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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)

This method was introduced in [67]. It is used on one or more collective variables. This method is also called dynamic reference restraining(DRR) [119] . A detailed description of this module can be found at [32] .

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) [68] 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 [41] . 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. The additional .zcount and .zgrad files contain the number of samples of \(\boldsymbol{\xi}\), and the negative of \(\boldsymbol{\xi}\)-averaged spring forces, respectively, which are mainly for inspecting and debugging purpose. To get PMF, the abf_integrate(https://github.com/Colvars/colvars/tree/master/colvartools) is useful for numerically integrating the .czar.grad file.

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 v2.10
phi: TORSION ATOMSthe four atoms involved in the torsional angle =5,7,9,15 
psi: TORSION ATOMSthe four atoms involved in the torsional angle =7,9,15,17 
eabf: DRR ...
   
   ARGthe input for this action is the scalar output from one or more other actions. =phi,psi 
   FULLSAMPLEScompulsory keyword ( default=500 )
number of samples in a bin prior to application of the ABF =500 
   GRID_MINcompulsory keyword 
the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =-pi,-pi 
   GRID_MAXcompulsory keyword 
the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =pi,pi 
   GRID_BINthe number of bins for the grid =180,180 
   FRICTIONcompulsory keyword ( default=8.0 )
add a friction to the variable, similar to extended Langevin Damping in Colvars =8.0,8.0 
   TAUcompulsory keyword ( default=0.5 )
specifies relaxation time on each of variables are, similar to extended Time Constant
in Colvars =0.5,0.5 
   OUTPUTFREQcompulsory keyword 
write results to a file every N steps =50000 
   HISTORYFREQsave history to a file every N steps =500000 
...
# monitor the two variables, their fictitious variables and applied forces.
PRINT STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output =10 ARGthe 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 FILEthe 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 v2.10





It's also possible to run extended generalized adaptive biasing force (egABF) described in [118] . An egABF example: 


 Click on the labels of the actions for more information on what each action computes 


tested on v2.10
phi: TORSION ATOMSthe four atoms involved in the torsional angle =5,7,9,15 
psi: TORSION ATOMSthe four atoms involved in the torsional angle =7,9,15,17 
gabf_phi: DRR ...
   
   ARGthe input for this action is the scalar output from one or more other actions. =phi 
   FULLSAMPLEScompulsory keyword ( default=500 )
number of samples in a bin prior to application of the ABF =500 
   GRID_MINcompulsory keyword 
the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =-pi 
   GRID_MAXcompulsory keyword 
the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =pi 
   GRID_BINthe number of bins for the grid =180 
   FRICTIONcompulsory keyword ( default=8.0 )
add a friction to the variable, similar to extended Langevin Damping in Colvars =8.0 
   TAUcompulsory keyword ( default=0.5 )
specifies relaxation time on each of variables are, similar to extended Time Constant
in Colvars =0.5 
   OUTPUTFREQcompulsory keyword 
write results to a file every N steps =50000 
   HISTORYFREQsave history to a file every N steps =500000 
...
gabf_psi: DRR ...
   
   ARGthe input for this action is the scalar output from one or more other actions. =psi 
   FULLSAMPLEScompulsory keyword ( default=500 )
number of samples in a bin prior to application of the ABF =500 
   GRID_MINcompulsory keyword 
the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =-pi 
   GRID_MAXcompulsory keyword 
the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =pi 
   GRID_BINthe number of bins for the grid =180 
   FRICTIONcompulsory keyword ( default=8.0 )
add a friction to the variable, similar to extended Langevin Damping in Colvars =8.0 
   TAUcompulsory keyword ( default=0.5 )
specifies relaxation time on each of variables are, similar to extended Time Constant
in Colvars =0.5 
   OUTPUTFREQcompulsory keyword 
write results to a file every N steps =50000 
   HISTORYFREQsave history to a file every N steps =500000 
...
gabf_2d: DRR ...
   
   ARGthe input for this action is the scalar output from one or more other actions. =phi,psi 
   EXTERNAL_FORCEuse forces from other action instead of internal spring force, this disable the extended
system! =gabf_phi.phi_springforce,gabf_psi.psi_springforce 
   EXTERNAL_FICTposition of external fictitious particles, useful for UIESTIMATOR =gabf_phi.phi_fictNoPBC,gabf_psi.psi_fictNoPBC 
   GRID_MINcompulsory keyword 
the lower bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =-pi,-pi 
   GRID_MAXcompulsory keyword 
the upper bounds for the grid (GRID_BIN or GRID_SPACING should be specified) =pi,pi 
   GRID_BINthe number of bins for the grid =180,180 
   NOBIAS( default=off ) DO NOT apply bias forces.  
   OUTPUTFREQcompulsory keyword 
write results to a file every N steps =50000 
   HISTORYFREQsave history to a file every N steps =500000 
...
PRINT STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output =10 ARGthe input for this action is the scalar output from one or more other actions. =phi,psi FILEthe 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)   



 FMT  specify format for outfiles files (useful for decrease the number of digits in regtests)