On the convergence improvement in the metadynamics simulations: A Wang-Landau recursion approach

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Abstract
As a popular tool in exploring free energy landscapes, the metadynamics method has been widely applied to elucidate various chemical or biochemical processes. As deeply discussed by Laio et al. [J. Phys. Chem. B109, 6714 (2005)], the size of the updating Gaussian function is pivotal to the free energy convergence toward the target free energysurface. For instance, a greater Gaussian height can facilitate the quick visit of a conformation region of interest; however, it may lead to a larger error of the calculated free energysurface. In contrast, a lower Gaussian height can guarantee a better resolution of the calculated free energysurface; however, it will take longer time for such a simulation to navigate through the defined conformational region. In order to reconcile such confliction, the authors present a method by implementing the Wang-Landau recursion scheme in the metadynamics simulations to adaptively update the height of the unit Gaussian function. As demonstrated in their model studies on both a toy system, and a realistic molecular system treated with the hybrid quantum mechanical and molecular mechanical (QM∕MM) potential, the present approach can quickly result in more decently converged free energysurfaces, compared with the classical metadynamics simulations employing the fixed Gaussian heights.