TETRAHEDRAL

This is part of the crystallization module | |

It is only available if you configure PLUMED with ./configure –enable-modules=crystallization . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Calculate the degree to which the environment about ions has a tetrahedral order.

We can measure the degree to which the atoms in the first coordination shell around any atom, \(i\) is is arranged like a tetrahedron using the following function.

\[ s(i) = \frac{1}{\sum_j \sigma( r_{ij} )} \sum_j \sigma( r_{ij} )\left[ \frac{(x_{ij} + y_{ij} + z_{ij})^3}{r_{ij}^3} + \frac{(x_{ij} - y_{ij} - z_{ij})^3}{r_{ij}^3} + \frac{(-x_{ij} + y_{ij} - z_{ij})^3}{r_{ij}^3} + \frac{(-x_{ij} - y_{ij} + z_{ij})^3}{r_{ij}^3} \right] \]

Here \(r_{ij}\) is the magnitude of the vector connecting atom \(i\) to atom \(j\) and \(x_{ij}\), \(y_{ij}\) and \(z_{ij}\) are its three components. The function \(\sigma( r_{ij} )\) is a switchingfunction that acts on the distance between atoms \(i\) and \(j\). The parameters of this function should be set so that the function is equal to one when atom \(j\) is in the first coordination sphere of atom \(i\) and is zero otherwise.

- Examples

The following command calculates the average value of the TETRAHEDRAL parameter for a set of 64 atoms all of the same type and outputs this quantity to a file called colvar.

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

tt:TETRAHEDRALSPECIES=1-64this keyword is used for colvars such as coordination number.SWITCH={RATIONAL D_0=1.3 R_0=0.2}This keyword is used if you want to employ an alternative to the continuous switching function defined above.MEANPRINTtake the mean of these variables.ARG=the input for this action is the scalar output from one or more other actions.tt.meanFILE=colvarthe name of the file on which to output these quantities

The following command calculates the number of TETRAHEDRAL parameters that are greater than 0.8 in a set of 10 atoms. In this calculation it is assumed that there are two atom types A and B and that the first coordination sphere of the 10 atoms of type A contains atoms of type B. The formula above is thus calculated for ten different A atoms and within it the sum over \(j\) runs over 40 atoms of type B that could be in the first coordination sphere.

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

tt:TETRAHEDRALSPECIESA=1-10this keyword is used for colvars such as the coordination number.SPECIESB=11-40this keyword is used for colvars such as the coordination number.SWITCH={RATIONAL D_0=1.3 R_0=0.2}This keyword is used if you want to employ an alternative to the continuous switching function defined above.MORE_THAN={RATIONAL R_0=0.8} PRINTcalculate the number of variables more than a certain target value.ARG=the input for this action is the scalar output from one or more other actions.tt.*FILE=colvarthe name of the file on which to output these quantities

- 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 |

altmin | ALT_MIN | the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

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. |

highest | HIGHEST | the highest of the quantities calculated by this action |

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. |

lowest | LOWEST | the lowest of the quantities calculated by this action |

max | MAX | the maximum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

mean | MEAN | the mean value. The output component can be referred to elsewhere in the input file by using the label.mean |

min | MIN | |

moment | MOMENTS | the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc. |

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

SPECIES | this keyword is used for colvars such as coordination number. In that context it specifies that plumed should calculate one coordination number for each of the atoms specified. Each of these coordination numbers specifies how many of the other specified atoms are within a certain cutoff of the central atom. You can specify the atoms here as another multicolvar action or using a MultiColvarFilter or ActionVolume action. When you do so the quantity is calculated for those atoms specified in the previous multicolvar. This is useful if you would like to calculate the Steinhardt parameter for those atoms that have a coordination number more than four for example |

- Or alternatively by using

SPECIESA | this keyword is used for colvars such as the coordination number. In that context it species that plumed should calculate one coordination number for each of the atoms specified in SPECIESA. Each of these coordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff. As with the species keyword the input can also be specified using the label of another multicolvar |

SPECIESB | this keyword is used for colvars such as the coordination number. It must appear with SPECIESA. For a full explanation see the documentation for that keyword |

- Compulsory keywords

NN | ( default=6 ) The n parameter of the switching function |

MM | ( default=0 ) The m parameter of the switching function; 0 implies 2*NN |

D_0 | ( default=0.0 ) The d_0 parameter of the switching function |

R_0 | The r_0 parameter of the switching function |

PHI | ( default=0.0 ) The Euler rotational angle phi |

THETA | ( default=0.0 ) The Euler rotational angle theta |

PSI | ( default=0.0 ) The Euler rotational angle psi |

- 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 |

UNORMALIZED | ( default=off ) calculate the sum of the components of the vector rather than the mean |

SWITCH | This keyword is used if you want to employ an alternative to the continuous switching function defined above. The following provides information on the switchingfunction that are available. When this keyword is present you no longer need the NN, MM, D_0 and R_0 keywords. |

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... |

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... |

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... |

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= \(\beta\)) The final value can be referenced using label.max. You can use multiple instances of this keyword i.e. MAX1, MAX2, MAX3... The corresponding values are then referenced using label.max-1, label.max-2, label.max-3... |

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= \(\beta\)) The final value can be referenced using label.min. You can use multiple instances of this keyword i.e. MIN1, MIN2, MIN3... The corresponding values are then referenced using label.min-1, label.min-2, label.min-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... |

MOMENTS | calculate the moments of the distribution of collective variables. The mth moment of a distribution is calculated using \(\frac{1}{N} \sum_{i=1}^N ( s_i - \overline{s} )^m \), where \(\overline{s}\) is the average for the distribution. The moments keyword takes a lists of integers as input or a range. Each integer is a value of \(m\). The final calculated values can be referenced using moment- \(m\). You can use the COMPONENT keyword in this action but the syntax is slightly different. If you would like the second and third moments of the third component you would use MOMENTS={COMPONENT=3 MOMENTS=2-3}. The moments would then be referred to using the labels moment-3-2 and moment-3-3. This syntax is also required if you are using numbered MOMENT keywords i.e. MOMENTS1, MOMENTS2... |

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= \(\beta\)). The final value can be referenced using label.altmin. You can use multiple instances of this keyword i.e. ALT_MIN1, ALT_MIN2, ALT_MIN3... The corresponding values are then referenced using label.altmin-1, label.altmin-2, label.altmin-3... |

LOWEST | this flag allows you to recover the lowest of these variables. The final value can be referenced using label.lowest |

HIGHEST | this flag allows you to recover the highest of these variables. The final value can be referenced using label.highest |