An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations

Abstract

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD=0.89kcal·mol^-1). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.

Keywords: Hydration free energy calculations; Implicit solvent; Non-Boltzmann Bennett.

Figure 1

The thermodynamic cycle used for indirect free energy calculations in this work.

Figure 2

The 21 molecules from the blind portion of the SAMPL4 hydration free energy challenge.

Figure 3

The thermodynamic cycle used for absolute pK_a calculations in this work.

Figure 4

Comparison of RMSD of different QM protocols based on pure QM optimized structures (abscissa) and MM trajectories that we analyzed with QM-NBB (ordinate). The use of MM trajectories consistently improves the results by accounting for conformational entropy.

Figure 5

Comparison of QM-NBB data against QM-Opt data for the M06-2X/6-31G(d) level of theory. Molecule 1 has been omitted from the figure and from the best fit line, because of its disproportionate influence. The titratable molecules 21, 22, 23 and 24 are explicitly labeled in red (QM-optimization) and blue (QM-NBB).

Figure 6

Comparison of the underlying implicit solvent free energies for conformations in the gas phase (gray) and in aqueous phase (turquoise) on the left side with the resulting QM-NBB results (red) on the right side. All data is based on the OLYP/DZP QM method with the SMD implicit solvent.