Metadynamics (MTD) is a very powerful technique to sample high-dimensionalfree energy landscapes, and due to its self-guiding property, the method hasbeen successful in studying complex reactions and conformational changes. MTDsampling is based on filling the free energy basins by biasing potentials andthus for cases with flat, broad and unbound free energy wells, thecomputational time to sample them becomes very large. To alleviate thisproblem, we combine the standard Umbrella Sampling (US) technique with MTD tosample orthogonal collective variables (CVs) in a simultaneous way. Within thisscheme, we construct the equilibrium distribution of CVs from biaseddistributions obtained from independent MTD simulations with umbrellapotentials. Reweighting is carried out by a procedure that combines USreweighting and Tiwary-Parrinello MTD reweighting within the Weighted HistogramAnalysis Method (WHAM). The approach is ideal for a controlled sampling of a CVin a MTD simulation, making it computationally efficient in sampling flat,broad and unbound free energy surfaces. This technique also allows for adistributed sampling of a high-dimensional free energy surface, furtherincreasing the computational efficiency in sampling. We demonstrate theapplication of this technique in sampling high-dimensional surface for variouschemical reactions using ab initio and QM/MM hybrid molecular dynamicssimulations. Further, in order to carry out MTD bias reweighting for computingforward reaction barriers in ab initio or QM/MM simulations, we propose acomputationally affordable approach that does not require recrossingtrajectories.
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