Locality of Interatomic Interactions in Tight Binding Models for Insulators

Poster: locality of interatomic forces in tight binding models

Exponentially localised site-energy decompositions for tight binding models of insulators (joint work with Christoph Ortner and Huajie Chen).
Poster
Conference
Author

Jack Thomas

Published

July 2020

Presented at:

Based on Ortner et al. (2020).

The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed into exponentially localised site energy contributions, thus providing qualitatively sharp estimates on the interatomic interaction range which justifies a range of multi-scale models. For insulators at finite Fermi-temperature we obtain locality estimates that are uniform in the zero-temperature limit. A particular feature of all our results is that they depend only weakly on the point spectrum. Numerical tests confirm our analytical results. This work extends and strengthens Chen and Ortner (2016) and Chen et al. (2018) for finite temperature models.

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References

Chen, Huajie, Jianfeng Lu, and Christoph Ortner. 2018. “Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding.” Archive for Rational Mechanics and Analysis 230 (2): 701–33. https://doi.org/10.1007/s00205-018-1256-y.
Chen, Huajie, and Christoph Ortner. 2016. “QM/MM Methods for Crystalline Defects. Part 1: Locality of the Tight Binding Model.” Multiscale Modeling &Amp; Simulation 14 (1): 232–64. https://doi.org/10.1137/15m1022628.
Ortner, Christoph, Jack Thomas, and Huajie Chen. 2020. “Locality of Interatomic Forces in Tight Binding Models for Insulators.” ESAIM: Mathematical Modelling and Numerical Analysis 54 (6): 2295–318. https://doi.org/10.1051/m2an/2020020.