# Pseudo-Fragment Approach for Extended Systems Derived from Linear-Scaling DFT

## TL;DR

This paper introduces a localized basis function approach for linear-scaling density functional theory, enabling efficient and accurate simulations of extended systems with controlled errors, applicable to various dimensionalities.

## Contribution

The method provides a new way to generate optimized localized basis functions for extended systems, reducing computational complexity while maintaining accuracy, and is adaptable to different system geometries.

## Key findings

- Effective reduction of computational degrees of freedom.
- Reliable error estimation for localized approaches.
- Applicable to various system dimensionalities.

## Abstract

We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are optimized either for the accurate description of pristine, bulk like Wannier functions, or for the \emph{in situ} treatment of deformations induced by defective constituents such as boundaries or impurities. Our method enables one to identify the regions of an extended system which require dedicated optimization of the Kohn-Sham degrees of freedom, and provides the user with a reliable estimation of the errors -- if any -- induced by the locality of the approach. Such a method facilitates on the one hand an effective reduction of the computational degrees of freedom needed to simulate systems at the nanoscale, while in turn providing a description that can be straightforwardly put in relation to effective models, like tight binding Hamiltonians. We present our methodology with SiC nanotube-like cages as a test bed. Nonetheless, the wavelet-based method employed in this paper makes possible calculation of systems with different dimensionalities, including slabs and fully periodic systems.