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Subsections

## Arithmetic path collective variables

The arithmetic path collective variable in CV space uses the same formula as the one proposed by Branduardi[55] et al., except that it computes and in CV space instead of RMSDs in Cartesian space. Moreover, this implementation allows different coefficients for each CV components as described in [56]. Assuming a path is composed of reference frames and defined in an -dimensional CV space, then the equations of and of the path are

 (13.15)

 (13.16)

where is the coefficient(weight) of the -th CV, is the value of -th CV of -th reference frame and is the value of -th CV of current frame. is a parameter to smooth the variation of and .

### aspathCV: progress along a path defined in CV space.

This colvar component computes the variable.

• weights Coefficients of the collective variables
Context: aspathCV and azpathCV
Acceptable values: space-separated numbers in a {...} block
Default value: {1.0 ...}
Description: Define the coefficients. The -th value in the {...} block corresponds the in the equations.

• lambda Smoothness of the variation of and
Context: aspathCV and azpathCV
Acceptable values: decimal
Default value: inverse of the mean square displacements of successive reference frames
Description: The value of in the equations.

• pathFile The file name of the path file.
Context: aspathCV and azpathCV
Acceptable values: UNIX filename
Description: Defines the nodes or images that constitutes the path in CV space. The CVs of an image are listed in a line of pathFile using space-seperated format. Lines from top to button in pathFile corresponds images from initial to last.

### azpathCV: distance from a path defined in CV space.

This colvar component computes the variable. Options are the same as in .

The usage of azpathCV and aspathCV is illustrated below:

colvar {
# Progress along the path
name as
# Path defined by the CV space of two dihedral angles
aspathCV {
pathFile ./path.txt
weights {1.0 1.0}
lambda 0.005
dihedral {
name 001
group1 {atomNumbers {5}}
group2 {atomNumbers {7}}
group3 {atomNumbers {9}}
group4 {atomNumbers {15}}
}
dihedral {
name 002
group1 {atomNumbers {7}}
group2 {atomNumbers {9}}
group3 {atomNumbers {15}}
group4 {atomNumbers {17}}
}
}
}
colvar {
# Distance from the path
name az
azpathCV {
pathFile ./path.txt
weights {1.0 1.0}
lambda 0.005
dihedral {
name 001
group1 {atomNumbers {5}}
group2 {atomNumbers {7}}
group3 {atomNumbers {9}}
group4 {atomNumbers {15}}
}
dihedral {
name 002
group1 {atomNumbers {7}}
group2 {atomNumbers {9}}
group3 {atomNumbers {15}}
group4 {atomNumbers {17}}
}
}
}

### Path collective variables in Cartesian coordinates

The path collective variables defined by Branduardi et al. [55] are based on RMSDs in Cartesian coordinates. Noting the RMSD between the current set of Cartesian coordinates and those of image number of the path:

 (13.17)

 (13.18)

where is the smoothing parameter.

These coordinates are implemented as Tcl-scripted combinations of rmsd components. The implementation is available as file colvartools/pathCV.tcl, and an example is provided in file examples/10_pathCV.namd of the Colvars public repository. It implements an optimization procedure, whereby the distance to a given image is only calculated if its contribution to the sum is larger than a user-defined tolerance parameter. All distances are calculated every freq timesteps to update the list of nearby images.

Next: Shared keywords for all Up: Defining collective variables Previous: Geometric path collective variables   Contents   Index
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