Tutorial 4: running convergence tests

While koopmans is a package primarily oriented towards performing Koopmans spectral functional calculations, it does have a couple of other useful functionalities. In this tutorial, we will make use of its convergence task to determine how large a cell size and energy cutoff is required to converge the PBE energy of the highest occupied molecular orbital (HOMO) of a water molecule.

The input file

In order to run this calculation, our workflow block needs a few particular keywords:

{
    "workflow": {
        "functional": "dft",
        "task": "convergence",
        "from_scratch": true,
        "convergence_observable": "homo energy",
        "convergence_threshold": "0.01 eV",
        "convergence_parameters": [
            "ecutwfc",
            "cell_size"
        ],

The important lines are highlighted. "task": "convergence" means that we will be performing a convergence test. The other three highlighted keywords specifying that we are going to converge the HOMO energy to within 0.01 eV, with respect to both the energy cutoff ecutwfc and the cell size. The full input file can be found here.

The output file

When you run the calculation, you should see something like this after the header:

 ecutwfc = 20.0, cell_size = 1.0
 -------------------------------
    Running ./dft... done

 ecutwfc = 20.0, cell_size = 1.1
 -------------------------------
    Running ./dft... done

 ecutwfc = 20.0, cell_size = 1.2
 -------------------------------
    Running ./dft... done

 ecutwfc = 30.0, cell_size = 1.0
 -------------------------------
    Running ./dft... done

 ecutwfc = 30.0, cell_size = 1.1
 -------------------------------
    Running ./dft... done

Here, the code is attempting to use progressively larger energy cutoffs and cell sizes. It will ultimately arrive at a converged solution, with a ecutwfc of 50.0 Ha and a cell 1.3 times larger than that provided in the .json input file.

Plotting

The individual Quantum ESPRESSO calculations reside in nested subdirectories. If you plot the HOMO energies from each of these, you should get something like this:

Plot of the HOMO energy of water with respect to the energy cutoff and cell size (generated using this script)

We can see that indeed the calculation with ecutwfc = 50.0 and cell_size = 1.3 is the one where the energy of the HOMO goes within (and stays within) 0.01 eV of the most accurate calculation.