Combination QM/MM Method To Calculate Isotope Effect In Chemical And Biological Reactions

Quantum mechanics is significant for understanding and interpreting chemical phenomena in complex systems.Furthermore,it is essential for quantitative determination of chemical properties.Unfortunately,direct application of accurate quantum chemical methods to condensed-phase and biological systems is prohibitively expensive.This is further exacerbated by the need to carry out these calculations repeatedly for millions of times in order to obtain statistical mechanical averages of the system through molecular dynamics or Monte Carlo simulations.Therefore,there are two computational bottlenecks when an accurate quantum mechanical method is applied to complex systems,namely,accurate quantum chemical calculation itself for large systems,which scales exponentially with size,and statistical sampling whose computational scaling is dictated by the Boltzmann distribution.Consequently,the development and application of multi-scale computational methods are essential and have been an inevitable trend in recent years,evidenced by the award of the 2013 Nobel Prize in Chemistry to those who contributed to the development of such a multiscale model.In this thesis,two important contributions to methodology developments and applications of combined quantum mechanical and Molecular mechanical?QM/MM?methods are presented from the studies in the past several years.First,Feynman path integral-free energy perturbation theory?PI-FEP?along with a combined QM/MM potential was used to determine equilibrium isotope effect?EIE?in the solution.In particular,the PI-FEP@QM/MM method,a two-layer quantum-classical methodology,was used for the first time in statistical mechanical simulations to compute isotope fractionation factors?IFF?of organic solutes in aqueous solution.The goal of this project was accurately evaluated the ¹⁸O/¹⁶O isotope distribution of organic aldehyde ketone compounds,as a model for biological sugars.To this end,traditional approaches for estimating IFF rely on geometry optimization of the compound of interest in the gas phase,followed by vibrational frequency calculation to obtain zero-point-energy difference and its thermal corrections between different isotopomers.Typically,contributions due to anharmonicity are ignored.On the other hand,our method includes both solvent effects and anharmonicity in statistical mechanical simulations.The examples illustrated in this project shows that PI-FEP@QM/MM is accurate and can be used as a computational tool to explain the changes of isotope enrichment in tree rings observed experimentally.The latter provides historical information on fluctuations of climate change,and computational studies may provide support to understanding of historical changes in the global ecosystem.In addition,isotopic effects on acidity constant have been computed using PI-FEP@QM/MM on a series of organic acids in aqueous solution.The computational results were found to be in good accord with experiments,and supporting that PI-FEP is an effective and accurate theoretical technique.Moreover,a correlation between computed equilibrium isotope effects and the acidity constant has been observed,providing further insight on solvent effects on isotope effects.The second project is original and novel from this study,involving the development and applications of the generalized diabatic-at-construction?GDAC?method.Diabatic representation of the potential energy surface?PES?can be useful in nonadiabatic dynamics simulations of photochemical processes.Much effort has been devoted to the construction diabatic sate.Since diabatic states are not unique,several dozens of different methods have been available from many research groups in the world.Nevertheless,a commonality of these methods is that they are obtained through orthogonal transformation from the adiabatic states from delocalized electronic structure calculations.In principle,one important characteristic of diabatic states is that their valence states are maintained at different geometries,but the diabatic states from orthogonal transformation are generally mixed configurations.The present GDAC method employs a different approach,from the opposite direction in comparison with other approaches.Making use of multistate density functional theory?MSDFT?,we first define a set of localized,valence-bond states,corresponding to the photochemical reaction products.These localized states are diabatic states by construction,and their valence bond characteristics are fully maintained at different geometries.In MSDFT,the adiabatic potential energy surfaces are obtained by using the method of configuration interaction?CI?,which can be validated in comparison with experimental observations.Using generalized singular value decomposition,we proved that the GDAC diabatic states correspond to the orthogonal projection of the adiabatic states in the space of the MSDFT states with specified valence character?such as the ground state,and the excitation reaction product states?.GDAC consists of the following three key features:?1?localized configurational states are constructed first as basis states,whereas the adiabatic states are obtained through CI next,i.e.,diabatic-then-adiabatic,?2?the completeness of the active space can be verified by comparison of the resulting adiabatic state energies against experimental observables,and?3?the valence character of the diabatic states are fully maintained and independent of geometry variations.The GDAC method was illustrated with three chemical reactions:the S_N1 dissociation reaction with double avoided curve crossings,the potential energy surfaces near the conical intersection region of ammonia dimer,and the potential energy curves of photodissociation of LiH.