# ABINIT tutorial. Lesson on the use of Wannier90 library...

## The Wannier90 interface tutorial.

This lesson 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.
It is supposed that you already know how to use ABINIT in the norm conserving pseudopotential case.

This lesson should take about 1 hour. And it is important to note that all the cases in the tutorial are not converged they are just examples to show how to use the code.

##### Copyright (C) 2000-2017 ABINIT group (TRangel)

### Lesson on the use of Wannier90 library. Table of content:

- 1. Summary of Wannier90 in ABINIT
- 2. A first example: the silicon case
- 3. A PAW case
- 4. Defining the initial projections
- 5. More on Wannier90 + ABINIT

### 1. 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:

MV

     N. Marzari and D. Vanderbilt, Maximally localized generalized
    Wannier functions for composite energy bands, Phys. Rev. B 56, 12847
    (1997)

SMV

     I. Souza, N. Marzari and D. Vanderbilt, Maximally localized
    Wannier functions for entangled energy bands, Phys. Rev. B 65,
    035109 (2002)

Wannier functions (WFs) can be obtained from Bloch states by means of the formulas 1-3 of SMV. As you may note there is a freedom of choice of Bloch orbital's phase which is reflected on the shape and spatial extent of the WF. i.e., 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 MV.
After a ground state calculation the Wannier90 code will obtain the MLWFs requiring just two ingredients:

- The overlaps between the cell periodic part of the Bloch states |u_nk>
  M_mn= < u_mk | u_nk+b >
  See Eq. 25 of MV.
- As a starting guess the projection of the Bloch states |psi_nk> onto trial localized orbitals |g_n>
  A_mn= < psi_mk | g_n >
  See section D of SMV.

What ABINIT do is to take the Bloch functions from a ground state calculation and compute these two ingredients. Then, Wannier90 is run. Wannier90 is included as a library and 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.
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### 2. A first example: the silicon case

Before starting make sure that you compiled abinit enabling Wannier90. You may have to recompile it using the flag --enable-wannier90.

Now we will compute a set of MLWFs for the silicon case. 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 lessons. Why not "Work_w90" ?

- mkdir Work_w90
- cd Work_w90

Copy the files tw90_1.files, tw90_1.in and wannier90.win from the tests/tutoplug directory to "Work_w90" :

- cp ../tw90_1.files .
- cp ../tw90_1.in .

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

- cp ../wannier90.win .

Now you are ready to run abinit. Please type in:

- abinit < tw90_1.files >& log

Let's examine the input file tw90_1.in, while the calculation is running.
The input file should look familiar to you. It is indeed the silicon case. 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 the secondary 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 to be used in the minimization of the spread to obtain the MLWF. In particular, num_wann tell us the number of Wannier functions to extract while num_iter sets the number of iterations. There are also variables to govern the disentanglement procedure outlined in SMV 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 is the main output file of the library. You should read it carefully to see the details of the calculation.
- wannier90.chk is required to restart a calculation is case you use Wannier90 in standalone mode. In our case it is not used.

If you want to obtain information about the disentanglement procedure 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

Similarly to obtain information about the steepest-descent minimization just issue:
- grep CONV wannier90.wout
You will obtain a table of the following form:

     +--------------------------------------------------------------------+<-- CONV
     | Iter  Delta Spread     RMS Gradient      Spread (Ang^2)      Time  |<-- CONV
     +--------------------------------------------------------------------+<-- CONV

You can verify that the final spread you get is around 4.0 ang^2

Visualize the Wannier functions

    You can see the Wannier functions in xcrysden format. Just type:
    xcrysden --xsf wannier90_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

Notes:

- 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 MV.
- 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.

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### 3. A PAW case

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

The PAW method is implemented in such a way that it is very easy to use. For the silicon case 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 files tw90_2.files and tw90_2.in into "Work_w90":

- cp ../tw90_2.files .
- cp ../tw90_2.in .

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

- abinit < tw90_2.files >& log

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.
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### 4. 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 sp3 hybrid orbitals of Silane SiH4. You can start by copying from the tests/tutoplug directory the following files:

- cp ../tw90_3.files .
- cp ../tw90_3.in .
- cp ../tw90_3o_DS2_w90.win .

Now run abinit

- abinit < tw90_3.files >& log

While it is running we can start to examine the input files.
Open the main input file tw90_3.in. 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 sp3 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).
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### 5. More on Wannier90 + ABINIT

Now we will going to 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.in .
- cp ../tw90_4.files .
- cp ../tw90_4o_DS3_w90.win .

Initial projections:

In this example we extract sp3 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 first two lines of the .win file:

    postproc_setup = .true.   !used to write .nnkp file at first run
    num_iter = 100
    wannier_plot = .true.
    wannier_plot_supercell = 3

And uncomment the following two lines:

    !restart = plot
    !bands_plot = .true.

Now run Wannier90:
- [abinit-home]/plugins/wannier90/wannier90.x tw90_4o_DS3_w90
The interpolated bandstructure is in: tw90_4o_DS3_w90_band.dat

Now you can continue discovering the capabilities of Wannier90.

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