Shortcut: Q4

Module	symfunc
Description	Usage
Calculate fourth order Steinhardt parameters.
output value	type
the norms of the vectors of spherical harmonic coefficients	vector

Output components

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

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

Input

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

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

Further details and examples

Calculate fourth order Steinhardt parameters.

The 4th order Steinhardt parameters allow us to measure the degree to which the first coordination shell around an atom is ordered. The Steinhardt parameter for atom, $i$ is complex vector whose components are calculated using the following formula:

$q_{4m}(i) = \frac{\sum_j \sigma( r_{ij} ) Y_{4m}(\mathbf{r}_{ij}) }{\sum_j \sigma( r_{ij} ) }$

where $Y_{4m}$ is one of the 4th order spherical harmonics so $m$ is a number that runs from $-4$ to $+4$ . The function $\sigma( r_{ij} )$ is a switching function that acts on the distance between atoms $i$ and $j$ . The parameters of this function should be set so that it the function is equal to one when atom $j$ is in the first coordination sphere of atom $i$ and is zero otherwise.

As discussed on this page, the Steinhardt parameters can be used to measure the degree of order in the system in a variety of different ways. The simplest way of measuring whether or not the coordination sphere is ordered is to simply take the norm of the above vector i.e.

$Q_4(i) = \sqrt{ \sum_{m=-4}^4 q_{4m}(i)^{*} q_{4m}(i) }$

This norm is small when the coordination shell is disordered and larger when the coordination shell is ordered. Furthermore, in inputs like the one shown below where the keywords LESS_THAN, MIN, MAX, HISTOGRAM, MEAN and so on are used with it is the distribution of these normed quantities that is investigated. You can investigate precisely what calculation is performed here by expaning the shortcuts in the input below.

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

q4The Q4 action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 vector the norms of the vectors of spherical harmonic coefficients
q4_mean scalar the mean of the colvars: Q4Calculate fourth order Steinhardt parameters. 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=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities
q4: Q4Calculate fourth order Steinhardt parameters. 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=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# q4: Q4 SPECIES=1-64 D_0=1.3 R_0=0.2 MEAN
# as follows (Click the red comment above to revert to the short version of the input):
q4_grpThe GROUP action with label q4_grp calculates the following quantities: Quantity    Type    Description  
q4_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
q4_matThe CONTACT_MATRIX action with label q4_mat calculates the following quantities: Quantity    Type    Description  
q4_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
q4_mat.x matrix the projection of the bond on the x axis
q4_mat.y matrix the projection of the bond on the y axis
q4_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=0.2 D_0 The d_0 parameter of the switching function=1.3 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 vectors connecting the atoms in the contact matrix
q4_shThe SPHERICAL_HARMONIC action with label q4_sh calculates the following quantities: Quantity    Type    Description  
q4_sh.rm-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.rm-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.rm-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.rm-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.rm-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.rm-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.rm-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.rm-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.rm-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities
q4_sh.im-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.im-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.im-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.im-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.im-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.im-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.im-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.im-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.im-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities: SPHERICAL_HARMONICCalculate the values of all the spherical harmonic funtions for a particular value of l. More details ARGthe values input to this function=q4_mat.x,q4_mat.y,q4_mat.z,q4_mat.w Lthe value of the angular momentum=4
q4_denom_onesThe CONSTANT action with label q4_denom_ones calculates the following quantities: Quantity    Type    Description  
q4_denom_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
q4_denomThe MATRIX_VECTOR_PRODUCT action with label q4_denom calculates the following quantities: Quantity    Type    Description  
q4_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=q4_mat.w,q4_denom_ones
q4_spThe MATRIX_VECTOR_PRODUCT action with label q4_sp calculates the following quantities: Quantity    Type    Description  
q4_sp.rm-n4 vector the product of the matrix q4_sh.rm-n4 and the vector q4_denom_ones
q4_sp.rm-n3 vector the product of the matrix q4_sh.rm-n3 and the vector q4_denom_ones
q4_sp.rm-n2 vector the product of the matrix q4_sh.rm-n2 and the vector q4_denom_ones
q4_sp.rm-n1 vector the product of the matrix q4_sh.rm-n1 and the vector q4_denom_ones
q4_sp.rm-0 vector the product of the matrix q4_sh.rm-0 and the vector q4_denom_ones
q4_sp.rm-p1 vector the product of the matrix q4_sh.rm-p1 and the vector q4_denom_ones
q4_sp.rm-p2 vector the product of the matrix q4_sh.rm-p2 and the vector q4_denom_ones
q4_sp.rm-p3 vector the product of the matrix q4_sh.rm-p3 and the vector q4_denom_ones
q4_sp.rm-p4 vector the product of the matrix q4_sh.rm-p4 and the vector q4_denom_ones
q4_sp.im-n4 vector the product of the matrix q4_sh.im-n4 and the vector q4_denom_ones
q4_sp.im-n3 vector the product of the matrix q4_sh.im-n3 and the vector q4_denom_ones
q4_sp.im-n2 vector the product of the matrix q4_sh.im-n2 and the vector q4_denom_ones
q4_sp.im-n1 vector the product of the matrix q4_sh.im-n1 and the vector q4_denom_ones
q4_sp.im-0 vector the product of the matrix q4_sh.im-0 and the vector q4_denom_ones
q4_sp.im-p1 vector the product of the matrix q4_sh.im-p1 and the vector q4_denom_ones
q4_sp.im-p2 vector the product of the matrix q4_sh.im-p2 and the vector q4_denom_ones
q4_sp.im-p3 vector the product of the matrix q4_sh.im-p3 and the vector q4_denom_ones
q4_sp.im-p4 vector the product of the matrix q4_sh.im-p4 and the vector q4_denom_ones: 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=q4_sh.*,q4_denom_ones
q4_norm2The COMBINE action with label q4_norm2 calculates the following quantities: Quantity    Type    Description  
q4_norm2 vector the vector obtained by doing an element-wise application of a linear compbination 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 POWERS the powers to which you are raising each of the arguments in your function=2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 ARGthe values input to this function=q4_sp.rm-n4,q4_sp.im-n4,q4_sp.rm-n3,q4_sp.im-n3,q4_sp.rm-n2,q4_sp.im-n2,q4_sp.rm-n1,q4_sp.im-n1,q4_sp.rm-0,q4_sp.im-0,q4_sp.rm-p1,q4_sp.im-p1,q4_sp.rm-p2,q4_sp.im-p2,q4_sp.rm-p3,q4_sp.im-p3,q4_sp.rm-p4,q4_sp.im-p4
q4_normThe CUSTOM action with label q4_norm calculates the following quantities: Quantity    Type    Description  
q4_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=q4_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
q4The CUSTOM action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 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=q4_norm,q4_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
q4_meanThe MEAN action with label q4_mean calculates the following quantities: Quantity    Type    Description  
q4_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=q4 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=q4.mean FILEthe name of the file on which to output these quantities=colvar

Another similar command is provided below. This time the histogram of Q4 parameters for the 64 atoms in a box of Lennard Jones is computed and printed to to a file called colvar:

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

q4The Q4 action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 vector the norms of the vectors of spherical harmonic coefficients
q4_between-1 scalar the number of colvars that have a value that lies in a particular interval
q4_between-2 scalar the number of colvars that have a value that lies in a particular interval
q4_between-3 scalar the number of colvars that have a value that lies in a particular interval
q4_between-4 scalar the number of colvars that have a value that lies in a particular interval
q4_between-5 scalar the number of colvars that have a value that lies in a particular interval
q4_between-6 scalar the number of colvars that have a value that lies in a particular interval
q4_between-7 scalar the number of colvars that have a value that lies in a particular interval
q4_between-8 scalar the number of colvars that have a value that lies in a particular interval
q4_between-9 scalar the number of colvars that have a value that lies in a particular interval
q4_between-10 scalar the number of colvars that have a value that lies in a particular interval
q4_between-11 scalar the number of colvars that have a value that lies in a particular interval
q4_between-12 scalar the number of colvars that have a value that lies in a particular interval
q4_between-13 scalar the number of colvars that have a value that lies in a particular interval
q4_between-14 scalar the number of colvars that have a value that lies in a particular interval
q4_between-15 scalar the number of colvars that have a value that lies in a particular interval
q4_between-16 scalar the number of colvars that have a value that lies in a particular interval
q4_between-17 scalar the number of colvars that have a value that lies in a particular interval
q4_between-18 scalar the number of colvars that have a value that lies in a particular interval
q4_between-19 scalar the number of colvars that have a value that lies in a particular interval
q4_between-20 scalar the number of colvars that have a value that lies in a particular interval: Q4Calculate fourth order Steinhardt parameters. 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=1.3 R_0The r_0 parameter of the switching function=0.2 HISTOGRAMcalculate a discretized histogram of the distribution of values={GAUSSIAN LOWER=0.0 UPPER=1.0 NBINS=20 SMEAR=0.1}
q4: Q4Calculate fourth order Steinhardt parameters. 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=1.3 R_0The r_0 parameter of the switching function=0.2 HISTOGRAMcalculate a discretized histogram of the distribution of values={GAUSSIAN LOWER=0.0 UPPER=1.0 NBINS=20 SMEAR=0.1}  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# q4: Q4 SPECIES=1-64 D_0=1.3 R_0=0.2 HISTOGRAM={GAUSSIAN LOWER=0.0 UPPER=1.0 NBINS=20 SMEAR=0.1}
# as follows (Click the red comment above to revert to the short version of the input):
q4_grpThe GROUP action with label q4_grp calculates the following quantities: Quantity    Type    Description  
q4_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
q4_matThe CONTACT_MATRIX action with label q4_mat calculates the following quantities: Quantity    Type    Description  
q4_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
q4_mat.x matrix the projection of the bond on the x axis
q4_mat.y matrix the projection of the bond on the y axis
q4_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=0.2 D_0 The d_0 parameter of the switching function=1.3 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 vectors connecting the atoms in the contact matrix
q4_shThe SPHERICAL_HARMONIC action with label q4_sh calculates the following quantities: Quantity    Type    Description  
q4_sh.rm-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.rm-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.rm-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.rm-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.rm-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.rm-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.rm-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.rm-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.rm-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities
q4_sh.im-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.im-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.im-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.im-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.im-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.im-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.im-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.im-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.im-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities: SPHERICAL_HARMONICCalculate the values of all the spherical harmonic funtions for a particular value of l. More details ARGthe values input to this function=q4_mat.x,q4_mat.y,q4_mat.z,q4_mat.w Lthe value of the angular momentum=4
q4_denom_onesThe CONSTANT action with label q4_denom_ones calculates the following quantities: Quantity    Type    Description  
q4_denom_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
q4_denomThe MATRIX_VECTOR_PRODUCT action with label q4_denom calculates the following quantities: Quantity    Type    Description  
q4_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=q4_mat.w,q4_denom_ones
q4_spThe MATRIX_VECTOR_PRODUCT action with label q4_sp calculates the following quantities: Quantity    Type    Description  
q4_sp.rm-n4 vector the product of the matrix q4_sh.rm-n4 and the vector q4_denom_ones
q4_sp.rm-n3 vector the product of the matrix q4_sh.rm-n3 and the vector q4_denom_ones
q4_sp.rm-n2 vector the product of the matrix q4_sh.rm-n2 and the vector q4_denom_ones
q4_sp.rm-n1 vector the product of the matrix q4_sh.rm-n1 and the vector q4_denom_ones
q4_sp.rm-0 vector the product of the matrix q4_sh.rm-0 and the vector q4_denom_ones
q4_sp.rm-p1 vector the product of the matrix q4_sh.rm-p1 and the vector q4_denom_ones
q4_sp.rm-p2 vector the product of the matrix q4_sh.rm-p2 and the vector q4_denom_ones
q4_sp.rm-p3 vector the product of the matrix q4_sh.rm-p3 and the vector q4_denom_ones
q4_sp.rm-p4 vector the product of the matrix q4_sh.rm-p4 and the vector q4_denom_ones
q4_sp.im-n4 vector the product of the matrix q4_sh.im-n4 and the vector q4_denom_ones
q4_sp.im-n3 vector the product of the matrix q4_sh.im-n3 and the vector q4_denom_ones
q4_sp.im-n2 vector the product of the matrix q4_sh.im-n2 and the vector q4_denom_ones
q4_sp.im-n1 vector the product of the matrix q4_sh.im-n1 and the vector q4_denom_ones
q4_sp.im-0 vector the product of the matrix q4_sh.im-0 and the vector q4_denom_ones
q4_sp.im-p1 vector the product of the matrix q4_sh.im-p1 and the vector q4_denom_ones
q4_sp.im-p2 vector the product of the matrix q4_sh.im-p2 and the vector q4_denom_ones
q4_sp.im-p3 vector the product of the matrix q4_sh.im-p3 and the vector q4_denom_ones
q4_sp.im-p4 vector the product of the matrix q4_sh.im-p4 and the vector q4_denom_ones: 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=q4_sh.*,q4_denom_ones
q4_norm2The COMBINE action with label q4_norm2 calculates the following quantities: Quantity    Type    Description  
q4_norm2 vector the vector obtained by doing an element-wise application of a linear compbination 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 POWERS the powers to which you are raising each of the arguments in your function=2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 ARGthe values input to this function=q4_sp.rm-n4,q4_sp.im-n4,q4_sp.rm-n3,q4_sp.im-n3,q4_sp.rm-n2,q4_sp.im-n2,q4_sp.rm-n1,q4_sp.im-n1,q4_sp.rm-0,q4_sp.im-0,q4_sp.rm-p1,q4_sp.im-p1,q4_sp.rm-p2,q4_sp.im-p2,q4_sp.rm-p3,q4_sp.im-p3,q4_sp.rm-p4,q4_sp.im-p4
q4_normThe CUSTOM action with label q4_norm calculates the following quantities: Quantity    Type    Description  
q4_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=q4_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
q4The CUSTOM action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 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=q4_norm,q4_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
q4_bt1The BETWEEN action with label q4_bt1 calculates the following quantities: Quantity    Type    Description  
q4_bt1 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0 UPPER=0.05 SMEAR=0.1}
q4_between-1The SUM action with label q4_between-1 calculates the following quantities: Quantity    Type    Description  
q4_between-1 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt2The BETWEEN action with label q4_bt2 calculates the following quantities: Quantity    Type    Description  
q4_bt2 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.05 UPPER=0.1 SMEAR=0.1}
q4_between-2The SUM action with label q4_between-2 calculates the following quantities: Quantity    Type    Description  
q4_between-2 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt3The BETWEEN action with label q4_bt3 calculates the following quantities: Quantity    Type    Description  
q4_bt3 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.1 UPPER=0.15 SMEAR=0.1}
q4_between-3The SUM action with label q4_between-3 calculates the following quantities: Quantity    Type    Description  
q4_between-3 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt4The BETWEEN action with label q4_bt4 calculates the following quantities: Quantity    Type    Description  
q4_bt4 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.15 UPPER=0.2 SMEAR=0.1}
q4_between-4The SUM action with label q4_between-4 calculates the following quantities: Quantity    Type    Description  
q4_between-4 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt5The BETWEEN action with label q4_bt5 calculates the following quantities: Quantity    Type    Description  
q4_bt5 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.2 UPPER=0.25 SMEAR=0.1}
q4_between-5The SUM action with label q4_between-5 calculates the following quantities: Quantity    Type    Description  
q4_between-5 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt6The BETWEEN action with label q4_bt6 calculates the following quantities: Quantity    Type    Description  
q4_bt6 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.25 UPPER=0.3 SMEAR=0.1}
q4_between-6The SUM action with label q4_between-6 calculates the following quantities: Quantity    Type    Description  
q4_between-6 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt7The BETWEEN action with label q4_bt7 calculates the following quantities: Quantity    Type    Description  
q4_bt7 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.3 UPPER=0.35 SMEAR=0.1}
q4_between-7The SUM action with label q4_between-7 calculates the following quantities: Quantity    Type    Description  
q4_between-7 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt8The BETWEEN action with label q4_bt8 calculates the following quantities: Quantity    Type    Description  
q4_bt8 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.35 UPPER=0.4 SMEAR=0.1}
q4_between-8The SUM action with label q4_between-8 calculates the following quantities: Quantity    Type    Description  
q4_between-8 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt8 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt9The BETWEEN action with label q4_bt9 calculates the following quantities: Quantity    Type    Description  
q4_bt9 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.4 UPPER=0.45 SMEAR=0.1}
q4_between-9The SUM action with label q4_between-9 calculates the following quantities: Quantity    Type    Description  
q4_between-9 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt9 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt10The BETWEEN action with label q4_bt10 calculates the following quantities: Quantity    Type    Description  
q4_bt10 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.45 UPPER=0.5 SMEAR=0.1}
q4_between-10The SUM action with label q4_between-10 calculates the following quantities: Quantity    Type    Description  
q4_between-10 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt10 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt11The BETWEEN action with label q4_bt11 calculates the following quantities: Quantity    Type    Description  
q4_bt11 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.5 UPPER=0.55 SMEAR=0.1}
q4_between-11The SUM action with label q4_between-11 calculates the following quantities: Quantity    Type    Description  
q4_between-11 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt11 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt12The BETWEEN action with label q4_bt12 calculates the following quantities: Quantity    Type    Description  
q4_bt12 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.55 UPPER=0.6 SMEAR=0.1}
q4_between-12The SUM action with label q4_between-12 calculates the following quantities: Quantity    Type    Description  
q4_between-12 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt12 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt13The BETWEEN action with label q4_bt13 calculates the following quantities: Quantity    Type    Description  
q4_bt13 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.6 UPPER=0.65 SMEAR=0.1}
q4_between-13The SUM action with label q4_between-13 calculates the following quantities: Quantity    Type    Description  
q4_between-13 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt13 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt14The BETWEEN action with label q4_bt14 calculates the following quantities: Quantity    Type    Description  
q4_bt14 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.65 UPPER=0.7 SMEAR=0.1}
q4_between-14The SUM action with label q4_between-14 calculates the following quantities: Quantity    Type    Description  
q4_between-14 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt14 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt15The BETWEEN action with label q4_bt15 calculates the following quantities: Quantity    Type    Description  
q4_bt15 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.7 UPPER=0.75 SMEAR=0.1}
q4_between-15The SUM action with label q4_between-15 calculates the following quantities: Quantity    Type    Description  
q4_between-15 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt15 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt16The BETWEEN action with label q4_bt16 calculates the following quantities: Quantity    Type    Description  
q4_bt16 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.75 UPPER=0.8 SMEAR=0.1}
q4_between-16The SUM action with label q4_between-16 calculates the following quantities: Quantity    Type    Description  
q4_between-16 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt16 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt17The BETWEEN action with label q4_bt17 calculates the following quantities: Quantity    Type    Description  
q4_bt17 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.8 UPPER=0.85 SMEAR=0.1}
q4_between-17The SUM action with label q4_between-17 calculates the following quantities: Quantity    Type    Description  
q4_between-17 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt17 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt18The BETWEEN action with label q4_bt18 calculates the following quantities: Quantity    Type    Description  
q4_bt18 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.85 UPPER=0.9 SMEAR=0.1}
q4_between-18The SUM action with label q4_between-18 calculates the following quantities: Quantity    Type    Description  
q4_between-18 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt18 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt19The BETWEEN action with label q4_bt19 calculates the following quantities: Quantity    Type    Description  
q4_bt19 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.9 UPPER=0.95 SMEAR=0.1}
q4_between-19The SUM action with label q4_between-19 calculates the following quantities: Quantity    Type    Description  
q4_between-19 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt19 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_bt20The BETWEEN action with label q4_bt20 calculates the following quantities: Quantity    Type    Description  
q4_bt20 vector the vector obtained by doing an element-wise application of a function that is one if the input falls within a particular range and zero otherwise to the input vectors: BETWEENUse a switching function to determine how many of the input variables are within a certain range. More details ARGthe values input to this function=q4 SWITCHThis keyword is used if you want to employ an alternative to the continuous function defined above={GAUSSIAN LOWER=0.95 UPPER=1 SMEAR=0.1}
q4_between-20The SUM action with label q4_between-20 calculates the following quantities: Quantity    Type    Description  
q4_between-20 scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=q4_bt20 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=q4.* FILEthe name of the file on which to output these quantities=colvar

The command below could be used to measure the Q4 parameters that describe the arrangement of chlorine ions around the sodium atoms in sodium chloride. The imagined system here is composed of 64 NaCl formula units and the atoms are arranged in the input with the 64 Na $^+$ ions followed by the 64 Cl $-$ ions. Once again the average Q4 parameter is calculated and output to a file called colvar

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

q4The Q4 action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 vector the norms of the vectors of spherical harmonic coefficients
q4_mean scalar the mean of the colvars: Q4Calculate fourth order Steinhardt parameters. 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=65-128 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities
q4: Q4Calculate fourth order Steinhardt parameters. 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=65-128 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# q4: Q4 SPECIESA=1-64 SPECIESB=65-128 D_0=1.3 R_0=0.2 MEAN
# as follows (Click the red comment above to revert to the short version of the input):
q4_grpThe GROUP action with label q4_grp calculates the following quantities: Quantity    Type    Description  
q4_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
q4_matThe CONTACT_MATRIX action with label q4_mat calculates the following quantities: Quantity    Type    Description  
q4_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
q4_mat.x matrix the projection of the bond on the x axis
q4_mat.y matrix the projection of the bond on the y axis
q4_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=65-128 R_0The r_0 parameter of the switching function=0.2 D_0 The d_0 parameter of the switching function=1.3 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 vectors connecting the atoms in the contact matrix
q4_shThe SPHERICAL_HARMONIC action with label q4_sh calculates the following quantities: Quantity    Type    Description  
q4_sh.rm-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.rm-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.rm-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.rm-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.rm-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.rm-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.rm-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.rm-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.rm-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities
q4_sh.im-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.im-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.im-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.im-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.im-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.im-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.im-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.im-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.im-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities: SPHERICAL_HARMONICCalculate the values of all the spherical harmonic funtions for a particular value of l. More details ARGthe values input to this function=q4_mat.x,q4_mat.y,q4_mat.z,q4_mat.w Lthe value of the angular momentum=4
q4_denom_onesThe CONSTANT action with label q4_denom_ones calculates the following quantities: Quantity    Type    Description  
q4_denom_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
q4_denomThe MATRIX_VECTOR_PRODUCT action with label q4_denom calculates the following quantities: Quantity    Type    Description  
q4_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=q4_mat.w,q4_denom_ones
q4_spThe MATRIX_VECTOR_PRODUCT action with label q4_sp calculates the following quantities: Quantity    Type    Description  
q4_sp.rm-n4 vector the product of the matrix q4_sh.rm-n4 and the vector q4_denom_ones
q4_sp.rm-n3 vector the product of the matrix q4_sh.rm-n3 and the vector q4_denom_ones
q4_sp.rm-n2 vector the product of the matrix q4_sh.rm-n2 and the vector q4_denom_ones
q4_sp.rm-n1 vector the product of the matrix q4_sh.rm-n1 and the vector q4_denom_ones
q4_sp.rm-0 vector the product of the matrix q4_sh.rm-0 and the vector q4_denom_ones
q4_sp.rm-p1 vector the product of the matrix q4_sh.rm-p1 and the vector q4_denom_ones
q4_sp.rm-p2 vector the product of the matrix q4_sh.rm-p2 and the vector q4_denom_ones
q4_sp.rm-p3 vector the product of the matrix q4_sh.rm-p3 and the vector q4_denom_ones
q4_sp.rm-p4 vector the product of the matrix q4_sh.rm-p4 and the vector q4_denom_ones
q4_sp.im-n4 vector the product of the matrix q4_sh.im-n4 and the vector q4_denom_ones
q4_sp.im-n3 vector the product of the matrix q4_sh.im-n3 and the vector q4_denom_ones
q4_sp.im-n2 vector the product of the matrix q4_sh.im-n2 and the vector q4_denom_ones
q4_sp.im-n1 vector the product of the matrix q4_sh.im-n1 and the vector q4_denom_ones
q4_sp.im-0 vector the product of the matrix q4_sh.im-0 and the vector q4_denom_ones
q4_sp.im-p1 vector the product of the matrix q4_sh.im-p1 and the vector q4_denom_ones
q4_sp.im-p2 vector the product of the matrix q4_sh.im-p2 and the vector q4_denom_ones
q4_sp.im-p3 vector the product of the matrix q4_sh.im-p3 and the vector q4_denom_ones
q4_sp.im-p4 vector the product of the matrix q4_sh.im-p4 and the vector q4_denom_ones: 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=q4_sh.*,q4_denom_ones
q4_norm2The COMBINE action with label q4_norm2 calculates the following quantities: Quantity    Type    Description  
q4_norm2 vector the vector obtained by doing an element-wise application of a linear compbination 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 POWERS the powers to which you are raising each of the arguments in your function=2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 ARGthe values input to this function=q4_sp.rm-n4,q4_sp.im-n4,q4_sp.rm-n3,q4_sp.im-n3,q4_sp.rm-n2,q4_sp.im-n2,q4_sp.rm-n1,q4_sp.im-n1,q4_sp.rm-0,q4_sp.im-0,q4_sp.rm-p1,q4_sp.im-p1,q4_sp.rm-p2,q4_sp.im-p2,q4_sp.rm-p3,q4_sp.im-p3,q4_sp.rm-p4,q4_sp.im-p4
q4_normThe CUSTOM action with label q4_norm calculates the following quantities: Quantity    Type    Description  
q4_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=q4_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
q4The CUSTOM action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 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=q4_norm,q4_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
q4_meanThe MEAN action with label q4_mean calculates the following quantities: Quantity    Type    Description  
q4_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=q4 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=q4.mean FILEthe name of the file on which to output these quantities=colvar

If you simply want to examine the values of the Q4 parameters for each of the atoms in your system you can do so by exploiting the command DUMPATOMS as shown in the example below. The following output file will output a file in an extended xyz format called q4.xyz for each frame of the analyzed MD trajectory. The first column in this file will contain a dummy name for each of the atoms, columns 2-4 will then contain the x, y and z positions of the atoms, column 5 will contain the value of the Q4 parameter, columns 6-12 will contain the real parts of the director of the $q_{4m}$ vector while columns 12-19 will contain the imaginary parts of this director.

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

q4The Q4 action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 vector the norms of the vectors of spherical harmonic coefficients
q4_mean scalar the mean of the colvars: Q4Calculate fourth order Steinhardt parameters. 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=65-128 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities
q4: Q4Calculate fourth order Steinhardt parameters. 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=65-128 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2 MEAN calculate the mean of all the quantities  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# q4: Q4 SPECIESA=1-64 SPECIESB=65-128 D_0=1.3 R_0=0.2 MEAN
# as follows (Click the red comment above to revert to the short version of the input):
q4_grpThe GROUP action with label q4_grp calculates the following quantities: Quantity    Type    Description  
q4_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
q4_matThe CONTACT_MATRIX action with label q4_mat calculates the following quantities: Quantity    Type    Description  
q4_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
q4_mat.x matrix the projection of the bond on the x axis
q4_mat.y matrix the projection of the bond on the y axis
q4_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=65-128 R_0The r_0 parameter of the switching function=0.2 D_0 The d_0 parameter of the switching function=1.3 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 vectors connecting the atoms in the contact matrix
q4_shThe SPHERICAL_HARMONIC action with label q4_sh calculates the following quantities: Quantity    Type    Description  
q4_sh.rm-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.rm-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.rm-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.rm-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.rm-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.rm-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.rm-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.rm-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.rm-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities
q4_sh.im-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.im-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.im-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.im-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.im-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.im-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.im-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.im-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.im-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities: SPHERICAL_HARMONICCalculate the values of all the spherical harmonic funtions for a particular value of l. More details ARGthe values input to this function=q4_mat.x,q4_mat.y,q4_mat.z,q4_mat.w Lthe value of the angular momentum=4
q4_denom_onesThe CONSTANT action with label q4_denom_ones calculates the following quantities: Quantity    Type    Description  
q4_denom_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
q4_denomThe MATRIX_VECTOR_PRODUCT action with label q4_denom calculates the following quantities: Quantity    Type    Description  
q4_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=q4_mat.w,q4_denom_ones
q4_spThe MATRIX_VECTOR_PRODUCT action with label q4_sp calculates the following quantities: Quantity    Type    Description  
q4_sp.rm-n4 vector the product of the matrix q4_sh.rm-n4 and the vector q4_denom_ones
q4_sp.rm-n3 vector the product of the matrix q4_sh.rm-n3 and the vector q4_denom_ones
q4_sp.rm-n2 vector the product of the matrix q4_sh.rm-n2 and the vector q4_denom_ones
q4_sp.rm-n1 vector the product of the matrix q4_sh.rm-n1 and the vector q4_denom_ones
q4_sp.rm-0 vector the product of the matrix q4_sh.rm-0 and the vector q4_denom_ones
q4_sp.rm-p1 vector the product of the matrix q4_sh.rm-p1 and the vector q4_denom_ones
q4_sp.rm-p2 vector the product of the matrix q4_sh.rm-p2 and the vector q4_denom_ones
q4_sp.rm-p3 vector the product of the matrix q4_sh.rm-p3 and the vector q4_denom_ones
q4_sp.rm-p4 vector the product of the matrix q4_sh.rm-p4 and the vector q4_denom_ones
q4_sp.im-n4 vector the product of the matrix q4_sh.im-n4 and the vector q4_denom_ones
q4_sp.im-n3 vector the product of the matrix q4_sh.im-n3 and the vector q4_denom_ones
q4_sp.im-n2 vector the product of the matrix q4_sh.im-n2 and the vector q4_denom_ones
q4_sp.im-n1 vector the product of the matrix q4_sh.im-n1 and the vector q4_denom_ones
q4_sp.im-0 vector the product of the matrix q4_sh.im-0 and the vector q4_denom_ones
q4_sp.im-p1 vector the product of the matrix q4_sh.im-p1 and the vector q4_denom_ones
q4_sp.im-p2 vector the product of the matrix q4_sh.im-p2 and the vector q4_denom_ones
q4_sp.im-p3 vector the product of the matrix q4_sh.im-p3 and the vector q4_denom_ones
q4_sp.im-p4 vector the product of the matrix q4_sh.im-p4 and the vector q4_denom_ones: 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=q4_sh.*,q4_denom_ones
q4_norm2The COMBINE action with label q4_norm2 calculates the following quantities: Quantity    Type    Description  
q4_norm2 vector the vector obtained by doing an element-wise application of a linear compbination 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 POWERS the powers to which you are raising each of the arguments in your function=2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 ARGthe values input to this function=q4_sp.rm-n4,q4_sp.im-n4,q4_sp.rm-n3,q4_sp.im-n3,q4_sp.rm-n2,q4_sp.im-n2,q4_sp.rm-n1,q4_sp.im-n1,q4_sp.rm-0,q4_sp.im-0,q4_sp.rm-p1,q4_sp.im-p1,q4_sp.rm-p2,q4_sp.im-p2,q4_sp.rm-p3,q4_sp.im-p3,q4_sp.rm-p4,q4_sp.im-p4
q4_normThe CUSTOM action with label q4_norm calculates the following quantities: Quantity    Type    Description  
q4_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=q4_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
q4The CUSTOM action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 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=q4_norm,q4_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
q4_meanThe MEAN action with label q4_mean calculates the following quantities: Quantity    Type    Description  
q4_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=q4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=q4 ARGthe labels of vectors that should be output in the xyz file=q4 FILEfile on which to output coordinates; extension is automatically detected=q4.xyz

References

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

Syntax

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

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

Quantity	Type	Description
q4	vector	the norms of the vectors of spherical harmonic coefficients
q4_mean	scalar	the mean of the colvars