Accurate and efficient linear scaling DFT calculations with universal applicability

TL;DR

This paper presents a new linear scaling DFT method within BigDFT that achieves high accuracy and broad applicability for large systems, overcoming previous limitations of accuracy and parameter tuning.

Contribution

The authors develop a linear scaling DFT approach using Daubechies wavelets that maintains high accuracy and universality without extensive parameter fine-tuning.

Findings

Achieves high accuracy comparable to traditional DFT methods

Enables simulations of large systems with moderate computational resources

Demonstrates broad applicability across different system types

Abstract

Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources.