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PLUMED manual

Shortcut: COORDINATIONNUMBER

Shortcut: COORDINATIONNUMBER

Module	symfunc
Description	Usage
Calculate the coordination numbers of atoms so that you can then calculate functions of the distribution of
output value	type
the coordination numbers of the specified atoms	vector

Details and examples

Calculate the coordination numbers of atoms so that you can then calculate functions of the distribution of coordination numbers such as the minimum, the number less than a certain quantity and so on.

The coordination number of a atom $i$ is the number of atoms that are within a certain cutoff distance of it. This quantity can be calculated as follows:

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

where $r_{ij}$ is the distance between atoms $i$ and $j$ and $\sigma$ is a switching function. The typical switching function that is used in metadynamics is this one:

$s(r) = \frac{ 1 - \left(\frac{r-d_0}{r_0}\right)^n } { 1 - \left(\frac{r-d_0}{r_0}\right)^m }$

The following example shows how you can use this shortcut action to calculate and print the coordination numbers of one hundred atoms with themselves:

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

cThe COORDINATIONNUMBER action with label c calculates the following quantities: Quantity    Type    Description  
c vector the coordination numbers of the specified atoms: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and it has hidden defaults. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-100 R_0The r_0 parameter of the switching function=1.0
c: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and uses the defaults shown here. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-100 R_0The r_0 parameter of the switching function=1.0  D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# c: COORDINATIONNUMBER SPECIES=1-100 R_0=1.0
# as follows (Click the red comment above to revert to the short version of the input):
c_grpThe GROUP action with label c_grp calculates the following quantities: Quantity    Type    Description  
c_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=1-100
c_matThe CONTACT_MATRIX action with label c_mat calculates the following quantities: Quantity    Type    Description  
c_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=1-100 R_0The r_0 parameter of the switching function=1.0 D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
c_onesThe CONSTANT action with label c_ones calculates the following quantities: Quantity    Type    Description  
c_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=100
cThe MATRIX_VECTOR_PRODUCT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=c_mat,c_ones
# --- End of included input --- DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=c ARGthe labels of vectors that should be output in the xyz file=c FILEfile on which to output coordinates; extension is automatically detected=coords.xyz

This input will produce an output file called coords that contains the coordination numbers of the 100 input atoms. The cutoff that is used to calculate the coordination number in this case is 1.0. In the input above we use a rational switching function with the parameters above. We would recommend using SWITCH syntax rather than the syntax above when giving the parameters for the switching function as you can then use any of the switching functions described in the documentation for LESS_THAN. More importantly, however, using this syntax allows you to set the D_MAX parameter for the switching function as demonstrated below:

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

cThe COORDINATIONNUMBER action with label c calculates the following quantities: Quantity    Type    Description  
c vector the coordination numbers of the specified atoms: 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=1-100 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}
# PLUMED interprets the command:
# c: COORDINATIONNUMBER SPECIES=1-100 SWITCH={RATIONAL R_0=1.0}
# as follows (Click the red comment above to revert to the short version of the input):
c_grpThe GROUP action with label c_grp calculates the following quantities: Quantity    Type    Description  
c_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=1-100
c_matThe CONTACT_MATRIX action with label c_mat calculates the following quantities: Quantity    Type    Description  
c_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=1-100 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}
c_onesThe CONSTANT action with label c_ones calculates the following quantities: Quantity    Type    Description  
c_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=100
cThe MATRIX_VECTOR_PRODUCT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=c_mat,c_ones
# --- End of included input --- DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=c ARGthe labels of vectors that should be output in the xyz file=c FILEfile on which to output coordinates; extension is automatically detected=coords.xyz

Setting the D_MAX can substantially improve PLUMED performance as it turns on the linked list algorithm that is discussed in the optimisation details part of the documentation for CONTACT_MATRIX.

The vectors that are output by the COORDINATIONNUMBER shortcut can be used in the input for many other functions that are within PLUMED. In addition, in order to ensure compatibility with older versions of PLUMED you can add additional keywords on the input line for COORDINATIONNUMBER in order to calculate various functions of the input. For example, the following input tells plumed ato calculate the coordination numbers of atoms 1-100 with themselves. The minimum coordination number is then calculated.

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

cThe COORDINATIONNUMBER action with label c calculates the following quantities: Quantity    Type    Description  
c vector the coordination numbers of the specified atoms
c_min scalar the minimum colvar: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and it has hidden defaults. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-100 R_0The r_0 parameter of the switching function=1.0 MINcalculate the minimum value={BETA=0.1}
c: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and uses the defaults shown here. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-100 R_0The r_0 parameter of the switching function=1.0 MINcalculate the minimum value={BETA=0.1}  D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# c: COORDINATIONNUMBER SPECIES=1-100 R_0=1.0 MIN={BETA=0.1}
# as follows (Click the red comment above to revert to the short version of the input):
c_grpThe GROUP action with label c_grp calculates the following quantities: Quantity    Type    Description  
c_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=1-100
c_matThe CONTACT_MATRIX action with label c_mat calculates the following quantities: Quantity    Type    Description  
c_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=1-100 R_0The r_0 parameter of the switching function=1.0 D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
c_onesThe CONSTANT action with label c_ones calculates the following quantities: Quantity    Type    Description  
c_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=100
cThe MATRIX_VECTOR_PRODUCT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=c_mat,c_ones
c_me_minThe CUSTOM action with label c_me_min calculates the following quantities: Quantity    Type    Description  
c_me_min vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c FUNCthe function you wish to evaluate=exp(0.1/x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c_mec_minThe SUM action with label c_mec_min calculates the following quantities: Quantity    Type    Description  
c_mec_min scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=c_me_min PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c_minThe CUSTOM action with label c_min calculates the following quantities: Quantity    Type    Description  
c_min scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c_mec_min FUNCthe function you wish to evaluate=0.1/log(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

By constrast, this input tells plumed to calculate how many atoms from 1-100 are within 3.0 of each of the atoms from 101-110. In the first 101 is the central atom, in the second 102 is the central atom and so on. The number of coordination numbers that are more than 6 is then computed.

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

cThe COORDINATIONNUMBER action with label c calculates the following quantities: Quantity    Type    Description  
c vector the coordination numbers of the specified atoms: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and it has hidden defaults. More details SPECIESAthe list of atoms for which the symmetry function is being calculated=101-110 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=1-100 R_0The r_0 parameter of the switching function=3.0
c: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and uses the defaults shown here. More details SPECIESAthe list of atoms for which the symmetry function is being calculated=101-110 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=1-100 R_0The r_0 parameter of the switching function=3.0  D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# c: COORDINATIONNUMBER SPECIESA=101-110 SPECIESB=1-100 R_0=3.0
# as follows (Click the red comment above to revert to the short version of the input):
c_grpThe GROUP action with label c_grp calculates the following quantities: Quantity    Type    Description  
c_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=101-110
c_matThe CONTACT_MATRIX action with label c_mat calculates the following quantities: Quantity    Type    Description  
c_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 GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=101-110 GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=1-100 R_0The r_0 parameter of the switching function=3.0 D_0 The d_0 parameter of the switching function=0.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
c_onesThe CONSTANT action with label c_ones calculates the following quantities: Quantity    Type    Description  
c_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=100
cThe MATRIX_VECTOR_PRODUCT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=c_mat,c_ones
# --- End of included input --- mtThe MORE_THAN action with label mt calculates the following quantities: Quantity    Type    Description  
mt vector the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=c SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL R_0=6.0 NN=6 MM=12 D_0=0}
sThe SUM action with label s calculates the following quantities: Quantity    Type    Description  
s scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=mt PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO

The MASK keyword

Supppose that you want to calculate the average coordination number for the atoms that are within a sphere in the center of your simulation box. You can do so by exploiting an input similar to the one shown below:

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

# Fixed virtual atom which serves as the probe volume's center (pos. in nm)
centerThe FIXEDATOM action with label center calculates the following quantities: Quantity    Type    Description  
center atoms virtual atom calculated by FIXEDATOM action: FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=2.5,2.5,2.5
center: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=2.5,2.5,2.5  SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0
# Vector in which element i is one if atom i is in sphere of interest and zero otherwise
sphereThe INSPHERE action with label sphere calculates the following quantities: Quantity    Type    Description  
sphere vector vector of numbers between 0 and 1 that measure the degree to which each atom is within the volume of interest: INSPHEREThis quantity can be used to calculate functions of the distribution of collective variables for the atoms that lie in a particular, user-specified part of of the cell. More details ATOMSthe group of atoms that you would like to investigate=1-400 CENTERthe atom whose vicinity we are interested in examining=center RADIUSthe switching function that tells us the extent of the sphereical region of interest. Options for this keyword are explained in the documentation for LESS_THAN.={GAUSSIAN D_0=0.5 R_0=0.01 D_MAX=0.52}
# Calculate the coordination numbers
ccThe COORDINATIONNUMBER action with label cc calculates the following quantities: Quantity    Type    Description  
cc vector the coordination numbers of the specified atoms: 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=1-400 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 D_0=3.0 R_0=1.5 D_MAX=6.0}
# PLUMED interprets the command:
# cc: COORDINATIONNUMBER SPECIES=1-400 SWITCH={RATIONAL D_0=3.0 R_0=1.5 D_MAX=6.0}
# as follows (Click the red comment above to revert to the short version of the input):
cc_grpThe GROUP action with label cc_grp calculates the following quantities: Quantity    Type    Description  
cc_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=1-400
cc_matThe CONTACT_MATRIX action with label cc_mat calculates the following quantities: Quantity    Type    Description  
cc_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=1-400 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 D_0=3.0 R_0=1.5 D_MAX=6.0}
cc_onesThe CONSTANT action with label cc_ones calculates the following quantities: Quantity    Type    Description  
cc_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=400
ccThe MATRIX_VECTOR_PRODUCT action with label cc calculates the following quantities: Quantity    Type    Description  
cc 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=cc_mat,cc_ones
# --- End of included input --- # Multiply fccubic parameters numbers by sphere vector
prodThe CUSTOM action with label prod calculates the following quantities: Quantity    Type    Description  
prod vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=cc,sphere FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Sum of coordination numbers for atoms that are in the sphere of interest
numerThe SUM action with label numer calculates the following quantities: Quantity    Type    Description  
numer scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=prod PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Number of atoms that are in sphere of interest
denomThe SUM action with label denom calculates the following quantities: Quantity    Type    Description  
denom scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=sphere PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Average coordination number for atoms in sphere of interest
avThe CUSTOM action with label av calculates the following quantities: Quantity    Type    Description  
av scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=numer,denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# And print out final CV to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=av FILEthe name of the file on which to output these quantities=colvar STRIDE the frequency with which the quantities of interest should be output=1

This calculation is slow because you have to calculate the coordination numbers of all the atoms even though only a small subset of these quanitties are required to compute the average coordination number in the sphere. To avoid all these unecessary calculations you use the MASK keyword as shown below:

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

# Fixed virtual atom which serves as the probe volume's center (pos. in nm)
centerThe FIXEDATOM action with label center calculates the following quantities: Quantity    Type    Description  
center atoms virtual atom calculated by FIXEDATOM action: FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=2.5,2.5,2.5
center: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=2.5,2.5,2.5  SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0
# Vector in which element i is one if atom i is in sphere of interest and zero otherwise
sphereThe INSPHERE action with label sphere calculates the following quantities: Quantity    Type    Description  
sphere vector vector of numbers between 0 and 1 that measure the degree to which each atom is within the volume of interest: INSPHEREThis quantity can be used to calculate functions of the distribution of collective variables for the atoms that lie in a particular, user-specified part of of the cell. More details ATOMSthe group of atoms that you would like to investigate=1-400 CENTERthe atom whose vicinity we are interested in examining=center RADIUSthe switching function that tells us the extent of the sphereical region of interest. Options for this keyword are explained in the documentation for LESS_THAN.={GAUSSIAN D_0=0.5 R_0=0.01 D_MAX=0.52}
# Calculate the coordination numbers
ccThe COORDINATIONNUMBER action with label cc calculates the following quantities: Quantity    Type    Description  
cc vector the coordination numbers of the specified atoms: 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=1-400 MASKthe label for a vector that is used to determine which rows of the matrix are computed=sphere 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 D_0=3.0 R_0=1.5 D_MAX=6.0}
# PLUMED interprets the command:
# cc: COORDINATIONNUMBER SPECIES=1-400 MASK=sphere SWITCH={RATIONAL D_0=3.0 R_0=1.5 D_MAX=6.0}
# as follows (Click the red comment above to revert to the short version of the input):
cc_grpThe GROUP action with label cc_grp calculates the following quantities: Quantity    Type    Description  
cc_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=1-400
cc_matThe CONTACT_MATRIX action with label cc_mat calculates the following quantities: Quantity    Type    Description  
cc_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=1-400 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 D_0=3.0 R_0=1.5 D_MAX=6.0} MASKa vector that is used to used to determine which rows of the adjancency matrix to compute=sphere
cc_onesThe CONSTANT action with label cc_ones calculates the following quantities: Quantity    Type    Description  
cc_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=400
ccThe MATRIX_VECTOR_PRODUCT action with label cc calculates the following quantities: Quantity    Type    Description  
cc 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=cc_mat,cc_ones
# --- End of included input --- # Multiply fccubic parameters numbers by sphere vector
prodThe CUSTOM action with label prod calculates the following quantities: Quantity    Type    Description  
prod vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=cc,sphere FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Sum of coordination numbers for atoms that are in the sphere of interest
numerThe SUM action with label numer calculates the following quantities: Quantity    Type    Description  
numer scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=prod PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Number of atoms that are in sphere of interest
denomThe SUM action with label denom calculates the following quantities: Quantity    Type    Description  
denom scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=sphere PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Average coordination number for atoms in sphere of interest
avThe CUSTOM action with label av calculates the following quantities: Quantity    Type    Description  
av scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=numer,denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# And print out final CV to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=av FILEthe name of the file on which to output these quantities=colvar STRIDE the frequency with which the quantities of interest should be output=1

Adding the instruction MASK=sphere to the CONTACT_MATRIX line in this input tells PLUMED to only calculate the $i$ th row in the adjacency matrix if the $i$ th element of the vector sphere is non-zero. In other words, by adding this command we have ensured that we are not calculating coordination numbers for atoms that are not in the sphere that is of interest. In this way we can thus reduce the computational expense of the calculation enormously.

Notice, that there are other places where we can use this same trick. Some further examples are given in the documentation for CONTACT_MATRIX.

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

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

Full list of keywords

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
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.
MASK	optional	not used	the label for a vector that is used to determine which rows of the matrix are computed

deprecated keywords

The keywords in the following table can still be used with this action but have been deprecated

Keyword	Description
LESS_THAN	calculate the number of variables that are less than a certain target value
MORE_THAN	calculate the number of variables that are more than a certain target value
ALT_MIN	calculate the minimum value
MIN	calculate the minimum value
MAX	calculate the maximum value
BETWEEN	calculate the number of values that are within a certain range
HIGHEST	this flag allows you to recover the highest of these variables
HISTOGRAM	calculate a discretized histogram of the distribution of values
LOWEST	this flag allows you to recover the lowest of these variables
SUM	calculate the sum of all the quantities
MEAN	calculate the mean of all the quantities
LOWMEM	Including this keyword in the input to this action makes no difference to the calculation performed it was used in older versions of PLUMED and is provided here for back compatibility only
MOMENTS	the list of moments that you would like to calculate

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)