Lowest eigenvalue of the distance matrix
========================================

The geometric distance matrix is defined as 

.. math::
    D =
    \begin{pmatrix}
        0      & d_{01} & d_{02} & ... & d_{0N} \\
        d_{10} & 0      & d_{12} & ... & d_{1N} \\
        d_{20} & d_{21} & 0      & ... & d_{2N} \\
        ...    & ...    & ...    & 0   & ...    \\
        d_{N0} & d_{N1} & d_{N2} & ... & 0
    \end{pmatrix}.

Similar to the :doc:`Wiener number <wiener>`, the lowest eigenvalue to the geometric distance \
matrix :math:`\epsilon_0` represents a topographical descriptor related to the shape of the molecule.

The use of :math:`\epsilon_0` is invoked by the following block in the `meta-config.json` file::

    "collective variables": [
      {
        "type": "firsteigenvalue",
        "name": "lowest eigenvalue to the distance matrix",
        "exclude_h": False
      },
      ...
    ]

The additional keyword ``"exclude_h"`` allows for the calculation of the distance matrix without \
considering distances from and to Hydrogen atoms.