Lowest eigenvalue of the distance matrix¶

The geometric distance matrix is defined as

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

Similar to the Wiener number, the lowest eigenvalue to the geometric distance matrix $\epsilon_0$ represents a topographical descriptor related to the shape of the molecule.

The use of $\epsilon_0$ 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.