A Python code for calculating the mean-value (Baldereschi's) point for any crystal structure

TL;DR

This paper introduces a Python tool for calculating the mean-value point in the Brillouin zone for any crystal structure, enabling efficient approximation of reciprocal space integrals with minimal accuracy loss.

Contribution

The paper presents a versatile Python code that computes the mean-value point for any crystal structure, expanding the applicability of Baldereschi's method.

Findings

MVP coordinates are provided for 14 Bravais lattices.

The code simplifies Brillouin zone integral approximations.

Theoretical discussion supports the method's validity.

Abstract

A python code (mvp.py) is presented for computing the mean-value point (MVP) in the Brillouin zone first introduced by Baldereschi [1]. The code allows calculations of the MVP for any input crystal structure. Having MVP allows approximating the Brillouin zone integrals of relatively smooth, periodic functions defined in the reciprocal space by the value of the same function at only one, mean-value, k-point. This approximation decreases computational cost at a relatively small decrease in accuracy. The MVP coordinates for the 14 Bravais lattices are evaluated and the underlying theory is discussed.