ANGLES
 This is part of the multicolvar module

Calculate functions of the distribution of angles .

You can use this command to calculate functions such as:

$f(x) = \sum_{ijk} g( \theta_{ijk} )$

Alternatively you can use this command to calculate functions such as:

$f(x) = \sum_{ijk} s(r_{ij})s(r_{jk}) g(\theta_{ijk})$

where $$s(r)$$ is a switchingfunction. This second form means that you can use this to calculate functions of the angles in the first coordination sphere of an atom / molecule [51].

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 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.lessthan-1, label.lessthan-2 etc. When doing this and, for clarity we have made the label of the components customizable. As such by using the LABEL keyword in the description of the keyword input you can customize the component name

 Quantity Keyword Description 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 refererred 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.
The atoms involved can be specified using
 ATOMS the atoms involved in each of the collective variables you wish to calculate. Keywords like ATOMS1, ATOMS2, ATOMS3,... should be listed and one CV will be calculated for each ATOM keyword you specify (all ATOM keywords should define the same number of atoms). The eventual number of quantities calculated by this action will depend on what functions of the distribution you choose to calculate. You can use multiple instances of this keyword i.e. ATOMS1, ATOMS2, ATOMS3...
Or alternatively by using
 GROUP Calculate angles for each distinct set of three atoms in the group
Or alternatively by using
 GROUPA A group of central atoms about which angles should be calculated GROUPB When used in conjuction with GROUPA this keyword instructs plumed to calculate all distinct angles involving one atom from GROUPA and two atoms from GROUPB. The atom from GROUPA is the central atom.
Or alternatively by using
 GROUPC This must be used in conjuction with GROUPA and GROUPB. All angles involving one atom from GROUPA, one atom from GROUPB and one atom from GROUPC are calculated. The GROUPA atoms are assumed to be the central atoms
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 parallelize LOWMEM ( default=off ) lower the memory requirements TIMINGS ( default=off ) output information on the timings of the various parts of the calculation VERBOSE ( default=off ) write a more detailed output MEAN ( default=off ) take the mean of these variables. The final value can be referenced using label.mean
 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... 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. 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... SWITCH A switching function that ensures that only angles between atoms that are within a certain fixed cutoff are calculated. The following provides information on the switchingfunction that are available. SWITCHA A switching function on the distance between the atoms in group A and the atoms in group B SWITCHB A switching function on the distance between the atoms in group A and the atoms in group B
Examples

The following example instructs plumed to find the average of two angles and to print it to a file

ANGLES ATOMS1=1,2,3 ATOMS2=4,5,6 MEAN LABEL=a1
PRINT ARG=a1.mean FILE=colvar


The following example tells plumed to calculate all angles involving at least one atom from GROUPA and two atoms from GROUPB in which the distances are less than 1.0. The number of angles between $$\frac{\pi}{4}$$ and $$\frac{3\pi}{4}$$ is then output

ANGLES GROUPA=1-10 GROUPB=11-100 BETWEEN={GAUSSIAN LOWER=0.25pi UPPER=0.75pi} SWITCH={GAUSSIAN R_0=1.0} LABEL=a1
PRINT ARG=a1.between FILE=colvar


This final example instructs plumed to calculate all the angles in the first coordination spheres of the atoms. A discretized-normalized histogram of the distribution is then output

ANGLES GROUP=1-38 HISTOGRAM={GAUSSIAN LOWER=0.0 UPPER=pi NBINS=20} SWITCH={GAUSSIAN R_0=1.0} LABEL=a1
PRINT ARG=a1.* FILE=colvar