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 [133].

Examples

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

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

a1: ANGLES 
ATOMS1
the atoms involved in each of the angles you wish to calculate. 
=1,2,3 
ATOMS2
the atoms involved in each of the angles you wish to calculate. 
=4,5,6 
MEAN
take the mean of these variables. 
 The ANGLES action with label a1 calculates a single scalar value
PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=a1.mean 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

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

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

a1: ANGLES 
GROUPA
A group of central atoms about which angles should be calculated 
=1-10 
GROUPB
When used in conjunction with GROUPA this keyword instructs plumed to calculate all
distinct angles involving one atom from GROUPA and two atoms from GROUPB. 
=11-100 
BETWEEN
calculate the number of values that are within a certain range. 
={GAUSSIAN LOWER=0.25pi UPPER=0.75pi}  
SWITCH
A switching function that ensures that only angles between atoms that are within
a certain fixed cutoff are calculated. 
={GAUSSIAN R_0=1.0}  The ANGLES action with label a1 calculates a single scalar value
PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=a1.between 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

This final example instructs plumed to calculate all the angles in the first coordination spheres of the atoms. The bins for a normalized histogram of the distribution is then output

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

a1: ANGLES 
GROUP
Calculate angles for each distinct set of three atoms in the group 
=1-38 
HISTOGRAM
calculate how many of the values fall in each of the bins of a histogram. 
={GAUSSIAN LOWER=0.0 UPPER=pi NBINS=20}  
SWITCH
A switching function that ensures that only angles between atoms that are within
a certain fixed cutoff are calculated. 
={GAUSSIAN R_0=1.0}  The ANGLES action with label a1 calculates the following quantities:

 Quantity   
 Description  
a1.between-1
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.  This is the 1th of these quantities
a1.between-2
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.  This is the 2th of these quantities
a1.between-3
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.  This is the 3th of these quantities
a1.between-4
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.  This is the 4th of these quantities
a1.between-5
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.  This is the 5th of these quantities
a1.between-6
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.  This is the 6th of these quantities
a1.between-7
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.  This is the 7th of these quantities
a1.between-8
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.  This is the 8th of these quantities
a1.between-9
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.  This is the 9th of these quantities
a1.between-10
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.  This is the 10th of these quantities
a1.between-11
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.  This is the 11th of these quantities
a1.between-12
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.  This is the 12th of these quantities
a1.between-13
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.  This is the 13th of these quantities
a1.between-14
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.  This is the 14th of these quantities
a1.between-15
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.  This is the 15th of these quantities
a1.between-16
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.  This is the 16th of these quantities
a1.between-17
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.  This is the 17th of these quantities
a1.between-18
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.  This is the 18th of these quantities
a1.between-19
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.  This is the 19th of these quantities
a1.between-20
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.  This is the 20th of these quantities


PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=a1.* 
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
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.

The atoms involved can be specified using

ATOMS

the atoms involved in each of the angles you wish to calculate. Keywords like ATOMS1, ATOMS2, ATOMS3,... should be listed and one angle will be calculated for each ATOM keyword you specify (all ATOM keywords should provide the indices of three 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 conjunction 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 conjunction 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 use MPI
LOWMEM	( default=off ) lower the memory requirements
TIMINGS	( default=off ) output information on the timings of the various parts of the calculation
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...
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...
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