Efficient Reconstruction of Complex Free Energy Landscapes by Multiple Walkers Metadynamics

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Abstract
Recently, we have introduced a new method, metadynamics, which is able to sample rarely occurring transitions and to reconstruct the free energy as a function of several variables with a controlled accuracy. This method has been successfully applied in many different fields, ranging from chemistry to biophysics and ligand docking and from material science to crystal structure prediction. We present an important development that speeds up metadynamics calculations by orders of magnitude and renders the algorithm much more robust. We use multiple interacting simulations, walkers, for exploring and reconstructing the same free energy surface. Each walker contributes to the history-dependent potential that, in metadynamics, is an estimate of the free energy. We show that the error on the reconstructed free energy does not depend on the number of walkers, leading to a fully linear scaling algorithm even on inexpensive loosely coupled clusters of PCs. In addition, we show that the accuracy and stability of the method are much improved by combining it with a weighted histogram analysis. We check the validity of our new method on a realistic application.