LOW-ORDER MOMENT EXPANSIONS TO TIGHT-BINDING FOR INTERATOMIC POTENTIALS - SUCCESSES AND FAILURES

We discuss the use of moment-based approximations to tight binding. Us ing a maximum entropy form for the electronic density of states, we sh ow that a general interatomic potential can be defined that is suitabl e for molecular-dynamics simulations and has several other desirable f eatures. For covalent materials (C and Si), properties where the atoms are in equivalent environments are well converged at low-order moment s. For defect environments, which offer a more critical (and relevant) test, the method is found to give less satisfactory results. For exam ple, the vacancy formation energy for Si is too low by similar to 2 eV at 10 moments relative to exact tight binding. Attempts to improve th e accuracy were unsuccessful, leading to the conclusion that potential s based on this approach are inadequate for covalent materials. We spe culate that this may be a deficiency of low-order moment methods in ge neral. For metals, in contrast to the covalent systems, we find that t he low-order moment approach is better behaved. This finding is consis tent with the success of existing empirical fourth-moment potentials f or metals.