SPRINT

This is part of the adjmat module | |

It is only available if you configure PLUMED with ./configure –enable-modules=adjmat . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Calculate SPRINT topological variables from an adjacency matrix.

The SPRINT topological variables are calculated from the largest eigenvalue, \(\lambda\) of an \(n\times n\) adjacency matrix and its corresponding eigenvector, \(\mathbf{V}\), using:

\[ s_i = \sqrt{n} \lambda v_i \]

You can use different quantities to measure whether or not two given atoms/molecules are adjacent or not in the adjacency matrix. The simplest measure of adjacency is is whether two atoms/molecules are within some cutoff of each other. Further complexity can be added by insisting that two molecules are adjacent if they are within a certain distance of each other and if they have similar orientations.

- Examples

This example input calculates the 7 SPRINT coordinates for a 7 atom cluster of Lennard-Jones atoms and prints their values to a file. In this input the SPRINT coordinates are calculated in the manner described in ?? so two atoms are adjacent if they are within a cutoff:

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

d1:DENSITYSPECIES=1-7this keyword is used for colvars such as coordination number.mat:CONTACT_MATRIXATOMS=The list of atoms for which you would like to calculate the contact matrix.d1SWITCH={RATIONAL R_0=0.1}This keyword is used if you want to employ an alternative to the continuous switching function defined above.ss:SPRINTMATRIX=compulsory keywordthe action that calculates the adjacency matrix vessel we would like to analyzematPRINTARG=the input for this action is the scalar output from one or more other actions.ss.*FILE=colvarthe name of the file on which to output these quantities

This example input calculates the 14 SPRINT coordinates for a molecule composed of 7 hydrogen and 7 carbon atoms. Once again two atoms are adjacent if they are within a cutoff:

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

c:DENSITYSPECIES=1-7this keyword is used for colvars such as coordination number.h:DENSITYSPECIES=8-14this keyword is used for colvars such as coordination number.mat:CONTACT_MATRIX ...ATOMS=The list of atoms for which you would like to calculate the contact matrix.c,hSWITCH11={RATIONAL R_0=2.6 NN=6 MM=12}This keyword is used if you want to employ an alternative to the continuous switching function defined above.SWITCH12={RATIONAL R_0=2.2 NN=6 MM=12}This keyword is used if you want to employ an alternative to the continuous switching function defined above.SWITCH22={RATIONAL R_0=2.2 NN=6 MM=12} ...ss:SPRINTMATRIX=compulsory keywordthe action that calculates the adjacency matrix vessel we would like to analyzematPRINTARG=the input for this action is the scalar output from one or more other actions.ss.*FILE=colvarthe name of the file on which to output these quantities

- Glossary of keywords and components

- Description of components

By default this Action calculates the following quantities. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

Quantity | Description |

coord | all \(n\) sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on |

In addition the following quantities can be calculated by employing the keywords listed below

Quantity | Keyword | Description |

gradient | GRADIENT | the gradient |

vmean | VMEAN | the norm of the mean vector. The output component can be referred to elsewhere in the input file by using the label.vmean |

vsum | VSUM | the norm of sum of vectors. The output component can be referred to elsewhere in the input file by using the label.vsum |

spath | SPATH | the position on the path |

gspath | GPATH | the position on the path calculated using trigonometry |

gzpath | GPATH | the distance from the path calculated using trigonometry |

zpath | ZPATH | the distance from the path |

altmin | ALT_MIN | the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

between | BETWEEN | the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

highest | HIGHEST | the highest of the quantities calculated by this action |

lessthan | LESS_THAN | the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

lowest | LOWEST | the lowest of the quantities calculated by this action |

max | MAX | the maximum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

mean | MEAN | the mean value. The output component can be referred to elsewhere in the input file by using the label.mean |

min | MIN | the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

moment | MOMENTS | the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc. |

morethan | MORE_THAN | the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

sum | SUM | the sum of values |

- Compulsory keywords

MATRIX | the action that calculates the adjacency matrix vessel we would like to analyze |

- 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 ) do the calculation in serial. Do not use MPI |

LOWMEM | ( default=off ) lower the memory requirements |

TIMINGS | ( default=off ) output information on the timings of the various parts of the calculation |