mirror of https://github.com/abinit/abinit.git
544 lines
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Markdown
544 lines
23 KiB
Markdown
---
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authors: XG, JWZ
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---
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# Second tutorial on DFPT:
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## Phonon band structures, thermodynamical properties.
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In this tutorial you will learn how to post-process the raw data of the Abinit DFPT calculations to
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get the following physical properties of periodic solids:
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* Interatomic forces constants
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* Phonon band structures
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* Thermodynamical properties
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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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This tutorial should take about 1 hour.
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WARNING : This tutorial has been updated by removing the use of the ANADDB input variable [[brav]] in
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trf2_4.abi, trf2_5.abi, and trf2_7.abi, with the accompanying modifications in the text of the tutorial.
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Also, due to the change of default values for [[rfdir]] and [[rfatpol]] in ABINITv9.8 with respect to the prior versions of ABINIT,
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the example input files from this tutorial will not work with such prior versions of ABINIT.
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Please, use ABINITv9.8 or more recent versions of ABINIT, or adjust the values of [[rfdir]] and [[rfatpol]].
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See point A.3 of the [v9.8 release notes](/about/release-notes/#98).
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[TUTORIAL_README]
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## 0 Generation of necessary input wavefunctions
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*Before beginning, you might consider working in a different subdirectory as
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for the other tutorials, in order to help keep track of all the files.
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Why not create Work_rf2 in \$ABI_TESTS/tutorespfn/Input?*
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As the DFPT equations at higher order always start from input wavefunctions
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obtained at lower order, we begin by generating the ground state wavefunctions
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and DDK wavefunctions for our system, AlAs. The ground state wavefunctions are needed
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for the phonon and electric field perturbations, and the electric field perturbation
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needs the DDK wavefunctions as well, as explained in the [first tutorial on DFPT](/tutorial/rf1).
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Copy file *trf2_1.abi* from \$ABI_TESTS/tutorespfn/Input* to *Work_rf2*:
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```sh
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cd $ABI_TESTS/tutorespfn/Input;
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mkdir Work_rf2;
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cd Work_rf2;
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cp ../trf2_1.abi
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```
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Execute this file with
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abinit trf2_1.abi >& log &
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Let us have a look at the input file *trf2_1.abi*.
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{% dialog tests/tutorespfn/Input/trf2_1.abi %}
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This input file consists of two datasets--the first generates the
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ground state wavefunctions, with tight convergence: these are output
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in the file *trf2_1o_DS1_WFK*. The second dataset uses these
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wavefunctions to generate the DDK wavefunctions, which are output in
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the files *trf2_1o_DS2_1WF7*, *trf2_1o_DS2_1WF8*, and
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*trf2_1o_DS2_1WF9*. Depending on the details of your build, these
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files might be appended with *.nc*, if they are produced in `netcdf`
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format.
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A note on the naming convention--the DDK files here are named 1WF7,
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1WF8, and 1WF9. The "1" signifies a first-order wavefunction. Then,
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ABINIT numbers each perturbation, such that the phonons are numbered
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1...3N, for an N atom system. Here N = 2 for AlAs. The DDK
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perturbations are numbered 3N+1, 3N+2, and 3N+3, for the three
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cartesian directions, giving in this case 7, 8, and 9.
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## 1 Generation of a derivative database
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With the necessary input wavefunctions generated, we are ready to compute the derivative
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database.
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Copy the file *trf2_2.abi* from \$ABI_TESTS/tutorespfn/Input* into your working directory:
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```sh
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cp ../trf2_2.abi .
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```
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Before you run it, you will have to name the input wavefunctions that you prepared in step 0
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appropriately, so ABINIT can find them.
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Examine the input file you are about to run:
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{% dialog tests/tutorespfn/Input/trf2_2.abi %}
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Notice the lines `ndtset 8`, `getddk 98`, and `getwfk 99`. Since we
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will be looping over multiple datasets (8, in fact), in order to
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compute multiple perturbations in a single file, we use multi dataset
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mode. But this requires that any file read in be given dataset
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numbers in the same format. We avoid low numbers because those are
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the new datasets we are about to run; it is thus convenient to relabel
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the ground state and DDK wavefunctions with the dataset labels 99 and
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98. Thus you can rename with
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```sh
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mv trf2_1o_DS1_WFK trf2_2o_DS99_WFK;
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mv trf2_1o_DS2_1WF7 trf2_2o_DS98_1WF7;
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mv trf2_1o_DS2_1WF8 trf2_2o_DS98_1WF8;
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mv trf2_1o_DS2_1WF9 trf2_2o_DS98_1WF9
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```
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Append each new file with ".nc" if the original files were ".nc" files.
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Now you can execute the file with
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abinit trf2_2.abi >& log &
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It takes about 1-2 minutes to be completed on a PC 2.8 GHz.
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In order to do interatomic force constant (IFC) calculations, and to
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compute associated phonon band structure and thermodynamical
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properties, you should first have some theoretical background. Let us
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assume that you have read the literature relative to the [first
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tutorial on DFPT](/tutorial/rf1). You might find additional material,
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related to the present section, in [[cite:Gonze1997a]] -especially
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section IX-, [[cite:Lee1995]] and [[cite:Baroni2001]]. If you haven't
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read parts of these references, we strongly advise you to take the time
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to read them now.
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In short, the idea is that, in order to compute properties for which
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the phonon frequencies are needed in the full Brillouin zone, one can
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use an elaborate Fourier interpolation, so that only few dynamical
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matrices need to be computed directly. Others will be computed by
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interpolation. A schematic representation of the different steps
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required to compute the dynamical matrix in the IBZ and post-process
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the results with anaddb is given below.
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The calculation is done for AlAs, the same crystalline material as for
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the first tutorial on DFPT. Many input parameters are also quite
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similar, both at the level of the description of the unit cell and for
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the choice of cut-off energy and k point grid. The input file
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`trf2_2.abi` consists of a loop over a small set of phonons, and all other
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phonons will be determined later by interpolation. Moreover, the electric
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field perturbation is also a long wavelength, hence Gamma phonon perturbation,
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and can be computed at the same time. Thus our first dataset in
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`trf2_2.abi` is the Gamma phonon and the electric field both, and the other
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datasets are the additional nonzero q point phonons we wish to consider explicitly.
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The values of the phonon q wavevectors are not determined arbitrarily.
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They must correspond to the q wavevectors needed by the ANADDB utility (see later),
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that is, they should form a reduced set of symmetry-inequivalent wavevectors,
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corresponding to a regularly spaced grid. In principle, they need not include
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the Gamma point, but it is **recommended** to have it in the set, in order for the
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Fourier interpolation not to introduce errors at that important point.
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!!! tip
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In order to minimize the number of preliminary non-self-consistent calculations,
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it is advised to take a q point mesh that is adjusted to the k point mesh used
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for the electronic structure: all q wavevectors should connect two k point
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wavevectors from this grid.
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Such a set of q wavevectors can be generated conveniently, and
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automatically, in the input file, using [[qptopt]], [[ngqpt]],
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[[nshiftq]], and [[shiftq]], quite analogously to what can be done
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with the k point grid. Look again at the file `trf2_2.abi` and note that
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[[ngqpt]] 4 4 4 is used, mirroring [[ngkpt]], but with [[nshiftq]] 1 and
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[[shiftq]] 0 0 0 to produce an unshifted set, which will include the Gamma point.
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!!! tip
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Never forget to use [[nqpt]] 1, whenever [[qpt]] is being input, either
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directly or implicitly. If [[nqpt]] is absent in the input file, it defaults to zero
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which leads to [[qpt]] being ignored.
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This approach is conveniently combined with [[ndtset]] and [[iqpt]] to
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step automatically through the generated q points, as is done in our
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file with [[ndtset]] 8 and [[iqpt]]: 1 [[iqpt]]+ 1. This raises the
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question, though, of how one would know in advance that there will be
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8 q points in the current set. For this one can use
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[abitk](/guide/abitk), a convenient tool built along with ABINIT and
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used to examine output files in `netcdf` format. Run it on our
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original ground state file as:
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abitk ibz trf2_1o_DS1_GSR.nc --ngkpt 4 4 4 --shiftk 0 0 0
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and you should obtain a list of the k points (equivalently q points) generated with a
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`4 4 4` unshifted mesh, for the current input structure. There are 8 of them, and the
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set includes the Gamma point, as desired.
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At this point, it might be worth examining in some detail one of the Derivative
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Databases that has been created by the trf2_2 run.
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We suppose that the file *trf2_2o_DS1_DDB* has already been created.
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It corresponds to the first dataset, namely the response to q = 0 and electric field.
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Open this file, and read the [[help:respfn#ddb|6.5 section]] of the respfn help file.
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Examine the *trf2_2o_DS1_DDB* file carefully.
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Seven other similar files will be generated by the trf2_2 run, containing the
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same header, but a different 2DTE block. It will be the job of the MRGDDB
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utility (described in the next section) to gather all these files and merge them into a single DDB file.
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## 2 Manipulation of the derivative databases (the MRGDDB utility)
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The use of the MRGDDB utility is described in its [[help:mrgddb|help file]], which
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you should read carefully now.
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Use MRGDDB to create the merged DDB from the eight DDB's corresponding to
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the datasets of the trf2_2 job, which contain the dynamical matrices for the
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8 q points, as well as the response to the electric field (dielectric tensor
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and Born effective charges). Name the new DDB *trf2_3.ddb.abo*.
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File *\$ABI_TESTS/tutorespfn/Input/trf2_3.abi* is an example of input file for MRGDDB.
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{% dialog tests/tutorespfn/Input/trf2_3.abi %}
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You can copy it in the *Work_rf2* directory, noting that if your DDB
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files were produced in `netcdf` format, you will need to include
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properly the `.nc` suffixes in the file names listed in trf2_3.abi.
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Then run the merge as follows:
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mrgddb < trf2_3.abi
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Note the chevron in the call: MRGDDB reads from standard input by
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default, so you can make it read instead from a file using the `<`
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operator.
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## 3 Analysis of the derivative databases
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An introduction to the use of the ANADDB utility is described in its
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[[help:anaddb|help file]]. Please, read it carefully.
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This ANADDB utility is able to perform many different tasks, each
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governed by a selected set of input variables, with also some input
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variables common to many of the different tasks. The list of tasks to
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be done in one run is governed by different flags. Here is the list
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of the commonly used flags:
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* [[anaddb:dieflag]]
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* [[anaddb:elaflag]]
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* [[anaddb:elphflag]]
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* [[anaddb:ifcflag]]
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* [[anaddb:instrflag]]
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* [[anaddb:nlflag]]
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* [[anaddb:piezoflag]]
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* [[anaddb:polflag]]
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* [[anaddb:thmflag]]
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Please, take some time to read the description of each of these flags.
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Note that some of these flags might be required to allow to run another task.
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In this tutorial, we will focus on the flags [[anaddb:ifcflag]] and [[anaddb:thmflag]].
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## 4 The computation of interatomic force constants
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You can copy the file *trf2_4.abi* from *\$ABI_TESTS/tutorespfn/Input* to the *Work_rf2* directory.
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Examine the file *trf2_4.abi*. Note that [[anaddb:ifcflag]] is activated. It also specifies
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the input ddb file, and output file naming ([[anaddb:ddb_filepath]], [[anaddb:output_file]], and
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[[anaddb:outdata_prefix]]).
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{% dialog tests/tutorespfn/Input/trf2_4.abi %}
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Related input variables can be split in three groups.
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The first group of variables define the grid of q wavevectors:
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* [[anaddb:brav]]
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* [[anaddb:ngqpt]]
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* [[anaddb:nqshft]]
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* [[anaddb:q1shft]]
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Unfortunately, the names of input variables and their meaning are not
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exactly the same as the names used to generate the k and q points in
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ABINIT. This is a shame, a remnant of history. Please read carefully
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the documentation that describes these input variables.
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The second group of variables allows to impose the acoustic sum rule on the
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dynamical matrices and the charge neutrality on Born effective charges before proceeding with the analysis:
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* [[anaddb:asr]]
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* [[anaddb:chneut]]
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Please, read carefully the explanation for these input variables.
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Finally, a third group of variables is related specifically to the analysis of the IFC:
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* [[anaddb:dipdip]]
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* [[anaddb:ifcana]]
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* [[anaddb:ifcout]]
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* [[anaddb:natifc]]
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* [[anaddb:atifc]]
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Here also, spend some time to read the associated documentation.
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Now, you should issue:
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anaddb trf2_4.abi > trf2_4.abi.log
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It will last only a few seconds.
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The file *trf2_4.abo* contains the list of interatomic force constants, as well as some analysis.
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{% dialog tests/tutorespfn/Refs/trf2_4.abo %}
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Open this file and find the following paragraph:
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Analysis of interatomic force constants
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Are given : column(1-3), the total force constant
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then column(4-6), the Ewald part
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then column(7-9), the short-range part
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Column 1, 4 and 7 are related to the displacement
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of the generic atom along x,
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column 2, 5 and 8 are related to the displacement
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of the generic atom along y,
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column 3, 6 and 9 are related to the displacement
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of the generic atom along z.
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The interatomic force constants are output for the nuclei specified by the
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input variable [[anaddb:atifc]]. Here, only atom 1 is considered. The IFCs
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with respect to the other nuclei is given, by order of increasing distance.
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For each pair of nuclei involving atom 1, there is first the output of the
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IFCs in cartesian coordinates, as well as their decomposition into an Ewald
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and a short-range part, then, the analysis with respect to a local system of
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coordinate. The latter is chosen such that it diagonalizes the IFC tensor, in
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case of the self-force constant, and in the other cases, the first vector is
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the vector joining the two nuclei, in order to decompose the IFC into a
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longitudinal and a transverse component.
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## 5 Computation of phonon band structures with efficient interpolation
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You can copy the file trf2_5.abi from $ABI_TESTS/tutorespfn/Input to the Work_rf2 directory.
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Then open *trf2_5.abi*.
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{% dialog tests/tutorespfn/Input/trf2_5.abi %}
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Note that [[anaddb:ifcflag]] is again activated.
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Indeed, in order to compute a phonon band structure using the Fourier
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interpolation, the IFCs are required. This is why the two first groups of
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variables, needed to generate the IFCs are still defined. The third group of
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variables is now restricted to [[anaddb:dipdip]] only.
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Then, come the input variables needed to define the list of q wavevectors in the band structure:
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* [[anaddb:eivec]]: flag to turn on the analysis of phonon eigenvectors
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* [[anaddb:nqpath]]: number of q-points defining the band structure path
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* [[anaddb:qpath]]: list of q-points defining the band structure path
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* [[anaddb:ndivsm]]: number of divisions in the shortest band structure path segment
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* [[anaddb:nph2l]]: number of q-directions for LO-TO correction
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* [[anaddb:qph2l]]: list of q-directions for LO-TO correction
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Now, you should issue:
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anaddb trf2_5.abi > trf2_5.log
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It will last only a few seconds. The variables [[anaddb:nqpath]],
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[[anaddb:qpath]], and [[anaddb:ndivsm]] have analogous counterparts in
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electronic band structure calculations, see the [3rd basic
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tutorial](/tutorial/base3).
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The file *trf2_5.abo* contains the list of eigenvalues, for all the needed
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q-wavevectors. You can open it, and have a look at the different sections of
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the file. Note that the interatomic force constants are computed (they are
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needed for the Fourier interpolation), but not printed.
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{% dialog tests/tutorespfn/Refs/trf2_5.abo %}
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Please, open also the other output file, named *trf2_5o_B2EPS.freq*.
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It contains the frequencies, in a format suitable for graphical output, using the program
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*band2eps* (the latter should be more documented, and will not be described in the present tutorial).
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You can copy the files *trf2_6.abi*, *trf2_6.files* and *trf2_6.in_freq* to the *Work_rf2* directory. Note that band2eps uses the old format using the files file. Then, issue
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band2eps < trf2_6.files > trf2_6.log
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{% dialog tests/tutorespfn/Input/trf2_6.files tests/tutorespfn/Input/trf2_6.abi %}
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The file *trf2_6.abo.eps* has been produced. It is an .eps file (eps stand for
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Encapsulated PostScript). You can use the program ghostview to visualize it.
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The command to issue will depend on the way you have configured your machine,
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but the following might perhaps do the work:
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gv trf2_6.abo.eps
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You should see a nice phonon band structure for AlAs. Well, not so nice, after
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all, because there are two strange dips for the highest phonon band, at the Gamma point.
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This is due to the lack of LO-TO splitting for the ANADDB treatment of the first list of vector.
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The correct phonon band structure is:
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You can correct the LO-TO splitting by the following little hack.
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Open the file *trf2_5o_B2EPS.freq*, and note that the value of the frequency, in
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the sixth column, has a discontinuity exactly for the Gamma point (the three
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first columns give the k point coordinates), that is, at lines 1 and 31:
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0.0000000000E+00 0.0000000000E+00 0.0000000000E+00 0.1568561346E-02 0.1568561346E-02 0.1568561346E-02
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Replace these values (sixth column, line 1 and 31) by the correct value,
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including the LO-TO splitting, that you can find in the file *trf2_5.abo*, at
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the end, second list of vector. That is, the lines 1 and 31 should now read:
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0.000000E+00 0.000000E+00 0.000000E+00 1.568561E-03 1.568561E-03 1.730570E-03
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Now, run *band2eps* again. Your phonon band structure should be perfect!
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It can be compared with the AlAs phonon band structure published in [[cite:Giannozzi1991]].
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Of course, one should make a convergence study, on the k and q point grids
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(separately!), as well as on the energy cut-off, and also test LDA and GGA...
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But this is left to the user! You can have a look at the paper [[cite:Petretto2018]]
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for a careful analysis of phonon dispersion convergence with Abinit.
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### Plotting phonon bands with AbiPy
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If |AbiPy| is installed on your machine, you can use the |abiopen| script
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with the `--expose` option to visualize the phonon band structure stored in the *PHBST.nc* file
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produced by *anaddb*.
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For instance:
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```sh
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abiopen.py trf2_5_PHBST.nc --expose --seaborn=talk
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```
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produces the following plot without LO-TO splitting:
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: (left) Phonon bands without LO-TO splitting
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(right) Plot with band connection estimated from the overlap of the eigenvectors at adjacent q-points
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Alternatively, we can start from the DDB file and use the |abiview| script.
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In this case, AbiPy will generate the anaddb input file
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with all the variables required to handle the plotting of the LO-TO splitting,
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invoke anaddb for us and finally plot the results.
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All of this with just two commands! First, copy the ddb file to a file with extension DDB,
|
|
then, execute abiview.py:
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|
|
|
```sh
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|
cp trf2_3.ddb.abo trf2_3_DDB;
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|
abiview.py ddb trf2_3_DDB -sns=talk
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|
```
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|
|
|
|
|
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We can also compare our results with the phonon band structure available on the |materials_project|.
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|
|
|
First of all, let's find the materials project identifier associated to this particular phase of AlAs.
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|
Of course, one could use the materials project web interface but we can also do it
|
|
from the shell by just passing our Abinit input file to the |abistruct| script:
|
|
|
|
abistruct.py mp_match trf2_1.abi
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|
|
|
# Found 1 structures in Materials Project database (use `verbose` to get further info)
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|
|
|
######################### abivars input for mp-2172 #########################
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|
# Full Formula (Al1 As1)
|
|
# Reduced Formula: AlAs
|
|
# abc : 4.054377 4.054377 4.054377
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|
# angles: 60.000000 60.000000 60.000000
|
|
#
|
|
# Spglib space group info (magnetic symmetries are not taken into account).
|
|
# Spacegroup: F-43m (216), Hall: F -4 2 3, Abinit spg_number: None
|
|
# Crystal_system: cubic, Lattice_type: cubic, Point_group: -43m
|
|
#
|
|
# Idx Symbol Reduced_Coords Wyck EqIdx
|
|
# ----- -------- -------------------------- ------ -------
|
|
# 0 Al +0.00000 +0.00000 +0.00000 a 0
|
|
# 1 As +0.25000 +0.25000 +0.25000 d 1
|
|
|
|
natom 2
|
|
ntypat 2
|
|
typat 1 2
|
|
znucl 13 33
|
|
xred
|
|
0.0000000000 0.0000000000 0.0000000000
|
|
0.2500000000 0.2500000000 0.2500000000
|
|
acell 1.0 1.0 1.0
|
|
rprim
|
|
6.6351943530 0.0000000000 3.8308312587
|
|
2.2117314510 6.2557212277 3.8308312587
|
|
0.0000000000 0.0000000000 7.6616624984
|
|
|
|
AbiPy found one entry in the MP database that matches the structure given in our input file
|
|
and has generated the corresponding input file.
|
|
Now we know that this phase of AlAs corresponds to `mp-2172` and we can
|
|
look at the phonon band structure computed by [[cite:Petretto2018a]] at
|
|
<https://materialsproject.org/materials/mp-2172/>
|
|
|
|
!!! tip
|
|
|
|
For further information on the AbiPy API, please consult the |DdbFileNb| .
|
|
To learn how to automate DFPT calculations with Python, see
|
|
[this jupyter notebook](https://nbviewer.jupyter.org/github/abinit/abitutorials/blob/master/abitutorials/dfpt/lesson_dfpt.ipynb).
|
|
|
|
|
|
## 6 Thermodynamical properties
|
|
|
|
We will give only a very short example of the use of ANADDB to compute
|
|
thermodynamical properties. This is because this part of ANADDB is likely the
|
|
farthest from a clean, stable, usage. By exploring the input variables, the
|
|
user should be able to produce figures and data like the ones for SiO2 quartz
|
|
and stishovite, published in [[cite:Lee1995]].
|
|
|
|
You can copy the file *trf2_7.abi* from *\$ABI_TESTS/tutorespfn/Input* to *Work_rf2*.
|
|
The same DDB as for trf2_4 and trf2_5 is used, namely *trf2_3.ddb.abo*.
|
|
|
|
{% dialog tests/tutorespfn/Input/trf2_7.abi %}
|
|
|
|
The following additional input variables are present:
|
|
|
|
* [[anaddb:thmflag]]
|
|
* [[anaddb:ng2qpt]]
|
|
* [[anaddb:ngrids]]
|
|
* [[anaddb:q2shft]]
|
|
* [[anaddb:nchan]]
|
|
* [[anaddb:nwchan]]
|
|
* [[anaddb:thmtol]]
|
|
* [[anaddb:ntemper]]
|
|
* [[anaddb:temperinc]]
|
|
* [[anaddb:tempermin]]
|
|
|
|
Examine the input file, the input variables, then run anaddb as usual.
|
|
Then, open the output file. You should be able to find the crucial section:
|
|
|
|
# At T F(J/mol-c) E(J/mol-c) S(J/(mol-c.K)) C(J/(mol-c.K)) Omega_mean(cm-1)
|
|
# (A mol-c is the abbreviation of a mole-cell, that is, the
|
|
# number of Avogadro times the atoms in a unit cell)
|
|
2.000E+01 8.1406018E+03 8.1484316E+03 3.9149240E-01 1.4057917E+00 7.2615609E+01
|
|
4.000E+01 8.1084535E+03 8.2384509E+03 3.2499352E+00 7.8730812E+00 9.4376064E+01
|
|
6.000E+01 8.0007856E+03 8.4587550E+03 7.6328229E+00 1.3972961E+01 1.1313071E+02
|
|
8.000E+01 7.8007781E+03 8.7924243E+03 1.2395577E+01 1.9312368E+01 1.3603493E+02
|
|
1.000E+02 7.5044659E+03 9.2281056E+03 1.7236397E+01 2.4166544E+01 1.5713727E+02
|
|
1.200E+02 7.1116611E+03 9.7549590E+03 2.2027483E+01 2.8405448E+01 1.7346361E+02
|
|
1.400E+02 6.6242892E+03 1.0359674E+04 2.6681323E+01 3.1951237E+01 1.8536427E+02
|
|
1.600E+02 6.0456925E+03 1.1028647E+04 3.1143464E+01 3.4844495E+01 1.9397760E+02
|
|
1.800E+02 5.3800094E+03 1.1749746E+04 3.5387425E+01 3.7181668E+01 2.0029176E+02
|
|
2.000E+02 4.6317003E+03 1.2512909E+04 3.9406045E+01 3.9067753E+01 2.0500949E+02
|
|
|
|
There, one finds, the phonon free energy, the phonon internal energy,
|
|
the phonon entropy and the phonon heat capacity. The atomic
|
|
temperature factors can also be computed. An example is presented in
|
|
[[test:v5_22]]
|
|
|
|
!!! important
|
|
|
|
Do not forget that we are working in the harmonic approximation; beyond some
|
|
temperature, anharmonic effects will have a sizable contributions.
|