.. _dcdft tut:

Calculating Delta-values
========================

.. note::

  We are currently moving to a new way to display our examples.
  For this example we have an updated version.
  The example on this page is deprecated and will be removed
  once all examples have been moved to
  the new format.

In this tutorial we compare the equation-of-state (EOS) calculated for 7 FCC
metals using values from :class:`~ase.calculators.emt.EMT`, WIEN2k and
experiment. Each EOS is described by three parameters:

* volume per atom
* bulk-modulus
* pressure derivative of bulk-modulus

Differences between two EOS'es can be measured by a single :math:`\Delta` value
defined as:

.. math::

    \sqrt{\frac{\int_{V_a}^{V_b}
                (E_1(V) - E_2(V))^2 dV}
          {V_b - V_a}},

where :math:`E_n(V)` is the energy per atom as a function of volume.
The :math:`\Delta` value can be calculated using the
:func:`ase.utils.deltacodesdft.delta` function:

.. autofunction:: ase.utils.deltacodesdft.delta

.. seealso::

    * Collection of ground-state elemental crystals: :ref:`dcdft`
    * Equation-of-state module: :mod:`ase.eos`

We get the WIEN2k and experimental numbers from the :ref:`dcdft` ASE-collection
and we calculate the EMT EOS using this script:

.. literalinclude:: calculate.py

And fit to a Birch-Murnaghan EOS:

.. literalinclude:: fit.py

Result for Pt:

.. image:: Pt.png

Volumes in Ang^3:

.. csv-table::
    :file: volume.csv

Bulk moduli in GPa:

.. csv-table::
    :file: B.csv

Pressure derivative of bulk-moduli:

.. csv-table::
    :file: Bp.csv

Now, we can calculate :math:`\Delta` between EMT and WIEN2k for Pt:

>>> from ase.utils.deltacodesdft import delta
>>> from ase.units import kJ
>>> delta(15.08, 278.67 * 1e-24 * kJ, 5.31,
...       15.64, 248.71 * 1e-24 * kJ, 5.46)
0.03205389052984122

Here are all the values (in meV/atom) calculated with the script below:

.. csv-table::
    :file: delta.csv

.. literalinclude:: tables.py