A free energy perturbation technique is described in which configurations from a classical simulation (molecular dynamics or Monte Carlo) with empirical solute-solvent interactions are used to calculate free energies with quantum mechanically derived solute-solvent interactions. This approach is much less costly than simulations with forces derived from quantum mechanics at each time step, since it only requires quantum energies to be calculated at classically determined configurations. The method is not limited to free energies of solvation, and can potentially be applied to calculations of activation energies and other condensed phase chemical transformations. As a test, this method was used to calculate the free energy of hydration of water at ambient conditions. With a good classical model the method gives accurate results with only 50 quantum calculations. The method is self-correcting in the sense that it can be used to recognize a bad classical model, and improved classical models can be derived by a least-squares fitting to the quantum energies. As a result, this method also provides novel information about the comparative strengths and weaknesses of classical solute models.