# TDepES

This page gives hints on how to calculate the temperature dependence of the electronic structure with the ABINIT package.

## Introduction¶

The electronic structure changes with temperature. In most materials, such changes are mainly driven by the electron-phonon interaction, which is also present at zero Kelvin, inducing the so-called zero-point motion renormalization (ZPR) of the eigenvalues. These effects can be computed thanks to the Allen-Heine-Cardona (AHC) theory [Allen1976], [Allen1981], [Allen1983], which is based on diagrammatic method of many-body perturbation theory. An extension to the standard AHC theory also gives access to the electronic lifetime and decay rates. These physical properties are available from ABINIT since v7.10.4.

The AHC formalism and the implemented equations can be found in [Ponce2014a]. An extended verification and validation study (also versus other first-principle codes) of the ABINIT implementation can be found in [Ponce2014]. The AHC implementation can be used with any XC functional working with the response-function (RF) part of the code, and requires the use of norm-conserving pseudopotentials. NetCDF support is mandatory.

The AHC implementation in ABINIT is still under heavy development. Most of the present information relates to the legacy implementation, although some also relates to the most recent procedure that relies on optdriver=7. The documentation of the new procedure is given mostly by the related tutorials. We do not describe the Frohlich model computations.

In the oldest, well-established, AHC implementation in ABINIT, the sum over highly energetic bands appearing in the AHC equations [Gonze2011] is efficiently computed. Such behavior is controlled by the input variable ieig2rf.

The **k** -point convergence can be strongly improved by restoring the charge
neutrality through the reading of the Born effective charge and dielectric
tensor (controlled by the input variable getddb). More information on the
importance of charge neutrality fulfillment can be found in
[Ponce2015]. The value of elph2_imagden sets the imaginary shifts
used to smooth numerical instabilities in the denominator of the sum-over-
states expression.

We have checked that the implementation correctly holds for arbitrarily small elph2_imagden parameters, [Ponce2015]. The input variable smdelta triggers the calculation of the electronic lifetime and the value of the smearing delta function can be specified through esmear.

A double grid can be used to speed-up the calculations with getwfkfine or irdwfkfine. The variable getgam_eig2nkq gives the contribution at Γ so that the Debye-Waller term can be computed. This variable is only relevant for calculations of AHC using the abinit program only. It is nonetheless recommended to use the provided python post-processing script temperature_para.py with its module rf_mods.py in the directory scripts/post_processing/ to allow for more flexibility. The python scripts support multi-threading.

The following steps are required to perform an AHC calculation:

- Perform a response function calculation at
**q**=Γ with electric field perturbation. - Perform phonon calculations and produce the EPC for a large set of wavevectors
**q**, reading the Born effective charge and dielectric tensor with getddb. - Gather and compute the impact of the electron-phonon coupling on the electronic eigenenergies using the temperature_para.py python script.

The outputs of the script are provided in text and NetCDF format to allow for later reading inside ABINIT. This could be used in the future developments of ABINIT to compute temperature-dependent optical properties for example.

For the temperature dependence of the Fermi energy, see topic_ElPhonTransport.

## Related Input Variables¶

*compulsory:*

*basic:*

- bdeigrf BanD for second-order EIGenvalues from Response-Function
- elph2_imagden ELectron-PHonon interaction at 2
^{nd}order: IMAGinary shift of the DENominator

*useful:*

- esmear Eigenvalue SMEARing
- getddb GET the DDB from…
- getgam_eig2nkq GET the GAMma phonon data EIG2NKQ from dataset
- getwfkfine GET the fine grid wavefunctions from _WFK file
- irdwfkfine Integer that governs the ReaDing of the grid _WFK file on the FINE grid

## Selected Input Files¶

*v5:*

*v6:*

- tests/v6/Input/t37.abi
- tests/v6/Input/t40.abi
- tests/v6/Input/t50.abi
- tests/v6/Input/t53.abi
- tests/v6/Input/t57.abi
- tests/v6/Input/t59.abi
- tests/v6/Input/t69.abi

*v7:*

- tests/v7/Input/t50.abi
- tests/v7/Input/t51.abi
- tests/v7/Input/t52.abi
- tests/v7/Input/t53.abi
- tests/v7/Input/t54.abi
- tests/v7/Input/t55.abi
- tests/v7/Input/t57.abi
- tests/v7/Input/t58.abi
- tests/v7/Input/t59.abi

## Tutorials¶

- (Legacy procedure) A tutorial is available at the temperature dependence of the electronic structure:.
- (New procedure) Two tutorials are available at an overview of the EPH code, and Zero-point renormalization of the band gap and temperature-dependent band gaps:.