MOVINGRESTRAINT
 This is part of the bias module

Add a time-dependent, harmonic restraint on one or more variables.

This form of bias can be used to performed steered MD [24] and Jarzynski sampling [27].

The harmonic restraint on your system is given by:

$V(\vec{s},t) = \frac{1}{2} \kappa(t) ( \vec{s} - \vec{s}_0(t) )^2$

The time dependence of $$\kappa$$ and $$\vec{s}_0$$ are specified by a list of STEP, KAPPA and AT keywords. These keywords tell plumed what values $$\kappa$$ and $$\vec{s}_0$$ should have at the time specified by the corresponding STEP keyword. Inbetween these times the values of $$\kappa$$ and $$\vec{s}_0$$ are linearly interpolated.

Additional material and examples can be also found in the tutorial Belfast tutorial: Out of equilibrium dynamics

Description of components

By default this Action calculates the following quantities. These quanties can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

 Quantity Description bias the instantaneous value of the bias potential work the total work performed changing this restraint force2 the instantaneous value of the squared force due to this bias potential _cntr one or multiple instances of this quantity will be refereceable elsewhere in the input file. these quantities will named with the arguments of the bias followed by the character string _cntr. These quantities give the instantaneous position of the center of the harmonic potential. _work one or multiple instances of this quantity will be refereceable elsewhere in the input file. These quantities will named with the arguments of the bias followed by the character string _work. These quantities tell the user how much work has been done by the potential in dragging the system along the various colvar axis. _kappa one or multiple instances of this quantity will be refereceable elsewhere in the input file. These quantities will named with the arguments of the bias followed by the character string _kappa. These quantities tell the user the time dependent value of kappa.
Compulsory keywords
 ARG the input for this action is the scalar output from one or more other actions. The particular scalars that you will use are referenced using the label of the action. If the label appears on its own then it is assumed that the Action calculates a single scalar value. The value of this scalar is thus used as the input to this new action. If * or *.* appears the scalars calculated by all the proceding actions in the input file are taken. Some actions have multi-component outputs and each component of the output has a specific label. For example a DISTANCE action labelled dist may have three componets x, y and z. To take just the x component you should use dist.x, if you wish to take all three components then use dist.*.More information on the referencing of Actions can be found in the section of the manual on the PLUMED Getting started. Scalar values can also be referenced using POSIX regular expressions as detailed in the section on Regular Expressions. To use this feature you you must compile PLUMED with the appropriate flag. VERSE ( default=B ) Tells plumed whether the restraint is only acting for CV larger (U) or smaller (L) than the restraint or whether it is acting on both sides (B) STEP This keyword appears multiple times as STEPx with x=0,1,2,...,n. Each value given represents the MD step at which the restraint parameters take the values KAPPAx and ATx. You can use multiple instances of this keyword i.e. STEP1, STEP2, STEP3... AT ATx is equal to the position of the restraint at time STEPx. For intermediate times this parameter is linearly interpolated. If no ATx is specified for STEPx then the values of AT are kept constant during the interval of time between STEPx-1 and STEPx. You can use multiple instances of this keyword i.e. AT1, AT2, AT3... KAPPA KAPPAx is equal to the value of the force constants at time STEPx. For intermediate times this parameter is linearly interpolated. If no KAPPAx is specified for STEPx then the values of KAPPAx are kept constant during the interval of time between STEPx-1 and STEPx. You can use multiple instances of this keyword i.e. KAPPA1, KAPPA2, KAPPA3...
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically
Examples
The following input is dragging the distance between atoms 2 and 4 from 1 to 2 in the first 1000 steps, then back in the next 1000 steps. In the following 500 steps the restraint is progressively switched off.
DISTANCE ATOMS=2,4 LABEL=d
MOVINGRESTRAINT ...
ARG=d
STEP0=0    AT0=1.0 KAPPA0=100.0
STEP1=1000 AT1=2.0
STEP2=2000 AT2=1.0
STEP3=2500         KAPPA3=0.0
... MOVINGRESTRAINT

The following input is progressively building restraints distances between atoms 1 and 5 and between atoms 2 and 4 in the first 1000 steps. Afterwards, the restraint is kept static.
DISTANCE ATOMS=1,5 LABEL=d1
DISTANCE ATOMS=2,4 LABEL=d2
MOVINGRESTRAINT ...
ARG=d1,d2
STEP0=0    AT0=1.0,1.5 KAPPA0=0.0,0.0
STEP1=1000 AT1=1.0,1.5 KAPPA1=1.0,1.0
... MOVINGRESTRAINT

The following input is progressively bringing atoms 1 and 2 close to each other with an upper wall
DISTANCE ATOMS=1,2 LABEL=d1
MOVINGRESTRAINT ...
ARG=d1
VERSE=U
STEP0=0    AT0=1.0 KAPPA0=10.0
STEP1=1000 AT1=0.0
... MOVINGRESTRAINT


By default the Action is issuing some values which are the work on each degree of freedom, the center of the harmonic potential, the total bias deposited