INSPHERE

This is part of the multicolvar module

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:

\[ \overline{s}_{\tau} = \frac{ \sum_i f(s_i) \sigma(r) }{ \sum_i \sigma(r) } \]

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 \(\sigma\) is a switchingfunction that acts on the distance between the point at which the collective is located \((x_i,y_i,z_i)\) and the position of the atom that was specified using the ORIGIN keyword. In other words:

\[ r = sqrt{ ( x_i - x_0)^2 + ( y_i - y_0)^2 + ( z_i - z_0)^2} \]

In short this function, \(\sigma(r_{xy})\), measures whether or not the CV is within a sphere that is centered on the position of the atom specified using the keyword ORIGIN.

The function \((s_i)\) can be any of the usual LESS_THAN, MORE_THAN, WITHIN etc that are used in all other multicolvars.

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

Examples

The input below can be use to calculate the average coordination numbers for those atoms that are within a sphere of radius 1.5 nm that is centered on the position of atom 101.

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

c1: COORDINATIONNUMBER 
SPECIES
this keyword is used for colvars such as coordination number. 
=1-100 
SWITCH
This keyword is used if you want to employ an alternative to the continuous switching
function defined above. 
={RATIONAL R_0=0.1}  The COORDINATIONNUMBER action with label c1
d2: INSPHERE 
ATOM
the atom whose vicinity we are interested in examining. 
=101 
DATA
compulsory keyword 
The multicolvar that calculates the set of base quantities that we are interested
in 
=c1 
RADIUS
compulsory keyword 
the switching function that tells us the extent of the spherical region of interest
={TANH R_0=1.5}  
MEAN
take the mean of these variables. 
 The INSPHERE action with label d2 calculates a single scalar value
PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=d2.* 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

Glossary of keywords and components

Description of components

When the label of this action is used as the input for a second you are not referring to a scalar quantity as you are in regular collective variables. The label is used to reference the full set of quantities calculated by the action. This is usual when using MultiColvar functions. Generally when doing this the previously calculated multicolvar will be referenced using the DATA keyword rather than ARG.

This Action can be used to calculate the following scalar quantities directly. These quantities are calculated by employing the keywords listed below. 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 of 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.lessthan-1, label.lessthan-2 etc. When doing this and, for clarity we have made it so that the user can set a particular label for each of the components. As such by using the LABEL keyword in the description of the keyword input you can customize the component name

Quantity	Keyword	Description
vmean	VMEAN	the norm of the mean vector. The output component can be referred to elsewhere in the input file by using the label.vmean
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.
lessthan	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.
mean	MEAN	the mean value. The output component can be referred to elsewhere in the input file by using the label.mean
morethan	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.
sum	SUM	the sum of values

The atoms involved can be specified using

ATOM	the atom whose vicinity we are interested in examining. For more information on how to specify lists of atoms see Groups and Virtual Atoms

Compulsory keywords

DATA	The multicolvar that calculates the set of base quantities that we are interested in
KERNEL	( default=gaussian ) the type of kernel function to be used
RADIUS	the switching function that tells us the extent of the spherical region of interest

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
NOPBC	( default=off ) ignore the periodic boundary conditions when calculating distances
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
OUTSIDE	( default=off ) calculate quantities for colvars that are on atoms outside the region of interest
VMEAN	calculate the norm of the mean vector. The final value can be referenced using label.vmean. You can use multiple instances of this keyword i.e. VMEAN1, VMEAN2, VMEAN3... The corresponding values are then referenced using label.vmean-1, label.vmean-2, label.vmean-3...
MEAN	take the mean of these variables. The final value can be referenced using label.mean. You can use multiple instances of this keyword i.e. MEAN1, MEAN2, MEAN3... The corresponding values are then referenced using label.mean-1, label.mean-2, label.mean-3...
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.lessthan. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.lessthan-1, label.lessthan-2, label.lessthan-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.morethan. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.morethan-1, label.morethan-2, label.morethan-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 how many of the values fall in each of the bins of a histogram. This shortcut allows you to calculates NBIN quantities like BETWEEN. The final value can be referenced using label.histogram. You can use multiple instances of this keyword i.e. HISTOGRAM1, HISTOGRAM2, HISTOGRAM3... The corresponding values are then referenced using label.histogram-1, label.histogram-2, label.histogram-3...
SUM	calculate the sum of all the quantities. The final value can be referenced using label.sum. You can use multiple instances of this keyword i.e. SUM1, SUM2, SUM3... The corresponding values are then referenced using label.sum-1, label.sum-2, label.sum-3...