Five different published semi-empirical total-energy methods, which were applicable to atomistic simulations of extended defects in body-centered cubic transition metals, were compared with theoretical ab initio (local density functional theory) and experimental  (high-resolution transmission electron microscopy) studies; for the specific case of the Σ = 5, (310)[001] symmetrical tilt grain boundaries in Nb and Mo. The semi-empirical real-space approaches which were considered were based upon various approximations to the tight-binding and related methods. These were the Finnis-Sinclair central-force potentials, non central-force bond-order potentials of Pettifor et al., and non central-force potentials which were based upon the Moriarty generalized pseudopotential theory. A very simple d-basis tight-binding model (Paxton), and an elaborate environment-dependent spd-basis orthogonal tight-binding model (Haas et al.), were included in the analysis as semi-empirical reciprocal-space methods. The advantages and disadvantages of these models, with regard to their ability to predict the translation states and interfacial energies of the Σ = 5, (310)[001] symmetrical tilt grain boundaries, were considered.

Symmetrical Tilt Grain Boundaries in BCC Transition Metals - Comparison of Semiempirical with ab initio Total-Energy Calculations. T.Ochs, C.Elsässer, M.Mrovec, V.Vitek, J.Belak, J.A.Moriarty: Philosophical Magazine A, 2000, 80[10], 2405-23