Locality of Interatomic Interactions in Self-Consistent Tight Binding Models

Abstract

A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability condition, we construct such a spatial decomposition for self-consistent tight binding models, extending recent results for linear tight binding models to the nonlinear setting.

Rigorous body-order approximations of an electronic structure potential energy landscape

“…In addition to justifying and supporting the development of new models for general atomic properties, our results establish generic properties of ab initio models that have broader consequences, e.g. for the study of the mechanical properties of atomistic materials [15,17,34,93]. The application of our results to the construction and analysis of practical parameterisations (approximation schemes) that exploit our results will be pursued elsewhere.…”

“…Supposing that v is a function of a self-consistent electronic density, we arrive at a non-linear model such as DFTB [35,61,80]. Abstract variants of these nonlinear models have been analysed, for example, in [32,93]. Through much of this article we will treat r, v as independent inputs into the Hamiltonian, but will discuss their connection and self-consistency in §2.7.…”

“…Through much of this article we will treat r, v as independent inputs into the Hamiltonian, but will discuss their connection and self-consistency in §2.7. For a finite system u, we consider analytic observables of the density of states [14,93]: for functions O : R → R that can be analytically continued into an open neighbourhood of σ H(u) , we consider…”

“…where one assumes that each E is local, i.e., it depends only weakly on atoms far away. In previous works we have made this rigorous for the case of tight-binding models of varying complexity [14,16,17,93]. In practise, one may therefore truncate the interaction by admitting only those atoms r k with r k < r cut as arguments.…”

“…• short-ranged. Following our work on locality of interaction [14,16,17,93] we will focus on a class of tight-binding models as the ab initio reference model. These can be seen either as discrete approximations to density functional theory [40] or alternatively as electronic structure toy models sharing many similarities with the more complex Kohn-Sham DFT and Hartree-Fock models.…”