Collective Variable-based Calculations

In today's molecular dynamics simulations, it is often useful to
reduce the great number of degrees of freedom of a into a few
parameters which can be either analyzed individually, or manipulated
in order to alter the dynamics in a controlled manner. These have
been called `order parameters', `collective variables', `(surrogate)
reaction coordinates', and many other terms. In this section, the
term `collective variable' (shortened to *colvar*) is used, and
it indicates any differentiable function of atomic Cartesian
coordinates,
, with between and , the total
number of atoms:

The colvars module in NAMD may be used in both MD simulation and energy minimization runs (except free energy methods). It offers several features:

- define an arbitrary number of colvars, and perform a
multidimensional analysis or biased simulation by accessing any
subset of colvars independently from the rest (see
10.1);
- combine different functions of Cartesian coordinates (herein
termed colvar
*components*) into a colvar defined as a polynomial of several such components, thereby implementing new functional forms at runtime; periodic, multidimensional and symmetric components are handled transparently (see 10.2.2); - calculate potentials of mean force (PMFs) for any set of
colvars, using different sampling methods: currently implemented are
the Adaptive Biasing Force (ABF) method (see
10.3.1), metadynamics (see
10.3.2), Steered Molecular Dynamics (SMD) and
Umbrella Sampling (US) via a flexible harmonic restraint bias (see
10.3.3);
- calculate statistical properties of the colvars, such as their
running averages and standard deviations, time correlation
functions, and multidimensional histograms, without the need to save
very large trajectory files.
- compute collective variable values from existing coordinates
(e.g. an MD trajectory): use NAMD's
`coorfile read`command, and perform a 0-timestep run for each set of coordinates, as illustrated in 16.

- General parameters and input/output files

- Declaring and using collective variables
- General collective variable options
- Collective variable components
- Periodic components.
- Non-scalar components.
- Calculating system forces.
- Syntax of a component definition.
- Component
`distance`: center-of-mass distance between two groups. - Component
`distanceZ`: projection of a distance vector on an axis. - Component
`distanceXY`: modulus of the projection of a distance vector on a plane. - Component
`distanceVec`: distance vector between two groups. - Component
`distanceDir`: distance unit vector between two groups. - Component
`angle`: angle between three groups. - Component
`dihedral`: torsional angle between four groups. - Component
`coordNum`: coordination number between two groups. - Component
`selfCoordNum`: coordination number between atoms within a group. - Component
`hBond`: hydrogen bond between two atoms. - Component
`rmsd`: root mean square displacement (RMSD) with respect to a reference structure. - Component
`eigenvector`: projection of the atomic coordinates on a vector. - Component
`gyration`: radius of gyration of a group of atoms. - Component
`orientation`: orientation from reference coordinates. - Component
`orientationAngle`: angle of rotation from reference coordinates. - Component
`alpha`: -helix content of a protein segment. - Component
`dihedralPC`: protein dihedral pricipal component

- Linear and polynomial combinations of components
- Defining atom groups
- Statistical analysis of individual collective variables

- Biasing and analysis methods