AROUND

This quantity can be used to calculate functions of the distribution of collective variables for the atoms that lie in a particular, user-specified part of of the cell.

Each of the base quantities calculated by a multicolvar can can be assigned to a particular point in three dimensional space. For example, if we have the coordination numbers for all the atoms in the system each coordination number can be assumed to lie on the position of the central atom. Because each base quantity can be assigned to a particular point in space we can calculate functions of the distribution of base quantities in a particular part of the box by using:

\[ \overline{s}_{\tau} = \frac{ \sum_i f(s_i) w(x_i,y_i,z_i) }{ \sum_i w(x_i,y_i,z_i) } \]

where the sum is over the collective variables, \(s_i\), each of which can be thought to be at \( (x_i,y_i,z_i)\). The function \( w(x_i,y_i,z_i) \) measures whether or not the system is in the subregion of interest. It is equal to:

\[ w(x_i,y_i,z_i) = \int_{xl}^{xu} \int_{yl}^{yu} \int_{zl}^{zu} \textrm{d}x\textrm{d}y\textrm{d}z K\left( \frac{x - x_i}{\sigma} \right)K\left( \frac{y - y_i}{\sigma} \right)K\left( \frac{z - z_i}{\sigma} \right) \]

where \(K\) is one of the kernel functions described on histogrambead and \(\sigma\) is a bandwidth parameter. The function \((s_i)\) can be any of the usual LESS_THAN, MORE_THAN, WITHIN etc that are used in all other multicolvars.

When AROUND is used with the DENSITY action the number of atoms in the specified region is calculated

Description of components

This Action can be used to calculate the following quantities by employing the keywords listed below. You must select which from amongst these quantities you wish to calculate - this command cannot be run unless one of the quantities below is being calculated.These quantities can then be referenced elsewhere in the input file by using this Action's label followed by a dot and the name of the quantity. Some amongst them can be calculated multiple times with different parameters. In this case the quantities calculated can be referenced elsewhere in the input by using the name of the quantity followed by a numerical identifier e.g. label.less_than-1, label.less_than-2 etc.

Quantity	Keyword	Description
more_than	MORE_THAN	the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
mean	MEAN	the mean value. The output component can be refererred to elsewhere in the input file by using the label.mean
less_than	LESS_THAN	the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
between	BETWEEN	the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.

The atoms involved can be specified using

ATOM	the atom whose vicinity we are interested in examining

Compulsory keywords

ARG	the label of the action that calculates the multicolvar we are interested in
SIGMA	the width of the function to be used for kernel density estimation
KERNEL	( default=gaussian ) the type of kernel function to be used
XLOWER	( default=0.0 ) the lower boundary in x relative to the x coordinate of the atom (0 indicates use full extent of box).
XUPPER	( default=0.0 ) the upper boundary in x relative to the x coordinate of the atom (0 indicates use full extent of box).
YLOWER	( default=0.0 ) the lower boundary in y relative to the y coordinate of the atom (0 indicates use full extent of box).
YUPPER	( default=0.0 ) the upper boundary in y relative to the y coordinate of the atom (0 indicates use full extent of box).
ZLOWER	( default=0.0 ) the lower boundary in z relative to the z coordinate of the atom (0 indicates use full extent of box).
ZUPPER	( default=0.0 ) the upper boundary in z relative to the z coordinate of the atom (0 indicates use full extent of box).

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
SERIAL	( default=off ) do the calculation in serial. Do not parallelize
MEAN	( default=off ) take the mean of these variables. The final value can be referenced using label.mean
OUTSIDE	( default=off ) calculate quantities for colvars that are on atoms outside the region of interest

TOL	this keyword can be used to speed up your calculation. When accumulating sums in which the individual terms are numbers inbetween zero and one it is assumed that terms less than a certain tolerance make only a small contribution to the sum. They can thus be safely ignored as can the the derivatives wrt these small quantities.
LESS_THAN	calculate the number of variables less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.less_than. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.less_than-1, label.less_than-2, label.less_than-3...
MORE_THAN	calculate the number of variables more than a certain target value. This quantity is calculated using \(\sum_i 1.0 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.more_than. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.more_than-1, label.more_than-2, label.more_than-3...
BETWEEN	calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead. The final value can be referenced using label.between. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3... The corresponding values are then referenced using label.between-1, label.between-2, label.between-3...
HISTOGRAM	calculate a discretized histogram of the distribution of values. This shortcut allows you to calculates NBIN quantites like BETWEEN.

Examples

The following commands tell plumed to calculate the average coordination number for the atoms that have x (in fractional coordinates) within 2.0 nm of the com of mass c1. The final value will be labeled s.mean.

COM ATOMS=1-100 LABEL=c1
COORDINATIONNUMBER SPECIES=1-100 R_0=1.0 LABEL=c
AROUND ARG=c ORIGIN=c1 XLOWER=-2.0 XUPPER=2.0 SIGMA=0.1 MEAN LABEL=s