MULTICOLVARDENS

This is part of the gridtools module

Evaluate the average value of a multicolvar on a grid.

This keyword allows one to construct a phase field representation for a symmetry function from an atomistic description. If each atom has an associated order parameter, \(\phi_i\) then a smooth phase field function \(\phi(r)\) can be computed using:

\[ \phi(\mathbf{r}) = \frac{\sum_i K(\mathbf{r}-\mathbf{r}_i) \phi_i }{ \sum_i K(\mathbf{r} - \mathbf{r}_i )} \]

where \(\mathbf{r}_i\) is the position of atom \(i\), the sums run over all the atoms input and \(K(\mathbf{r} - \mathbf{r}_i)\) is one of the kernelfunctions implemented in plumed. This action calculates the above function on a grid, which can then be used in the input to further actions.

Examples

The following example shows perhaps the simplest way in which this action can be used. The following input computes the density of atoms at each point on the grid and outputs this quantity to a file. In other words this input instructs plumed to calculate \(\rho(\mathbf{r}) = \sum_i K(\mathbf{r} - \mathbf{r}_i )\)

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

dens: DENSITY 
SPECIES
compulsory keyword 
the atoms in the group 
=1-100  You cannot view the components that are calculated by each action for this input file. Sorry 
grid: MULTICOLVARDENS 
DATA
the multicolvar which you would like to calculate the density profile for 
=dens 
ORIGIN
compulsory keyword 
we will use the position of this atom as the origin 
=1 
DIR
compulsory keyword 
the direction in which to calculate the density profile 
=xyz 
NBINS
the number of bins to use in each direction (alternative to GRID_NBIN) 
=100,100,100 
BANDWIDTH
the bandwidths for kernel density esimtation 
=0.05,0.05,0.05 
STRIDE
compulsory keyword ( default=1 )
the frequency with which to accumulate the densities 
=1  You cannot view the components that are calculated by each action for this input file. Sorry 
DUMPGRID 
GRID
the grid you would like to print (can also use ARG for specifying what is being printed)
=grid 
STRIDE
compulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. 
=500 
FILE
compulsory keyword ( default=density )
the file on which to write the grid. 
=density  You cannot view the components that are calculated by each action for this input file. Sorry 

In the above example density is added to the grid on every step. The PRINT_GRID instruction thus tells PLUMED to output the average density at each point on the grid every 500 steps of simulation. Notice that the that grid output on step 1000 is an average over all 1000 frames of the trajectory. If you would like to analyze these two blocks of data separately you must use the CLEAR flag.

This second example computes an order parameter (in this case FCCUBIC) and constructs a phase field model for this order parameter using the equation above.

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

contract shortcuts

fcc: FCCUBIC 
SPECIES
this keyword is used for colvars such as coordination number. 
=1-5184 
SWITCH
the switching function that it used in the construction of the contact matrix 
={CUBIC D_0=1.2 D_MAX=1.5}  
ALPHA
compulsory keyword ( default=3.0 )
The alpha parameter of the angular function that is used for FCCUBIC 
=27 The FCCUBIC action with label fcc calculates a single scalar value
dens: MULTICOLVARDENS 
DATA
the multicolvar which you would like to calculate the density profile for 
=fcc 
ORIGIN
compulsory keyword 
we will use the position of this atom as the origin 
=1 
DIR
compulsory keyword 
the direction in which to calculate the density profile 
=xyz 
NBINS
the number of bins to use in each direction (alternative to GRID_NBIN) 
=14,14,28 
BANDWIDTH
the bandwidths for kernel density esimtation 
=1.0,1.0,1.0 
STRIDE
compulsory keyword ( default=1 )
the frequency with which to accumulate the densities 
=1 
CLEAR
compulsory keyword ( default=0 )
the frequency with which to clear the density 
=1 The MULTICOLVARDENS action with label dens calculates a single scalar value
DUMPCUBE 
GRID
the grid you would like to print (can also use ARG for specifying what is being printed)
=dens 
STRIDE
compulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. 
=1 
FILE
compulsory keyword ( default=density )
the file on which to write the grid. 
=dens.cube The DUMPCUBE action with label 

fcc_grp: GROUP 
ATOMS
the numerical indexes for the set of atoms in the group. 
=1-5184 The GROUP action with label fcc_grp defines a group of atoms so that they can be referred to later in the input
fcc_mat: CONTACT_MATRIX 
GROUP
specifies the list of atoms that should be assumed indistinguishable. 
=1-5184 
SWITCH
specify the switching function to use between two sets of indistinguishable atoms.
=CUBIC,D_0=1.2,D_MAX=1.5 
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix 
 The CONTACT_MATRIX action with label fcc_mat
In this example the phase field model is computed and output to a file on every step of the simulation. Furthermore, because the CLEAR=1 keyword is set on the MULTICOLVARDENS line each Gaussian cube file output is a phase field model for a particular trajectory frame. The average value accumulated thus far is cleared at the start of every single timestep and there is no averaging over trajectory frames in this case.
Glossary of keywords and components

Compulsory keywords



 STRIDE  
( default=1 ) the frequency with which to accumulate the densities   

 CLEAR  
( default=0 ) the frequency with which to clear the density   

 ORIGIN  
we will use the position of this atom as the origin   

 DIR  
the direction in which to calculate the density profile   

 KERNEL  
( default=GAUSSIAN ) the kernel function you are using. More details on the kernels available in plumed plumed can be found in kernelfunctions.   

Options



 UNORMALIZED  
( default=off ) do not divide by the density  



 BANDWIDTH  
the bandwidths for kernel density esimtation   

 NBINS  
the number of bins to use in each direction (alternative to GRID_NBIN)   

 DATA  
the multicolvar which you would like to calculate the density profile for   

 ATOMS  
if you are calculating a atomic density you use this keyword to specify the atoms that are involved   

 NORMALIZATION  
set true/false to determine how to the data is normalised