Free energy landscape from metadynamics

Bussi, G., Gervasio, E., Laio, A., Parrinello, M. Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics. J. Am. Chem. Soc. 128, 13435 (2006)... 

Fig. 2.8 Free energy landscape and main configurations of the O atoms adsorbed on an exposed Si(lOO) surface as provided by metadynamics in which two collective variables are used. These are the distances of the two atoms of an approaching O2 molecule from Si sites. The initial position of the non-dissociated oxygen dimer shown on top of the figure can evolve into two possible dissociated forms corresponding to the two minima B and C on the free energy surface. The associated barrier is about...

As a final remark, we note that the theoretically perfect scaling of multiple walkers metadynamics can be reached only if the walkers are started from independent configurations taken from the proper equilibrium distribution. This can be a difficult task, as the free-energy landscape is not known a priori. 

Using BEMD it is thus possible to replace an (unfeasible) metadynamics that would use ten or twenty CVs with ten or twenty weakly coupled one-dimensional metadynamics simulations and retain an accuracy that is determined by the replica containing the optimal CV. Moreover, the statistics of each of the replicas benehts from the exchange. Accordingly, the exploration of phase space by each replica is much higher compared to that of a simple MetaD. We hnally point out that in BEMD the statistics produced by all the replicas should be used to calculate the final free-energy landscape via a reweighting procedure. 

G. Bussi, F. L. Gervasio, A. Laio, and M. Parrinello, /. Ant. Ghent. Soc., 128(41), 13435-13441 (2006). Free-Energy Landscape for /J-Hairpin Folding from Combined Parallel Tempering and Metadynamics. 

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