Free energy profile (FE Profile) is an essential quantity for the estimation of reaction rate and the validation of reaction mechanism. For chemical reactions in condensed phase or enzymatic reactions, the computation of FE profile at the ab initio (ai) quantum mechanical/molecular mechanics (QM/MM) level is still far too expensive. Although semiempirical (SE) method can be hundreds or thousands of times faster than the ai methods, the accuracy of SE methods is often unsatisfactory due to the approximations that have been adopted in these methods. In this work, we propose a new method termed MBAR +wTP in which the ai QM/MM free energy profile is computed by a weighted thermodynamic perturbation (TP) correction to the SE profile generated by the multistate Bennett acceptance ratio (MBAR) analysis of the trajectories from umbrella samplings (US). The weight factors used in the TP calculations are a byproduct of the MBAR analysis in the postprocessing of the US trajectories, which are often discarded after the free energy calculations. The raw ai QM/MM free energy profile is then smoothed using Gaussian process regression in which the noise of each datum is set to be inversely proportional to the exponential of the reweighting entropy. The results show that this approach can enhance the efficiency of ai FE profile calculations by several orders of magnitude with only a slight loss of accuracy. This method can significantly enhance the applicability of ai QM/MM methods in the studies of chemical reactions in condensed phase and enzymatic reactions.

In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.

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.

The Fenna-Matthews-Olson (FMO) light-harvesting complex is now one of the primary model systems for the study of excitation energy transfer (EET). However, the mechanism of the EET in this system is still controversial. In this work, molecular dynamics simulations and the electrostatic-embedding quantum-mechanics/molecular-mechanics single-point calculations have been employed to predict the energy transfer pathways utilizing the polarized protein-specific charge (PPC), which provides a more realistic description of Coulomb interaction potential in the protein than conventional mean-field charge scheme. The recently discovered eighth pigment has also been included in this study. Comparing with the conventional mean-field charges, more stable structures of FMO complex were found under PPC scheme during molecular dynamic simulation. Based on the electronic structure calculations, an exciton model was constructed to consider the couplings during excitation. The results show that pigments 3 and 4 dominate the lowest exciton levels whereas the highest exciton level are mainly constituted of pigments 1 and 6. This observation agrees well with the assumption based on the spatial distribution of the pigments. Moreover, the obtained spectral density in this study gives a reliable description of the diverse local environment embedding each pigment.

An efficient approach that combines the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method with conductor-like polarizable continuum model (CPCM), termed EE-GMFCC-CPCM, is developed for ab initio calculation of the electrostatic solvation energy of proteins. Compared with the previous MFCC-CPCM study [Y. Mei, C. G. Ji, and J. Z. H. Zhang, J. Chem. Phys. 125, 094906 (2006)], quantum mechanical (QM) calculation is applied to deal with short-range non-neighboring interactions replacing the classical treatment. Numerical studies are carried out for proteins up to 3837 atoms at the HF/6-31G* level. As compared to standard full system CPCM calculations, EE-GMFCC-CPCM shows clear improvement over the MFCC-CPCM method for both the total electrostatic solvation energy and its components (the polarized solute-solvent reaction field energy and wavefunction distortion energy of the solute). For large proteins with 1000-4000 atoms, where the standard full system ab initio CPCM calculations are not affordable, the EE-GMFCC-CPCM gives larger relative wavefunction distortion energies and weaker relative electrostatic solvation energies for proteins, as compared to the corresponding energies calculated by the Divide-and-Conquer Poisson-Boltzmann (D&C-PB) method. Notwithstanding, a high correlation between EE-GMFCC-CPCM and D&C-PB is observed. This study demonstrates that the linear-scaling EE-GMFCC-CPCM approach is an accurate and also efficient method for the calculation of electrostatic solvation energy of proteins.