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PLUMED manual

Shortcut: HEXACTIC_PARAMETER

Shortcut: HEXACTIC_PARAMETER

Module	symfunc
Description	Usage
Calculate the hexatic order parameter
output value	type
the value of the cylindrical harmonic for each bond vector specified	matrix

Details and examples

Calculate the hexatic order parameter

This symmetry function can be used to understand phase transitions in two dimensional systems. The symmetry function for atom $k$ is calculated using:

$s_k = \left| \frac{\sum_j \sigma(r_{kj}) e^{6i\theta_j} }{\sum_j \sigma(r_{kj})} \right|$

In this expression, the sum run over all the atoms of interest and $r_{kj}$ is the distance between atom $k$ and atom $j$ and $\sigma$ is a switching function that acts upon this distance. $\theta_j$ is the angle between either the $x$ , $y$ or $z$ axis and the bond connecting atom $k$ and atom $j$ . This angle is multiplied by the imaginary number $i$ - the square root of minus one. In the code, we thus calculate $e^{i\theta_j}$ as follows:

$e^{i\theta_j} = \frac{x_{kj}}{r_{kj}} + i \frac{y_{kj}}{r_{kj}}$

We then take the 6th power of this complex number directly before compupting the magnitude by multiplying the result by its complex conjugate. Notice, furthermore, that we can replace $x_{kj}$ or $y_{kj}$ with $z_{kj}$ by using PLANE=xz or PLANE=yz in place of PLANE=xy.

An example that shows how you can use this shortcut is shown below:

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

hexThe CYLINDRICAL_HARMONIC action with label hex calculates the following quantities: Quantity    Type    Description  
hex.rm matrix the real part of the cylindrical harmonic
hex.im matrix the imaginary part of the cylindrical harmonic: HEXACTIC_PARAMETERCalculate the hexatic order parameter 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 PLANEthe plane to use when calculating the value of the order parameter should be xy, xz or yz=xy R_0The r_0 parameter of the switching function=0.2 D_0 The d_0 parameter of the switching function=1.4 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=12
# PLUMED interprets the command:
# hex: HEXACTIC_PARAMETER SPECIES=1-400 PLANE=xy R_0=0.2 D_0=1.4 NN=6 MM=12
# as follows (Click the red comment above to revert to the short version of the input):
hex_grpThe GROUP action with label hex_grp calculates the following quantities: Quantity    Type    Description  
hex_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
hex_matThe CONTACT_MATRIX action with label hex_mat calculates the following quantities: Quantity    Type    Description  
hex_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
hex_mat.x matrix the projection of the bond on the x axis
hex_mat.y matrix the projection of the bond on the y axis
hex_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 R_0The r_0 parameter of the switching function=0.2 D_0 The d_0 parameter of the switching function=1.4 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=12 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
hex: CYLINDRICAL_HARMONIC_MATRIX More details DEGREEthe value of the n parameter in the equation above=6 ARGthe labels of the scalar and matrices that on which the function is being calculated elementwise=hex_mat.x,hex_mat.y,hex_mat.w
hex_onesThe CONSTANT action with label hex_ones calculates the following quantities: Quantity    Type    Description  
hex_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
hex_rmThe MATRIX_VECTOR_PRODUCT action with label hex_rm calculates the following quantities: Quantity    Type    Description  
hex_rm 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=hex.rm,hex_ones
hex_imThe MATRIX_VECTOR_PRODUCT action with label hex_im calculates the following quantities: Quantity    Type    Description  
hex_im 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=hex.im,hex_ones
hex_denomThe MATRIX_VECTOR_PRODUCT action with label hex_denom calculates the following quantities: Quantity    Type    Description  
hex_denom 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=hex_mat.w,hex_ones
hex_rmnThe CUSTOM action with label hex_rmn calculates the following quantities: Quantity    Type    Description  
hex_rmn 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=hex_rm,hex_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
hex_imnThe CUSTOM action with label hex_imn calculates the following quantities: Quantity    Type    Description  
hex_imn 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=hex_im,hex_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
hex_norm2The COMBINE action with label hex_norm2 calculates the following quantities: Quantity    Type    Description  
hex_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmn,hex_imn POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_normThe CUSTOM action with label hex_norm calculates the following quantities: Quantity    Type    Description  
hex_norm 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=hex_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- hex_meanThe MEAN action with label hex_mean calculates the following quantities: Quantity    Type    Description  
hex_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=hex_norm 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=hex_mean FILEthe name of the file on which to output these quantities=colvar

As you can see if you expand the shortcut above, this input calculates the quantity defined in the equation above for the 400 atoms in the simulated system and stores them in a vector. The elements of this vector are then added together so the mean value can be computed.

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

hexThe CYLINDRICAL_HARMONIC action with label hex calculates the following quantities: Quantity    Type    Description  
hex.rm matrix the real part of the cylindrical harmonic
hex.im matrix the imaginary part of the cylindrical harmonic: HEXACTIC_PARAMETERCalculate the hexatic order parameter 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 PLANEthe plane to use when calculating the value of the order parameter should be xy, xz or yz=xy 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=1.4 R_0=0.2 D_MAX=3.0}
# PLUMED interprets the command:
# hex: HEXACTIC_PARAMETER SPECIES=1-400 PLANE=xy SWITCH={RATIONAL D_0=1.4 R_0=0.2 D_MAX=3.0}
# as follows (Click the red comment above to revert to the short version of the input):
hex_grpThe GROUP action with label hex_grp calculates the following quantities: Quantity    Type    Description  
hex_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
hex_matThe CONTACT_MATRIX action with label hex_mat calculates the following quantities: Quantity    Type    Description  
hex_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
hex_mat.x matrix the projection of the bond on the x axis
hex_mat.y matrix the projection of the bond on the y axis
hex_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=1.4 R_0=0.2 D_MAX=3.0} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
hex: CYLINDRICAL_HARMONIC_MATRIX More details DEGREEthe value of the n parameter in the equation above=6 ARGthe labels of the scalar and matrices that on which the function is being calculated elementwise=hex_mat.x,hex_mat.y,hex_mat.w
hex_onesThe CONSTANT action with label hex_ones calculates the following quantities: Quantity    Type    Description  
hex_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
hex_rmThe MATRIX_VECTOR_PRODUCT action with label hex_rm calculates the following quantities: Quantity    Type    Description  
hex_rm 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=hex.rm,hex_ones
hex_imThe MATRIX_VECTOR_PRODUCT action with label hex_im calculates the following quantities: Quantity    Type    Description  
hex_im 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=hex.im,hex_ones
hex_denomThe MATRIX_VECTOR_PRODUCT action with label hex_denom calculates the following quantities: Quantity    Type    Description  
hex_denom 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=hex_mat.w,hex_ones
hex_rmnThe CUSTOM action with label hex_rmn calculates the following quantities: Quantity    Type    Description  
hex_rmn 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=hex_rm,hex_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
hex_imnThe CUSTOM action with label hex_imn calculates the following quantities: Quantity    Type    Description  
hex_imn 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=hex_im,hex_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
hex_norm2The COMBINE action with label hex_norm2 calculates the following quantities: Quantity    Type    Description  
hex_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmn,hex_imn POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_normThe CUSTOM action with label hex_norm calculates the following quantities: Quantity    Type    Description  
hex_norm 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=hex_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- hex_meanThe MEAN action with label hex_mean calculates the following quantities: Quantity    Type    Description  
hex_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=hex_norm 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=hex_mean 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.

The VMEAN and VSUM options

If you expand the inputs in the previous section you will see that the value hex_norm that we are calculating the average of is a vector that contains the magnitude of the complex number defined in the equation above. If you would like to add up the vector of complex numbers directly (or take an average of the vector) before computing the magnitude of the complex number you can use the VSUM and VMEAN flags as sillstrated below:

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

hexThe CYLINDRICAL_HARMONIC action with label hex calculates the following quantities: Quantity    Type    Description  
hex.rm matrix the real part of the cylindrical harmonic
hex.im matrix the imaginary part of the cylindrical harmonic: HEXACTIC_PARAMETERCalculate the hexatic order parameter 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 PLANEthe plane to use when calculating the value of the order parameter should be xy, xz or yz=xy 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=1.4 R_0=0.2} VMEAN calculate the norm of the mean vector VSUM calculate the norm of the sum of all the vectors
# PLUMED interprets the command:
# hex: HEXACTIC_PARAMETER SPECIES=1-400 PLANE=xy SWITCH={RATIONAL D_0=1.4 R_0=0.2} VMEAN VSUM
# as follows (Click the red comment above to revert to the short version of the input):
hex_grpThe GROUP action with label hex_grp calculates the following quantities: Quantity    Type    Description  
hex_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
hex_matThe CONTACT_MATRIX action with label hex_mat calculates the following quantities: Quantity    Type    Description  
hex_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
hex_mat.x matrix the projection of the bond on the x axis
hex_mat.y matrix the projection of the bond on the y axis
hex_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=1.4 R_0=0.2} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
hex: CYLINDRICAL_HARMONIC_MATRIX More details DEGREEthe value of the n parameter in the equation above=6 ARGthe labels of the scalar and matrices that on which the function is being calculated elementwise=hex_mat.x,hex_mat.y,hex_mat.w
hex_onesThe CONSTANT action with label hex_ones calculates the following quantities: Quantity    Type    Description  
hex_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
hex_rmThe MATRIX_VECTOR_PRODUCT action with label hex_rm calculates the following quantities: Quantity    Type    Description  
hex_rm 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=hex.rm,hex_ones
hex_imThe MATRIX_VECTOR_PRODUCT action with label hex_im calculates the following quantities: Quantity    Type    Description  
hex_im 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=hex.im,hex_ones
hex_denomThe MATRIX_VECTOR_PRODUCT action with label hex_denom calculates the following quantities: Quantity    Type    Description  
hex_denom 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=hex_mat.w,hex_ones
hex_rmnThe CUSTOM action with label hex_rmn calculates the following quantities: Quantity    Type    Description  
hex_rmn 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=hex_rm,hex_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
hex_imnThe CUSTOM action with label hex_imn calculates the following quantities: Quantity    Type    Description  
hex_imn 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=hex_im,hex_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
hex_rmsThe MEAN action with label hex_rms calculates the following quantities: Quantity    Type    Description  
hex_rms scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=hex_rmn PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_imsThe MEAN action with label hex_ims calculates the following quantities: Quantity    Type    Description  
hex_ims scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=hex_imn PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_vmean2The COMBINE action with label hex_vmean2 calculates the following quantities: Quantity    Type    Description  
hex_vmean2 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rms,hex_ims POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_vmeanThe CUSTOM action with label hex_vmean calculates the following quantities: Quantity    Type    Description  
hex_vmean scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hex_vmean2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_rmzThe SUM action with label hex_rmz calculates the following quantities: Quantity    Type    Description  
hex_rmz 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=hex_rmn PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_imzThe SUM action with label hex_imz calculates the following quantities: Quantity    Type    Description  
hex_imz 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=hex_imn PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_vsum2The COMBINE action with label hex_vsum2 calculates the following quantities: Quantity    Type    Description  
hex_vsum2 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmz,hex_imz POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_vsumThe CUSTOM action with label hex_vsum calculates the following quantities: Quantity    Type    Description  
hex_vsum scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hex_vsum2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hex_norm2The COMBINE action with label hex_norm2 calculates the following quantities: Quantity    Type    Description  
hex_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmn,hex_imn POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_normThe CUSTOM action with label hex_norm calculates the following quantities: Quantity    Type    Description  
hex_norm 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=hex_norm2 FUNCthe function you wish to evaluate=sqrt(x) 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=hex_vmean,hex_vsum FILEthe name of the file on which to output these quantities=colvar

If you expand the shortcut in the input above you will see that this input adds the complex numbers together directly before calculating the modulus. This contrasts with the approach in the inputs above, which computes a vector that contains the square moduli for each of the individual hexatic order parameters and then computes the average from this vector.

Using two types of atom

If you would like to calculate the hexatic parameters using the directors 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

hexThe CYLINDRICAL_HARMONIC action with label hex calculates the following quantities: Quantity    Type    Description  
hex.rm matrix the real part of the cylindrical harmonic
hex.im matrix the imaginary part of the cylindrical harmonic: HEXACTIC_PARAMETERCalculate the hexatic order parameter This action is a shortcut. More details SPECIESAthe list of atoms for which the symmetry function is being calculated=1-200 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=201-400 PLANEthe plane to use when calculating the value of the order parameter should be xy, xz or yz=xy 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=1.4 R_0=0.2 D_MAX=3.0}
# PLUMED interprets the command:
# hex: HEXACTIC_PARAMETER SPECIESA=1-200 SPECIESB=201-400 PLANE=xy SWITCH={RATIONAL D_0=1.4 R_0=0.2 D_MAX=3.0}
# as follows (Click the red comment above to revert to the short version of the input):
hex_grpThe GROUP action with label hex_grp calculates the following quantities: Quantity    Type    Description  
hex_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=1-200
hex_matThe CONTACT_MATRIX action with label hex_mat calculates the following quantities: Quantity    Type    Description  
hex_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
hex_mat.x matrix the projection of the bond on the x axis
hex_mat.y matrix the projection of the bond on the y axis
hex_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=1-200 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=201-400 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=1.4 R_0=0.2 D_MAX=3.0} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
hex: CYLINDRICAL_HARMONIC_MATRIX More details DEGREEthe value of the n parameter in the equation above=6 ARGthe labels of the scalar and matrices that on which the function is being calculated elementwise=hex_mat.x,hex_mat.y,hex_mat.w
hex_onesThe CONSTANT action with label hex_ones calculates the following quantities: Quantity    Type    Description  
hex_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=200
hex_rmThe MATRIX_VECTOR_PRODUCT action with label hex_rm calculates the following quantities: Quantity    Type    Description  
hex_rm 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=hex.rm,hex_ones
hex_imThe MATRIX_VECTOR_PRODUCT action with label hex_im calculates the following quantities: Quantity    Type    Description  
hex_im 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=hex.im,hex_ones
hex_denomThe MATRIX_VECTOR_PRODUCT action with label hex_denom calculates the following quantities: Quantity    Type    Description  
hex_denom 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=hex_mat.w,hex_ones
hex_rmnThe CUSTOM action with label hex_rmn calculates the following quantities: Quantity    Type    Description  
hex_rmn 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=hex_rm,hex_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
hex_imnThe CUSTOM action with label hex_imn calculates the following quantities: Quantity    Type    Description  
hex_imn 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=hex_im,hex_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
hex_norm2The COMBINE action with label hex_norm2 calculates the following quantities: Quantity    Type    Description  
hex_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmn,hex_imn POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_normThe CUSTOM action with label hex_norm calculates the following quantities: Quantity    Type    Description  
hex_norm 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=hex_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- hex_meanThe MEAN action with label hex_mean calculates the following quantities: Quantity    Type    Description  
hex_mean scalar the MEAN of the elements in the input value: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe vector/matrix/grid whose elements shuld be added together=hex_norm 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=hex_mean FILEthe name of the file on which to output these quantities=colvar

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 hexatic 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
hexThe CYLINDRICAL_HARMONIC action with label hex calculates the following quantities: Quantity    Type    Description  
hex.rm matrix the real part of the cylindrical harmonic
hex.im matrix the imaginary part of the cylindrical harmonic: HEXACTIC_PARAMETERCalculate the hexatic order parameter 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 PLANEthe plane to use when calculating the value of the order parameter should be xy, xz or yz=xy
   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:
# hex: HEXACTIC_PARAMETER ...
#    SPECIES=1-400 MASK=sphere PLANE=xy
#    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):
hex_grpThe GROUP action with label hex_grp calculates the following quantities: Quantity    Type    Description  
hex_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
hex_matThe CONTACT_MATRIX action with label hex_mat calculates the following quantities: Quantity    Type    Description  
hex_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
hex_mat.x matrix the projection of the bond on the x axis
hex_mat.y matrix the projection of the bond on the y axis
hex_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
hex: CYLINDRICAL_HARMONIC_MATRIX More details DEGREEthe value of the n parameter in the equation above=6 ARGthe labels of the scalar and matrices that on which the function is being calculated elementwise=hex_mat.x,hex_mat.y,hex_mat.w
hex_onesThe CONSTANT action with label hex_ones calculates the following quantities: Quantity    Type    Description  
hex_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
hex_rmThe MATRIX_VECTOR_PRODUCT action with label hex_rm calculates the following quantities: Quantity    Type    Description  
hex_rm 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=hex.rm,hex_ones
hex_imThe MATRIX_VECTOR_PRODUCT action with label hex_im calculates the following quantities: Quantity    Type    Description  
hex_im 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=hex.im,hex_ones
hex_denomThe MATRIX_VECTOR_PRODUCT action with label hex_denom calculates the following quantities: Quantity    Type    Description  
hex_denom 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=hex_mat.w,hex_ones
hex_rmnThe CUSTOM action with label hex_rmn calculates the following quantities: Quantity    Type    Description  
hex_rmn 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=hex_rm,hex_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
hex_imnThe CUSTOM action with label hex_imn calculates the following quantities: Quantity    Type    Description  
hex_imn 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=hex_im,hex_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
hex_norm2The COMBINE action with label hex_norm2 calculates the following quantities: Quantity    Type    Description  
hex_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=hex_rmn,hex_imn POWERS the powers to which you are raising each of the arguments in your function=2,2
hex_normThe CUSTOM action with label hex_norm calculates the following quantities: Quantity    Type    Description  
hex_norm 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=hex_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- # Multiply hexatic parameters by sphere vector
prod_rmThe CUSTOM action with label prod_rm calculates the following quantities: Quantity    Type    Description  
prod_rm 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=hex_rm,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
prod_imThe CUSTOM action with label prod_im calculates the following quantities: Quantity    Type    Description  
prod_im 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=hex_im,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
numer_rmThe SUM action with label numer_rm calculates the following quantities: Quantity    Type    Description  
numer_rm 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_rm PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
numer_imThe SUM action with label numer_im calculates the following quantities: Quantity    Type    Description  
numer_im 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_im 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
av_rmThe CUSTOM action with label av_rm calculates the following quantities: Quantity    Type    Description  
av_rm scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=numer_rm,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
av_imThe CUSTOM action with label av_im calculates the following quantities: Quantity    Type    Description  
av_im scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=numer_im,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
# Take the square modulus
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=av_rm,av_im FUNCthe function you wish to evaluate=x*x+y*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 (complex) hexatic parameter for only those atoms that are within a spherical region that is centered on the point $(2.5,2.5,2.5)$ . The square modulus of this average is then output.

Using nearest neighbours

In papers where symmetry functions similar to this one have been used a switching function is not employed. The sums over $j$ in the expression above are replaced by sums over the six nearest neighbours to each atom. If you would like to calculate this quantity using PLUMED you can use an input like this:

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

dmatThe DISTANCE_MATRIX action with label dmat calculates the following quantities: Quantity    Type    Description  
dmat.w matrix a matrix containing the weights for the bonds between each pair of atoms
dmat.x matrix the projection of the bond on the x axis
dmat.y matrix the projection of the bond on the y axis
dmat.z matrix the projection of the bond on the z axis: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action has hidden defaults. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-400 CUTOFF ignore distances that have a value larger than this cutoff=3.0 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
dmat: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-400 CUTOFF ignore distances that have a value larger than this cutoff=3.0 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix  NL_CUTOFF The cutoff for the neighbor list=0.0 NL_STRIDE The frequency with which we are updating the atoms in the neighbor list=1
neighThe NEIGHBORS action with label neigh calculates the following quantities: Quantity    Type    Description  
neigh matrix a matrix in which the ij element is one if the ij-element of the input matrix is one of the NLOWEST/NHIGHEST elements on that row of the input matrix and zero otherwise: NEIGHBORSBuild a matrix with ones in for the N nearest neighbours of an atom This action has hidden defaults. More details ARGthe label of an adjacency/distance matrix that will be used to find the nearest neighbors=dmat.w NLOWEST in each row of the output matrix set the elements that correspond to the n lowest elements in each row of the input matrix equal to one=6
neigh: NEIGHBORSBuild a matrix with ones in for the N nearest neighbours of an atom This action uses the defaults shown here. More details ARGthe label of an adjacency/distance matrix that will be used to find the nearest neighbors=dmat.w NLOWEST in each row of the output matrix set the elements that correspond to the n lowest elements in each row of the input matrix equal to one=6  NHIGHEST in each row of the output matrix set the elements that correspond to the n highest elements in each row of the input matrix equal to one=0
harmThe CYLINDRICAL_HARMONIC action with label harm calculates the following quantities: Quantity    Type    Description  
harm.rm matrix the real part of the cylindrical harmonic
harm.im matrix the imaginary part of the cylindrical harmonic: CYLINDRICAL_HARMONICCalculate the cylindrical harmonic function More details DEGREEthe value of the n parameter in the equation above=6 ARGthe values input to this function=dmat.x,dmat.y
rprodThe CUSTOM action with label rprod calculates the following quantities: Quantity    Type    Description  
rprod 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=neigh,harm.rm 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
iprodThe CUSTOM action with label iprod calculates the following quantities: Quantity    Type    Description  
iprod 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=neigh,harm.im 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
hex2_onesThe ONES action with label hex2_ones calculates the following quantities: Quantity    Type    Description  
hex2_ones vector a vector of ones with the required number of elements: ONESCreate a constant vector with all elements equal to one This action is a shortcut. More details SIZEthe number of ones that you would like to create=400
# PLUMED interprets the command:
# hex2_ones: ONES SIZE=400
# as follows (Click the red comment above to revert to the short version of the input):
hex2_onesThe CONSTANT action with label hex2_ones calculates the following quantities: Quantity    Type    Description  
hex2_ones vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NOLOG do not report all the read in scalars in the log VALUESthe numbers that are in your constant value=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
# --- End of included input --- hex2_denomThe MATRIX_VECTOR_PRODUCT action with label hex2_denom calculates the following quantities: Quantity    Type    Description  
hex2_denom 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=neigh,hex2_ones
harm_rmThe MATRIX_VECTOR_PRODUCT action with label harm_rm calculates the following quantities: Quantity    Type    Description  
harm_rm 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=rprod,hex2_ones
harm_imThe MATRIX_VECTOR_PRODUCT action with label harm_im calculates the following quantities: Quantity    Type    Description  
harm_im 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=iprod,hex2_ones
hex2_rmnThe CUSTOM action with label hex2_rmn calculates the following quantities: Quantity    Type    Description  
hex2_rmn 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=harm_rm,hex2_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
hex2_imnThe CUSTOM action with label hex2_imn calculates the following quantities: Quantity    Type    Description  
hex2_imn 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=harm_im,hex2_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
DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=1-400 ARGthe labels of vectors that should be output in the xyz file=hex2_rmn,hex2_imn,hex2_denom FILEfile on which to output coordinates; extension is automatically detected=hexparam.xyz

This input outputs the values of the order parameters for all the atoms to an extended xyz file .

Broken virial

Virial is not working currently

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
_vmean	scalar	VMEAN	the norm of the mean vector
_vsum	scalar	VSUM	the norm of the mean vector

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
PLANE	compulsory	none	the plane to use when calculating the value of the order parameter should be xy, xz or yz
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
VMEAN	optional	false	calculate the norm of the mean vector
VSUM	optional	false	calculate the norm of the sum of all the vectors

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

References

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