mirror of https://github.com/abinit/abinit.git
624 lines
27 KiB
Markdown
624 lines
27 KiB
Markdown
---
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authors: SP, LMac
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---
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# Tutorial EPH Temperature-Dependence (Legacy)
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## Electron-phonon Temperature-DEPendence of the Electronic Structure.
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This tutorial aims to show how to get the following physical properties for periodic solids:
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* The zero-point-motion renormalization (ZPR) of eigenenergies
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* The temperature-dependence of eigenenergies
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* The lifetime/broadening of eigenenergies
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It should take about 1 hour.
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WARNING : This tutorial concerns an outdated procedure of obtaining the temperature-dependence of the electronic structure, as indicated by the "legacy" qualifier.
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For the theory related to temperature-dependent calculations, please read
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the following papers: [[cite:Ponce2015]], [[cite:Ponce2014]] and [[cite:Ponce2014a]].
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There are three ways to compute the temperature dependence with Abinit:
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* **Using Anaddb**: historically the first implementation.
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* **Using a post-processing python scripts**: This route provides more options and is more efficient (i.e., requires less disk space and less memory), but it **requires Netcdf** (both in Abinit and python). The current tutorial focuses on this approach.
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* **Using an interpolation of the perturbed potential**: This new method is covered
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in the [ZPR and T-dependent band structures](/tutorial/eph4zpr) tutorial.
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!!! important
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In order to run the python script you need:
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* python3
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* numpy 1.7.1 or higher
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* netCDF4 and netCDF4 for python
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* scipy 0.12.0 or higher
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This can be done with:
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sudo apt-get install netcdf-bin
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sudo apt-get install python-dev
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pip3 install numpy
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pip3 install scipy
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pip3 install netcdf4
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A list of configuration files for clusters is available in the
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[abiconfig repository](https://github.com/abinit/abiconfig)
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If you have a prebuilt abinit executable, use:
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./abinit -b
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to get the list of libraries/options activated in the build.
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You should see netcdf in the `TRIO flavor` section:
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=== Connectors / Fallbacks ===
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LINALG flavor : netlib
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FFT flavor : goedecker
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HDF5 : yes
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NetCDF : yes
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NetCDF Fortran : yes
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LibXC : yes
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Wannier90 : no
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[TUTORIAL_README]
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Visualisation tools are NOT covered in this tutorial.
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Powerful visualisation procedures have been developed in the Abipy context,
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relying on matplotlib. See the README of [Abipy](https://github.com/abinit/abipy)
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and the [Abipy tutorials](https://github.com/abinit/abitutorials).
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## 1 Calculation of the ZPR of eigenenergies at q=Γ.
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The reference input files for this tutorial are located in
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~/abinit/tests/tutorespfn/Input and the corresponding reference output files
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are in ~/abinit/tests/tutorespfn/Refs.
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The prefix for files is **teph_tdep_legacy**. As usual, we use the shorthand `~/abinit` to indicate
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the root directory where the abinit package has been deployed, but most often
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consider the paths relative to this directory.
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First, examine the [[tests/tutorespfn/Input/teph_tdep_legacy_1.abi]] input file.
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{% dialog tests/tutorespfn/Input/teph_tdep_legacy_1.abi %}
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Note that there are three datasets ([[ndtset]]=3). The first dataset corresponds to a standard
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self-consistent calculation, with an unshifted eight k-point grid,
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producing e.g. the ground-state eigenvalue file teph_tdep_legacy_1o_DS1_EIG.nc ,
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as well as the density file teph_tdep_legacy_1o_DS1_DEN. The latter is read ([[getden]]2=1)
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to initiate the second dataset calculation,
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which is a non-self-consistent run, specifically at the Gamma point only (there is no real recomputation
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with respect to the dataset 1, it only extract a subset of the eight k-point grid).
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This second dataset produces the wavefunction file teph_tdep_legacy_1o_DS2_WFQ, that is read by the third dataset ([[getwfq]]3=2),
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as well as the teph_tdep_legacy_1o_DS1_WFK file from the first dataset ([[getwfk]]3=1).
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The third dataset corresponds to a DFPT phonon calculation ([[rfphon]]3=1)
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with displacement of all atoms ([[rfatpol]]3= 1 2) in all directions ([[rfdir]]3= 1 1 1), which are the default values.
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This induces the creation of the Derivative DataBase file teph_tdep_legacy_1o_DS3_DDB.
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The electron-phonon matrix elements are produced because of [[ieig2rf]]3=5 ,
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this option generating the needed netCDF files teph_tdep_legacy_1o_DS3_EIGR2D.nc and teph_tdep_legacy_1o_DS3_GKK.nc .
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In order to run abinit, we suggest that you create a working directory, why not call it `Work`,
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as subdirectory of ~/abinit/tests/tutorespfn/Input, then
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copy/modify the relevant files. Explicitly:
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cd ~/abinit/tests/tutorespfn/Input
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mkdir Work
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cd Work
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cp ../teph_tdep_legacy*in .
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Finally, issue
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abinit teph_tdep_legacy_1.abi > teph_tdep_legacy_1.log
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The calculation will produce several _EIG.nc, _DDB, EIGR2D.nc and EIGI2D.nc files,
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that contain respectively the eigenvalues (GS or perturbed),
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the second-order derivative of the total energy with respect to
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two atomic displacements, the electron-phonon matrix elements used to compute
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the renormalization of the eigenenergies and the electron-phonon matrix
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elements used to compute the lifetime of the electronic states.
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You can now copy three post-processing python files from
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~/abinit/scripts/.
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Make sure you are in the directory containing the output files produced by the code and issue:
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cp ~/abinit/scripts/post_processing/temperature-dependence/temperature_final.py .
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cp ~/abinit/scripts/post_processing/temperature-dependence/rf_mods.py .
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cp ~/abinit/scripts/post_processing/plot_bs.py .
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in which ~/abinit has been replaced by your own path to the abinit directory.
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<!--
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as well as the python file
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containing the required classes from ~abinit/scripts/post_processing/mrgeignc.py
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into the directory where you did the calculations.
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-->
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You can then simply run the python script with the following command:
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python temperature_final.py
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and enter the information asked by the script, typically the following
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(data contained in ~abinit/tests/tutorespfn/Input/teph_tdep_legacy_1_temperature.in):
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```
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1 # Number of cpus
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2 # Static ZPR computed in the Allen-Heine-Cardona theory
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temperature_1 # Prefix for output files
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0.1 # Value of the smearing parameter for AHC (in eV)
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0.1 # Gaussian broadening for the Eliashberg function and PDOS (in eV)
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0 0.5 # Energy range for the PDOS and Eliashberg calculations (in eV)
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0 1000 50 # min, max temperature and temperature step
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1 # Number of Q-points we have (here we only computed $\Gamma$)
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teph_tdep_legacy_1o_DS3_DDB # Name of the response-funtion (RF) DDB file
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teph_tdep_legacy_1o_DS2_EIG.nc # Eigenvalues at $\mathbf{k+q}$
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teph_tdep_legacy_1o_DS3_EIGR2D.nc # Second-order electron-phonon matrix element
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teph_tdep_legacy_1o_DS3_GKK.nc # Name of the 0 GKK file
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teph_tdep_legacy_1o_DS1_EIG.nc # Name of the unperturbed EIG.nc file with Eigenvalues at $k$
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```
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Alternatively, copy this example file in the Work directory if not yet done, and then run
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python temperature_final.py < teph_tdep_legacy_1_temperature.in
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{% dialog tests/tutorespfn/Input/teph_tdep_legacy_1_temperature.in %}
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!!! warning
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Remember to install the libraries required by the script before running.
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For pip, use:
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pip install netcdf4
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or:
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conda install netcdf4
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if you are using [conda](https://docs.conda.io/en/latest/miniconda.html)
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You should see on the screen an output similar to:
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```shell
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Start on 21/12/2020 at 15h21
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____ ____ _ _
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| _ \| _ \ | |_ ___ _ __ ___ _ __ ___ _ __ __ _| |_ _ _ _ __ ___
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| |_) | |_) |____| __/ _ \ '_ ` _ \| '_ \ / _ \ '__/ _` | __| | | | '__/ _ \
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| __/| __/_____| || __/ | | | | | |_) | __/ | | (_| | |_| |_| | | | __/
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|_| |_| \__\___|_| |_| |_| .__/ \___|_| \__,_|\__|\__,_|_| \___|
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|_| Version 1.5
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This script compute the static/dynamic zero-point motion
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and the temperature dependence of eigenenergies due to electron-phonon interaction.
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The electronic lifetime can also be computed.
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WARNING: The first Q-point MUST be the Gamma point.
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Enter the number of cpu on which you want to multi-thread
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Define the type of calculation you want to perform. Type:
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1 if you want to run a non-adiabatic AHC calculation
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2 if you want to run a static AHC calculation
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3 if you want to run a static AHC calculation without control on active space (not recommended !)
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Note that for 1 & 2 you need _EIGR2D.nc and _GKK.nc files obtained through ABINIT option "ieig2rf 5"
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Enter name of the output file
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Enter value of the smearing parameter for AHC (in eV)
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Enter value of the Gaussian broadening for the Eliashberg function and PDOS (in eV)
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Enter the energy range for the PDOS and Eliashberg calculations (in eV): [e.g. 0 0.5]
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Introduce the min temperature, the max temperature and the temperature steps. e.g. 0 200 50 for (0,50,100,150)
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Enter the number of Q-points you have
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Enter the name of the 0 DDB file
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Enter the name of the 0 eigq file
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Enter the name of the 0 EIGR2D file
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Enter the name of the 0 GKK file
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Enter the name of the unperturbed EIG.nc file at Gamma
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Inside the dynamic_zpm_temp def
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Q-point: 0 with wtq = 1.0 and reduced coord. [0. 0. 0.]
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WARNING: An eigenvalue is negative with value: -2.8630004909173537e-10 ... but proceed with value 0.0
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Now compute active space ...
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Now compute generalized g2F Eliashberg electron-phonon spectral function ...
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End on 21/12/2020 at 15 h 21
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Runtime: 0 seconds (or 0.0 minutes)
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```
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The python code has generated the following files:
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**temperature_1.txt**
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: This text file contains the zero-point motion renormalization (ZPR) at each k-point for each band.
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It also contain the evolution of each band with temperature at k=$\Gamma$.
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At the end of the file, the Fan/DDW contribution is also reported.
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**temperature_1_EP.nc**
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: This netcdf file contains a number for each k-point,
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for each band and each temperature. The real part of this number is the ZPR correction
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and the imaginary part is the lifetime.
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<!--
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**temperature_BRD.txt**
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: This text file contains the lifetime of the electronic states
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at each k-point for each band. It also contains the evolution of each band with temperature at k=$\Gamma$.
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-->
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We can for example visualize the temperature dependence at k=$\Gamma$ of the LUMO bands
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(`Band: 4` section in the **temperature_1.txt** file, that you can examine)
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with the contribution of only q=$\Gamma$.
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As you can see, the LUMO correction goes down with temperature.
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If the calculations were converged, the HOMO eigenenergies correction should go up with temperature.
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In general, the ZPR correction as well as their temperature dependence usually closes the gap
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of semiconductors.
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As usual, checking whether the input parameters give converged values is of course important.
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<!-- OBSOLETE
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### If Abinit is **not** compiled with Netcdf ...
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In this case, we should first use [[help:mrgddb|mrgddb]] to merge the _DDB and _EIGR2D/_EIGI2D
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but since we only have one q-point we do not have to perform this step.
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The static temperature dependence and the G2F can be computed thanks to anaddb
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with the files file teph_tdep_legacy_2.files and the input
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file [[tests/tutorespfn/Input/teph_tdep_legacy_2.abi]].
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The information contained in the files file can be understood by looking at the echo
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if its reading in the standard output:
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```
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Give name for formatted input file:
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- teph_tdep_legacy_2.abi
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Give name for formatted output file:
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- teph_tdep_legacy_2.out
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Give name for input derivative database:
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- teph_tdep_legacy_1o_DS3_DDB
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Give name for output molecular dynamics:
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- dummyo.md
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Give name for input elphon matrix elements (GKK file):
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- teph_tdep_legacy_1o_DS3_EIGR2D
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Give root name for elphon output files:
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- teph_tdep_legacy_1_ana
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Give name for file containing ddk filenames for elphon/transport:
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- dummy.ddk
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```
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{% dialog tests/tutorespfn/Input/teph_tdep_legacy_2.abi %}
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As concern the anaddb input file, note that the electron-phonon analysis is triggered by
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[[anaddb:thmflag]] 3, as well as [[anaddb:telphint]] 1 .
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Launch anaddb by the command
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anaddb teph_tdep_legacy_2.abi
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(where `anaddb` might have to be replaced by the proper location of the anaddb executable).
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The run will generate 3 files:
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**teph_tdep_legacy_2.out_ep_G2F**
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: This g2F spectral function represents the contribution of the phononic modes of energy E
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to the change of electronic eigenenergies according to the equation
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**teph_tdep_legacy_2.out_ep_PDS**
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: This file contains the phonon density of states
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**teph_tdep_legacy_2.out_ep_TBS**
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: This file contains the eigenenergy corrections as well
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as the temperature dependence one.
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You can check that the results are the same as with the python script approach here above.
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END OF OBSOLETE
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-->
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## 2 Converging the calculation with respect to the grid of phonon wavevectors
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Convergence studies with respect to most of the parameters will rely on obvious modifications
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of the input file detailed in the previous section. However, using more than one
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q-point phonon wavevector needs a non-trivial generalisation of this procedure.
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This is because each q-point needs to be treated in a different dataset in the current version of ABINIT.
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<!--
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From now on we will only describe the approach with Abinit **compiled with Netcdf support**.
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The approach with Anaddb is similar to what we described in the previous sections.
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Note, however, that Anaddb only supports integration with homogenous q-point grids.
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-->
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The code can perform the q-wavevector integration either with random q-points or
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homogenous Monkhorst-Pack meshes.
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Both grids have been used in the Ref. [[cite:Ponce2014]], see e.g. Fig. 3 of this paper.
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For the random integration method you
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should create a script that generates random q-points, perform the Abinit
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calculations at these points, gather the results and analyze them.
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The temperature_final.py script will detect that you used random
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integration thanks to the weight of the q-point stored in the _EIGR2D.nc file
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and perform the integration accordingly.
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The random integration converges slowly but in a smooth manner.
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However, since this method is a little bit less user-friendly than the one based on homogeneous grids,
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we will focus on this homogenous integration.
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In this case, the user must specify in the ABINIT input file the homogeneous q-point grid,
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using input variables like
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[[ngqpt]], [[qptopt]], [[shiftq]], [[nshiftq]], ..., i.e. variables whose names
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are similar to those used to specify the k-point grid (for electrons).
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There are several difficulties here.
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First, since we focus on the k=$\Gamma$ point, we expect to be able to use symmetries to decrease the computational
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load, as $\Gamma$ is invariant under all symmetry operations of the crystal. The symmetry operations of the crystal will be used
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to decrease the number of q-wavevectors, but they cannot be used as well to decrease the k-point grid during the corresponding
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self-consistent phonon computation.
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How this different behaviour of k-grids and q-grids can be handled by ABINIT ?
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By convention, in such case, with [[nsym]]=1 the k-point grid will be generated in the Full Brillouin zone,
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without use of symmetries, while the q-point grid with [[qptopt]]=1 with be generated in the irreducible Brillouin Zone,
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despite [[nsym]]=1. In order to generate q-point grids that are not folded in the irreducible Brillouin Zone, one need to use another value of [[qptopt]].
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In particular [[qptopt]]=3 has to be used to generate q points in the full Brillouin zone.
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Second, the number of ABINIT datasets is expected to be given in the input file, by the user,
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but not determined on-the-flight by ABINIT. Still, this number of datasets is determined by the number of q points.
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Thus, the user will have to compute it before being able to launch the real q-point calculations, since it determines [[ndtset]].
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How to determine the number of irreducible q points ?
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Well, the easiest procedure is to compute it for an equivalent k-point grid, by a quick run.
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An example will clarify this.
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Suppose that one is looking for the number of q-points corresponding to
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ngqpt 4 4 4
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qptopt 1
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nshiftq 1
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shiftq 0.0 0.0 0.0
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One make a quick ABINIT run with [[tests/tutorespfn/Input/teph_tdep_legacy_2.abi]].
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Note that several input variables have been changed with respect to [[tests/tutorespfn/Input/teph_tdep_legacy_1.abi]]:
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ndtset 1
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nstep 0
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prtebands 0
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ngkpt 4 4 4
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nshiftk 1
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shiftk 0.0 0.0 0.0
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nsym 0
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In this example, the new values of [[ndtset]] and [[nstep]], and the definition of [[prtebands]]
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allow a fast run ([[nline]]==0 might be specified as well,
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or even, the run might be interrupted after a few seconds, since the number of k points is very quickly available).
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Then, the k-point grid is
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specified thanks to [[ngkpt]], [[nshiftk]], [[shiftk]], replacing the corresponding input variables for the q-point
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grid. The use of symmetries has been reenabled thanks to [[nsym]]=0.
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To run it, issue:
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abinit teph_tdep_legacy_2.abi
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Now, the number of points can be seen in the output file :
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```
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nkpt 8
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```
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the list of these eight k-points being given in
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```
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kpt 0.00000000E+00 0.00000000E+00 0.00000000E+00
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2.50000000E-01 0.00000000E+00 0.00000000E+00
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5.00000000E-01 0.00000000E+00 0.00000000E+00
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2.50000000E-01 2.50000000E-01 0.00000000E+00
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5.00000000E-01 2.50000000E-01 0.00000000E+00
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-2.50000000E-01 2.50000000E-01 0.00000000E+00
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5.00000000E-01 5.00000000E-01 0.00000000E+00
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-2.50000000E-01 5.00000000E-01 2.50000000E-01
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```
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We are now ready to launch the determination of the
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_EIG.nc, _DDB, EIGR2D.nc and EIGI2D.nc files, with 8 q-points.
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As for the $\Gamma$ calculation of the previous section, we will rely on three
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datasets for each q-point. This permits a well-structured set of calculations,
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although there is some redundancy. Indeed, the first of these datasets will correspond
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to an unperturbed ground-state calculation identical for all q. It is done very quickly because
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the converged wavefunctions are already available. The second dataset will correspond to
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a non-self-consistent ground-state calculation at k+q (it is also quick thanks to previously available wavefunctions),
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and the third dataset will correspond to the DFPT calculations at k+q (this is the CPU intensive part) .
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So, compared to the first run in this tutorial, we have to replace
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ndtset 3 by ndtset 24 udtset 8 3
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in the input file [[tests/tutorespfn/Input/teph_tdep_legacy_3.abi]], and adjusted accordingly all input variables that were dataset-dependent.
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{% dialog tests/tutorespfn/Input/teph_tdep_legacy_3.abi %}
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Please, refer to the
|
|
[[help:abinit#35-defining-a-double-loop-dataset|explanation of the usage of a double-loop of datasets]]
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|
if you are confused about the meaning of [[udtset]], and the usage of the corresponding metacharacters.
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We have indeed also introduced
|
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|
iqpt:? 1
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iqpt+? 1
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that translates into
|
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|
iqpt11 1
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|
iqpt12 1
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|
iqpt13 1
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|
iqpt21 2
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iqpt22 2
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|
iqpt23 2
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|
iqpt31 3
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...
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allowing to perform calculations for three datasets at each q-point.
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Then issue:
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abinit teph_tdep_legacy_3.abi
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|
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This is a significantly longer ABINIT run (still less than two minutes), also producing many files.
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|
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When the run is finished, copy the file [[tests/tutorespfn/Input/teph_tdep_legacy_3_temperature.in]] in the
|
|
working directory (if not yet done) and launch the python script with:
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./temperature_final.py < teph_tdep_legacy_3_temperature.in
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|
|
|
{% dialog tests/tutorespfn/Input/teph_tdep_legacy_3_temperature.in %}
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|
|
|
Examination of the same HOMO and LUMO bands at k=$\Gamma$ for a 4x4x4 q-point grid gives a very different result
|
|
than previously.
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The zero-point renormalization (ZPR) is the change of the bandgap at 0 K and was (band 5 - band 4):
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|
-0.012507 - 0.017727 = -0.030234 eV
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and is now:
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|
-0.351528 - 0.095900 = -0.447428 eV
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|
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|
This means that the bandgap was closing by 30 meV at 0 K and is now closing by 447 meV at 0 K.
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For comparison, the converged direct bandgap ZPR of diamond is 438.6 meV from Ref. [[cite:Ponce2015]].
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|
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|
As a matter of fact, diamond requires an extremely dense q-point grid (40x40x40) to be converged.
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On the bright side, each q-point calculation is independent and thus the parallel scaling is ideal.
|
|
Running separate jobs for different q-points is quite easy thanks to the dtset approach.
|
|
|
|
## 3 Calculation of the eigenenergy corrections along high-symmetry lines
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|
|
|
The calculation of the electronic eigenvalue correction due to electron-phonon
|
|
coupling along high-symmetry lines requires the use of 6 datasets per q-point.
|
|
Moreover, the choice of an arbitrary k-wavevector breaks all symmetries of the crystal.
|
|
Different datasets are required to compute the following quantites:
|
|
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|
$\Psi^{(0)}_{kHom}$ : The ground-state wavefunctions on the Homogeneous k-point sampling.
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|
$\Psi^{(0)}_{kBS}$ : The ground-state wavefunctions computed along the bandstructure k-point sampling.
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|
$\Psi^{(0)}_{kHom+q}$ : The ground-state wavefunctions on the shifted Homogeneous k+q-point sampling.
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|
$n^{(1)}$ : The perturbed density integrated over the homogeneous k+q grid.
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|
$\Psi^{(0)}_{kBS+q}$ : The ground-state wavefunctions obtained from reading the perturbed density of the previous dataset.
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|
|
|
Reading the previous quantity we obtain the el-ph matrix elements along the bandstructure with all physical
|
|
quantities integrated over a homogeneous grid.
|
|
|
|
We will use the [[tests/tutorespfn/Input/teph_tdep_legacy_4.abi]] input file
|
|
|
|
{% dialog tests/tutorespfn/Input/teph_tdep_legacy_4.abi %}
|
|
|
|
Note the use of the usual input variables to define a path in the Brillouin Zone to build an electronic band structure:
|
|
[[kptbounds]], [[kptopt]], and [[ndivsm]]. Note also that we have defined [[qptopt]]=3. The number of q-points
|
|
is thus very easy to determine, as being the product of [[ngqpt]] values times [[nshiftq]]. Here a very rough 2*2*2 grid has been chosen,
|
|
even less dense than the one for section 2.
|
|
|
|
Then issue:
|
|
|
|
abinit teph_tdep_legacy_4.abi
|
|
|
|
This is a significantly longer ABINIT run (5-10 minutes), also producing many files.
|
|
|
|
|
|
then use [[tests/tutorespfn/Input/teph_tdep_legacy_4_temperature.in]] for the python script.
|
|
|
|
{% dialog tests/tutorespfn/Input/teph_tdep_legacy_4_temperature.in %}
|
|
|
|
with the usual syntax:
|
|
|
|
./temperature_final.py < teph_tdep_legacy_4_temperature.in
|
|
|
|
<!-- THIS SECTION DOES NOT SEEM CORRECT : there is no other k point computed in section 2 ...
|
|
Of course, the high symmetry points computed in section 2 have the same value here.
|
|
It is a good idea to check it by running the script with the file teph_tdep_legacy_3bis.files.
|
|
|
|
-->
|
|
|
|
You can now copy the plotting script (Plot-EP-BS) python file from
|
|
~abinit/scripts/post_processing/plot_bs.py into the directory where you did all the calculations.
|
|
Now run the script:
|
|
|
|
./plot_bs.py
|
|
|
|
with the following input data:
|
|
|
|
```
|
|
temperature_4_EP.nc
|
|
L \Gamma X W K L W X K \Gamma
|
|
-20 30
|
|
0
|
|
```
|
|
|
|
or more directly
|
|
|
|
./plot_bs.py < teph_tdep_legacy_4_plot_bs.abi
|
|
|
|
This should give the following bandstructure
|
|
|
|
|
|
|
|
where the solid black lines are the traditional electronic bandstructure, the
|
|
dashed lines are the electronic eigenenergies with electron-phonon
|
|
renormalization at a defined temperature (here 0K). Finally the area around
|
|
the dashed line is the lifetime of the electronic eigenstates.
|
|
|
|
Notice all the spikes in the electron-phonon case. This
|
|
is because we did a completely under-converged calculation
|
|
with respect to the q-point sampling.
|
|
|
|
It is possible to converge the calculations using [[ecut]]=30 Ha, a [[ngkpt]]
|
|
grid of 6x6x6 and an increasing [[ngqpt]] grid to get converged results:
|
|
|
|
| Convergence study ZPR and inverse lifetime(1/τ) [eV] at 0K |
|
|
| q-grid | Nb qpt | Γ25' | Γ15 | Min Γ-X |
|
|
| | in IBZ | ZPR | 1/τ | ZPR | 1/τ | ZPR | 1/τ |
|
|
| 4x4x4 | 8 | 0.1175 | 0.0701 | -0.3178 | 0.1916 | -0.1570 | 0.0250 |
|
|
| 10x10x10 | 47 | 0.1390 | 0.0580 | -0.3288 | 0.1847 | -0.1605 | 0.0308 |
|
|
| 20x20x20 | 256 | 0.1446 | 0.0574 | -0.2691 | 0.1823 | -0.1592 | 0.0298 |
|
|
| 26x26x26 | 511 | 0.1448 | 0.0573 | -0.2736 | 0.1823 | -0.1592 | 0.0297 |
|
|
| 34x34x34 | 1059 | 0.1446 | 0.0573 | -0.2699 | 0.1821 | -0.1591 | 0.0297 |
|
|
| 43x43x43 | 2024 | 0.1447 | 0.0572 | -0.2650 | 0.1821 | -0.1592 | 0.0297 |
|
|
|
|
As you can see the limiting factor for the convergence study is the
|
|
convergence of the LUMO band at $\Gamma$. This band is not the lowest in energy (the
|
|
lowest is on the line between $\Gamma$ and X) and therefore this band is rather
|
|
unstable. This can also be seen by the fact that it has a large electronic
|
|
broadening, meaning that this state will decay quickly into another state.
|
|
|
|
Using the relatively dense q-grid of 43x43x43 we can obtain the following
|
|
converged bandstructure, at a high temperature (1900K):
|
|
|
|
|
|
|
|
Here we show the renormalization at a very high temperature of 1900K in order
|
|
to highlight more the broadening and renormalization that occurs. If you want
|
|
accurate values of the ZPR at 0K you can look at the table above.
|
|
|
|
|
|
!!! Important
|
|
|
|
If you use an extremely fine q-point grid, the acoustic phonon frequencies for
|
|
q-points close to $\Gamma$ will be wrongly determined by Abinit. Indeed in order to
|
|
have correct phonon frequencies close to $\Gamma$, one has to impose the acousting sum rule
|
|
with anaddb and [[asr@anaddb]].
|
|
However, this feature is not available in the python script. Instead, the script reject the
|
|
contribution of the acoustic phonon close to $\Gamma$ if their phonon frequency is
|
|
lower than 1E-6 Ha. Otherwise one gets unphysically large contribution.
|
|
|
|
One can tune this parameter by editing the variable "tol6 = 1E-6" in the beginning of the script.
|
|
|
|
For example, for the last 43x43x43 calculation, it was set to 1E-4.
|
|
|
|
!!! important
|
|
|
|
It is possible to speed up the convergence with respect to increasing q-point density by noticing
|
|
that the renormalization behaves analytically with increasing q-point grid and smaller broadening.
|
|
|
|
It is therefore possible to extrapolate the results. Different analytical behavior extists depending
|
|
if the material is polar and if the state we are considering is a band extrema or not.
|
|
More information can be found in Ref. [[cite:Ponce2015]]
|
|
|