DISTANCES
 This is part of the multicolvar module

Calculate the distances between one or many pairs of atoms. You can then calculate functions of the distribution of distances such as the minimum, the number less than a certain quantity and so on.

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
 ATOMS the atoms involved in each of the collective variables you wish to calculate. Keywords like ATOMS1, ATOMS2, ATOMS3,... should be listed and one CV will be calculated for each ATOM keyword you specify (all ATOM keywords should define the same number of atoms). The eventual number of quantities calculated by this action will depend on what functions of the distribution you choose to calculate. You can use multiple instances of this keyword i.e. ATOMS1, ATOMS2, ATOMS3...
Or alternatively by using
 GROUP Calculate the distance between each distinct pair of atoms in the group
Or alternatively by using
 GROUPA Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB. This must be used in conjuction with GROUPB. GROUPB Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB. This must be used in conjuction with GROUPA.
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 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 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... 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... 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... 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... 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... 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. 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 $$m$$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- $$m$$.
Examples

The following input tells plumed to calculate the distances between atoms 3 and 5 and between atoms 1 and 2 and to print the minimum for these two distances.

DISTANCES ATOMS1=3,5 ATOMS2=1,2 MIN={BETA=0.1} LABEL=d1
PRINT ARG=d1.min


The following input tells plumed to calculate the distances between atoms 3 and 5 and between atoms 1 and 2 and then to calculate the number of these distances that are less than 0.1 nm. The number of distances less than 0.1nm is then printed to a file.

DISTANCES ATOMS1=3,5 ATOMS2=1,2 LABEL=d1 LESS_THAN={RATIONAL R_0=0.1}
PRINT ARG=d1.lt0.1


The following input tells plumed to calculate all the distances between atoms 1, 2 and 3 (i.e. the distances between atoms 1 and 2, atoms 1 and 3 and atoms 2 and 3). The average of these distances is then calculated.

DISTANCES GROUP=1-3 MEAN LABEL=d1
PRINT ARG=d1.mean


The following input tells plumed to calculate all the distances between the atoms in GROUPA and the atoms in GROUPB. In other words the distances between atoms 1 and 2 and the distance between atoms 1 and 3. The number of distances more than 0.1 is then printed to a file.

DISTANCES GROUPA=1 GROUPB=2,3 MORE_THAN={RATIONAL R_0=0.1}
PRINT ARG=d1.gt0.1


Calculating minimum distances

To calculate and print the minimum distance between two groups of atoms you use the following commands

d1: DISTANCES GROUPA=1-10 GROUPB=11-20 MIN={BETA=500.}
PRINT ARG=d1.min FILE=colvar STRIDE=10


(see DISTANCES and PRINT)

In order to ensure differentiability the minimum is calculated using the following function:

$s = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) }$

where $$\beta$$ is a user specified parameter.

This input is used rather than a separate MINDIST colvar so that the same routine and the same input style can be used to calculate minimum coordinatetion numbers (see COORDINATIONNUMBER), minimum angles (see ANGLES) and many other variables.

This new way of calculating mindist is part of plumed 2's multicolvar functionality. These special actions allow you to calculate multiple functions of a distribution of simple collective variables. As an example you can calculate the number of distances less than 1.0, the minimum distance, the number of distances more than 2.0 and the number of distances between 1.0 and 2.0 by using the following command:

DISTANCES ...
GROUPA=1-10 GROUPB=11-20
LESS_THAN={RATIONAL R_0=1.0}
MORE_THAN={RATIONAL R_0=2.0}
BETWEEN={GAUSSIAN LOWER=1.0 UPPER=2.0}
MIN={BETA=500.}
... DISTANCES
PRINT ARG=d1.lessthan,d1.morethan,d1.between,d1.min FILE=colvar STRIDE=10


(see DISTANCES and PRINT)

A calculation performed this way is fast because the expensive part of the calculation - the calculation of all the distances - is only done once per step. Furthermore, it can be made faster by using the TOL keyword to discard those distance that make only a small contributions to the final values together with the NL_STRIDE keyword, which ensures that the distances that make only a small contribution to the final values aren't calculated at every step.