Coordination number¶

The coordination number of an atom $i$ with respect to a set of reference atoms $k,l,m,...$ is defined as

$\mathrm{CN} = \sum_{j=k,l,m,...} \frac{(1-r_{ij}/d)^n}{(1-r_{ij}/d)^m},$

with the exponents $m>n$ . If only a single bond is taken into account, $\mathrm{CN}$ takes values close to 1, if $r_{ij}<d$ and gets approximately zero, if $r_{ij}>>d$ . The threshold $d$ therefore is a constant that can be diferent for every pair of atoms.

The use of the coordination number is invoked by the following block in the meta-config.json file:

"collective variables": [
  {
    "type": "bond",
    "name": "bond length between two atoms",
    "atom": i,
    "reference": [k, l, m, ...],
    "n": 6,
    "m": 12,
    "d": "auto"
  },
  ...
]

If "d": "auto", the distance thresholds are determined for each pair of atoms as the sum of their covalent radii. Other possibilities are to provide a single float number "d": d_0 that is used for all pairs or a list of floats corresponding to all pairs of atom $i$ and reference atoms $k,l,m,...$ "d": [d_ik, d_il, d_im, ...].

The choice of parameters can be checked by running the check_cn_parameters() function from the metafalcon.cvs.cvfunctions module:

from metafalcon.cvs.cvfunctions import check_cn_parameters

check_cn_parameters(n=6, m=12, d=1.0)

A file cv_parameters.png will be saved that looks like the following and allows for the critical evaluation of the parameters.