Shortcut: COORDINATION_MOMENTS

Module	symfunc
Description	Usage
Calculate moments of the distribution of distances in the first coordination sphere
output value	type
the coordination numbers of the specified atoms	vector

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Keyword	Description
lessthan	scalar	LESS_THAN	the number of colvars that have a value less than a threshold
morethan	scalar	MORE_THAN	the number of colvars that have a value more than a threshold
altmin	scalar	ALT_MIN	the minimum value of the cv
min	scalar	MIN	the minimum colvar
max	scalar	MAX	the maximum colvar
between	scalar	BETWEEN	the number of colvars that have a value that lies in a particular interval
highest	scalar	HIGHEST	the largest of the colvars
lowest	scalar	LOWEST	the smallest of the colvars
sum	scalar	SUM	the sum of the colvars
mean	scalar	MEAN	the mean of the colvars
moment	scalar	MOMENTS	the moments of the distribution

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
SPECIES	atoms	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	atoms	the list of atoms for which the symmetry function is being calculated
SPECIESB	atoms	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated

Further details and examples

Calculate moments of the distribution of distances in the first coordination sphere

This is the CV that was developed by White and Voth and is described in the paper in the bibliograhy below. This action provides a way of indirectly biasing radial distribution functions and computes the following function

$s_i = \sum_j \sigma(r_{ij})r_{ij}^k$

where $k$ is the value that is input using the R_POWER keyword, $r_{ij}$ is the distance between atoms $i$ and $j$ and $\sigma$ is a switching function.

The following example shows how this action can be used.

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

cn0The COORDINATIONNUMBER action with label cn0 calculates the following quantities: Quantity    Type    Description  
cn0 vector the coordination numbers of the specified atoms
cn0_mean scalar the mean of the colvars: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-10 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8} MEAN calculate the mean of all the quantities
# PLUMED interprets the command:
# cn0: COORDINATIONNUMBER SPECIES=1-10 SWITCH={RATIONAL R_0=1.0 D_MAX=8} MEAN
# as follows (Click the red comment above to revert to the short version of the input):
cn0_grpThe GROUP action with label cn0_grp calculates the following quantities: Quantity    Type    Description  
cn0_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=1-10
cn0_matThe CONTACT_MATRIX action with label cn0_mat calculates the following quantities: Quantity    Type    Description  
cn0_mat matrix a matrix containing the weights for the bonds between each pair of atoms: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-10 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8}
cn0_onesThe CONSTANT action with label cn0_ones calculates the following quantities: Quantity    Type    Description  
cn0_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=10
cn0The MATRIX_VECTOR_PRODUCT action with label cn0 calculates the following quantities: Quantity    Type    Description  
cn0 vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details  ARGthe label for the matrix and the vector/scalar that are being multiplied=cn0_mat,cn0_ones
cn0_caverageThe MEAN action with label cn0_caverage calculates the following quantities: Quantity    Type    Description  
cn0_caverage scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn0 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
cn0_meanThe MEAN action with label cn0_mean calculates the following quantities: Quantity    Type    Description  
cn0_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn0 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- cn1The COORDINATION_MOMENTS action with label cn1 calculates the following quantities: Quantity    Type    Description  
cn1 vector the coordination numbers of the specified atoms
cn1_mean scalar the mean of the colvars: COORDINATION_MOMENTSCalculate moments of the distribution of distances in the first coordination sphere This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-10 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8} R_POWERthe power to which you want to raise the distance=1 MEAN calculate the mean of all the quantities
# PLUMED interprets the command:
# cn1: COORDINATION_MOMENTS SPECIES=1-10 SWITCH={RATIONAL R_0=1.0 D_MAX=8} R_POWER=1 MEAN
# as follows (Click the red comment above to revert to the short version of the input):
cn1_grpThe GROUP action with label cn1_grp calculates the following quantities: Quantity    Type    Description  
cn1_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=1-10
cn1_matThe CONTACT_MATRIX action with label cn1_mat calculates the following quantities: Quantity    Type    Description  
cn1_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
cn1_mat.x matrix the projection of the bond on the x axis
cn1_mat.y matrix the projection of the bond on the y axis
cn1_mat.z matrix the projection of the bond on the z axis: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-10 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8} COMPONENTS also calculate the components of the vectors connecting the atoms in the contact matrix
cn1_onesThe CONSTANT action with label cn1_ones calculates the following quantities: Quantity    Type    Description  
cn1_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=10
cn1_powThe CUSTOM action with label cn1_pow calculates the following quantities: Quantity    Type    Description  
cn1_pow matrix the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=cn1_mat.x,cn1_mat.y,cn1_mat.z,cn1_mat.w VARthe names to give each of the arguments in the function=x,y,z,w PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=w*(sqrt(x*x+y*y+z*z)^1)
cn1The MATRIX_VECTOR_PRODUCT action with label cn1 calculates the following quantities: Quantity    Type    Description  
cn1 vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details  ARGthe label for the matrix and the vector/scalar that are being multiplied=cn1_pow,cn1_ones
cn1_caverageThe MEAN action with label cn1_caverage calculates the following quantities: Quantity    Type    Description  
cn1_caverage scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
cn1_meanThe MEAN action with label cn1_mean calculates the following quantities: Quantity    Type    Description  
cn1_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- cn2The COORDINATION_MOMENTS action with label cn2 calculates the following quantities: Quantity    Type    Description  
cn2 vector the coordination numbers of the specified atoms
cn2_mean scalar the mean of the colvars: COORDINATION_MOMENTSCalculate moments of the distribution of distances in the first coordination sphere This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-10 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8} R_POWERthe power to which you want to raise the distance=2 MEAN calculate the mean of all the quantities
# PLUMED interprets the command:
# cn2: COORDINATION_MOMENTS SPECIES=1-10 SWITCH={RATIONAL R_0=1.0 D_MAX=8} R_POWER=2 MEAN
# as follows (Click the red comment above to revert to the short version of the input):
cn2_grpThe GROUP action with label cn2_grp calculates the following quantities: Quantity    Type    Description  
cn2_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=1-10
cn2_matThe CONTACT_MATRIX action with label cn2_mat calculates the following quantities: Quantity    Type    Description  
cn2_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
cn2_mat.x matrix the projection of the bond on the x axis
cn2_mat.y matrix the projection of the bond on the y axis
cn2_mat.z matrix the projection of the bond on the z axis: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-10 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=1.0 D_MAX=8} COMPONENTS also calculate the components of the vectors connecting the atoms in the contact matrix
cn2_onesThe CONSTANT action with label cn2_ones calculates the following quantities: Quantity    Type    Description  
cn2_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=10
cn2_powThe CUSTOM action with label cn2_pow calculates the following quantities: Quantity    Type    Description  
cn2_pow matrix the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=cn2_mat.x,cn2_mat.y,cn2_mat.z,cn2_mat.w VARthe names to give each of the arguments in the function=x,y,z,w PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=w*(sqrt(x*x+y*y+z*z)^2)
cn2The MATRIX_VECTOR_PRODUCT action with label cn2 calculates the following quantities: Quantity    Type    Description  
cn2 vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details  ARGthe label for the matrix and the vector/scalar that are being multiplied=cn2_pow,cn2_ones
cn2_caverageThe MEAN action with label cn2_caverage calculates the following quantities: Quantity    Type    Description  
cn2_caverage scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
cn2_meanThe MEAN action with label cn2_mean calculates the following quantities: Quantity    Type    Description  
cn2_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=cn2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=cn0.mean,cn1.mean,cn2.mean STRIDE the frequency with which the quantities of interest should be output=1 FILEthe name of the file on which to output these quantities=cn_out

As you can see, it works similarlly to COORDINATIONNUMBER.

References

More information about how this action can be used is available in the following articles: - A. D. White, G. A. Voth, Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data. Journal of Chemical Theory and Computation. 10, 3023–3030 (2014)

Syntax

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
SPECIES	input	none	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	input	none	the list of atoms for which the symmetry function is being calculated
SPECIESB	input	none	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated
NN	compulsory	6	The n parameter of the switching function
MM	compulsory	0	The m parameter of the switching function; 0 implies 2*NN
D_0	compulsory	0.0	The d_0 parameter of the switching function
R_0	compulsory	none	The r_0 parameter of the switching function
R_POWER	compulsory	none	the power to which you want to raise the distance
SWITCH	optional	not used	the switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.
LESS_THAN	optional	not used	calculate the number of variables that are less than a certain target value. Options for this keyword are explained in the documentation for LESS_THAN.
MORE_THAN	optional	not used	calculate the number of variables that are more than a certain target value. Options for this keyword are explained in the documentation for MORE_THAN.
ALT_MIN	optional	not used	calculate the minimum value
MIN	optional	not used	calculate the minimum value
MAX	optional	not used	calculate the maximum value
BETWEEN	optional	not used	calculate the number of values that are within a certain range. Options for this keyword are explained in the documentation for BETWEEN.
HIGHEST	optional	false	this flag allows you to recover the highest of these variables
HISTOGRAM	optional	not used	calculate a discretized histogram of the distribution of values
LOWEST	optional	false	this flag allows you to recover the lowest of these variables
SUM	optional	false	calculate the sum of all the quantities
MEAN	optional	false	calculate the mean of all the quantities
LOWMEM	optional	false	this flag does nothing and is present only to ensure back-compatibility
MOMENTS	optional	not used	the list of moments that you would like to calculate

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Quantity	Type	Description
cn0	vector	the coordination numbers of the specified atoms
cn0_mean	scalar	the mean of the colvars