# Tutorial on the use of Wannier90 library¶

## The Wannier90 interface tutorial¶

This tutorial aims at showing how to use the Wannier90 interface to compute Maximally Localized Wannier Functions (MLWFs).

You will learn how to get MLWFs with ABINIT and Wannier90 and what are the basic variables to govern the numerical efficiency.

This tutorial should take about 1 hour and it is important to note that the examples in this tutorial are not converged, they are just examples to show how to use the code.

Note

Supposing you made your own installation of ABINIT, the input files to run the examples are in the ~abinit/tests/ directory where ~abinit is the absolute path of the abinit top-level directory. If you have NOT made your own install, ask your system administrator where to find the package, especially the executable and test files.

In case you work on your own PC or workstation, to make things easier, we suggest you define some handy environment variables by executing the following lines in the terminal:

export ABI_HOME=Replace_with_absolute_path_to_abinit_top_level_dir # Change this line
export PATH=$ABI_HOME/src/98_main/:$PATH      # Do not change this line: path to executable
export ABI_TESTS=$ABI_HOME/tests/ # Do not change this line: path to tests dir export ABI_PSPDIR=$ABI_TESTS/Psps_for_tests/  # Do not change this line: path to pseudos dir


Examples in this tutorial use these shell variables: copy and paste the code snippets into the terminal (remember to set ABI_HOME first!) or, alternatively, source the set_abienv.sh script located in the ~abinit directory:

source ~abinit/set_abienv.sh


The ‘export PATH’ line adds the directory containing the executables to your PATH so that you can invoke the code by simply typing abinit in the terminal instead of providing the absolute path.

To execute the tutorials, create a working directory (Work*) and copy there the input files of the lesson.

Most of the tutorials do not rely on parallelism (except specific tutorials on parallelism). However you can run most of the tutorial examples in parallel with MPI, see the topic on parallelism.

## Summary of Wannier90 in ABINIT¶

Wannier90 is a code that computes MLWFs (see www.wannier.org ). Wannier90 uses the methodology introduced by N. Marzari and D. Vanderbilt in 1997 and it is highly recommended to read the following papers to understand its basics: [Marzari1997] and [Souza2002a].

Wannier functions (WFs) can be obtained from Bloch states by means of the formulas 1-3 of [Souza2002a]. As you may note there is a freedom of choice in the Bloch orbital’s phase which is reflected in the shape and the spatial extent of the WF. This means that for different phases there will be WFs with different spatial localizations.

To obtain the MLWFs we minimize the spread of the WF with respect to the choice of phase. This is done by using a steepest-descent algorithm, see section D of [Marzari1997]. After a ground state calculation the Wannier90 code will obtain the MLWFs requiring just two ingredients:

• The overlaps $M_{mn} = \langle u_{mk} | u_{nk+b} \rangle$ between the cell periodic part of the Bloch states $|u_{nk}\rangle$. See Eq. 25 of [Marzari1997]).

• As a starting guess the projection, $A_{mn} = \langle \psi_{mk} | g_{n} \rangle$, of the Bloch states $|\psi_{nk} \rangle$ onto trial localized orbitals $|g_{n}\rangle$ (See section D of [Souza2002a])

What ABINIT does is to take the Bloch functions from a ground state calculation and compute these two ingredients. Then, Wannier90 is executed. Wannier90 is included as a library in ABINIT and the process is automatic, so that in a single run you can do both the ground state calculation and the computation of MLWFs.

## A first example: silicon¶

Before starting make sure that you compiled abinit enabling Wannier90. You may have to recompile the code with

configure --with-config-file=myconf.ac9


where myconf.ac9 defines:

#Install prefix of the PSML I/O library (e.g.
#                          /usr/local).
with_wannier90="/usr/local"


Now we will compute a set of MLWFs for silicon. We are going to extract the Wannier functions corresponding to the four valence states of silicon.

Before beginning, you might consider to work in a different sub-directory as for the other tutorials. Why not Work_w90? Then copy the files tw90_1.abi and wannier90.win from the $ABI_TESTS/tutoplugs/Input directory to Work_w90: cd$ABI_TESTS/tutoplugs/Input
mkdir Work_w90
cd Work_w90
cp ../tw90_1.abi .


Wannier90 also uses a secondary input file called wannier90.win. Therefore, you must include this file in the folder:

cp ../wannier90.win .


abinit  tw90_1.abi > log 2> err &


Let’s examine the input file tw90_1.abi, while the calculation is running.

The input file should look familiar to you. It is indeed the primitive cell of silicon. It has two data sets: first a SCF calculation and then a NSCF calculation which will call the Wannier90 library. The only new input variable is prtwant which has to be set to 2 in order to use the Wannier90 utility.

Now lets look at the second input file wannier90.win.

This is a mandatory input file required by the Wannier90 library. There are many variables that can be defined inside this file. In our case we used num_wann and num_iter. These variables are used in the minimization of the spread to obtain the MLWF. In particular, num_wann defines the number of Wannier functions to extract while num_iter sets the maximum number of iterations. There are also variables to govern the disentanglement procedure outlined in [Souza2002a] which are not used in this simple case. The complete list of input variables can be found in the Wannier90 user guide (see www.wannier.org).

We can now examine the log file. After the convergence of the SCF cycle is reached. We can see that the Wannier90 library is called. You will find the following lines:

  Calculation of overlap and call to Wannier90 library
to obtain Maximally Localized Wannier functions
- wannier90.win is a mandatory secondary input
- wannier90.wout is the output for the library
- wannier90.amn contains projections
- wannier90random.amn contains random projections
- wannier90.mmn contains the overlap
- wannier90.eig contains the eigenvalues


This is an explanation of the input and output files for the Wannier90 library. As you can see many new files were created. The input files for Wannier90 which were created by ABINIT are:

wannier90random.amn
Contains a list of projections to be used as a starting guess of the WF. This is the $A_{mn}$ matrix which was mentioned before in this tutorial.
wannier90.eig
Contains a list of eigenvalues for each k-point and band.
wannier90.mmn
Contains the overlaps between the cell periodic part of the Bloch states. This is the M_mn matrix mentioned before in this tutorial.
UNK
Files containing the wavefunction in real space for every k-point. Once these files were computed by ABINIT the Wannier90 library was used. The output files of Wannier90 are:
wannier90.wout
This is the main output file of the library. You should read it carefully to see the details of the calculation.
wannier90.chk
This file is required to restart a calculation is case you use Wannier90 in standalone mode. In our case it is not used.

To obtain information about the steepest-descent minimization just issue:

grep CONV tw90_1o_DS2_w90.wout


You will obtain a table of the following form:

 +--------------------------------------------------------------------+<-- CONV
+--------------------------------------------------------------------+<-- CONV
0     0.438E+02     0.0000000000       43.7939618280       0.08  <-- CONV
1    -0.946E+01    10.5484513508       34.3387915333       0.09  <-- CONV


You can verify that the final spread you get is around 4.0 Å$^2$.

Similarly to obtain information about the disentanglement procedure (not used in this example) just type:

grep DIS wannier90.wout


You will obtain a table of the following form:

 +---------------------------------------------------------------------+<-- DIS
|  Iter     Omega_I(i-1)      Omega_I(i)      Delta (frac.)    Time   |<-- DIS
+---------------------------------------------------------------------+<-- DIS


Tip

If AbiPy is installed on your machine, you can use the abiopen script with the wout command and the --expose option to visualize the iterations

abiopen.py tw90_1o_DS2_w90.wout --expose -sns


### Visualize the Wannier functions¶

You can see the Wannier functions in XCrysDen format. Just type:

xcrysden --xsf tw90_1o_DS2_w90_00001.xsf


To see the isosurface click on: Tools->Data Grid -> OK And modify the isovalue, put, for instance, 0.3 and check the option “Render ± isovalue” then click on OK Alternatively, one can read the xsf file with vesta . MacOsx users can use the command line:

open tw90_1o_DS2_w90_00003.xsf -a vesta


to invoke vesta directly from the terminal:

Important

• It is important to set istwfk equal to 1 for every k-point avoiding using symmetries. The reason is that the formalism used to extract the MLWF assumes that you have a uniform grid of k-points. See section IV of [Marzari1997].

• The number of Wannier functions to extract should be minor or equal to the number of bands. If nband > nwan then the disentanglement routines will be called.

• The number of k-points should be equal to ngkpt(1)*ngkpt(2)*ngkpt(3). This is achieved by using the input variables kptopt= 3, ngkpt and nshiftk= 1.

• The prefix of all wannier90 files in this sample case is wannier90. Other possible prefixes are w90_ and abo __w90_ , where abo is the fourth line on your .file file. To setup the prefix, ABINIT will first look for a file named abo __w90.win_ if it is not found then it will look for w90.win and finally for wannier90.win.

## The PAW case¶

Before starting it is assumed that you have already completed the tutorials PAW1 and PAW2.

For silicon, we just have to add the variable pawecutdg and the PAW Atomic Data is included in the pseudopotential file. An example has already been prepared.

Just copy the file tw90_2.abi into Work_w90:

cp ../tw90_2.abi .


We are going to reuse the wannier90.win of the previous example. Now, just run abinit again

abinit tw90_2.abi > log 2> err &


As it is expected, the results should be similar than those of the PW case.

Important

For the PAW case the UNK files are not those of the real wavefunctions. The contribution inside the spheres is not computed, however, they can be used to plot the Wannier functions.

## Defining the initial projections¶

Up to now we have obtained the MLWF for the four valence bands of silicon. It is important to note that for valence states the MLWF can be obtained starting from a random initial position. However, for conduction states we have to give a very accurate starting guess to get the MLWF.

We are going to extract the $sp^3$ hybrid orbitals of Silane SiH$_4$. You can start by copying from the tests/tutoplugs directory the following files:

cp ../tw90_3.abi .
cp ../tw90_3o_DS2_w90.win .


Now run abinit

abinit  tw90_3.abi > log 2> err &


While it is running, we can start to examine the input files. Open the main input file tw90_3.abi. The file is divided into three datasets.

First a SCF calculation is done. What follows is a NSCF calculation including more bands. Finally, in the third dataset we just read the wavefunction from the previous one and the Wannier90 library is called. w90iniprj is a keyword used to indicate that the initial projections will be given in the .win file.

Note

You may notice that the .win file is now called tw90_3o_DS2_w90.win. It has the following form: prefix_dataset_w90.win, where the prefix is taken from the third line of your .file file. and dataset is the dataset number at which you call Wannier90 (dataset 2 in this example).

Now open the .win file. The initial projections will be the $sp^3$ hybrid orbitals centered in the position of the silicon atom. This is written explicitly as:

begin projections
Si:sp3
end projections


There is an enormous freedom of choice for the initial projections. For instance, you can define the centers in Cartesian coordinates or rotate the axis. Please refer to the Wannier90 user guide and see the part related to projections (see www.wannier90.org).

## More on Wannier90 + ABINIT¶

Now we will redo the silicon case but defining different initial projections.

This calculation will be more time consuming, so you can start by running the calculation while reading:

cp ../tw90_4.abi .
cp ../tw90_4o_DS3_w90.win .
abinit  tw90_4.abi > log 2> err &


Initial projections:

In this example we extract sp$^3$ orbitals centered on the silicon atoms. But you could also extract bonding and anti-bonding orbitals by uncommenting and commenting the required lines as it is indicated in tw90_4o_DS3_w90.win.

You can see that we are using r=4 in the initial projections block. This is to indicate that the radial part will be a Gaussian function whose width can be controlled by the value of the variable zona. The main advantage over radial functions in the form of hydrogenic orbitals is that the time to write the .amn file will be reduced.

Interpolated band structure

We are going to run Wannier90 in standalone mode. Just comment out the following lines of the .win file:

postproc_setup = .true.   !used to write .nnkp file at first run
num_iter = 100


And uncomment the following two lines:

!restart = plot
!bands_plot = .true.


Now run Wannier90:

\$ABI_HOME/fallbacks/exports/bin/wannier90.x-abinit tw90_4o_DS3_w90


The interpolated band structure is in tw90_4o_DS3_w90_band.dat

To plot the bands, open gnuplot in the terminal and type:

load "tw90_4o_DS3_w90_band.gnu"