Enhanced QM/MM Free Energy Calculations For Chemical Processes In Condensed Phase

For chemical reactions in the condensed phase,free energy profile(FE Profile)is an essential quantity for the estimation of reaction rate and the validation of the reaction mechanism.However,the computation of FE profile at ab initio(ai)quantum mechanical/molecular mechanics(QM/MM)level is formidably expensive.Although the semiempirical(SE)method can be hundreds or thousands of times faster than ai methods,the accuracy of SE methods is often unsatisfactory,due to the approximations that have been adopted in these methods.Recently,we propose a new method termed MBAR+wTP,which can be used to obtain the ai QM/MM free energy profile with much-enhanced efficiency.In this dissertation,I will explain this method in detail,and discuss its applicability,limitations and our perspective on future development.In chapter two,this MBAR+wTP method is explained in detail,in which the ai QM/MM free energy profile is computed by a weighted thermodynamic perturbation(wTP)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 wTP calculations are a byproduct of the MBAR analysis in the post-processing 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(GPR)method,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 the condensed phase and enzymatic reactions.In chapter three,this MBAR+wTP method is utilized and extended to obtain the twodimensional FE surfaces of two Diels-Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level.For both Diels-Alder(DA)reactions in solution,accurate and converged free energy surfaces at ai QM/MM level are imperative for the understanding of reaction mechanism.However,this kind of computations is still far too expensive.The calculated accurate activation free energies at the ai QM/MM level by our method,which are much closer to the experimental measurements than those calculated by other methods,indicate that this MBAR+wTP method can be applied in the studies of complex reactions in condensed phase with markedly-enhanced efficiency.In chapter four,we further apply this MBAR+wTP method to investigate the endo/exo stereoselectivity of the Diels-Alder reaction between cyclopentadiene(CP)and methyl vinyl ketone(MVK),which requires an accurate free energy landscape.The results indicate that this method can yield more accurate activation free energies than the semiempirical Hamiltonian PM6 and the “sampling-free” quantum mechanical methods at B3 LYP and MP2 levels using a polarizable continuous solvent model(PCM).This stereoselectivity mainly comes from the solvation effect.Nonetheless,in terms of the stereoselectivity,we can obtain an endo/exo ratio of 2 from this method,which is still one order of magnitude smaller than the experimental measurement.Although the endo/exo ratio from the MP2/PCM calculation agrees well with the experiment,the absolute reaction barriers deviate by about 5 kcal/mol.At present,in the field of computational biophysics and biochemistry,many research groups are devoted to the development of methods for enhancing the calculations of free energies at ai QM/MM level.However,compared with these existing methods,implementation of our method is very easy.Nonetheless,we have also discovered some limitations of this method.In chapter five,we point out the challenges that our method is facing,and envision its further improvement in the near future.