atomistics

The atomistics package consists of two primary components. On the one hand it provides interfaces to atomistic simulation codes - named calculators. The supported simulation codes in alphabetical order are:

• Abinit - Plane wave density functional theory
• EMT - Effective medium theory potential
• GPAW - Density functional theory Python code based on the projector-augmented wave method
• LAMMPS - Molecular Dynamics
• Quantum Espresso - Integrated suite of Open-Source computer codes for electronic-structure calculations
• Siesta - Electronic structure calculations and ab initio molecular dynamics
• SPHInX - Plane wave DFT with interactive tools, charged defect correction and spin constraints

For majority of these simulation codes the atomistics package use the Atomic Simulation Environment to interface the underlying C/ C++ and Fortran Codes with the Python programming language. Still this approach limits the functionality of the simulation code to calculating the energy and forces, so by adding custom interfaces the atomistics package can support built-in features of the simulation code like structure optimization and molecular dynamics.

On the other hand the atomistics package also provides workflows to calculate material properties on the atomistic scales, these include:

• Equation of State - to calculate equilibrium properties like the equilibrium energy, equilibrium volume, equilibrium bulk modulus and its pressure derivative.
• Elastic Matrix - to calculate the elastic constants and elastic moduli.
• Harmonic and Quasi-harmonic Approximation - to calculate the density of states, vibrational free energy and thermal expansion based on the finite displacements method implemented in phonopy.
• Molecular Dynamics - to calculate finite temperature properties like thermal expansion including the anharmonic contributions.

All these workflows can be coupled with all the simulation codes implemented in the atomistics package. In contrast to the Atomic Simulation Environment which provides similar functionality the focus of the atomistics package is not to reimplement existing functionality but rather simplify the process of coupling existing simulation codes with existing workflows. Here the phonopy workflow is a great example to enable the calculation of thermodynamic properties with the harmonic and quasi-harmonic approximation.

Example

Use the equation of state to calculate the equilibrium properties like the equilibrium volume, equilibrium energy, equilibrium bulk modulus and its derivative using the GPAW simulation code

from ase.build import bulk
from atomistics.workflows import get_tasks_for_energy_volume_curve

task_dict = get_tasks_for_energy_volume_curve(
    structure=bulk("Al", a=4.05, cubic=True),
    num_points=11,
    vol_range=0.05,
    axes=["x", "y", "z"],
)
print(task_dict)

>>> {'calc_energy': OrderedDict([
>>>     (0.95, Atoms(symbols='Al4', pbc=True, cell=[3.9813426685908118, 3.9813426685908118, 3.9813426685908118])),
>>>     (0.96, Atoms(symbols='Al4', pbc=True, cell=[3.9952635604153612, 3.9952635604153612, 3.9952635604153612])),
>>>     (0.97, Atoms(symbols='Al4', pbc=True, cell=[4.009088111958974, 4.009088111958974, 4.009088111958974])),
>>>     (0.98, Atoms(symbols='Al4', pbc=True, cell=[4.022817972936038, 4.022817972936038, 4.022817972936038])),
>>>     (0.99, Atoms(symbols='Al4', pbc=True, cell=[4.036454748321015, 4.036454748321015, 4.036454748321015])),
>>>     (1.0, Atoms(symbols='Al4', pbc=True, cell=[4.05, 4.05, 4.05])),
>>>     (1.01, Atoms(symbols='Al4', pbc=True, cell=[4.063455248345461, 4.063455248345461, 4.063455248345461])),
>>>     (1.02, Atoms(symbols='Al4', pbc=True, cell=[4.076821973718458, 4.076821973718458, 4.076821973718458])),
>>>     (1.03, Atoms(symbols='Al4', pbc=True, cell=[4.0901016179023415, 4.0901016179023415, 4.0901016179023415])),
>>>     (1.04, Atoms(symbols='Al4', pbc=True, cell=[4.1032955854717175, 4.1032955854717175, 4.1032955854717175])),
>>>     (1.05, Atoms(symbols='Al4', pbc=True, cell=[4.1164052451001565, 4.1164052451001565, 4.1164052451001565]))
>>> ])}

In the first step the EnergyVolumeCurveWorkflow object is initialized including all the parameters to generate the strained structures and afterwards fit the resulting energy volume curve. This allows the user to see all relevant parameters at one place. After the initialization the function generate_structures() is called without any additional parameters. This function returns the task dictionary task_dict which includes the tasks which should be executed by the calculator. In this case the task is to calculate the energy calc_energy of the eleven generated structures. Each structure is labeled by the ratio of compression or elongation. In the second step the task_dict is evaluate with the GPAW simulation code using the evaluate_with_ase() function:

from atomistics.calculators import evaluate_with_ase
from gpaw import GPAW, PW

result_dict = evaluate_with_ase(
    task_dict=task_dict, ase_calculator=GPAW(xc="PBE", mode=PW(300), kpts=(3, 3, 3))
)
print(result_dict)

>>> {'energy': {
>>>     0.95: -14.895378072824752,
>>>     0.96: -14.910819737657118,
>>>     0.97: -14.922307241122466,
>>>     0.98: -14.930392279321056,
>>>     0.99: -14.935048569964911,
>>>     1.0: -14.936666396364169,
>>>     1.01: -14.935212782128556,
>>>     1.02: -14.931045138839849,
>>>     1.03: -14.924165445706581,
>>>     1.04: -14.914703574005678,
>>>     1.05: -14.902774559134226
>>> }}

In analogy to the task_dict which defines the tasks to be executed by the simulation code the result_dict summarizes the results of the calculations. In this case the energies calculated for the specific strains. By ordering both the task_dict and the result_dict with the same labels, the EnergyVolumeCurveWorkflow object is able to match the calculation results to the corresponding structure. Finally, in the third step the analyse_structures() function takes the result_dict as an input and fits the Equation of State with the fitting parameters defined in the first step:

from atomistics.workflows import analyse_results_for_energy_volume_curve

fit_dict = analyse_results_for_energy_volume_curve(
    output_dict=result_dict,
    task_dict=task_dict,
    fit_type="polynomial",
    fit_order=3,
)
print(fit_dict)

>>> {'poly_fit': array([-9.30297838e-05,  2.19434659e-02, -1.68388816e+00,  2.73605421e+01]),
>>>  'fit_type': 'polynomial',
>>>  'fit_order': 3,
>>>  'volume_eq': 66.44252286131888,
>>>  'energy_eq': -14.93670322204575,
>>>  'bulkmodul_eq': 72.38919826304497,
>>>  'b_prime_eq': 4.45383655040775,
>>>  'least_square_error': 4.432974529908853e-09,
>>>  'volume': [63.10861874999998, 63.77291999999998, ..., 69.75163125000002],
>>>  'energy': [-14.895378072824752, -14.910819737657118, ..., -14.902774559134226]
>>> }

As a result the equilibrium parameters are returned plus the parameters of the polynomial and the set of volumes and energies which were fitted to achieve these results. The important step here is that while the interface between the first and the second as well as between the second and the third step is clearly defined independent of the specific workflow, the initial parameters for the workflow to initialize the EnergyVolumeCurveWorkflow object as well as the final output of the fit_dict are workflow specific.

Disclaimer

While we try to develop a stable and reliable software library, the development remains a opensource project under the BSD 3-Clause License without any warranties:

BSD 3-Clause License

Copyright (c) 2023, Jan Janssen
All rights reserved.

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Documentation

• Installation
  • conda-based Installation
  • pypi-based Installation
• Simulation Codes
  • ASE
  • LAMMPS
  • Quantum Espresso
• Workflows
  • Elastic Matrix
  • Energy Volume Curve
  • Molecular Dynamics
  • Harmonic Approximation
  • Structure Optimization
• Materials Properties
  • Elastic Properties
  • Thermal Expansion
  • Helmholtz Free Energy
  • Phase Diagram