Point defects in tight binding models for insulators

Abstract

We consider atomistic geometry relaxation in the context of linear tight binding models for point defects. A limiting model as Fermi-temperature is sent to zero is formulated, and an exponential rate of convergence for the nuclei configuration is established. We also formulate the thermodynamic limit model at zero Fermi-temperature, extending the results of [H. Chen, J. Lu and C. Ortner, Thermodynamic limit of crystal defects with finite temperature tight binding, Arch. Ration. Mech. Anal. 230 (2018) 701–733]. We discuss the non-trivial relationship between taking zero temperature and thermodynamic limits in the finite Fermi-temperature models.

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

“…Recall from § 2.1.3 (see in particular Fig. 2) that this gives rise to a discrete spectrum, which "pollutes" the band gap [72]. Thus, the spectral gap is reduced and a naive application of Theorem 2.3 leads to a reduction in the convergence rate of the body-ordered approximation.…”

“…The choice of potential in (TB) defines a hierarchy of tight binding models. If v = const, (TB) defines a linear tight binding model, a simple yet common model [14,16,17,72]. In this case, we implicitly assume that the Coulomb interactions have been screened, a typical assumption made in practice for a wide variety of materials [20,70,73,74].…”

“…where (λ s , ψ s ) are normalised eigenpairs of H(u). Many properties of the system, including the particle number functional and Helmholtz free energy, may be written in this form [14,16,72,93]. By distributing these quantities amongst atomic positions, we obtain a well-known spatial decomposition [14,16,37,40],…”

“…The total grand potential is defined as G β (u) [14,72]. For β < ∞, the functions F β ( • ) and G β ( • ) are analytic in a strip of width πβ −1 about the real axis [17,Lemma 5.1].…”

QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned Interatomic Potentials

“…We consider the site potential to be a collection of mappings V : (R d ) Λ− → R, which represent the energy distributed to each atomic site. We make the following assumptions on the regularity and locality of the site potentials, which has been justified for some basic quantum mechanic models [7,9,11,34]. We refer to [8, §2.3 and §4] for discussions of more general site potentials.…”