Combining Fast Exploration with Accurate Reweighting in the OPES-eABF Hybrid Sampling Method

On-the-fly probability enhanced sampling (OPES) has recently been introduced [Invernizzi, M.; Parrinello, M. <i>J. Chem. Theory Comput.</i> 2022, 18, 3988-3996], with important improvements over the highly popular metadynamics methods. In our work, we introduce a new combination of OPES with the extended-system adaptive biasing force (eABF) method. We show that the resulting OPES-eABF hybrid is highly robust to the choice of input parameters, while ensuring faster exploration of configuration space than the original OPES. The only critical parameter of OPES-eABF is the coupling width to the extended-system, for which we introduce an automatic algorithm based on a short initial unbiased simulation, such that OPES-eABF requires minimal user intervention. Additionally, we show that due to the decoupling of the physical system from the time-dependent potential, unbiased probabilities of visited configurations are recovered highly accurately.