Efficient Computation of Free Energy Surfaces of Diels⁻Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level.

Fengjiao Liu,Wenxin Hu,Xiangyu Jia,Yihan Shao,Jun Zheng,Pengfei Li,Ye Mei

doi:10.3390/molecules23102487

Abstract

For Diels–Alder (DA) reactions in solution, an accurate and converged free energy (FE) surface at ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) level is imperative for the understanding of reaction mechanism. However, this computation is still far too expensive. In a previous work, we proposed a new method termed MBAR+wTP, with which the computation of the ai FE profile can be accelerated by several orders of magnitude via a three-step procedure: (I) an umbrella sampling (US) using a semi-empirical (SE) QM/MM Hamiltonian is performed; (II) the FE profile is generated using the Multistate Bennett Acceptance Ratio (MBAR) analysis; and (III) a weighted Thermodynamic Perturbation (wTP) from the SE Hamiltonian to the ai Hamiltonian is performed to obtain the ai QM/MM FE profile using weight factors from the MBAR analysis. In this work, this method is extended to the calculations of two-dimensional FE surfaces of two Diels–Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level. The accurate activation free energies at the ai QM/MM level, 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 much-enhanced efficiency.

Highlights

The Diels–Alder (DA) reactions are one category of organic chemical reactions (a [4+2]cycloaddition) between a conjugated diene and a dienophile, which involve a dual carbon–carbon bond-forming process
In the Multistate Bennett Acceptance Ratio (MBAR)+weighted Thermodynamic Perturbation (wTP) method, there are two key factors that are critical to the reliability of the results
The first one is the similarity between the Hamiltonians for neighboring windows in the two-dimensional umbrella sampling (US). It can be characterized by the overlap of the samples in the phase space, which can be quantitatively measured by, for instance, the overlap matrix proposed by Klimovich et al [52]

Summary

Introduction

The Diels–Alder (DA) reactions are one category of organic chemical reactions (a [4+2]cycloaddition) between a conjugated diene and a dienophile, which involve a dual carbon–carbon bond-forming process. Hybrid quantum mechanical/molecular mechanical (QM/MM) method, which was proposed by Warshel and Levitt in 1976 [9], is a mature method that can be used to study chemical reactions taking place in condensed phase such as aqueous solution or enzymatic environment [10,11,12,13]. In this approach, only reactive region is treated quantum mechanically, and the remaining part is described by molecular mechanical force field. Despite the continuous development in computer technology and enhanced sampling methods, investigation of reaction mechanism in solution or enzymes using direct ai QM/MM simulations is still a daunting task

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