The tight-binding bond model

Abstract

The authors present a tight-binding model of cohesion and interatomic forces which exploits the variational principle of density functional theory. The binding energy of a solid is expressed as a sum of four terms, each of which has a clear physical meaning. The first two terms are the covalent bond and promotion energies, which are found by solving the electronic Hamiltonian to obtain the density matrix. The remaining two terms describe changes in the total electrostatic and exchange-correlation energies on forming the solid from isolated atoms. The variational principle allows these two terms to be expressed as functionals of a superposition of frozen atomic charge densities. The authors show that they may then be approximated by a sum of pair potentials. The importance of self-consistency in tight-binding models is discussed with particular attention to the evaluation of the bulk modulus and certain interatomic force constants by frozen-phonon calculations. It is shown that serious errors may arise in non-self-consistent models due to the violation of charge conservation and the neglect of variations in the potential caused by charge flow. The authors advocate local charge neutrality as the simplest approximation to self-consistency which overcomes these problems. This assumption leads to a remarkably simple expression for the force on an atom due to its neighbours, which is both physically transparent and computationally efficient. These concepts are illustrated for three-dimensional solids by calculations of covalent bond energies in BCC, FCC and HCP transition metals using a canonical d-band model. Model one-dimensional calculations are also presented which illustrate the computation of covalent bond energies and interatomic forces at surfaces and interfaces, and the importance of local charge neutrality in the model.