Shortcut: CENTER

Module	vatom
Description	Usage
Calculate the center for a group of atoms, with arbitrary weights.
output value	type
the position of the center of mass	atom

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
ATOMS	atoms	the group of atoms that you are calculating the Gyration Tensor for

Further details and examples

Calculate the center for a group of atoms, with arbitrary weights.

The position of the center ${r}_{\rm COM}$ given by:

${r}_{\rm COM}=\frac{\sum_{i=1}^{n} {r}_i\ w_i }{\sum_i^{n} w_i}$

In these expressions $r_i$ indicates the position of atom $i$ and $w_i$ is the weight for atom $i$ . The following input shows how you can calculate the expressions for a set of atoms by using PLUMED:

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

# This action calculates the position of the point on the line connecting atoms 1 and 10 that is
# twice as far atom 10 as it is from atom 1
c1The CENTER_FAST action with label c1 calculates the following quantities: Quantity    Type    Description  
c1 atoms virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1,1,10
# this is another way of calculating this position
c1bisThe CENTER_FAST action with label c1bis calculates the following quantities: Quantity    Type    Description  
c1bis atoms virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1,10 WEIGHTSwhat weights should be used when calculating the center=2,1

DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=c1,c1bis FILEfile on which to output coordinates; extension is automatically detected=atoms.xyz

Notice that center's position is stored as a virtual atom. The positions of the centers in the above input used in the DUMPATOMS command by using the labels for the CENTER actions. Notice, furthermore, that the mass and charge of this new center are equal to the sums of the masses and charges of the input atoms.

The input below shows how you can use the CENTER action in place of the COM action to calculate the center of mass for a group of atoms.

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

cThe CENTER_FAST action with label c calculates the following quantities: Quantity    Type    Description  
c atoms virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-5 MASS calculate the center of mass

Center is more powerful than COM because you can use arbitrary vectors of weights as in the first example above or vector of weights that are calculated by another action as has been done in the input below.

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

fccThe FCCUBIC action with label fcc calculates the following quantities: Quantity    Type    Description  
fcc vector the symmetry function for each of the specified atoms: FCCUBICMeasure how similar the environment around atoms is to that found in a FCC structure. 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=1-1000 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}
fcc: FCCUBICMeasure how similar the environment around atoms is to that found in a FCC structure. 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=1-1000 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}  PHI The Euler rotational angle phi=0.0 THETA The Euler rotational angle theta=0.0 PSI The Euler rotational angle psi=0.0 ALPHA The alpha parameter of the angular function that is used for FCCUBIC=3.0
# PLUMED interprets the command:
# fcc: FCCUBIC SPECIES=1-1000 SWITCH={RATIONAL D_0=3.0 R_0=1.5}
# as follows (Click the red comment above to revert to the short version of the input):
fcc_grpThe GROUP action with label fcc_grp calculates the following quantities: Quantity    Type    Description  
fcc_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=1-1000
fcc_matThe CONTACT_MATRIX action with label fcc_mat calculates the following quantities: Quantity    Type    Description  
fcc_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
fcc_mat.x matrix the projection of the bond on the x axis
fcc_mat.y matrix the projection of the bond on the y axis
fcc_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=1-1000 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} COMPONENTS also calculate the components of the vectors connecting the atoms in the contact matrix
fcc_vfuncThe FCCUBIC_FUNC action with label fcc_vfunc calculates the following quantities: Quantity    Type    Description  
fcc_vfunc matrix the matrix obtained by doing an element-wise application of a function that measures the similarity with an fcc environment to the input matrix: FCCUBIC_FUNCMeasure how similar the environment around atoms is to that found in a FCC structure. More details ARGthe values input to this function=fcc_mat.x,fcc_mat.y,fcc_mat.z ALPHA The alpha parameter of the angular function=3.0
fcc_wvfuncThe CUSTOM action with label fcc_wvfunc calculates the following quantities: Quantity    Type    Description  
fcc_wvfunc matrix the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=fcc_vfunc,fcc_mat.w FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
fcc_onesThe CONSTANT action with label fcc_ones calculates the following quantities: Quantity    Type    Description  
fcc_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=1000
fccThe MATRIX_VECTOR_PRODUCT action with label fcc calculates the following quantities: Quantity    Type    Description  
fcc 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=fcc_wvfunc,fcc_ones
fcc_denomThe MATRIX_VECTOR_PRODUCT action with label fcc_denom calculates the following quantities: Quantity    Type    Description  
fcc_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=fcc_mat.w,fcc_ones
fcc_nThe CUSTOM action with label fcc_n calculates the following quantities: Quantity    Type    Description  
fcc_n 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=fcc,fcc_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
# --- End of included input --- sfccThe MORE_THAN action with label sfcc calculates the following quantities: Quantity    Type    Description  
sfcc vector the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=fcc SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL R_0=0.5}
cThe ARGS2VATOM action with label c calculates the following quantities: Quantity    Type    Description  
c.x scalar the x coordinate of the virtual atom
c.y scalar the y coordinate of the virtual atom
c.z scalar the z coordinate of the virtual atom
c.mass scalar the mass of the virtual atom
c.charge scalar the charge of the virtual atom: CENTERCalculate the center for a group of atoms, with arbitrary weights. This action is a shortcut. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-1000 WEIGHTSwhat weights should be used when calculating the center=sfcc
# PLUMED interprets the command:
# c: CENTER ATOMS=1-1000 WEIGHTS=sfcc
# as follows (Click the red comment above to revert to the short version of the input):
c_mThe MASS action with label c_m calculates the following quantities: Quantity    Type    Description  
c_m vector the MASS for each set of specified atoms: MASSGet the mass of one or multiple atoms More details ATOMSthe atom numbers that you would like to store the masses and charges of=1-1000
c_massThe SUM action with label c_mass calculates the following quantities: Quantity    Type    Description  
c_mass scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments 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=c_m
c_qThe CHARGE action with label c_q calculates the following quantities: Quantity    Type    Description  
c_q vector the CHARGE for each set of specified atoms: CHARGEGet the charges of one or multiple atoms More details ATOMSthe atom numbers that you would like to store the masses and charges of=1-1000
c_chargeThe SUM action with label c_charge calculates the following quantities: Quantity    Type    Description  
c_charge scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments 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=c_q
c_wnormThe SUM action with label c_wnorm calculates the following quantities: Quantity    Type    Description  
c_wnorm scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments 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=sfcc
c_weightsThe CUSTOM action with label c_weights calculates the following quantities: Quantity    Type    Description  
c_weights vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c_wnorm,sfcc FUNCthe function you wish to evaluate=y/x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c_posThe POSITION action with label c_pos calculates the following quantities: Quantity    Type    Description  
c_pos.x vector the x-component of the atom position
c_pos.y vector the y-component of the atom position
c_pos.z vector the z-component of the atom position: POSITIONCalculate the components of the position of an atom or atoms. More details WHOLEMOLECULES if this is a vector of positions do you want to make the positions into a whole before ATOMSthe atom numbers that you would like to use the positions of=1-1000
c_xwvecThe CUSTOM action with label c_xwvec calculates the following quantities: Quantity    Type    Description  
c_xwvec vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c_weights,c_pos.x 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
c_ywvecThe CUSTOM action with label c_ywvec calculates the following quantities: Quantity    Type    Description  
c_ywvec vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c_weights,c_pos.y 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
c_zwvecThe CUSTOM action with label c_zwvec calculates the following quantities: Quantity    Type    Description  
c_zwvec vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c_weights,c_pos.z 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
c_xThe SUM action with label c_x calculates the following quantities: Quantity    Type    Description  
c_x 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=c_xwvec PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c_yThe SUM action with label c_y calculates the following quantities: Quantity    Type    Description  
c_y 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=c_ywvec PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c_zThe SUM action with label c_z calculates the following quantities: Quantity    Type    Description  
c_z 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=c_zwvec PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c: ARGS2VATOMCreate a virtual atom from the input scalars More details XPOSthe value to use for the x position of the atom=c_x YPOSthe value to use for the y position of the atom=c_y ZPOSthe value to use for the z position of the atom=c_z  MASSthe value to use for the mass of the atom=c_mass CHARGEthe value to use for the charge of the atom=c_charge 
# --- End of included input --- DUMPATOMSDump selected atoms on a file. More details ATOMSthe atom indices whose positions you would like to print out=c FILEfile on which to output coordinates; extension is automatically detected=atom.xyz

This input assumes you have a cluster of solid atoms in a liquid. The actions with labels fcc and sfcc are used to differentiate between atoms in solid-like and liquid-like atoms. sfcc is thus a vector with one element for each atom. These elements are equal to one if the environment around the corresponding atom are solid like and zero if the environment around the atom is liquid like.

A note on periodic boundary conditions

If you run with periodic boundary conditions these are taken into account automatically when computing the center of mass. The way this is handled is akin to the way molecules are rebuilt in the WHOLEMOLECULES command. However, at variance to WHOLEMOLECULES, the copies of the atomic positions in this action are modified. The global positions (i.e. those that are used in all other actions) are not changed when the alignment is performed.

If you believe that PBC should not be applied when calculating the position fo the center of mass you can use the NOPBC flag.

An additional way of managing periodic boundary conditions is offered in CENTER by using the PHASES keyword as shown in the example input below

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

cThe CENTER_FAST action with label c calculates the following quantities: Quantity    Type    Description  
c atoms virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-100 PHASES use trigonometric phases when computing position of center

The scaled value for the $x$ component of the position of the center is calculated from the scaled components of the input atoms, $x_i$ , using the following expression when the PHASES option is employed

$x_\textrm{com} = \frac{1}{2\pi} \atan\left( \frac{\sum_{i=1}^n w_i \sin(2 \pi x_i ) }{ \sum_{i=1}^n w_i \cos(2 \pi x_i ) } \right)$

Similar, expressions are used to calculae the values of the scaled $y$ and $z$ components. The final cartesian coordinates of the center are then computed by multiplying these scaled components by the cell vectors. Notice that by construction this center position is not invariant with respect to rotations of the atoms at fixed cell lattice. In addition, for symmetric Bravais lattices, it is not invariant with respect to special symmetries. E.g., if you have an hexagonal cell, the center will not be invariant with respect to rotations of 120 degrees. On the other hand, it might make the treatment of PBC easier in difficult cases.

Syntax

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

Keyword	Type	Default	Description
ATOMS	input	none	the group of atoms that you are calculating the Gyration Tensor for
TYPE	compulsory	RADIUS	The type of calculation relative to the Gyration Tensor you want to perform
NOPBC	optional	false	ignore the periodic boundary conditions when calculating distances
WEIGHTS	optional	not used	what weights should be used when calculating the center
PHASES	optional	false	use trigonometric phases when computing position of center
SAFE_PHASES	optional	false	use trignomentric phases when computing position of center but also compute the center in ths usual way and use this when the pbc are not set
MASS	optional	false	calculate the center of mass

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Quantity	Type	Description
c1	atoms	virtual atom calculated by CENTER_FAST action