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 actuality, \(s_{ij}\) is replaced with a switching function so as to ensure that the calculated CV has continuous derivatives. 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".

- 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 neighbor list is used to make this calculation faster, this neighbor list is updated every 100 steps.

Click on the labels of the actions for more information on what each action computes

COORDINATIONGROUPA=1-10First list of atoms.GROUPB=20-100Second list of atoms (if empty, N*(N-1)/2 pairs in GROUPA are counted).R_0=0.3could not find this keywordNLIST( default=off ) Use a neighbor list to speed up the calculationNL_CUTOFF=0.5The cutoff for the neighbor listNL_STRIDE=100The frequency with which we are updating the atoms in the neighbor list

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.

Click on the labels of the actions for more information on what each action computes

c:COORDINATIONGROUPA=1First list of atoms.GROUPB=1Second list of atoms (if empty, N*(N-1)/2 pairs in GROUPA are counted).R_0=0.3 PRINTcould not find this keywordARG=the input for this action is the scalar output from one or more other actions.cSTRIDE=10compulsory keyword ( default=1 )the frequency with which the quantities of interest should be output

Here's an example that shows what happens when providing COORDINATION with a single group:

Click on the labels of the actions for more information on what each action computes

# define some huge group:group:GROUPATOMS=1-1000 # Here's coordination of a group against itself:the numerical indexes for the set of atoms in the group.c1:COORDINATIONGROUPA=First list of atoms.groupGROUPB=Second list of atoms (if empty, N*(N-1)/2 pairs in GROUPA are counted).groupR_0=0.3 # Here's coordination within a single group:could not find this keywordx:COORDINATIONGROUPA=First list of atoms.groupR_0=0.3 # This is just multiplying times 2 the variable x:could not find this keywordc2:COMBINEARG=the input for this action is the scalar output from one or more other actions.xCOEFFICIENTS=2compulsory keyword ( default=1.0 )the coefficients of the arguments in your functionPERIODIC=NO # 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. PRINTcompulsory keywordif the output of your function is periodic then you should specify the periodicity of the function.ARG=the input for this action is the scalar output from one or more other actions.c1,c2STRIDE=10compulsory keyword ( default=1 )the frequency with which the quantities of interest should be output

- Glossary of keywords and components

- 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 neighbor list to speed up the calculation |

NL_CUTOFF | The cutoff for the neighbor list |

NL_STRIDE | The frequency with which we are updating the atoms in the neighbor list |

SWITCH | This keyword is used if you want to employ an alternative to the continuous switching 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. |