ANGLES

This is part of the multicolvar module

Calculate an angle.

This command can be used to compute the angle between three atoms. Alternatively if four atoms appear in the atom specification it calculates the angle between two vectors identified by two pairs of atoms.

If three atoms are given, the angle is defined as:

\[ \theta=\arccos\left(\frac{ {\bf r}_{21}\cdot {\bf r}_{23}}{ |{\bf r}_{21}| |{\bf r}_{23}|}\right) \]

Here \( {\bf r}_{ij}\) is the distance vector among the i-th and the j-th listed atom.

If four atoms are given, the angle is defined as:

\[ \theta=\arccos\left(\frac{ {\bf r}_{21}\cdot {\bf r}_{34}}{ |{\bf r}_{21}| |{\bf r}_{34}|}\right) \]

Notice that angles defined in this way are non-periodic variables and their value is limited by definition between 0 and \(\pi\).

The vectors \( {\bf r}_{ij}\) are by default evaluated taking periodic boundary conditions into account. This behavior can be changed with the NOPBC flag.

Examples

This command tells plumed to calculate the angle between the vector connecting atom 1 to atom 2 and the vector connecting atom 2 to atom 3 and to print it on file COLVAR1. At the same time, the angle between vector connecting atom 1 to atom 2 and the vector connecting atom 3 to atom 4 is printed on file COLVAR2.

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

a: ANGLE 
ATOMS
the list of atoms involved in this collective variable (either 3 or 4 atoms). 
=1,2,3 The ANGLE action with label a calculates a single scalar value
# equivalently one could state:
# a: ANGLE ATOMS=1,2,2,3
b: ANGLE 
ATOMS
the list of atoms involved in this collective variable (either 3 or 4 atoms). 
=1,2,3,4 The ANGLE action with label b calculates a single scalar value
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=a 
FILE
the name of the file on which to output these quantities 
=COLVAR1 The PRINT action with label 
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=b 
FILE
the name of the file on which to output these quantities 
=COLVAR2 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 a discretized histogram of the distribution of values. 
={GAUSSIAN LOWER=0.0 UPPER=pi NBINS=20}  
SWITCH
the switching function specifies that only those bonds that have a length that is
less than a certain threshold are considered 
={GAUSSIAN R_0=1.0}   You cannot view the components that are calculated by each action for this input file. Sorry 
PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=a1.* 
FILE
the name of the file on which to output these quantities 
=colvar  You cannot view the components that are calculated by each action for this input file. Sorry 

Glossary of keywords and components

Description of components

Quantity	Description
.#!value	the ANGLE for each set of three atoms that were specified

In addition the following quantities can be calculated by employing the keywords listed below

Quantity	Keyword	Description
lessthan	LESS_THAN	the number of colvars that have a value less than a threshold
morethan	MORE_THAN	the number of colvars that have a value more than a threshold
altmin	ALT_MIN	the minimum value of the cv
min	MIN	the minimum colvar
max	MAX	the maximum colvar
between	BETWEEN	the number of colvars that have a value that lies in a particular interval
highest	HIGHEST	the largest of the colvars
lowest	LOWEST	the smallest of the colvars
sum	SUM	the sum of the colvars
mean	MEAN	the mean of the colvars

The atoms involved can be specified 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

HIGHEST	( default=off ) this flag allows you to recover the highest of these variables.
LOWEST	( default=off ) this flag allows you to recover the lowest of these variables.
SUM	( default=off ) calculate the sum of all the quantities.
MEAN	( default=off ) calculate the mean of all the quantities.
SWITCH	the switching function specifies that only those bonds that have a length that is less than a certain threshold are considered
LESS_THAN	calculate the number of variables that are less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3...
MORE_THAN	calculate the number of variables that are more than a certain target value. This quantity is calculated using \(\sum_i 1 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3...
ALT_MIN	calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = -\frac{1}{\beta} \log \sum_i \exp\left( -\beta s_i \right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)).
MIN	calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) } \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\))
MAX	calculate the maximum value. To make this quantity continuous the maximum is calculated using \( \textrm{max} = \beta \log \sum_i \exp\left( \frac{s_i}{\beta}\right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\))
BETWEEN	calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead.. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3...
HISTOGRAM	calculate a discretized histogram of the distribution of values. This shortcut allows you to calculates NBIN quantites like BETWEEN.