SPRINT

	This is part of the sprint module
	It is only available if you configure PLUMED with ./configure –enable-modules=sprint . 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: DENSITY 
SPECIES
compulsory keyword 
the atoms in the group 
=1-7  You cannot view the components that are calculated by each action for this input file. Sorry 
mat: CONTACT_MATRIX 
ATOMS
the atoms for which you would like to calculate the adjacency matrix. 
=d1 
SWITCH
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=0.1}   You cannot view the components that are calculated by each action for this input file. Sorry 
ss: SPRINT 
MATRIX
the matrix that you would like to perform SPRINT on 
=mat  You cannot view the components that are calculated by each action for this input file. Sorry 
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=ss.* 
FILE
the name of the file on which to output these quantities 
=colvar  You cannot view the components that are calculated by each action for this input file. Sorry 

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

contract shortcuts

c: DENSITY 
SPECIES
compulsory keyword 
the atoms in the group 
=1-7 The DENSITY action with label c
h: DENSITY 
SPECIES
compulsory keyword 
the atoms in the group 
=8-14 The DENSITY action with label h
mat: CONTACT_MATRIX ...
   
ATOMS
the atoms for which you would like to calculate the adjacency matrix. 
=c,h 
   
SWITCH11
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.6 NN=6 MM=12}  
   
SWITCH12
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.2 NN=6 MM=12}  
   
SWITCH22
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.2 NN=6 MM=12}  
   
...The CONTACT_MATRIX action with label mat calculates a single scalar value
ss: SPRINT 
MATRIX
the matrix that you would like to perform SPRINT on 
=mat The SPRINT action with label ss
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=ss.* 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

c: GROUP 
ATOMS
the numerical indexes for the set of atoms in the group. 
=1-7 The GROUP action with label c defines a group of atoms so that they can be referred to later in the input
h: GROUP 
ATOMS
the numerical indexes for the set of atoms in the group. 
=8-14 The GROUP action with label h defines a group of atoms so that they can be referred to later in the input
mat: CONTACT_MATRIX ...
   
ATOMS
the atoms for which you would like to calculate the adjacency matrix. 
=c,h 
   
SWITCH11
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.6 NN=6 MM=12}  
   
SWITCH12
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.2 NN=6 MM=12}  
   
SWITCH22
specify the switching function to use between two sets of indistinguishable atoms.
={RATIONAL R_0=2.2 NN=6 MM=12}  
   
...The CONTACT_MATRIX action with label mat calculates a single scalar value
ss_diag: DIAGONALIZE 
ARG
compulsory keyword 
the input matrix 
=mat 
VECTORS
compulsory keyword ( default=all )
the eigenvalues and vectors that you would like to calculate. 
=1 The DIAGONALIZE action with label ss_diag calculates the following quantities:

 Quantity   
 Description  
ss_diag.vals-1
the eigevalues of the input matrix  This is the 1th of these quantities
ss_diag.vecs-1
the eigenvectors of the input matrix  This is the 1th of these quantities


ss_sp: CUSTOM 
ARG
compulsory keyword 
the values input to this function 
=ss_diag.vals-1,ss_diag.vecs-1 
FUNC
compulsory keyword 
the function you wish to evaluate 
=sqrt(14)*x*y 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label ss_sp calculates a single scalar value
ss_selection1: SELECT_COMPONENTS 
ARG
compulsory keyword 
the value from which we are selecting components 
=ss_sp 
COMPONENTS
compulsory keyword 
the components in the input value that you woul like to build a new vector from 
=1,2,3,4,5,6,7 The SELECT_COMPONENTS action with label ss_selection1 calculates a single scalar value
ss1: SORT 
ARG
compulsory keyword 
the values input to this function 
=ss_selection1 The SORT action with label ss1 calculates the following quantities:

 Quantity   
 Description  
ss1.1
the 1th largest element of the vector ss_selection1
ss1.2
the 2th largest element of the vector ss_selection1
ss1.3
the 3th largest element of the vector ss_selection1
ss1.4
the 4th largest element of the vector ss_selection1
ss1.5
the 5th largest element of the vector ss_selection1
ss1.6
the 6th largest element of the vector ss_selection1
ss1.7
the 7th largest element of the vector ss_selection1


ss_coord-0: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.1 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-0 calculates a single scalar value
ss_coord-1: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.2 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-1 calculates a single scalar value
ss_coord-2: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.3 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-2 calculates a single scalar value
ss_coord-3: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.4 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-3 calculates a single scalar value
ss_coord-4: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.5 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-4 calculates a single scalar value
ss_coord-5: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.6 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-5 calculates a single scalar value
ss_coord-6: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss1.7 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-6 calculates a single scalar value
ss_selection2: SELECT_COMPONENTS 
ARG
compulsory keyword 
the value from which we are selecting components 
=ss_sp 
COMPONENTS
compulsory keyword 
the components in the input value that you woul like to build a new vector from 
=8,9,10,11,12,13,14 The SELECT_COMPONENTS action with label ss_selection2 calculates a single scalar value
ss2: SORT 
ARG
compulsory keyword 
the values input to this function 
=ss_selection2 The SORT action with label ss2 calculates the following quantities:

 Quantity   
 Description  
ss2.1
the 1th largest element of the vector ss_selection2
ss2.2
the 2th largest element of the vector ss_selection2
ss2.3
the 3th largest element of the vector ss_selection2
ss2.4
the 4th largest element of the vector ss_selection2
ss2.5
the 5th largest element of the vector ss_selection2
ss2.6
the 6th largest element of the vector ss_selection2
ss2.7
the 7th largest element of the vector ss_selection2


ss_coord-7: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.1 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-7 calculates a single scalar value
ss_coord-8: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.2 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-8 calculates a single scalar value
ss_coord-9: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.3 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-9 calculates a single scalar value
ss_coord-10: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.4 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-10 calculates a single scalar value
ss_coord-11: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.5 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-11 calculates a single scalar value
ss_coord-12: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.6 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-12 calculates a single scalar value
ss_coord-13: COMBINE 
ARG
compulsory keyword 
the values input to this function 
=ss2.7 
PERIODIC
compulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The COMBINE action with label ss_coord-13 calculates a single scalar value
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=ss.* 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 
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  
the sprint coordinates   

Options



 MATRIX  
the matrix that you would like to perform SPRINT on   

 GROUP  
specifies the list of atoms that should be assumed indistinguishable. You can use multiple instances of this keyword i.e. GROUP1, GROUP2, GROUP3...   

 SWITCH  
specify the switching function to use between two sets of indistinguishable atoms. You can use multiple instances of this keyword i.e. SWITCH1, SWITCH2, SWITCH3...