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 ATOMSthe list of atoms involved in this collective variable (either 3 or 4 atoms). =1,2,3
# equivalently one could state:
# a: ANGLE ATOMS=1,2,2,3
b: ANGLE ATOMSthe list of atoms involved in this collective variable (either 3 or 4 atoms). =1,2,3,4
PRINT ARGthe input for this action is the scalar output from one or more other actions. =a FILEthe name of the file on which to output these quantities =COLVAR1
PRINT ARGthe input for this action is the scalar output from one or more other actions. =b FILEthe name of the file on which to output these quantities =COLVAR2


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 GROUPCalculate angles for each distinct set of three atoms in the group =1-38 HISTOGRAMcalculate a discretized histogram of the distribution of values. ={GAUSSIAN LOWER=0.0 UPPER=pi NBINS=20}  SWITCHthe 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}
PRINT ARGthe input for this action is the scalar output from one or more other actions. =a1.* FILEthe name of the file on which to output these quantities =colvar

Glossary of keywords and components
Description of components
 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.