Calculating a minimum distance

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

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.less_than,d1.more_than,d1.between,d1.min FILE=colvar STRIDE=10

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.

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