This is part of the bias module

Calculate weights for ensemble averages that negate the effect the bias has on the region of phase space explored

If a static or pseudo-static bias \(V(x,t')\) is acting on the system we can remove the bias and get the unbiased probability distribution using:

\[ \langle P(s',t) \rangle = \frac{ \sum_{t'}^t \delta( s(x) - s' ) \exp\left( +\frac{V(x,t')}{k_B T} \right) }{ \sum_t'^t \exp\left( +\frac{V(x,t')}{k_B T} \right) } \]

The weights calculated by this action are equal to \(\exp\left( +\frac{V(x,t')}{k_B T} \right)\) these weights can then be used in any action that computes ensemble averages. For example this action can be used in tandem with HISTOGRAM or AVERAGE.

Examples

In the following example there is a fixed restraint on the distance between atoms 1 and 2. Clearly, this restraint will have an effect on the region of phase space that will be sampled when an MD simulation is run using this variable. Consequently, when the histogram as a function of the distance, \(x\), is accumulated, we use reweighting into order to discount the effect of the bias from our final histogram.

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

x: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=1,2 The DISTANCE action with label x calculates a single scalar value
RESTRAINT ARGthe input for this action is the scalar output from one or more other actions. 
=x SLOPEcompulsory keyword ( default=0.0 )
specifies that the restraint is linear and what the values of the force constants
on each of the variables are 
=1.0 ATcompulsory keyword 
the position of the restraint 
=0.0 The RESTRAINT action with label 
bias: REWEIGHT_BIAS TEMPthe system temperature. 
=300 The REWEIGHT_BIAS action with label bias calculates a single scalar value
hB: HISTOGRAM ...
   ARGthe input for this action is the scalar output from one or more other actions. 
=x 
   GRID_MINcompulsory keyword 
the lower bounds for the grid =0.0 
   GRID_MAXcompulsory keyword 
the upper bounds for the grid =3.0 
   GRID_BINthe number of bins for the grid =100 
   BANDWIDTHcompulsory keyword 
the bandwidths for kernel density estimation =0.1 
   LOGWEIGHTSlist of actions that calculates log weights that should be used to weight configurations
when calculating averages 
=bias 
   
...The HISTOGRAM action with label hB
DUMPGRID GRIDcompulsory keyword 
the action that creates the grid you would like to output 
=hB FILEcompulsory keyword ( default=density )
the file on which to write the grid. 
=histoB STRIDEcompulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. 
=1 FMTthe format that should be used to output real numbers 
=%8.4f The DUMPGRID action with label

Glossary of keywords and components

Compulsory keywords

ARG

( default=*.bias ) the biases that must be taken into account when reweighting

Options

TEMP

the system temperature. This is not required if your MD code passes this quantity to PLUMED