Effect of overlap on semiempirical potentials derived from tight binding

Abstract

Overlap must explicitly be included when empirical interatomic potentials for use in environments of low symmetry are derived using tight-binding theory. We derive a simplified real-space total-energy expression that takes into account the first and second moments of the density of states including overlap. It uses the extended Huckel theory and Taylor and Pade truncations for the inverse of the overlap matrix. Our approximate expression is tested for an s-band nearest-neighbor model by carrying out nurnerical integrations over exact densities of states for many lattices of different dimensionality and coordination number. Within a two-body simplification the inclusion of overlap leads to a new functional form for use in developing embedded-atom functionals. Quantitative accuracy is improved, however, when the three-body Pade-approximation-derived form is used.

Transferability of Orthogonal and Nonorthogonal Tight-Binding Models for Aluminum Clusters and Nanoparticles

“…Comparing the best TB to NTB parametrizations shows that the TB models are both more accurate and more transferable than the NTB ones. Several theoretical analyses of the effect of including the overlap in TB have appeared in the literature, ,,,− ,− many of which focus on the bulk band structure. We do not attempt another such analysis here, but we do note that, whenever the effect of including overlap has been discussed, there is an implicit assumption or explicit working hypothesis, sometimes based on experience, that including overlap should make the model more realistic.…”

Analytic Environment-Dependent Tight-Binding Bond Integrals: Application toMoSi2

“…This expresses the elements of the Green's function matrix G͑E͒ ͑EI 2 H͒ 21 in a rapidly convergent real-space manner by imposing the physical constraint that at any level of approximation the poles of the intersite Green's function G ij are the same as those of the average on-site Green's function ͑1͞2͒ ͑G ii 1 G jj ͒. Putting [23] E 1 and H 2O within this constrained BOP formalism to three-levels of Lanczos recursion [14], we find that the inverse matrix elements can be written as…”

Valence–Bond Order (VBO): A New Approach to Modeling Reactive Potential Energy Surfaces for Complex Systems, Materials, and Nanoparticles

“…Tight-binding theory − ,,, may be justified − as an approximation to density functional theory, especially by using the noniterative formulation of Harris and Foulkes. − Tight-binding theory has been developed to simulate materials systems directly, − ,,,,,− but it can also be further approximated to motivate analytic potentials. In particular, the closely related functional forms of the quasiatom theory, the Gupta potential, the embedded-atom model (EAM), the modified EAM (MEAM), the second-nearest-neighbor EAM (2NN-EAM), the Finnis-Sinclair scheme, the effective medium theory, and the bond order potential can all be motivated by the second moment approximation to tight binding theory. − These methods are closely related to each other, and they are also closely related to the Tersoff potential and hence to the Brenner and ReaxFF ,− potentials . The relationship of EAM to the Pauling bond order has also been discussed …”

“…In particular, the closely related functional forms of the quasiatom theory, 87 the Gupta potential, 88 the embedded-atom model (EAM), 89 the modified EAM (MEAM), 90 the secondnearest-neighbor EAM (2NN-EAM), 91 the Finnis-Sinclair scheme, 92 the effective medium theory, 93 and the bond order potential 94 can all be motivated by the second moment approximation to tight binding theory. [95][96][97][98][99][100][101][102][103][104][105] These methods are closely related to each other, and they are also closely related to the Tersoff potential 106 and hence to the Brenner 23 and ReaxFF 25,[27][28][29] potentials. 107 The relationship of EAM to the Pauling bond order has also been discussed.…”