Comparison of QM/MM Methods To Obtain Ligand-Binding Free Energies

We have compared two approaches to calculate relative binding free energies employing molecular dynamics simulations at the combined quantum-mechanical/molecular mechanics (QM/MM) level. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavitand host system. The ligand is treated with the semiempirical PM6-DH+ QM method. In the first approach, we perform direct alchemical QM/MM free energy perturbation (FEP). In the second, reference-potential approach, we convert the ligands with FEP at the molecular mechanics (MM) level and then perform also MM → QM/MM FEP for each ligand. We show that the two approaches give identical results within statistical uncertainty. For the reference-potential approach, the MM → QM/MM perturbation converges in terms of energies, uncertainties, and overlap measures with two intermediate states, giving a precision of 0.5-0.9 kJ/mol for all eight transformations considered. On the other hand, the QM/MM-FEP approach requires 17-18 intermediate states, showing that the reference-potential approach is more effective. Previous calculations with single-step exponential averaging (i.e., entirely avoiding QM/MM simulations) required fewer QM/MM energy calculations, but they gave worse precision and involved approximations with an unclear effect on the results.