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

This Action can be used to calculate the following quantities by employing the keywords listed below. You must select which from amongst these quantities you wish to calculate - this command cannot be run unless one of the quantities below is being calculated.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.less_than-1, label.less_than-2 etc.

Quantity	Keyword	Description
more_than	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.
min	MIN	the minimum 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
less_than	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.
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.
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.
dhenergy	DHENERGY	the Debye-Huckel interaction energy. 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
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

TOL	this keyword can be used to speed up your calculation. When accumulating sums in which the individual terms are numbers inbetween zero and one it is assumed that terms less than a certain tolerance make only a small contribution to the sum. They can thus be safely ignored as can the the derivatives wrt these small quantities.
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.
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.less_than. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.less_than-1, label.less_than-2, label.less_than-3...
DHENERGY	calculate the Debye-Huckel interaction energy. This is a alternative implementation of DHENERGY that is particularly useful if you want to calculate the Debye-Huckel interaction energy and some other function of set of distances between the atoms in the two groups. The input for this keyword should read DHENERGY={I= \(I\) TEMP= \(T\) EPSILON= \(\epsilon\)}. You can use multiple instances of this keyword i.e. DHENERGY1, DHENERGY2, DHENERGY3...
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.more_than. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.more_than-1, label.more_than-2, label.more_than-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.
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

(See also PRINT).

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

(See also PRINT switchingfunction).

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 AVERAGE LABEL=d1
PRINT ARG=d1.average

(See also PRINT)

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

(See also PRINT switchingfunction)