This is part of the multicolvar 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 SPECIESthis keyword is used for colvars such as coordination number. =1-100 The DENSITY action with label dens
grid: MULTICOLVARDENS DATAcompulsory keyword 
the multicolvar which you would like to calculate the density profile for =dens ORIGINwe will use the position of this atom as the origin. =1 DIRcompulsory keyword 
the direction in which to calculate the density profile =xyz NBINSthe number of bins to use to represent the density profile =100,100,100 BANDWIDTHcompulsory keyword 
the bandwidths for kernel density estimation =0.05,0.05,0.05 STRIDEcompulsory keyword ( default=1 )
the frequency with which the data should be collected and added to the quantity being
averaged =1 The MULTICOLVARDENS action with label grid
DUMPGRID GRIDcompulsory keyword 
the action that creates the grid you would like to output =grid STRIDEcompulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. =500 FILEcompulsory keyword ( default=density )
the file on which to write the grid. =density The DUMPGRID action with label

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

fcc: FCCUBIC SPECIESthis keyword is used for colvars such as coordination number. =1-5184 SWITCHThis keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={CUBIC D_0=1.2 D_MAX=1.5}  ALPHAcompulsory keyword ( default=3.0 )
The alpha parameter of the angular function =27 The FCCUBIC action with label fcc
dens: MULTICOLVARDENS DATAcompulsory keyword 
the multicolvar which you would like to calculate the density profile for =fcc ORIGINwe will use the position of this atom as the origin. =1 DIRcompulsory keyword 
the direction in which to calculate the density profile =xyz NBINSthe number of bins to use to represent the density profile =14,14,28 BANDWIDTHcompulsory keyword 
the bandwidths for kernel density estimation =1.0,1.0,1.0 STRIDEcompulsory keyword ( default=1 )
the frequency with which the data should be collected and added to the quantity being
averaged =1 CLEARcompulsory keyword ( default=0 )
the frequency with which to clear all the accumulated data. =1 The MULTICOLVARDENS action with label dens
DUMPCUBE GRIDcompulsory keyword 
the action that creates the grid you would like to output =dens STRIDEcompulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. =1 FILEcompulsory keyword ( default=density )
the file on which to write the grid. =dens.cube The DUMPCUBE action with label

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

The atoms involved can be specified using

ORIGIN

we will use the position of this atom as the origin. For more information on how to specify lists of atoms see Groups and Virtual Atoms

Compulsory keywords

STRIDE	( default=1 ) the frequency with which the data should be collected and added to the quantity being averaged
CLEAR	( default=0 ) the frequency with which to clear all the accumulated data. The default value of 0 implies that all the data will be used and that the grid will never be cleared
NORMALIZATION	( default=true ) This controls how the data is normalized it can be set equal to true, false or ndata. The differences between these options are explained in the manual page for HISTOGRAM
BANDWIDTH	the bandwidths for kernel density estimation
KERNEL	( default=gaussian ) the kernel function you are using. More details on the kernels available in plumed plumed can be found in kernelfunctions.
DATA	the multicolvar which you would like to calculate the density profile for
DIR	the direction in which to calculate the density profile

Options

SERIAL	( default=off ) do the calculation in serial. Do not use MPI
LOWMEM	( default=off ) lower the memory requirements
TIMINGS	( default=off ) output information on the timings of the various parts of the calculation
FRACTIONAL	( default=off ) use fractional coordinates for the various axes
XREDUCED	( default=off ) limit the calculation of the density/average to a portion of the z-axis only
YREDUCED	( default=off ) limit the calculation of the density/average to a portion of the y-axis only
ZREDUCED	( default=off ) limit the calculation of the density/average to a portion of the z-axis only
LOGWEIGHTS	list of actions that calculates log weights that should be used to weight configurations when calculating averages
CONCENTRATION	the concentration parameter for Von Mises-Fisher distributions
NBINS	the number of bins to use to represent the density profile
SPACING	the approximate grid spacing (to be used as an alternative or together with NBINS)
XLOWER	this is required if you are using XREDUCED. It specifies the lower bound for the region of the x-axis that for which you are calculating the density/average
XUPPER	this is required if you are using XREDUCED. It specifies the upper bound for the region of the x-axis that for which you are calculating the density/average
YLOWER	this is required if you are using YREDUCED. It specifies the lower bound for the region of the y-axis that for which you are calculating the density/average
YUPPER	this is required if you are using YREDUCED. It specifies the upper bound for the region of the y-axis that for which you are calculating the density/average
ZLOWER	this is required if you are using ZREDUCED. It specifies the lower bound for the region of the z-axis that for which you are calculating the density/average
ZUPPER	this is required if you are using ZREDUCED. It specifies the upper bound for the region of the z-axis that for which you are calculating the density/average