Integrated Boltzmann Sampling: A Few-State Approach for Efficient Multistate Free Energy Calculations

Free energy calculations underpin a wide spectrum of tasks in computational chemistry, from scanning free energy surfaces along collective variables to ranking affinities of ligands in computer-aided drug discovery. Their routine use, however, is constrained by the high cost of sampling an extensive set of thermodynamic states with replicas. We introduce here Integrated Boltzmann Sampling (IBS), a few-state framework that integrates multistate thermodynamic sampling into a small set of artificial ensembles. Trajectories generated from these ensembles are reweighted to recover the full thermodynamic information for dozens of alchemical and tempered states, reducing the formal sampling cost from <i>K</i> · <i>S</i> to (1 - ϵ + <i>Kϵ</i>) · <i>S</i>, ϵ ≪ 1, where <i>K</i> counts the number of thermodynamic states involved, and <i>S</i> represents the computational effort required to sample a single state. On the SAMPL6 host-guest benchmark and a 13-ligand Farnesoid X receptor panel, IBS achieves accuracy comparable to replica-based free energy methods while lowering wall time by approximately 50-60%. These results demonstrate that achieving chemically accurate free energy predictions does not require exhaustive replica sampling and that IBS offers an efficient, drop-in alternative for computational applications that rely on accurate free energy differences.