# Structural and electronic properties of the incommensurate host-guest Bi-III phase

## TL;DR

This study uses large-scale DFT calculations to model the complex incommensurate Bi-III phase of bismuth, revealing how atomic modulations influence electronic properties and stability, with results aligning well with experimental data.

## Contribution

It introduces a method to accurately model the incommensurate Bi-III phase using commensurate approximants and highlights the importance of large unit-cells for electronic and structural accuracy.

## Key findings

- Large unit-cells are essential for accurate geometric and electronic modeling.
- The equation of state of Bi-III matches experimental results when using a relativistic model.
- Pseudopotential and exchange-correlation choices significantly affect the equation of state.

## Abstract

At high pressure, bismuth acquires a complex incommensurate host-guest structure, only recently discovered. Characterizing the structure and properties of this incommensurate phase from first principles is challenging owing to its non-periodic nature. In this study we use large scale DFT calculations to model commensurate approximants to the Bi-III phase, and in particular to describe the atomic modulations with respect to their ideal positions, shown here to strongly affect the electronic structure of the lattice and its stability. The equation of state and range of stability of Bi-III are reproduced in excellent agreement with experiment using a fully relativistic model. We demonstrate the importance of employing large unit-cells for the accurate description of the geometric and electronic configuration of Bi-III. In contrast, accurate description of the equation of state of bismuth is found to be primarily sensitive to the choice of pseudopotential and exchange-correlation function, while almost completely insensitive to the commensurate approximation.