Tutorial TDDFT

Authors: Xavier Andrade and Alfredo Correa

In this tutorial you will learn how to do an Ehrenfest-TDDFT molecular-dynamics simulation with Qball. We will be doing a calculation of electronic stopping of a proton in Aluminum. This is the force that fast particule feels when entering a material.

Ground state calculation

First, we generate a file with the coordinates of an aluminum supercell with 32 atoms (for actual calculations you probably need a larger cell). Call it al32.sys and copy the following content:

 set cell 15.306 0.0 0.0 0.0 15.306 0.0 0.0 0.0 15.306
 species aluminum Al.xml
 atom   Al1   aluminum   0.000000    0.000000    0.000000
 atom   Al2   aluminum   3.826500    3.826500    0.000000
 atom   Al3   aluminum   3.826500    0.000000    3.826500
 atom   Al4   aluminum   0.000000    3.826500    3.826500
 atom   Al5   aluminum  -7.653000    0.000000    0.000000
 atom   Al6   aluminum  -3.826500    3.826500    0.000000
 atom   Al7   aluminum  -3.826500    0.000000    3.826500
 atom   Al8   aluminum  -7.653000    3.826500    3.826500
 atom   Al9   aluminum   0.000000   -7.653000    0.000000
 atom   Al10  aluminum   3.826500   -3.826500    0.000000
 atom   Al11  aluminum   3.826500   -7.653000    3.826500
 atom   Al12  aluminum   0.000000   -3.826500    3.826500
 atom   Al13  aluminum   0.000000    0.000000   -7.653000
 atom   Al14  aluminum   3.826500    3.826500   -7.653000
 atom   Al15  aluminum   3.826500    0.000000   -3.826500
 atom   Al16  aluminum   0.000000    3.826500   -3.826500
 atom   Al17  aluminum   0.000000   -7.653000   -7.653000
 atom   Al18  aluminum   3.826500   -3.826500   -7.653000
 atom   Al19  aluminum   3.826500   -7.653000   -3.826500
 atom   Al20  aluminum   0.000000   -3.826500   -3.826500
 atom   Al21  aluminum  -7.653000    0.000000   -7.653000
 atom   Al22  aluminum  -3.826500    3.826500   -7.653000
 atom   Al23  aluminum  -3.826500    0.000000   -3.826500
 atom   Al24  aluminum  -7.653000    3.826500   -3.826500
 atom   Al25  aluminum  -7.653000   -7.653000    0.000000
 atom   Al26  aluminum  -3.826500   -3.826500    0.000000
 atom   Al27  aluminum  -3.826500   -7.653000    3.826500
 atom   Al28  aluminum  -7.653000   -3.826500    3.826500
 atom   Al29  aluminum  -7.653000   -7.653000   -7.653000
 atom   Al30  aluminum  -3.826500   -3.826500   -7.653000
 atom   Al31  aluminum  -3.826500   -7.653000   -3.826500
 atom   Al32  aluminum  -7.653000   -3.826500   -3.826500

Make sure you understand what the commands in the file do. You will need the Al.xml pseudopotential file.

Now, lets create the input file for a ground state calculation. You could call it gs.i. First, you need to force Qball to use complex wave-functions with the force_complex variable.

 set force_complex_wf ON

This is necessary since in TDDFT the wave-functions are always complex.

Then we load the atoms of the aluminum supercell, simply by putting the name of the file

 al32.sys

Now we need to add the proton to the system. First you will need a pseudopotential for hydrogen, you can find it here. Place the proton at coordinates 0.00000 1.91325 1.91325 using the atom command. To add an atom without electrons we have to append a + sign to the name of the atom, for example call it "+proton".

Now add the standard commands to set a ground state calculation, using an energy cutoff of 30 Rydberg, a preconditioner cutoff of 4 Rydberg, and a threshold of 1e-6 for 5 steps. If you don't know how to set this, we recommend you to have a look the ground state tutorial.

Since the system is metallic we have to adjust a few parameters. First, we will use the PSDA diagonalizer (wf_dyn variable). We need to add some empty states with

  set nempty 12

and now add some smearing with an electronic temperature of 1000 K (0.006333621 Rydberg). This is done with the commands

  set smearing fermi
  set smearing_width 0.006333621

Finally we reduce a bit the amount of charge mixing with

  set charge_mix_coeff 0.6

(the default is 0.5).

We now can randomize the wave-functions and issue the run command, this time we tell qball to do 5 optimization steps per SCF iteration by passing a third value to run as this

  run 0 200 5

We still have to add a few command so after the calculation is done, the results are saved to use them as a starting point for the real-time calculation. First we save the coordinates using the savesys command

  savesys md.sys

This will generate an file in the Qball input format, that we can load from other input files. Then, we save the wave-functions with the save command

  save -states restart/md

This command saves several files, one per state, in the restart/ directory.

You can now go ahead and tell Qball to execute the newly created input file. After it is done, I recommend you to have a look to the md.sys to see what it is saved there.

Real-time calculation

Now that we have the set of ground-state orbitals, we can setup the real-time calculation. Create a new input file for this, call it td.i.

As before, we need to set the force_complex_wf variable to force Qball to work with complex states.