 (minor revision 18 October 2007) Introduction The purpose of these notes is: 1. to illustrate the main aspects of the tight-binding (TB) method; 2. to sketch how TB molecular dynamics is done in practice; 3. to show how TB supplies ideas useful for the construction of empirical potentials. In TB approaches one works within the one-electron, self-consistent field approximation (Kohn-Sham equations in the density functional theory frame- work). There are several kinds of TB models, differing in the kind of approxima- tions made to the full density functional total energy expression. The common denominator is the use of a minimal basis of local orbitals. I will not consider the more accurate approaches, which definitely fall in the class of first-principle methods, and focus the attention on the more approximate approaches—which are of course those that allow molecular dynamics calculations with large num- ber of particles. It should also be noted that TB treatments in elementary solid state books are focused on perfect crystals, and usually show how the band structure arises within this scheme when applied to situations with translational symmetry (in- troducing the k vector, constructing Bloch functions, etc.). I will not follow this road here, as we are mainly interested in applying this formalism to molecular dynamics calculations for systems that do not present in general any particular symmetry. We will therefore focus on a real space description, and ignore the aspects related with band theory. So, no k vector appears in these notes. These note