# On nearsightedness in metallic systems for $\mathcal{O}(N)$ Density Functional Theory calculations: A case study on Aluminum

## TL;DR

This study examines how electronic interactions in aluminum influence the efficiency of $ ext{O}(N)$) Density Functional Theory calculations, revealing exponential convergence and specific truncation sizes needed for accuracy, enabling scalable simulations of large systems.

## Contribution

It provides a detailed analysis of locality in aluminum's electronic interactions, demonstrating how smearing affects convergence and scaling in $ ext{O}(N)$ DFT calculations.

## Key findings

- Exponential convergence with truncation size
- Truncation of 48-64 Bohr achieves chemical accuracy
- Scaling becomes $ ext{O}(N)$ for systems over 1000 atoms

## Abstract

We investigate the locality of electronic interactions in aluminum as a function of smearing/electronic temperature in the context of $\mathcal{O}(N)$ Density Functional Theory calculations. Specifically, we determine the convergence in energy and atomic forces with truncation region size for smearing of $0.001-0.15$ Ha. We find exponential convergence accompanied by a rate that increases sub-linearly with smearing, with truncation region sizes of $48-64$ Bohr required to achieve chemical accuracy for typical smearing values of $0.001-0.01$ Ha. This translates to $\mathcal{O}(N)$ scaling for systems larger than $\mathcal{O}(1000)$ atoms.