TD_PRODUCT_COMBINATION
This is part of the ves module
It is only available if you configure PLUMED with ./configure –enable-modules=ves . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Target distribution given by product combination of distributions (static or dynamic).

Employ a target distribution that is a product combination of the other distributions, defined as

\[ p(\mathbf{s}) = \frac{\prod_{i} p_{i}(\mathbf{s})} {\int d \mathbf{s} \prod_{i} p_{i}(\mathbf{s})} \]

where the distributions \(p_{i}(\mathbf{s})\) are in full dimensional space of the arguments used.

Note the difference between this target distribution and the one defined in TD_PRODUCT_DISTRIBUTION. Here we have a non-separable distribution given as a product of distribution \(p_{i}(\mathbf{s})\) which are in full dimensional space of the arguments used.

The labels of the distributions \(p_{i}(\mathbf{s})\) to be used in the product combination are given in the DISTRIBUTIONS keyword.

The target distribution resulting from the product combination will be automatically normalized. Therefore, the product combination needs to be a proper distribution that is non-negative and that can be normalized. The code will perform checks to make sure that this is indeed the case.

The product combination will be a dynamic target distribution if one or more of the distributions used is a dynamic distribution. Otherwise it will be a static distribution.

Examples

In the following example the overall interval on which the target distribution is defined is from 0.23 to 0.8. We employ a product combination of a well-tempered distribution and a uniform distribution that decays to zero at 0.6. This results in a target distribution that is well-tempered from 0.23 to 0.6 and then decays to zero. In other words, we cut off the tail of the well-tempered distribution at 0.6

Click on the labels of the actions for more information on what each action computes
tested on v2.7
td_welltemp: TD_WELLTEMPERED 
BIASFACTOR
compulsory keyword The bias factor used for the well-tempered distribution.
=5 td_uniform: TD_UNIFORM
MINIMA
The minimum of the intervals where the target distribution is taken as uniform.
=0.23
MAXIMA
The maximum of the intervals where the target distribution is taken as uniform.
=0.6
SIGMA_MAXIMA
The standard deviation parameters of the Gaussian switching functions for the maximum of the intervals.
=0.05 td_combination: TD_PRODUCT_COMBINATION
DISTRIBUTIONS
compulsory keyword The labels of the target distribution actions to be used in the product combination.
=td_uniform,td_welltemp

In the following example the overall interval on which the target distribution is defined is from -4 to 4. We employ a product of a Gaussian distribution with two centers and distribution that is uniform on the interval -3 to 3 and then smoothly decays to zero outside that interval. The overall effect will then be to cut off the tails of the Gaussian distribution

Click on the labels of the actions for more information on what each action computes
tested on v2.7
td_gauss: TD_GAUSSIAN ...
   
CENTER1
The centers of the Gaussian distributions.
=-2.9
SIGMA1
The standard deviations of the Gaussian distributions.
=1.0
CENTER2
The centers of the Gaussian distributions.
=+2.9
SIGMA2
The standard deviations of the Gaussian distributions.
=0.4 ... td_uni: TD_UNIFORM ...
MINIMA
The minimum of the intervals where the target distribution is taken as uniform.
=-3.0
SIGMA_MINIMA
The standard deviation parameters of the Gaussian switching functions for the minima of the intervals.
=0.20
MAXIMA
The maximum of the intervals where the target distribution is taken as uniform.
=+3.0
SIGMA_MAXIMA
The standard deviation parameters of the Gaussian switching functions for the maximum of the intervals.
=0.15 ... td_pc: TD_PRODUCT_COMBINATION
DISTRIBUTIONS
compulsory keyword The labels of the target distribution actions to be used in the product combination.
=td_gauss,td_uni
Glossary of keywords and components
Compulsory keywords
DISTRIBUTIONS The labels of the target distribution actions to be used in the product combination.
Options
SHIFT_TO_ZERO

( default=off ) Shift the minimum value of the target distribution to zero. This can for example be used to avoid negative values in the target distribution. If this option is active the distribution will be automatically normalized.

WELLTEMPERED_FACTOR Broaden the target distribution such that it is taken as [p(s)]^(1/ \(\gamma\)) where \(\gamma\) is the well tempered factor given here. If this option is active the distribution will be automatically normalized.