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Open AccessArticle

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

by Pengfei Li 1, Fengjiao Liu 1, Xiangyu Jia 1,†, Yihan Shao 2, Wenxin Hu 3,*, Jun Zheng 3 and Ye Mei 1,2,4,*
1
State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China
2
Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019, USA
3
The Computer Center, School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China
4
NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
*
Authors to whom correspondence should be addressed.
Current address: NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China.
Molecules 2018, 23(10), 2487; https://doi.org/10.3390/molecules23102487
Received: 5 September 2018 / Revised: 25 September 2018 / Accepted: 26 September 2018 / Published: 28 September 2018
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. View Full-Text
Keywords: Diels–Alder reaction; free energy surface; ab initio; reference-potential method; umbrella sampling Diels–Alder reaction; free energy surface; ab initio; reference-potential method; umbrella sampling
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MDPI and ACS Style

Li, P.; Liu, F.; Jia, X.; Shao, Y.; Hu, W.; Zheng, J.; Mei, Y. Efficient Computation of Free Energy Surfaces of Diels–Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level. Molecules 2018, 23, 2487.

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