Well-tempered metadynamics

Standard MetaD, introduced in the previous section, has two well-known problems  

As discussed, both these problems have been recognized and tackled respectively by taking time averages and by using restraining potentials. 

An alternative method that addresses both the problems in an elegant fashion. 

In WTMetaD, the rule for the bias update (Eq. [13]) is modified slightly to  

Equivalently, each Gaussian, when deposited, is scaled down by a factor 

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Barducci, A., Bussi, G., Parrinello, M. Well-tempered metadynamics a smoothly converging and mnable free-energy method. Phys. Rev. Lett 100, 020603 (2008)... 

Well-Tempered Metadynamics Using Gyration Radius... 

Well-Tempered Metadynamics Using Dihedral Angle ... 

As a last example we report the use of WTMetaD as discussed in Section Well-Tempered Metadynamics Using Dihedral Angle O. ... 

A. Barducd, G. Bussi, and M. Parrinello, Phys. Rev. Lett., 100(2), 020603 (2008). Well-Tempered Metadynamics A Smoothly-Converging and Tunable Free-Energy Method. 

M. Bonomi, A. Barducci, and M. Parrinello,/. Comput. Chem., 30(11), 1615—1621 (2009). Reconstructing the Equilibrium Boltzmann Distribution from Well-Tempered Metadynamics. 

The added bias potential, t), is added to the overall potential energy and is repulsive, Gaussian-shaped, and centered on the CV at the time of addition. This results in a net force that prevents the system from exploring previously visited states and instead encourages it to explore new regions of the CVs. To achieve smooth convergence of the bias potential, we use the well-tempered variant of metadynamics (WTM) [32] ... 

Multiple walkers metadynamics can also be used in the well-tempered algorithm. In the long time fimit the error prefactor will be decreased when increasing the number of walkers because the walkers will provide independent statistics biased by the same potential. 

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