# Real-world example - Equation of state¶

Now that we’ve discussed the concepts of workflows in AiiDA using some basic examples, let’s move on to something more interesting: calculating the equation of state of silicon. An equation of state consists of calculating the total energy (E) as a function of the unit cell volume (V). The minimal energy is reached at the equilibrium volume. Equivalently, the equilibrium is defined by a vanishing pressure: $$p=-dE/dV$$. In the vicinity of the minimum, the functional form of the equation of state can be approximated by a parabola. Such an approximation greatly simplifies the calculation of the bulk modulus, which is proportional to the second derivative of the energy (a more advanced treatment requires fitting the curve with, e.g., the Birch–Murnaghan expression).

Note

The approach of the workflows in this module is not necessarily the optimal one! However, the material is meant be instructive in understanding how to write work chains before you get started on your own.

## Importing a structure from the COD¶

First, we’ll need the structure of bulk silicon. Instead of loading the structure from a .cif file, we show you how to load it from the Crystallography Open Database (COD). Similar to data, calculation, and workflows, a database importer class can be loaded using the corresponding factory and entry point:

In [1]: from aiida.plugins import DbImporterFactory
...: CodDbImporter = DbImporterFactory('cod')


Now that we have the CodDbImporter class loaded, let’s initialize an instance of the class:

In [2]: cod = CodDbImporter()


Next, we’ll load the conventional unit cell of silicon, which has the COD id = 1526655:

In [3]: results = cod.query(id='1526655')
...: structure = results[0].get_aiida_structure()


Let’s have a look at the structure variable:

In [4]: structure
Out[4]: <StructureData: uuid: 3d4ab03b-4149-4c31-88ef-180640f1f79a (unstored)>


We can see that the structure variable contains an instance of StructureData, but that it hasn’t been stored in the AiiDA database. Before doing so, let’s double check that we have the right structure. The StructureData class has several methods for obtaining information about the structure, such as get_formula():

In [5]: structure.get_formula()
Out[5]: 'Si8'


That looks alright! Let’s store the node in the database:

In [6]: structure.store()
Out[6]: <StructureData: uuid: 3d4ab03b-4149-4c31-88ef-180640f1f79a (pk: 2804)>


## Rescaling the structure¶

For the equation of state you need another function that takes as input a StructureData object and a rescaling factor, and returns a StructureData object with the rescaled lattice parameter:

from aiida.engine import calcfunction

@calcfunction
def rescale(structure, scale):
"""Calculation function to rescale a structure

:param structure: An AiiDA StructureData to rescale
:param scale: The scale factor (for the lattice constant)
:return: The rescaled structure
"""
from aiida.orm import StructureData

ase_structure = structure.get_ase()
scale_value = scale.value

new_cell = ase_structure.get_cell() * scale_value
ase_structure.set_cell(new_cell, scale_atoms=True)

return StructureData(ase=ase_structure)


This calculation function should be familiar to you from the section on calculation function from the work functions module. Copy the code snippet above into a Python file, (e.g. rescale.py). Next, open a verdi shell, load the StructureData node for silicon that you just stored, and generate a set of rescaled structures:

In [1]: from rescale import rescale
...:
...: structure = load_node(pk=<PK>)  # If you still have the structure variable loaded, not need to load it again!
...: rescaled_structures = [rescale(structure, Float(factor)) for factor in (0.98, 0.99, 1.0, 1.01, 1.02)]


Note

Notice that we have supplied the rescale method with two inputs that are both Data nodes: StructureData and Float.

Now let’s check the contents of the rescaled_structures variable:

In [2]: rescaled_structures
Out[2]:
[<StructureData: uuid: a1801ec8-35c8-4e1d-bbbf-36fbcef7d034 (pk: 2807)>,
<StructureData: uuid: e2714063-63ce-492b-b003-b05323c70a22 (pk: 2810)>,
<StructureData: uuid: 842aa50b-c6ce-429c-b089-96a1480cea9f (pk: 2813)>,
<StructureData: uuid: 78bb6406-ec94-425d-a396-9a7cc7ffbacf (pk: 2816)>,
<StructureData: uuid: 8f9c876e-d5e9-4018-9bb5-9e52c335fe0c (pk: 2819)>]


Notice that all of the StructureData nodes of the rescaled structures are already stored in the database with their own PK. This is because they are the output nodes of the rescale calculation function.

## Equation of state work function¶

Now that we have our initial structure and a calculation function for rescaling the unit cell, we can put this together with the PwCalculation from the session on running calculations to calculate the equation of state. For this part of the tutorial, we provide some utility functions that get the correct pseudopotentials and generate the input for a PwCalculation:

These inputs are defined in a similar way to how you have prepared them in the running computations hands on.

Important

The workflow scripts for the rest of this section rely on the methods in rescale.py and utils.py to function. Make sure the Python files with the workflows are in the same directory as these two files.

In the script shown below, a work function has been implemented that generates a scaled structure and calculates its energy for a range of 5 scaling factors:

# -*- coding: utf-8 -*-
"""Simple workflow example"""
from aiida.engine import run, Process, calcfunction, workfunction
from aiida.orm import Dict, Float, load_group
from aiida.plugins import CalculationFactory

from rescale import rescale
from utils import generate_scf_input_params

# Load the calculation class 'PwCalculation' using its entry point 'quantumespresso.pw'
PwCalculation = CalculationFactory("quantumespresso.pw")

@calcfunction
def create_eos_dictionary(**kwargs):
"""Create a single Dict node from the Dict output parameters of completed PwCalculations.

The dictionary will contain a list of tuples, where each tuple contains the volume, total energy and its units
of the results of a calculation.

:return: Dict node with the equation of state results
"""
eos = [
(result.dict.volume, result.dict.energy, result.dict.energy_units)
for label, result in kwargs.items()
]
return Dict(dict={"eos": eos})

@workfunction
def run_eos_wf(code, pseudo_family_label, structure):
"""Run an equation of state of a bulk crystal structure for the given element."""

# This will print the pk of the work function
print("Running run_eos_wf<{}>".format(Process.current().pid))

scale_factors = (0.96, 0.98, 1.0, 1.02, 1.04)
labels = ["c1", "c2", "c3", "c4", "c5"]

calculations = {}

# Loop over the label and scale_factor pairs
for label, factor in list(zip(labels, scale_factors)):

# Generated the scaled structure from the initial structure
rescaled_structure = rescale(structure, Float(factor))

# Generate the inputs for the PwCalculation
inputs = generate_scf_input_params(rescaled_structure, code, pseudo_family)

# Launch a PwCalculation for each scaled structure
print(
"Running a scf for {} with scale factor {}".format(
structure.get_formula(), factor
)
)
calculations[label] = run(PwCalculation, **inputs)

# Bundle the individual results from each PwCalculation in a single dictionary node.
# Note: since we are 'creating' new data from existing data, we *have* to go through a calcfunction, otherwise
# the provenance would be lost!
inputs = {
label: result["output_parameters"] for label, result in calculations.items()
}
eos = create_eos_dictionary(**inputs)

# Finally, return the eos Dict node
return eos


Copy the contents of this script into a Python file, for example eos_workfunction.py , or simply download it. Next, let’s open up a verdi shell and run the equation of state workflow. In case you no longer have it stored, load the silicon structure you imported earlier using its PK:

In [1]: structure = load_node(pk=<PK>)


Next, load the Quantum ESPRESSO pw code you used previously to run calculations:

In [2]: code = load_code('pw@localhost')


To run the workflow, we also have to specify the label of the family of pseudopotentials as an AiiDA Str node:

In [3]: pseudo_family_label = Str('SSSP/1.1/PBE/efficiency')


Finally, we are ready to import the run_eos() work function and run it!

In [4]: from eos_workfunction import run_eos_wf
...: result = run_eos_wf(code, pseudo_family_label, structure)


The work function will start running and print one line of output for each scale factor used. Once it is complete, the output will look something like this:

Running run_eos_wf<2821>
Running a scf for Si8 with scale factor 0.96
Running a scf for Si8 with scale factor 0.98
Running a scf for Si8 with scale factor 1.0
Running a scf for Si8 with scale factor 1.02
Running a scf for Si8 with scale factor 1.04


Similar to the simple arithmetic work function run in the work function module, running the eos_wf work function means that the Python interpreter will be blocked during the whole workflow. In this case, this will take the time required to launch the calculations, the actual time needed by Quantum ESPRESSO to perform the calculation and the time taken to retrieve the results. If you interrupt the workflow at any point, you will experience some unpleasant consequences: intermediate calculation results are potentially lost and it is extremely difficult to restart a workflow from the exact place where it stopped. This is exactly the motivation for writing such a workflow as a work chain.

That said, we can still have a look at the result!

In [5]: result
Out[5]:
<Dict: uuid: 4a8cdde5-a2ff-4c97-9a13-28096b1d9b91 (pk: 2878)>


We can see that the work function returns a Dict node with the results for the equation of state. Let’s have a look at the contents of this node:

In [6]: result.get_dict()
Out[6]:
{'eos': [[137.84870014835, -1240.4759003187, 'eV'],
[146.64498086438, -1241.4786547651, 'eV'],
[155.807721341, -1242.0231198534, 'eV'],
[165.34440034884, -1242.1847659475, 'eV'],
[175.26249665852, -1242.0265883524, 'eV']]}


We can see that the dictionary contains the volume, calculated energy and its units for each scaled structure. Of course, this information is much better represented with a graph, so let’s plot the equation of state and fit it with a Birch-Murnaghan equation. For this purpose, we have provided the plot_eos script in the utils.py file that takes the PK of the run_eos_wf work function as an input and plots the equation of state:

In [7]: from utils import plot_eos
...: plot_eos(<PK>)


## Submitting the workflow: Workchains¶

Clearly, when writing workflows that involve the use of an ab initio code like Quantum ESPRESSO, it is better to use a work chain. Below you can find an incomplete snippet for the corresponding EquationOfState work chain. It is almost completely implemented, all that it is missing is its define method.

# -*- coding: utf-8 -*-
"""Equation of State WorkChain."""
from aiida.engine import WorkChain, ToContext, calcfunction
from aiida.orm import Code, Dict, Float, Str, StructureData, load_group
from aiida.plugins import CalculationFactory

from rescale import rescale
from utils import generate_scf_input_params

PwCalculation = CalculationFactory("quantumespresso.pw")
scale_facs = (0.96, 0.98, 1.0, 1.02, 1.04)
labels = ["c1", "c2", "c3", "c4", "c5"]

@calcfunction
def get_eos_data(**kwargs):
"""Store EOS data in Dict node."""
eos = [
(result.dict.volume, result.dict.energy, result.dict.energy_units)
for label, result in kwargs.items()
]
return Dict(dict={"eos": eos})

class EquationOfState(WorkChain):
"""WorkChain to compute Equation of State using Quantum ESPRESSO."""

@classmethod
def define(cls, spec):
"""Specify inputs and outputs."""

def run_eos(self):
"""Run calculations for equation of state."""
# Create basic structure and attach it as an output
structure = self.inputs.structure

calculations = {}

for label, factor in zip(labels, scale_facs):

rescaled_structure = rescale(structure, Float(factor))
inputs = generate_scf_input_params(
rescaled_structure, self.inputs.code, pseudo_family
)

self.report(
"Running an SCF calculation for {} with scale factor {}".format(
structure.get_formula(), factor
)
)
calcjob_node = self.submit(PwCalculation, **inputs)
calculations[label] = calcjob_node

# Ask the workflow to continue when the results are ready and store them in the context

def results(self):
"""Process results."""
inputs = {
label: self.ctx[label].get_outgoing().get_node_by_label("output_parameters")
for label in labels
}
eos = get_eos_data(**inputs)

# Attach Equation of State results as output node to be able to plot the EOS later
self.out("eos", eos)


Warning

WorkChains need to be defined in a separate file from the script used to run them. E.g. save your WorkChain in eos_workchain.py and use from eos_workchain import EquationOfState to import the work chain in your script.

Let’s reiterate some differences between the run_eos_wf work function and the EquationOfState:

• Instead of using a workfunction-decorated function you need to define a class, inheriting from a prototype class called WorkChain that is provided by AiiDA in the aiida.engine module.

class EquationOfState(WorkChain):

• For the WorkChain, you need to split your main code into methods, which are the steps of the workflow.

    def run_eos(self):
"""Run calculations for equation of state."""

    def results(self):
"""Process results."""


Here we have to decide where should the code be split for the equation of state workflow. The splitting points should be put where you would normally block the execution of the script for collecting results in a standard work function. For example here we split after submitting the PwCalculation’s.

• Any submission within the workflow should not call the normal run or submit functions, but self.submit to which you have to pass the process class, and a dictionary of inputs.

            calcjob_node = self.submit(PwCalculation, **inputs)


This submission in run_eos returns a calcjob_node that represents actual calculation, but at that point in time we have only just launched the calculation to the daemon and it is not yet completed.

• We need to add these calcjob_node to the context, so that in the next step of the workchain, when the calculations are in fact completed, we can access their results and continue the work. To do this, we can use the ToContext class:

        # Ask the workflow to continue when the results are ready and store them in the context


This class takes a dictionary, where the values are the calcjob_nodes and the keys will be the names under which the corresponding calculations will be made available in the context when they are done. By returning the ToContext object in run_eos, the work chain will implicitly wait for the results of all the calcjob_nodes you have specified, and then call the next step only when all calcjob_node have completed.

• In the results step, the results are obtained from the ctx attribute through self.ctx:

        inputs = {
label: self.ctx[label].get_outgoing().get_node_by_label("output_parameters")
for label in labels
}


Since the context is nothing more than a special kind of dictionary, you can also access the value of a context variable as self.ctx.varname instead of self.ctx['varname'].

• While in normal process functions you attach output nodes to the node by invoking the return statement, the work chain calls self.out(link_name, node) for each node you want to return. An advantage of this different syntax is that you can start emitting output nodes already in the middle of the execution, and not necessarily at the very end as it happens for normal functions (return is always the last instruction executed in a function or method).

Note

Once you have called self.out(link_name, node) on a given link_name, you can no longer call self.out() on the same link_name: this will raise an exception.

### Exercise¶

As an exercise, try to complete the define method. In this method you specify the main information on the workchain, in particular:

• The inputs that the workchain expects. This is obtained by means of the spec.input() method, which provides as the key feature the automatic validation of the input types via the valid_type argument. The same holds true for outputs, as you can use the spec.output() method to state what output types are expected to be returned by the workchain.

• The outline consisting in a list of ‘steps’ that you want to run, put in the right sequence. This is obtained by means of the method spec.outline() which takes as input the steps. Note: in this example we just split the main execution in two sequential steps, that is, first run_eos then results.

You can look at the define method of the MultiplyAddWorkChain as an example. If you get stuck, you can also download the complete script here.

Once you have completed the define method, you can submit the EquationOfState to the daemon. However, in this case the work chain will need to be globally importable so the daemon can load it. To achieve this, the directory containing the work chain definition (i.e. the Python file) needs to be in the PYTHONPATH in order for the AiiDA daemon to find it. When your eos_workchain.py is in e.g. /home/aiida/workflows, add a line export PYTHONPATH=$PYTHONPATH:/home/max/workchains to your .bashrc in the home directory. Or, if the .py file is in your current directory: $ echo "export PYTHONPATH=\$PYTHONPATH:$PWD" >> ~/.bashrc


Next, it is very important to restart the daemon, so it can successfully set up the PYTHONPATH and find the EquationOfState work chain:

$verdi daemon restart --reset  Once the daemon has been restarted, it is time to submit the EquationOfState work chain from the verdi shell: In [1]: from eos_workchain import EquationOfState ...: from aiida.engine import submit ...: submit(EquationOfState, code=load_code('pw@localhost'), pseudo_family_label=Str('SSSP/1.1/PBE/efficiency'), structure=load_node(pk=<PK>)) Out[1]: <WorkChainNode: uuid: 9e5c7c48-a47c-49fc-a8ab-fff081f250ee (pk: 665) (eos.workchain.EquationOfState)>  Note that similar as for the MultiplyAddWorkChain, the submit function returns the WorkChain instance for our equation of state workflow. Now, leave the verdi shell and check the status of the work chain with verdi process list. Depending on what stage of the work chain you are in, you will see something like the following output: (aiida) max@quantum-mobile:~/wf_basic$ verdi process list
PK  Created    Process label    Process State    Process status
----  ---------  ---------------  ---------------  ----------------------------------------------------
346  26s ago    EquationOfState  ⏵ Waiting        Waiting for child processes: 352, 358, 364, 370, 376
352  25s ago    PwCalculation    ⏵ Waiting        Monitoring scheduler: job state RUNNING
358  25s ago    PwCalculation    ⏵ Waiting        Monitoring scheduler: job state RUNNING
364  24s ago    PwCalculation    ⏵ Waiting        Monitoring scheduler: job state RUNNING
370  24s ago    PwCalculation    ⏵ Waiting        Monitoring scheduler: job state RUNNING
376  23s ago    PwCalculation    ⏵ Waiting        Monitoring scheduler: job state RUNNING

Total results: 6

Info: last time an entry changed state: 20s ago (at 21:00:35 on 2020-06-07)


Note

If you run into issues, it might be helpful to have a look at the debugging module.