NOON gap
========

The gap between two natural orbital occupation numbers (NOONs)  :math:`n_i,n_j` is defined as

.. math::
    \Delta n = n_j-n_i

The use of the energy gap is invoked by the following block in the `meta-config.json` \
file::

    "collective variables": [
      {
        "type": "noongap",
        "name": "noon gap between two natural orbitals",
        "no_index1": j,
        "no_index2": i,
        "do_multistate": False
        "nproc": 1
      },
      ...
    ]

``"no_index1"`` is the keyword for the orbital with the lower occupation number and ``"no_index2"``
is the keyword for the orbital with the higher occupation number. Orbital counting starts at 0.
Gradients are calculated numerically. This is step is parallelized using the :mod:`multiprocessing`
python package. The number of used processors is specified with the ``"nproc"`` keyword.
Currently, only the :doc:`Molpro <../interfaces/molpro>` calculator interface can be used in
combination with this CV and it has to provide natural orbital occupation numbers. For this purpose,
Molpro has to print an xml file with the name `natural.xml` containing the natural orbital
information. Include the following code in your Molpro tail file::

    put,xml,natural.xml;orb,2141.2

`2141.2` is the directive in the Molpro wavefunction file where the natural orbital information is
stored.

The Multistate Metadynamics extension is used, when ``"do_multistate"`` is set to ``True``. In this \
case, the configuration for a second metadynamics instance has to be provided under the \
``"metadynamics_multistate"`` keyword in the `meta-config.json` file.