Shortcut: COORDINATION_SHELL_FUNCTION

Module	symfunc
Description	Usage
Calculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom
output value	type
the symmetry function for each of the specified atoms	vector

Details and examples

Calculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom

This shortcut allows you to calculate the sum for an arbitrary function of the bond vectors that connect an atom to each of its neighbours. In other words, this action allows you to compute the following:

$s_i = \sum_{i \ne j} \sigma(r_{ij}) f(x_{ij}, y_{ij}, z_{ij}, r_{ij}) )$

In this expression, $x_{ij}, y_{ij}, z_{ij}$ are the components of the vector connecting atoms $i$ and $j$ and $r_{ij}$ is the magnitude of this vector. $\sigma(r_{ij})$ is then a switching function that ensures that the aritrary function $f$ is only evaluated for if atom $j$ is within a certain cutoff distance of atom $i$ .

Below you can see a simple example that shows how this action can be used in practise.

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

cvThe COORDINATION_SHELL_FUNCTION action with label cv calculates the following quantities: Quantity    Type    Description  
cv vector the symmetry function for each of the specified atoms: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-64 D_0 The d_0 parameter of the switching function=3.0 R_0The r_0 parameter of the switching function=1.5 FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
cv: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-64 D_0 The d_0 parameter of the switching function=3.0 R_0The r_0 parameter of the switching function=1.5 FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0 PHI The Euler rotational angle phi=0.0 THETA The Euler rotational angle theta=0.0 PSI The Euler rotational angle psi=0.0
# PLUMED interprets the command:
# cv: COORDINATION_SHELL_FUNCTION SPECIES=1-64 D_0=3.0 R_0=1.5 FUNCTION=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
# as follows (Click the red comment above to revert to the short version of the input):
cv_grpThe GROUP action with label cv_grp calculates the following quantities: Quantity    Type    Description  
cv_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=1-64
cv_matThe CONTACT_MATRIX action with label cv_mat calculates the following quantities: Quantity    Type    Description  
cv_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
cv_mat.x matrix the projection of the bond on the x axis
cv_mat.y matrix the projection of the bond on the y axis
cv_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=1-64 R_0The r_0 parameter of the switching function=1.5 D_0 The d_0 parameter of the switching function=3.0 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
cv_rThe CUSTOM action with label cv_r calculates the following quantities: Quantity    Type    Description  
cv_r 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=cv_mat.x,cv_mat.y,cv_mat.z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z)
cv_vfuncThe CUSTOM action with label cv_vfunc calculates the following quantities: Quantity    Type    Description  
cv_vfunc 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=cv_mat.x,cv_mat.y,cv_mat.z,cv_r VARthe names to give each of the arguments in the function=x,y,z,r PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
cv_wvfuncThe CUSTOM action with label cv_wvfunc calculates the following quantities: Quantity    Type    Description  
cv_wvfunc 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=cv_vfunc,cv_mat.w 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
cv_onesThe CONSTANT action with label cv_ones calculates the following quantities: Quantity    Type    Description  
cv_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=64
cvThe MATRIX_VECTOR_PRODUCT action with label cv calculates the following quantities: Quantity    Type    Description  
cv 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=cv_wvfunc,cv_ones
# --- 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=cv FILEthe name of the file on which to output these quantities=colvar

The above input calculates 64 $s_i$ values - one $s_i$ values for each of the atoms specified using the SPECIES keyword. These 64 numbers are then output to a file. The function of x, y, z and r to be evaluated is specified using the FUNCTION keyword. Obviously, if your function does not depend on all four of these variables they can be excluded from your function.

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

cvThe COORDINATION_SHELL_FUNCTION action with label cv calculates the following quantities: Quantity    Type    Description  
cv vector the symmetry function for each of the specified atoms: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-64 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=7.0}
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
...
cv: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-64 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=7.0}
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
 PHI The Euler rotational angle phi=0.0 THETA The Euler rotational angle theta=0.0 PSI The Euler rotational angle psi=0.0
...
# PLUMED interprets the command:
# cv: COORDINATION_SHELL_FUNCTION ...
#    SPECIES=1-64 SWITCH={RATIONAL D_0=3.0 R_0=1.5 D_MAX=7.0}
#    FUNCTION=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
# ...
# as follows (Click the red comment above to revert to the short version of the input):
cv_grpThe GROUP action with label cv_grp calculates the following quantities: Quantity    Type    Description  
cv_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=1-64
cv_matThe CONTACT_MATRIX action with label cv_mat calculates the following quantities: Quantity    Type    Description  
cv_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
cv_mat.x matrix the projection of the bond on the x axis
cv_mat.y matrix the projection of the bond on the y axis
cv_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=1-64 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=7.0} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
cv_rThe CUSTOM action with label cv_r calculates the following quantities: Quantity    Type    Description  
cv_r 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=cv_mat.x,cv_mat.y,cv_mat.z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z)
cv_vfuncThe CUSTOM action with label cv_vfunc calculates the following quantities: Quantity    Type    Description  
cv_vfunc 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=cv_mat.x,cv_mat.y,cv_mat.z,cv_r VARthe names to give each of the arguments in the function=x,y,z,r PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
cv_wvfuncThe CUSTOM action with label cv_wvfunc calculates the following quantities: Quantity    Type    Description  
cv_wvfunc 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=cv_vfunc,cv_mat.w 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
cv_onesThe CONSTANT action with label cv_ones calculates the following quantities: Quantity    Type    Description  
cv_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=64
cvThe MATRIX_VECTOR_PRODUCT action with label cv calculates the following quantities: Quantity    Type    Description  
cv 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=cv_wvfunc,cv_ones
# --- 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=cv FILEthe name of the file on which to output these quantities=colvar

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.

Rotating the reference frame

As discussed in this paper it is sometimes useful to rotate the bond vectors before computing the arbitrary function $f$ in the above expression. To perform such rotations you use the PHI, THETA and PSI keywords. The $x_{ij}, y_{ij}$ and $z_{ij}$ values that enter $f$ in the expression above are then calculated as:

$\left( \begin{matrix} x_{ij} \\ y_{ij} \\ z_{ij} \end{matrix} \right) = \left( \begin{matrix} \cos(\psi)\cos(\phi) - \cos(\theta)\sin(\phi)\sin(\psi) & \cos(\psi)*\sin(\phi)+\cos(\theta)*\cos(\phi)*\sin(\psi) & \sin(\psi)*sin(\theta) \\ -\sin(\psi)*\cos(\phi)-\cos(\theta)*\sin(\phi)*\cos(\psi) & -\sin(\psi)*\sin(\phi)+\cos(\theta)*\cos(\phi)*std::cos(\psi), & \cos(\psi)*\sin(\theta) \\ \sin(\theta)*\sin(\phi) & \sin(\theta)*\cos(\phi) & \cos(\theta) \end{matrix} \right) \left( \begin{matrix} x_{ij}' \\ y_{ij}' \\ z_{ij}' \end{matrix} \right)$

$x_{ij}', y_{ij}'$ and $z_{ij}'$ in this expression are the bond vectors that are calculated in the lab frame. The matrix in the above expression is thus just a rotation matrix that converts the lab frame to some frame of interest.

Working with two types of atom

If you would like to calculate a function of the bonds connecting the atoms in GROUPA to the atoms in GROUPB you can use an input like the one shown below:

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

dThe COORDINATION_SHELL_FUNCTION action with label d calculates the following quantities: Quantity    Type    Description  
d vector the symmetry function for each of the specified atoms: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom This action is a shortcut and it has hidden defaults. More details ...
   SPECIESAthe list of atoms for which the symmetry function is being calculated=1-64 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=65-200
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
   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}
...
d: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-64 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=65-200
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
   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}
 PHI The Euler rotational angle phi=0.0 THETA The Euler rotational angle theta=0.0 PSI The Euler rotational angle psi=0.0
...
# PLUMED interprets the command:
# d: COORDINATION_SHELL_FUNCTION ...
#    SPECIESA=1-64 SPECIESB=65-200
#    FUNCTION=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
#    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):
d_grpThe GROUP action with label d_grp calculates the following quantities: Quantity    Type    Description  
d_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=1-64
d_matThe CONTACT_MATRIX action with label d_mat calculates the following quantities: Quantity    Type    Description  
d_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
d_mat.x matrix the projection of the bond on the x axis
d_mat.y matrix the projection of the bond on the y axis
d_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 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=1-64 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=65-200 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} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
d_rThe CUSTOM action with label d_r calculates the following quantities: Quantity    Type    Description  
d_r 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=d_mat.x,d_mat.y,d_mat.z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z)
d_vfuncThe CUSTOM action with label d_vfunc calculates the following quantities: Quantity    Type    Description  
d_vfunc 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=d_mat.x,d_mat.y,d_mat.z,d_r VARthe names to give each of the arguments in the function=x,y,z,r PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
d_wvfuncThe CUSTOM action with label d_wvfunc calculates the following quantities: Quantity    Type    Description  
d_wvfunc 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=d_vfunc,d_mat.w 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
d_onesThe CONSTANT action with label d_ones calculates the following quantities: Quantity    Type    Description  
d_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=136
dThe MATRIX_VECTOR_PRODUCT action with label d calculates the following quantities: Quantity    Type    Description  
d 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=d_wvfunc,d_ones
# --- End of included input --- ltThe MORE_THAN action with label lt calculates the following quantities: Quantity    Type    Description  
lt 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=d SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL R_0=0.5}
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=lt PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=s FILEthe name of the file on which to output these quantities=colv

The MASK keyword

You can use the MASK keyword with this action in the same way that it is used with COORDINATIONNUMBER. This keyword thus expects a vector in input, which tells PLUMED the atoms for which you do not need to calculate the function. As illustrated below, this is useful if you are using functionality from the volumes module to calculate the average value of the TETRAHEDRAL parameter for only those atoms that lie in a certain part of the simulation box.

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 tetrahedral parameter of the atoms
dThe COORDINATION_SHELL_FUNCTION action with label d calculates the following quantities: Quantity    Type    Description  
d vector the symmetry function for each of the specified atoms: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-400 MASKthe label for a vector that is used to determine which rows of the matrix are computed=sphere
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
   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}
...
d: COORDINATION_SHELL_FUNCTIONCalculate an arbitrary function of all the bond vectors in the first coordination sphere of an atom 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=1-400 MASKthe label for a vector that is used to determine which rows of the matrix are computed=sphere
   FUNCTIONthe function of the bond vectors that you would like to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
   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}
 PHI The Euler rotational angle phi=0.0 THETA The Euler rotational angle theta=0.0 PSI The Euler rotational angle psi=0.0
...
# PLUMED interprets the command:
# d: COORDINATION_SHELL_FUNCTION ...
#    SPECIES=1-400 MASK=sphere
#    FUNCTION=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
#    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):
d_grpThe GROUP action with label d_grp calculates the following quantities: Quantity    Type    Description  
d_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
d_matThe CONTACT_MATRIX action with label d_mat calculates the following quantities: Quantity    Type    Description  
d_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
d_mat.x matrix the projection of the bond on the x axis
d_mat.y matrix the projection of the bond on the y axis
d_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=1-400 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} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix MASKa vector that is used to used to determine which rows of the adjancency matrix to compute=sphere
d_rThe CUSTOM action with label d_r calculates the following quantities: Quantity    Type    Description  
d_r 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=d_mat.x,d_mat.y,d_mat.z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z)
d_vfuncThe CUSTOM action with label d_vfunc calculates the following quantities: Quantity    Type    Description  
d_vfunc 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=d_mat.x,d_mat.y,d_mat.z,d_r VARthe names to give each of the arguments in the function=x,y,z,r PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=((x+y+z)/r)^3+((x-y-z)/r)^3+((-x+y-z)/r)^3+((-x-y+z)/r)^3
d_wvfuncThe CUSTOM action with label d_wvfunc calculates the following quantities: Quantity    Type    Description  
d_wvfunc 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=d_vfunc,d_mat.w 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
d_onesThe CONSTANT action with label d_ones calculates the following quantities: Quantity    Type    Description  
d_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
dThe MATRIX_VECTOR_PRODUCT action with label d calculates the following quantities: Quantity    Type    Description  
d 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=d_wvfunc,d_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=d,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 input calculate the average value of the function for only those atoms that are within a spherical region that is centered on the point $(2.5,2.5,2.5)$ .

Deprecated syntax

More information on the deprecated keywords that are given below is available in the documentation for the DISTANCES command.

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

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
FUNCTION	compulsory	none	the function of the bond vectors that you would like to evaluate
PHI	compulsory	0.0	The Euler rotational angle phi
THETA	compulsory	0.0	The Euler rotational angle theta
PSI	compulsory	0.0	The Euler rotational angle psi
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
USEGPUThis keyword do not have examples	optional	false	run part of this calculation on the GPU

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

References

More information about how this action can be used is available in the following articles:

Quantity	Type	Description
cv	vector	the symmetry function for each of the specified atoms