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:DISTANCEATOMS=1,2 RESTRAINTthe pair of atom that we are calculating the distance between.ARG=the values the harmonic restraint acts upon.xSLOPE=1.0compulsory keyword ( default=0.0 )specifies that the restraint is linear and what the values of the force constants on each of the variables areAT=0.0compulsory keywordthe position of the restraintbias:REWEIGHT_BIASTEMP=300the system temperature.hB:HISTOGRAM ...ARG=the quantities that are being used to construct the histogramxGRID_MIN=0.0compulsory keyword ( default=auto )the lower bounds for the gridGRID_MAX=3.0compulsory keyword ( default=auto )the upper bounds for the gridGRID_BIN=100the number of bins for the gridBANDWIDTH=0.1the bandwidths for kernel density esimtationLOGWEIGHTS=the logarithm of the quantity to use as the weights when calculating averagesbias... DUMPGRIDGRID=the grid you would like to print (can also use ARG for specifying what is being printed)hBFILE=histoBcompulsory keyword ( default=density )the file on which to write the grid.STRIDE=1compulsory keyword ( default=0 )the frequency with which the grid should be output to the file.FMT=%8.4fthe format that should be used to output real numbers

- 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 |