   COORDINATION
 This is part of the colvar module

Calculate coordination numbers.

This keyword can be used to calculate the number of contacts between two groups of atoms and is defined as

$\sum_{i\in A} \sum_{i\in B} s_{ij}$

where $$s_{ij}$$ is 1 if the contact between atoms $$i$$ and $$j$$ is formed, zero otherwise. In practise, $$s_{ij}$$ is replaced with a switching function to make it differentiable. The default switching function is:

$s_{ij} = \frac{ 1 - \left(\frac{{\bf r}_{ij}-d_0}{r_0}\right)^n } { 1 - \left(\frac{{\bf r}_{ij}-d_0}{r_0}\right)^m }$

but it can be changed using the optional SWITCH option.

To make your calculation faster you can use a neighbor list, which makes it that only a relevant subset of the pairwise distance are calculated at every step.

If GROUPB is empty, it will sum the $$\frac{N(N-1)}{2}$$ pairs in GROUPA. This avoids computing twice permuted indexes (e.g. pair (i,j) and (j,i)) thus running at twice the speed.

Notice that if there are common atoms between GROUPA and GROUPB the switching function should be equal to one. These "self contacts" are discarded by plumed (since version 2.1), so that they actually count as "zero".

The atoms involved can be specified using
 GROUPA First list of atoms. For more information on how to specify lists of atoms see Groups and Virtual Atoms GROUPB Second list of atoms (if empty, N*(N-1)/2 pairs in GROUPA are counted). For more information on how to specify lists of atoms see Groups and Virtual Atoms
Compulsory keywords
 NN ( default=6 ) The n parameter of the switching function MM ( default=0 ) The m parameter of the switching function; 0 implies 2*NN D_0 ( default=0.0 ) The d_0 parameter of the switching function R_0 The r_0 parameter of the switching function
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically NOPBC ( default=off ) ignore the periodic boundary conditions when calculating distances SERIAL ( default=off ) Perform the calculation in serial - for debug purpose PAIR ( default=off ) Pair only 1st element of the 1st group with 1st element in the second, etc NLIST ( default=off ) Use a neighbour list to speed up the calculation NL_CUTOFF The cutoff for the neighbour list NL_STRIDE The frequency with which we are updating the atoms in the neighbour list SWITCH This keyword is used if you want to employ an alternative to the continuous swiching function defined above. The following provides information on the switchingfunction that are available. When this keyword is present you no longer need the NN, MM, D_0 and R_0 keywords.
Examples

The following example instructs plumed to calculate the total coordination number of the atoms in group 1-10 with the atoms in group 20-100. For atoms 1-10 coordination numbers are calculated that count the number of atoms from the second group that are within 0.3 nm of the central atom. A neighbour list is used to make this calculation faster, this neighbour list is updated every 100 steps.

COORDINATION GROUPA=1-10 GROUPB=20-100 R_0=0.3 NLIST NL_CUTOFF=0.5 NL_STRIDE=100


The following is a dummy example which should compute the value 0 because the self interaction of atom 1 is skipped. Notice that in plumed 2.0 "self interactions" were not skipped, and the same calculation should return 1.

c: COORDINATION GROUPA=1 GROUPB=1 R_0=0.3
PRINT ARG=c STRIDE=10

c1: COORDINATION GROUPA=1-10 GROUPB=1-10 R_0=0.3
x: COORDINATION GROUPA=1-10 R_0=0.3
c2: COMBINE ARG=x COEFFICIENTS=2
# the two variables c1 and c2 should be identical, but the calculation of c2 is twice faster
# since it runs on half of the pairs. Notice that to get the same result you
# should double it
PRINT ARG=c1,c2 STRIDE=10