REWEIGHT_BIAS
 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
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
bias: REWEIGHT_BIAS TEMPthe system temperature. =300
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

...
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

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