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Combine Gaussians for multiple-walkers metadynamics before applying well-tempered scaling #819

@giacomofiorin

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@giacomofiorin

Multiple-walkers metadynamics (Raiteri et al, 2005) and well-tempered metadynamics (Barducci et al, 2008) are two separate variants that are occasionally combined together. The Barducci paper didn't explicitly state which biasing potential (partial or total) is scaled by the bias factor. Colvars scales the partial biasing potential of each replica, whereas PLUMED scales the total one, as mentioned in #815.

Independently from that, however, the write_pmf() function in Colvars uses the total biasing potential to extract the free-energy landscape:

if (well_tempered) {
cvm::real const well_temper_scale = (bias_temperature + proxy->target_temperature()) / bias_temperature;
pmf->multiply_constant(well_temper_scale);
}

Because fixing this inconsistency would break backward compatibility, it would be better to adopt the same convention that PLUMED uses.

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