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 
ATOMS
the pair of atom that we are calculating the distance between. 
=1,2  You cannot view the components that are calculated by each action for this input file. Sorry 
RESTRAINT 
ARG
the values the harmonic restraint acts upon. 
=x 
SLOPE
compulsory 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 
AT
compulsory keyword 
the position of the restraint 
=0.0  You cannot view the components that are calculated by each action for this input file. Sorry 
bias: REWEIGHT_BIAS 
TEMP
the system temperature. 
=300  You cannot view the components that are calculated by each action for this input file. Sorry 
hB: HISTOGRAM ...
   
ARG
the quantities that are being used to construct the histogram 
=x 
   
GRID_MIN
compulsory keyword ( default=auto )
the lower bounds for the grid 
=0.0 
   
GRID_MAX
compulsory keyword ( default=auto )
the upper bounds for the grid 
=3.0 
   
GRID_BIN
the number of bins for the grid 
=100 
   
BANDWIDTH
the bandwidths for kernel density esimtation 
=0.1 
   
LOGWEIGHTS
the logarithm of the quantity to use as the weights when calculating averages 
=bias 
   
... You cannot view the components that are calculated by each action for this input file. Sorry 
DUMPGRID 
GRID
the grid you would like to print (can also use ARG for specifying what is being printed)
=hB 
FILE
compulsory keyword ( default=density )
the file on which to write the grid. 
=histoB 
STRIDE
compulsory keyword ( default=0 )
the frequency with which the grid should be output to the file. 
=1 
FMT
the format that should be used to output real numbers 
=%8.4f  You cannot view the components that are calculated by each action for this input file. Sorry 

Glossary of keywords and components

Description of components

This action calculates the logarithm of a weight for reweighting

Quantity	Description
.#!value	the weight to use for this frame to negate the effect the bias

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