Defining collective variables and their properties

In the configuration file each colvar is defined by the keyword colvar, followed by its configuration options within curly braces: colvar { ... }. One of these options is the name of a colvar component: for example, including rmsd { ... } defines the colvar as a RMSD function. In most applications, only one component is used, and the component is equal to the colvar.

The full list of colvar components can be found in Section 10.4, with the syntax to select atoms in Section 10.3. The following section lists several options to control the behavior of a single colvar, regardless of its type.

General options for a collective variable

The following options are not required by default; however, the first four are very frequently used:

• name $<$ (colvar context) Name of this colvar $>$
  Acceptable Values: string
  Default Value: ``colvar'' + numeric id
  Description: The name is an unique case-sensitive string which allows the colvar module to identify this colvar unambiguously; it is also used in the trajectory file to label to the columns corresponding to this colvar.

• width $<$ (colvar context) Expected fluctuations amplitude, and resolution for grid-based methods $>$
  Acceptable Values: positive decimal
  Default Value: 1.0
  Description: This number is a user-provided estimate of the fluctuation amplitude for the colvar. For example, it is recommended to set this number smaller than or equal to the standard deviation of the colvar during a very short simulation run. Biasing algorithms use this parameter for different purposes: harmonic restraints (10.5.3) use it to set the physical unit of the force constant, the histogram (10.5.4) and ABF biases (10.5.1) interpret it as the grid spacing in the direction of this variable, and metadynamics (10.5.2) uses it to set the width of newly added hills. This number is expressed in the same physical unit as the colvar value.

• lowerBoundary $<$ (colvar context) Lower boundary of the colvar $>$
  Acceptable Values: decimal
  Description: Defines the lowest end of the interval of ``relevant'' values for the colvar. This number can be either a true physical boundary, or a user-defined number. Together with upperBoundary and width, it is used to define a grid of values along the colvar (not available for colvars based on distanceDir, distanceVec, and orientation). This option does not affect dynamics: to confine a colvar within a certain interval, the options lowerWall and lowerWallConstant should be used.

• upperBoundary $<$ (colvar context) Upper boundary of the colvar $>$
  Acceptable Values: decimal
  Description: Similarly to lowerBoundary, defines the highest possible or allowed value.

• hardLowerBoundary $<$ (colvar context) Whether the lower boundary is the physical lower limit $>$
  Acceptable Values: boolean
  Default Value: off
  Description: This option does not affect simulation results, but enables some internal optimizations. Depending on its mathematical definition, a colvar may have ``natural'' boundaries: for example, a distance colvar has a ``natural'' lower boundary at 0. Setting this option instructs the colvars module that the user-defined lower boundary is ``natural''. See Section 10.4 for the physical ranges of values of each component.

• hardUpperBoundary $<$ (colvar context) Whether the upper boundary is the physical upper limit of the colvar's values $>$
  Acceptable Values: boolean
  Default Value: off
  Description: Analogous to hardLowerBoundary.

• expandBoundaries $<$ (colvar context) Allow to expand the two boundaries if needed $>$
  Acceptable Values: boolean
  Default Value: off
  Description: If defined, biasing and analysis methods may keep their own copies of lowerBoundary and upperBoundary, and expand them to accommodate values that do not fit in the initial range. Currently, this option is used by the metadynamics bias (10.5.2) to keep all of its hills fully within the grid. This option cannot be used when the initial boundaries already span the full period of a periodic colvar.

Artificial boundary potentials (walls)

The following options are useful to define restraints (confining potentials) for this colvar. To apply moving restraints, or restraints to more than one colvar simultaneously, a more convenient option is to use the harmonic bias (10.5.3).

• lowerWallConstant $<$ (colvar context) Lower wall force constant (kcal/mol) $>$
  Acceptable Values: positive decimal
  Description: Defines the force constant for a confining restraint on the colvar, in the form of a ``half-harmonic'' potential. The potential starts at lowerWall if it is defined, or lowerBoundary otherwise. The energy unit of the constant is kcal/mol, while the spatial unit is that of the colvar.

• lowerWall $<$ (colvar context) Position of the lower wall $>$
  Acceptable Values: decimal
  Default Value: lowerBoundary
  Description: Defines the value below which a confining restraint on the colvar is applied, in the form of a ``half-harmonic'' potential. Allows to use a different position of the wall than lowerBoundary.

• upperWallConstant $<$ (colvar context) Upper wall force constant (kcal/mol) $>$
  Acceptable Values: positive decimal
  Description: Analogous to lowerWallConstant.

• upperWall $<$ (colvar context) Position of the upper wall $>$
  Acceptable Values: decimal
  Default Value: upperBoundary
  Description: Analogous to lowerWall.

Trajectory output

• outputValue $<$ (colvar context) Output a trajectory for this colvar $>$
  Acceptable Values: boolean
  Default Value: on
  Description: If colvarsTrajFrequency is non-zero, the value of this colvar is written to the trajectory file every colvarsTrajFrequency steps in the column labeled ``$<$ name$>$ ''.

• outputVelocity $<$ (colvar context) Output a velocity trajectory for this colvar $>$
  Acceptable Values: boolean
  Default Value: off
  Description: If colvarsTrajFrequency is defined, the finite-difference calculated velocity of this colvar are written to the trajectory file under the label ``v_$<$ name$>$ ''.

• outputEnergy $<$ (colvar context) Output an energy trajectory for this colvar $>$
  Acceptable Values: boolean
  Default Value: off
  Description: This option applies only to extended Lagrangian colvars. If colvarsTrajFrequency is defined, the kinetic energy of the extended degree and freedom and the potential energy of the restraining spring are are written to the trajectory file under the labels ``Ek_$<$ name$>$ '' and ``Ep_$<$ name$>$ ''.

• outputSystemForce $<$ (colvar context) Output a system force trajectory for this colvar $>$
  Acceptable Values: boolean
  Default Value: off
  Description: If colvarsTrajFrequency is defined, the total system force on this colvar (i.e. the projection of all interatomic forces except constraint forces on this colvar -- see equation (53) in section 10.5.1) are written to the trajectory file under the label ``fs_$<$ name$>$ ''. Note: not all components support this option. The physical unit for this force is kcal/mol, divided by the colvar unit.

• outputAppliedForce $<$ (colvar context) Output an applied force trajectory for this colvar $>$
  Acceptable Values: boolean
  Default Value: off
  Description: If colvarsTrajFrequency is defined, the total force applied on this colvar by biases within the colvar module are written to the trajectory under the label ``fa_$<$ name$>$ ''. The physical unit for this force is kcal/mol divided by the colvar unit.

Extended Lagrangian.

The following options enable extended-system dynamics, where a colvar is coupled to an additional degree of freedom (fictitious particle) by a harmonic spring.

• extendedLagrangian $<$ (colvar context) Add extended degree of freedom $>$
  Acceptable Values: boolean
  Default Value: off
  Description: Adds a fictitious particle to be coupled to the colvar by a harmonic spring. The fictitious mass and the force constant of the coupling potential are derived from the parameters extendedTimeConstant and extendedFluctuation, described below. Biasing forces on the colvar are applied to this fictitious particle, rather than to the atoms directly. This implements the extended Lagrangian formalism used in some metadynamics simulations [34]. The energy associated with the extended degree of freedom is reported under the MISC title in NAMD's energy output.

• extendedFluctuation $<$ (colvar context) Standard deviation between the colvar and the fictitious particle (colvar unit) $>$
  Acceptable Values: positive decimal
  Default Value: width
  Description: Defines the spring stiffness for the extendedLagrangian mode, by setting the typical deviation between the colvar and the extended degree of freedom due to thermal fluctuation. The spring force constant is calculated internally as $k_B T / \sigma^2$ , where $\sigma$ is the value of extendedFluctuation.

• extendedTimeConstant $<$ (colvar context) Oscillation period of the fictitious particle (fs) $>$
  Acceptable Values: positive decimal
  Default Value: 200
  Description: Defines the inertial mass of the fictitious particle, by setting the oscillation period of the harmonic oscillator formed by the fictitious particle and the spring. The period should be much larger than the MD time step to ensure accurate integration of the extended particle's equation of motion. The fictitious mass is calculated internally as $k_B T (\tau/2 \pi \sigma)^2$ , where $\tau$ is the period and $\sigma$ is the typical fluctuation (see above).

• extendedTemp $<$ (colvar context) Temperature for the extended degree of freedom (K) $>$
  Acceptable Values: positive decimal
  Default Value: thermostat temperature
  Description: Temperature used for calculating the coupling force constant of the extended coordinate (see extendedFluctuation) and, if needed, as a target temperature for extended Langevin dynamics (see extendedLangevinDamping). This should normally be left at its default value.

• extendedLangevinDamping $<$ (colvar context) Damping factor for extended Langevin dynamics (ps$^{-1}$ ) $>$
  Acceptable Values: positive decimal
  Default Value: 1.0
  Description: If this is non-zero, the extended degree of freedom undergoes Langevin dynamics at temperature extendedTemp. The friction force is minus extendedLangevinDamping times the velocity. This is useful because the extended dynamics coordinate may heat up in the transient non-equilibrium regime of ABF. Use moderate damping values, to limit viscous friction (potentially slowing down diffusive sampling) and stochastic noise (increasing the variance of statistical measurements). In doubt, use the default value.

Statistical analysis of collective variables

When the global keyword analysis is defined in the configuration file, run-time calculations of statistical properties for individual colvars can be performed. At the moment, several types of time correlation functions, running averages and running standard deviations are available.

• corrFunc $<$ (colvar context) Calculate a time correlation function? $>$
  Acceptable Values: boolean
  Default Value: off
  Description: Whether or not a time correlaction function should be calculated for this colvar.

• corrFuncWithColvar $<$ (colvar context) Colvar name for the correlation function $>$
  Acceptable Values: string
  Description: By default, the auto-correlation function (ACF) of this colvar, $\xi_{i}$ , is calculated. When this option is specified, the correlation function is calculated instead with another colvar, $\xi_{j}$ , which must be of the same type (scalar, vector, or quaternion) as $\xi_{i}$ .

• corrFuncType $<$ (colvar context) Type of the correlation function $>$
  Acceptable Values: velocity, coordinate or coordinate_p2
  Default Value: velocity
  Description: With coordinate or velocity, the correlation function $C_{i,j}(t)$  = $\left\langle \Pi\left(\xi_{i}(t_{0}), \xi_{j}(t_{0}+t)\right) \right\rangle$ is calculated between the variables $\xi_{i}$ and $\xi_{j}$ , or their velocities. $\Pi(\xi_{i}, \xi_{j})$ is the scalar product when calculated between scalar or vector values, whereas for quaternions it is the cosine between the two corresponding rotation axes. With coordinate_p2, the second order Legendre polynomial, $(3\cos(\theta)^{2}-1)/2$ , is used instead of the cosine.

• corrFuncNormalize $<$ (colvar context) Normalize the time correlation function? $>$
  Acceptable Values: boolean
  Default Value: on
  Description: If enabled, the value of the correlation function at $t$  = 0 is normalized to 1; otherwise, it equals to $\left\langle O\left(\xi_{i}, \xi_{j}\right) \right\rangle$ .

• corrFuncLength $<$ (colvar context) Length of the time correlation function $>$
  Acceptable Values: positive integer
  Default Value: 1000
  Description: Length (in number of points) of the time correlation function.

• corrFuncStride $<$ (colvar context) Stride of the time correlation function $>$
  Acceptable Values: positive integer
  Default Value: 1
  Description: Number of steps between two values of the time correlation function.

• corrFuncOffset $<$ (colvar context) Offset of the time correlation function $>$
  Acceptable Values: positive integer
  Default Value: 0
  Description: The starting time (in number of steps) of the time correlation function (default: $t$  = 0). Note: the value at $t$  = 0 is always used for the normalization.

• corrFuncOutputFile $<$ (colvar context) Output file for the time correlation function $>$
  Acceptable Values: UNIX filename
  Default Value: $<$ name$>$ .corrfunc.dat
  Description: The time correlation function is saved in this file.

• runAve $<$ (colvar context) Calculate the running average and standard deviation $>$
  Acceptable Values: boolean
  Default Value: off
  Description: Whether or not the running average and standard deviation should be calculated for this colvar.

• runAveLength $<$ (colvar context) Length of the running average window $>$
  Acceptable Values: positive integer
  Default Value: 1000
  Description: Length (in number of points) of the running average window.

• runAveStride $<$ (colvar context) Stride of the running average window values $>$
  Acceptable Values: positive integer
  Default Value: 1
  Description: Number of steps between two values within the running average window.

• runAveOutputFile $<$ (colvar context) Output file for the running average and standard deviation $>$
  Acceptable Values: UNIX filename
  Default Value: $<$ name$>$ .runave.dat
  Description: The running average and standard deviation are saved in this file.