# Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System

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## Abstract

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## 1. Introduction

## 2. Methodology

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Two pairs of distinct structures (

**a**–

**d**), where we can find central atoms (shown as cubes) that are in virtually identical short range chemical environments, with fingerprint distances of $\mathsf{\Delta}F{P}_{OM}\approx {10}^{-2}$. Due to long range effects, the atomic charges and atomic energies are, however, quite different. The atoms in the first and second row are coloured according to their atomic charges and energies respectively. $\mathsf{\Delta}E=0.11$ Ha and $\mathsf{\Delta}Q=0.08$ electrons for the pair in the left column and $\mathsf{\Delta}E=0.21$ Ha and $\mathsf{\Delta}Q=0.12$ electrons for the pair in the right column.

**Figure 2.**The correlation plot between OM and SOAP fingerprint distances among atomic environments and the differences in atomic charge (Equation (2)), atomic energy (Equation (3)), and the atom projected DOS (Equation (4)) of the central atoms of these environments. The colour coding indicates the density of correlation pairs. Within our chosen resolution, there are about 200,000 points on the x-axis, which corresponds to about 0.001 percent of the total number of points.

**Figure 3.**The correlation between fingerprint distances and the atomic charge differences calculated in PBE0 and HF. The color coding indicates the density of correlation pairs.

**Figure 4.**(

**Left**): The correlation between OM and CSOM fingerprints. (

**Right**): The correlation between distances calculated with the charge-sensitive OM fingerprint (CSOM) and the atomic energy differences.

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**MDPI and ACS Style**

Parsaeifard, B.; De, D.S.; Finkler, J.A.; Goedecker, S. Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System. *Condens. Matter* **2021**, *6*, 9.
https://doi.org/10.3390/condmat6010009

**AMA Style**

Parsaeifard B, De DS, Finkler JA, Goedecker S. Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System. *Condensed Matter*. 2021; 6(1):9.
https://doi.org/10.3390/condmat6010009

**Chicago/Turabian Style**

Parsaeifard, Behnam, Deb Sankar De, Jonas A. Finkler, and Stefan Goedecker. 2021. "Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System" *Condensed Matter* 6, no. 1: 9.
https://doi.org/10.3390/condmat6010009