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We present an approach that extends the theory of targeted free energyperturbation (TFEP) to calculate free energy differences and free energysurfaces at an accurate quantum mechanical level of theory from a cheaperreference potential. The convergence is accelerated by a mapping function thatincreases the overlap between the target and the reference distributions.Building on recent work, we show that this map can be learned with anormalizing flow neural network, without requiring simulations with theexpensive target potential but only a small number of single-pointcalculations, and, crucially, avoiding the systematic error that was foundpreviously. We validate the method by numerically evaluating the free energydifference in a system with a double-well potential and by describing the freeenergy landscape of a simple chemical reaction in the gas phase.

Targeted free energy perturbation revisited: Accurate free energies from mapped reference potentials