# Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

## TL;DR

This paper introduces an  ab initio Langevin dynamics method based on stochastic density functional theory with an embedded saturated fragment formalism, enabling scalable simulations of large covalently bonded nanostructures like silicon nanocrystals.

## Contribution

It develops a linear-scaling, stochastic DFT-based Langevin dynamics approach applicable to large covalent systems using an embedded fragment formalism.

## Key findings

- Successfully simulated silicon nanocrystals up to 3 nm in diameter.
- Generated canonical configurations across a range of temperatures.
- Analyzed surface structure and geometry reconstruction of nanocrystals.

## Abstract

An \emph{ab initio} Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new \emph{embedded saturated } \emph{fragment }formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation\textendash dissipation relation. The overall approach scales linearly with system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to $3$nm corresponding to $N_{e}=3000$ electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.