This is part of the mapping module

Path collective variables with a more flexible framework for the distance metric being used.

The Path Collective Variables developed by Branduardi and co-workers [10] allow one to compute the progress along a high-dimensional path and the distance from the high-dimensional path. The progress along the path (s) is computed using:

\[ s = \frac{ \sum_{i=1}^N i \exp( -\lambda R[X - X_i] ) }{ \sum_{i=1}^N \exp( -\lambda R[X - X_i] ) } \]

while the distance from the path (z) is measured using:

\[ z = -\frac{1}{\lambda} \ln\left[ \sum_{i=1}^N \exp( -\lambda R[X - X_i] ) \right] \]

In these expressions \(N\) high-dimensional frames ( \(X_i\)) are used to describe the path in the high-dimensional space. The two expressions above are then functions of the distances from each of the high-dimensional frames \(R[X - X_i]\). Within PLUMED there are multiple ways to define the distance from a high-dimensional configuration. You could calculate the RMSD distance or you could calculate the ammount by which a set of collective variables change. As such this implementation of the path cv allows one to use all the difference distance metrics that are discussed in Distances from reference configurations. This is as opposed to the alternative implementation of path (PATHMSD) which is a bit faster but which only allows one to use the RMSD distance.

Compulsory keywords
REFERENCE a pdb file containing the set of reference configurations
TYPE ( default=OPTIMAL-FAST ) the manner in which distances are calculated. More information on the different metrics that are available in PLUMED can be found in the section of the manual on Distances from reference configurations
LAMBDA the value of the lambda parameter for paths
NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically
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
DISABLE_CHECKS ( default=off ) disable checks on reference input structures.
NOZPATH ( default=off ) do not calculate the zpath position

( default=off ) do not calculate the spath position