GaAs Total Energy Tight Binding Hamiltonians for use in Molecular Dynamics

ABSTRACTA self-consistent non-orthogonal semi-empirical tight binding Hamiltonian is proposed for GaAs, or any sp system, which is simple, reliable, transferable, accurate and fast to evaluate. Matrix elements are functions of charges, distances between atoms and simple cosines of angles between s and p-electron densities and interatomic vectors which maintain the simplicity of Slater-Koster parameterizations. The tight binding scheme is fit against a large data base of local density functional derived total energies for systems of differing coordination and geometry. The Hamiltonian fulfills the correct Virial constraint, invokes the physically correct relationship between overlap and kinetic energy matrix elements and defines charges via Mulliken or Löwdin schemes. Such Hamiltonians will allow the reliable simulation of statistical mechanically interesting systems of order hundred or more atoms over physically useful periods of time of order tens to hundreds of thousands of time steps within not unreasonable supercomputer budgets.