Electron-phonon potential from supercells

The computation of the electron-phonon potential, $\partial_{\nu \mathbf{q}} V(\mathbf{r})$, is a prerequisite for the calculation of the electron-phonon matrix element:

$g_{mn \mathbf{k}, \nu \mathbf{q}} \equiv \langle \psi_{m \mathbf{k} + \mathbf{q}} | \partial_{\nu \mathbf{q}} V | \psi_{n \mathbf{k}} \rangle .$

In the direct interpolation approach, $\partial_{\nu \mathbf{q}} V$ is computed from a supercell calculation by means of Fourier interpolation while the Bloch orbitals, $\psi_{n \mathbf{k}}(\mathbf{r})$, are computed directly in the primitive cell. Naturally, this process involves multiple VASP calculations in different cells, which can introduce additional complexities compared to just a single execution of VASP. This page tries to give a high-level overview of the general workflow associated with electron-phonon calculations using the direct interpolation approach.

Finite displacements in the supercell

The electron-phonon potential is computed from finite atomic displacements in a sufficiently large supercell. In this case, sufficient means that the effects of an atomic displacement become negligible at about half the supercell size. Usually, converging the phonon frequencies is a good way of finding a supercell that is sufficiently large. Polar materials can exhibit long-range electrostatic interactions that go beyond reasonable supercell sizes. In this case, a correction scheme exists that explicitly treats the long-range dipole interactions and works with smaller cells. More information can be found on the theory page.

Currently, two ways exist to calculate the electron-phonon potential. One relies solely on VASP, while the other uses VASP in combination with the phelel python package. Both approaches calculate the derivative of the Kohn-Sham potential in real space via the displacement of atoms. However, they may differ in terms of flexibility and computational performance. Below, we describe the general workflow of each approach and highlight their advantages and disadvantages.

Regardless of which approach is chosen, the output is then written to the phelel_params.hdf5 binary file. This file can then be read during a VASP calculation in the primitive unit cell to compute electron-phonon interactions. The entire workflow of initializing a calculation, computing the electron-phonon potential in the supercell and performing subsequent electron-phonon calculations in the primitive cell can be facilitated by the velph command-line tool. It helps guide you through the process step by step and ensures a certain level of consistency between the required VASP calculations.

VASP internal driver

This way of calculating the electron-phonon potential utilizes the VASP-internal finite-difference driver that is activated by setting IBRION = 6 in the INCAR file. The atomic displacement directions are automatically determined by VASP. As usual, POTIM and NFREE can be used to control the displacement amount and finite-difference stencil, respectively.