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 first coordination shell around any atom, $$i$$ is tetrahedrally ordered 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 fo 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.

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 amongst 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 the label of the components customizable. 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 lowest of the quantitities 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 quantitities 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 refererred to elsewhere in the input file by using the label.mean min MIN the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. 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.
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 cooordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff 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=12 ) The m parameter of the switching function D_0 ( default=0.0 ) The d_0 parameter of the switching function R_0 The r_0 parameter of the switching function
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 parallelize LOWMEM ( default=off ) lower the memory requirements TIMINGS ( default=off ) output information on the timings of the various parts of the calculation VERBOSE ( default=off ) write a more detailed output MEAN ( default=off ) take the mean of these variables. The final value can be referenced using label.mean LOWEST ( default=off ) calculate the lowest of these variables. The final value can be referenced using label.lowest HIGHEST ( default=off ) calculate the highest of these variables. The final value can be referenced using label.highest
 SWITCH This keyword is used if you want to employ an alternative to the continuous swiching 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. 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. 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. 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 a discretized histogram of the distribution of values. This shortcut allows you to calculates NBIN quantites like BETWEEN. MOMENTS calculate the moments of the distribution of collective variables. The $$m$$th 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- $$m$$. 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.
Examples

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

tt: TETRAHEDRAL SPECIES=1-64 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MEAN
PRINT ARG=tt.mean FILE=colvar


The following command calculates the number of tetrahedrality 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.

tt: TETRAHEDRAL SPECIESA=1-10 SPECIESB=11-40 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MORE_THAN={RATIONAL R_0=0.8}
PRINT ARG=tt.* FILE=colvar