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:ANGLEATOMS=1,2,3 # equivalently one could state: # a: ANGLE ATOMS=1,2,2,3the list of atoms involved in this collective variable (either 3 or 4 atoms).b:ANGLEATOMS=1,2,3,4 PRINTthe list of atoms involved in this collective variable (either 3 or 4 atoms).ARG=the input for this action is the scalar output from one or more other actions.aFILE=COLVAR1 PRINTthe name of the file on which to output these quantitiesARG=the input for this action is the scalar output from one or more other actions.bFILE=COLVAR2the name of the file on which to output these quantities

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:ANGLESGROUP=1-38Calculate angles for each distinct set of three atoms in the groupHISTOGRAM={GAUSSIAN LOWER=0.0 UPPER=pi NBINS=20}calculate a discretized histogram of the distribution of values.SWITCH={GAUSSIAN R_0=1.0} PRINTthe switching function specifies that only those bonds that have a length that is less than a certain threshold are consideredARG=the input for this action is the scalar output from one or more other actions.a1.*FILE=colvarthe name of the file on which to output these quantities

- 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. |