Efficient Strategy for the Calculation of Solvation Free Energies in Water and Chloroform at the Quantum Mechanical/Molecular Mechanical Level

Abstract

The partitioning of solute molecules between immiscible solvents with significantly different polarities is of great importance. The polarization between the solute and solvent molecules plays an essential role in determining the solubility of the solute, which makes computational studies utilizing molecular mechanics (MM) rather difficult. In contrast, quantum mechanics (QM) can provide more reliable predictions. In this work, the partition coefficients of the side chain analogs of some amino acids between water and chloroform were computed. The QM solvation free energies were calculated indirectly via a series of MM states using the multistate Bennett acceptance ratio (MBAR) and the MM-to-QM corrections were applied at the two endpoints using thermodynamic perturbation (TP). Previously, it has been shown (Jia et al. J. Chem. Theory Comput. 2016, 12, 499-511) that this method provides the minimal variance in the results without running QM simulations. However, if there is insufficient overlap in phase space between the MM and QM Hamiltonians, this method fails. In this work, we propose, for the first time, a quantity termed the reweighting entropy that serves as a metric for the reliability of the TP calculations. If the reweighting entropy is below a certain threshold (0.65 for the solvation free energy calculations in this work), this MM-to-QM correction should be avoided and two alternative methods can be employed by either introducing a semiempirical state or conducting nonequilibrium simulations. However, the results show that the QM methods are not guaranteed to yield better results than the MM methods. Further improvement of the QM methods are imperative, especially the treatment of the van der Waals and the electrostatic interactions between the QM region and the MM region in the first shell. We also propose a scheme for the calculation of the van der Waals parameters for the solute molecules in nonaqueous solvent, which improves the quality of the computed thermodynamic properties. Furthermore, the force field parameters for the sulfur-containing molecules are also optimized.

Solvation Free Energy Calculations: The Combination between the Implicitly Polarized Fixed‐charge Model and the Reference Potential Strategy

“…Solvation free energy is the free energy change of the solute molecule transferring from gas phase to the pure liquid. As it is one part of the absolute binding free energy calculation and also associated with many physical properties such as relative solubility, partition coefficient, and activity coefficient, many theoretical efforts have been devoted to give an accurate prediction of the solvation free energy . However, the predicted results sensitively depend on the Hamiltonians for the interaction potential …”

Predicting Relative Binding Affinity Using Nonequilibrium QM/MM Simulations

“…It was pioneered by Gao, Warshel and co-workers, [21][22][23][24][25] followed by implementations and enhancement by many other groups. [26][27][28][29][30][31][32][33][34][35] These methods are based on the thermodynamic cycle shown in Fig. 1.…”

“…1). 23,27,36 The free energy difference between the MM and QM/MM Hamiltonians can be obtained by single-step exponential averaging (ssEA) 27,33,34 and non-Boltzmann Bennett (NBB) calculations. 32,37 Thereby, sampling at the QM/MM level of theory can be avoided.…”

Optimization and benchmarking of a perturbative Metropolis Monte Carlo quantum mechanics/molecular mechanics program

“…In general, a reasonable agreement is observed, meaning that the model captures the majority of interactions at play. In a recent study 50 with the solvents water and chloroform, it has been noted as well that QM/MM does not always improve upon the MM results and that the accuracy may be, for this particular application, comparable. The advantage over other approaches is that very few parameters are required for the setup.…”