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.

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

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.

x: DISTANCE ATOMS=1,2
RESTRAINT ARG=x SLOPE=1.0 AT=0.0
bias: REWEIGHT_BIAS TEMP=300

HISTOGRAM ...
  ARG=x
  GRID_MIN=0.0
  GRID_MAX=3.0
  GRID_BIN=100
  BANDWIDTH=0.1
  LOGWEIGHTS=bias
  LABEL=hB
... HISTOGRAM

DUMPGRID GRID=hB FILE=histoB STRIDE=1 FMT=%8.4f