DRR
This is part of the drr module
It is only available if you configure PLUMED with ./configure –enable-modules=drr . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Used to performed extended-system adaptive biasing force(eABF) [81] method on one or more collective variables. This method is also called dynamic reference restraining(DRR) [145] . A detailed description of this module can be found at [40] .

For each collective variable \(\xi_i\), a fictitious variable \(\lambda_i\) is attached through a spring. The fictitious variable \(\lambda_i\) undergoes overdamped Langevin dynamics just like EXTENDED_LAGRANGIAN. The ABF algorithm applies bias force on \(\lambda_i\). The bias force acts on \(\lambda_i\) is the negative average spring force on \(\lambda_i\), which enhances the sampling of \(\lambda_i\).

\[ F_{bias}(\lambda_i)=k(\lambda_i-\langle\xi_i\rangle_{\lambda_i}) \]

If spring force constant k is large enough, then \(\xi_i\) synchronizes with \(\lambda_i\). The naive(ABF) estimator is just the negative average spring force of \(\lambda_i\).

The naive(ABF) estimator is biased. There are unbiased estimators such as CZAR(Corrected z-averaged restraint) [82] and UI(Umbrella Integration). The CZAR estimates the gradients as:

\[ \frac{\partial{A}}{\partial{\xi_i}}\left({\xi}\right)=-\frac{1}{\beta}\frac{\partial\ln\tilde{\rho}\left(\xi\right)}{\partial{\xi_i}}+k\left(\langle\lambda_i\rangle_\xi-\xi_i\right) \]

The UI estimates the gradients as:

\[ A'(\xi^*)=\frac{{\sum_\lambda}N\left(\xi^*,\lambda\right)\left[\frac{\xi^*-\langle\xi\rangle_\lambda}{\beta\sigma_\lambda^2}-k(\xi^*-\lambda)\right]}{{\sum_\lambda}N\left(\xi^*,\lambda\right)} \]

The code performing UI(colvar_UIestimator.h) is contributed by Haohao Fu [52] . It may be slow. I only change the Boltzmann constant and output precision in it. For new version and issues, please see: https://github.com/fhh2626/colvars

After running eABF/DRR, the drr_tool utility can be used to extract the gradients and counts files from .drrstate. Naive(ABF) estimator's result is in .abf.grad and .abf.count files and CZAR estimator's result is in .czar.grad and .czar.count files. To get PMF, the abf_integrate(https://github.com/Colvars/colvars/tree/master/colvartools) is useful.

Examples

The following input tells plumed to perform a eABF/DRR simulation on two torsional angles.

Click on the labels of the actions for more information on what each action computes
tested on master
phi: TORSION 
ATOMS
the four atoms involved in the torsional angle
=5,7,9,15 psi: TORSION
ATOMS
the four atoms involved in the torsional angle
=7,9,15,17 eabf: DRR ...
ARG
the input for this action is the scalar output from one or more other actions.
=phi,psi
FULLSAMPLES
compulsory keyword ( default=500 ) number of samples in a bin prior to application of the ABF
=500
GRID_MIN
compulsory keyword the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=-pi,-pi
GRID_MAX
compulsory keyword the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=pi,pi
GRID_BIN
the number of bins for the grid
=180,180
FRICTION
compulsory keyword ( default=8.0 ) add a friction to the variable, similar to extended Langevin Damping in Colvars
=8.0,8.0
TAU
compulsory keyword ( default=0.5 ) specifies relaxation time on each of variables are, similar to extended Time Constant in Colvars
=0.5,0.5
OUTPUTFREQ
compulsory keyword write results to a file every N steps
=50000
HISTORYFREQ
save history to a file every N steps
=500000 ... # monitor the two variables, their fictitious variables and applied forces. PRINT
STRIDE
compulsory keyword ( default=1 ) the frequency with which the quantities of interest should be output
=10
ARG
the input for this action is the scalar output from one or more other actions.
=phi,psi,eabf.phi_fict,eabf.psi_fict,eabf.phi_biasforce,eabf.psi_biasforce
FILE
the name of the file on which to output these quantities
=COLVAR

The following input tells plumed to perform a eABF/DRR simulation on the distance of atom 10 and 92. The distance is restraint by LOWER_WALLS and UPPER_WALLS.

Click on the labels of the actions for more information on what each action computes
tested on master
dist1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=10,92 eabf_winall: DRR
ARG
the input for this action is the scalar output from one or more other actions.
=dist1
FULLSAMPLES
compulsory keyword ( default=500 ) number of samples in a bin prior to application of the ABF
=2000
GRID_MIN
compulsory keyword the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=1.20
GRID_MAX
compulsory keyword the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=3.20
GRID_BIN
the number of bins for the grid
=200
FRICTION
compulsory keyword ( default=8.0 ) add a friction to the variable, similar to extended Langevin Damping in Colvars
=8.0
TAU
compulsory keyword ( default=0.5 ) specifies relaxation time on each of variables are, similar to extended Time Constant in Colvars
=0.5
OUTPUTFREQ
compulsory keyword write results to a file every N steps
=5000
HISTORYFREQ
save history to a file every N steps
=500000 uwall: UPPER_WALLS
ARG
the input for this action is the scalar output from one or more other actions.
=eabf_winall.dist1_fict
AT
compulsory keyword the positions of the wall.
=3.2
KAPPA
compulsory keyword the force constant for the wall.
=418.4 lwall: LOWER_WALLS
ARG
the input for this action is the scalar output from one or more other actions.
=eabf_winall.dist1_fict
AT
compulsory keyword the positions of the wall.
=1.2
KAPPA
compulsory keyword the force constant for the wall.
=418.4 PRINT
STRIDE
compulsory keyword ( default=1 ) the frequency with which the quantities of interest should be output
=10
ARG
the input for this action is the scalar output from one or more other actions.
=dist1,eabf_winall.dist1_fict,eabf_winall.dist1_biasforce
FILE
the name of the file on which to output these quantities
=COLVAR

It's also possible to run extended generalized adaptive biasing force (egABF) described in [144] . An egABF example:

Click on the labels of the actions for more information on what each action computes
tested on master
phi: TORSION 
ATOMS
the four atoms involved in the torsional angle
=5,7,9,15 psi: TORSION
ATOMS
the four atoms involved in the torsional angle
=7,9,15,17 gabf_phi: DRR ...
ARG
the input for this action is the scalar output from one or more other actions.
=phi
FULLSAMPLES
compulsory keyword ( default=500 ) number of samples in a bin prior to application of the ABF
=500
GRID_MIN
compulsory keyword the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=-pi
GRID_MAX
compulsory keyword the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=pi
GRID_BIN
the number of bins for the grid
=180
FRICTION
compulsory keyword ( default=8.0 ) add a friction to the variable, similar to extended Langevin Damping in Colvars
=8.0
TAU
compulsory keyword ( default=0.5 ) specifies relaxation time on each of variables are, similar to extended Time Constant in Colvars
=0.5
OUTPUTFREQ
compulsory keyword write results to a file every N steps
=50000
HISTORYFREQ
save history to a file every N steps
=500000 ... gabf_psi: DRR ...
ARG
the input for this action is the scalar output from one or more other actions.
=psi
FULLSAMPLES
compulsory keyword ( default=500 ) number of samples in a bin prior to application of the ABF
=500
GRID_MIN
compulsory keyword the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=-pi
GRID_MAX
compulsory keyword the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=pi
GRID_BIN
the number of bins for the grid
=180
FRICTION
compulsory keyword ( default=8.0 ) add a friction to the variable, similar to extended Langevin Damping in Colvars
=8.0
TAU
compulsory keyword ( default=0.5 ) specifies relaxation time on each of variables are, similar to extended Time Constant in Colvars
=0.5
OUTPUTFREQ
compulsory keyword write results to a file every N steps
=50000
HISTORYFREQ
save history to a file every N steps
=500000 ... gabf_2d: DRR ...
ARG
the input for this action is the scalar output from one or more other actions.
=phi,psi
EXTERNAL_FORCE
use forces from other action instead of internal spring force, this disable the extended system!
=gabf_phi.phi_springforce,gabf_psi.psi_springforce
EXTERNAL_FICT
position of external fictitious particles, useful for UIESTIMATOR
=gabf_phi.phi_fictNoPBC,gabf_psi.psi_fictNoPBC
GRID_MIN
compulsory keyword the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=-pi,-pi
GRID_MAX
compulsory keyword the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
=pi,pi
GRID_BIN
the number of bins for the grid
=180,180
NOBIAS
( default=off ) DO NOT apply bias forces.
OUTPUTFREQ
compulsory keyword write results to a file every N steps
=50000
HISTORYFREQ
save history to a file every N steps
=500000 ... PRINT
STRIDE
compulsory keyword ( default=1 ) the frequency with which the quantities of interest should be output
=10
ARG
the input for this action is the scalar output from one or more other actions.
=phi,psi
FILE
the name of the file on which to output these quantities
=COLVAR
Glossary of keywords and components
Description of components

By default this Action calculates the following quantities. These quantities 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
_fict one or multiple instances of this quantity can be referenced elsewhere in the input file. These quantities will named with the arguments of the bias followed by the character string _tilde. It is possible to add forces on these variable.
_vfict one or multiple instances of this quantity can be referenced elsewhere in the input file. These quantities will named with the arguments of the bias followed by the character string _tilde. It is NOT possible to add forces on these variable.
_biasforce The bias force from eABF/DRR of the fictitious particle.
_springforce Spring force between real CVs and extended CVs
_fictNoPBC the positions of fictitious particles (without PBC).
Compulsory keywords
TAU ( default=0.5 ) specifies relaxation time on each of variables are, similar to extended Time Constant in Colvars
FRICTION ( default=8.0 ) add a friction to the variable, similar to extended Langevin Damping in Colvars
GRID_MIN the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
GRID_MAX the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified)
REFLECTINGWALL ( default=0 ) whether add reflecting walls for each CV at GRID_MIN and GRID_MAX. Setting non-zero values will enable this feature
FULLSAMPLES ( default=500 ) number of samples in a bin prior to application of the ABF
MAXFACTOR ( default=1.0 ) maximum scaling factor of biasing force
OUTPUTFREQ write results to a file every N steps
Options
NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically
NOCZAR ( default=off ) disable the CZAR estimator
UI ( default=off ) enable the umbrella integration estimator
NOBIAS ( default=off ) DO NOT apply bias forces.
TEXTOUTPUT ( default=off ) use text output for grad and count files instead of boost::serialization binary output
MERGEHISTORYFILES

( default=off ) output all historic results to a single file rather than multiple .drrstate files. This option is effective only when textOutput is on.

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 proceeding 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 components 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. You can use multiple instances of this keyword i.e. ARG1, ARG2, ARG3...
KAPPA specifies that the restraint is harmonic and what the values of the force constants on each of the variables are (default to \(k_BT\)/(GRID_SPACING)^2)
GRID_BIN the number of bins for the grid
GRID_SPACING the approximate grid spacing (to be used as an alternative or together with GRID_BIN)
ZGRID_MIN the lower bounds for the grid (ZGRID_BIN or ZGRID_SPACING should be specified)
ZGRID_MAX the upper bounds for the grid (ZGRID_BIN or ZGRID_SPACING should be specified)
ZGRID_BIN the number of bins for the grid
ZGRID_SPACING the approximate grid spacing (to be used as an alternative or together with ZGRID_BIN)
EXTERNAL_FORCE use forces from other action instead of internal spring force, this disable the extended system!
EXTERNAL_FICT position of external fictitious particles, useful for UIESTIMATOR
HISTORYFREQ save history to a file every N steps
UIRESTARTPREFIX specify the restart files for umbrella integration
OUTPUTPREFIX specify the output prefix (default to the label name)
TEMP the system temperature - needed when FRICTION is present. If not provided will be taken from MD code (if available)
EXTTEMP the temperature of extended variables (default to system temperature)
DRR_RFILE specifies the restart file (.drrstate file)