# Introduction

Welcome to **PyEPFD** - A Python library for computing Electron-Phonon
renormalizations from Finite Displacements (EPFD).

## Aims

PyEPFD provides a set of tools to compute electronic properties, such as fundamental gap, at a finite temperature where nuclear quantum effects are incorporated using harmonic approximation. For that purpose, an additional ab-initio code is required that computes the ab-initio forces and electronic properties such as eigenenergies of the bands. PyEPFD also provides tools to analyze the validity of the harmonic approximation if a Molecular Dynamics and/or Monte Carlo trajectories are available. Currently, for the ab-initio part, PyEPFD depends on Qbox code (http://qboxcode.org/). However, it is very easy to use pyEPFD with any ab-inito code of your choice.

## Features:

PyEPFD can perform the following tasks:

(1) Compute normal-modes, dynamical matrix (mass-weighted Hessian matrix) using Cartesian Displacements.

(2) Compute normal-modes, dynamical matrix (mass-weighted Hessian matrix) using normal-mode Displacements.

(3) Compute phonon-renormalized electronic properties using a frozen-phonon approach. [1]

(4) Perform stochastic displacements (e.g. thermal line sampling, Zacharias-Giustino’s special displacement, etc.) on normal-modes [1-4] to compute thermally averaged properties at 0 K (including zero-point quantum fluctuations) or any finite temperature.

(5) If Molecular Dynamics or Monte Carlo trajectories (positions and/or forces) are available, vibrational densities along normal modes (see section S6 of ref. 5 for an example) or anharmonic measure [6] can be computed to understand the impact of anharmonicity.

## Citation

Hope, you will find PyEPFD helpful for your research. If you have used PyEPFD for obtaining exciting results that you cannot wait to see published, please acknowledge us by citing the follwoing papers:

(1) Kundu, A.; Govoni, M.; Yang, H.; Ceriotti, M.; Gygi, F.; Galli, G.
Quantum vibronic effects on the electronic properties of solid and
molecular carbon.
*Phys. Rev. Materials* **2021**, *5*, L070801
[Link].
(arXiv:2104.11065).

(2) Kundu, A.; Galli, G.
Quantum vibronic effects on the electronic properties of molecular
crystals. *J. Chem. Theory Comput.* **2023**, *19(13)*, 4011.
[Link]
(arXiv:2304.13687.)

## References

[1] Monserrat, B. Electron-phonon coupling from finite differences.
*J. Phys: Condens, Matter* **2018**, *30*, 083001.

[2] Monserrat, B. Vibrational averages along thermal lines.
*Phys. Rev. B* **2016**, *93*, 014302.

[3] Zacharias, M.; Patrick, C. E; Giustino, F.
Stochastic approach to phonon-assisted optical absorption.
*Phys. Rev. Lett.* **2015**, *115*, 177401.

[4] Zacharias, M.; Giustino, F.
One-shot calculation of temperature-dependent optical spectra
and phonon-induced band-gap renormalization.
*Phys. Rev. B* **2016**, *94*, 075125

[5] Kundu, A.; Govoni, M.; Yang, H.; Ceriotti, M.; Gygi, F.; Galli, G.
Quantum vibronic effects on the electronic properties of solid and
molecular carbon.
*Phys. Rev. Materials* **2021**, *5*, L070801.

[6] Knoop, F.; Purcell, T. A. R.; Scheffler, M., Carbogno, C.
Anharmonicity measure for materials **2020**, *4*, 083809.