Replica exchange with Smart Monte Carlo and Hybrid Monte Carlo in manifolds

Several Smart Monte Carlo (SMC) and Hybrid Monte Carlo (HMC) simulations coupled with the Replica Exchange (RE) strategy are compared in multidimensional flat and curved manifolds characterized by extremely rugged potential energy surfaces, to quantify their convergence properties with respect to walk length and overall cost. We learn that the HMC coupled with a sampling enhancing method is much more efficient in manifolds mapped with unconventional coordinates than SMC. This is due to an inherent difficulty in conserving energy in curved spaces directly mapped, and the lack of such strict requirement for HMC.