1
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Rey J, Chizallet C, Rocca D, Bučko T, Badawi M. Reference-Quality Free Energy Barriers in Catalysis from Machine Learning Thermodynamic Perturbation Theory. Angew Chem Int Ed Engl 2024; 63:e202312392. [PMID: 38055209 DOI: 10.1002/anie.202312392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Revised: 11/11/2023] [Accepted: 12/06/2023] [Indexed: 12/07/2023]
Abstract
For the first time, we report calculations of the free energies of activation of cracking and isomerization reactions of alkenes that combine several different electronic structure methods with molecular dynamics simulations. We demonstrate that the use of a high level of theory (here Random Phase Approximation-RPA) is necessary to bridge the gap between experimental and computed values. These transformations, catalyzed by zeolites and proceeding via cationic intermediates and transition states, are building blocks of many chemical transformations for valorization of long chain paraffins originating, e.g., from plastic waste, vegetable oils, Fischer-Tropsch waxes or crude oils. Compared with the free energy barriers computed at the PBE+D2 production level of theory via constrained ab initio molecular dynamics, the barriers computed at the RPA level by the application of Machine Learning thermodynamic Perturbation Theory (MLPT) show a significant decrease for isomerization reaction and an increase of a similar magnitude for cracking, yielding an unprecedented agreement with the results obtained by experiments and kinetic modeling.
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Affiliation(s)
- Jérôme Rey
- Laboratoire de Physique et Chimie Théoriques LPCT UMR 7019-CNRS, Université de Lorraine, Vandœuvre-lés-Nancy, France
| | - Céline Chizallet
- IFP Energies nouvelles, Rond-Point de l'Ēchangeur de Solaize, BP3, 69360, Solaize, France
| | - Dario Rocca
- Laboratoire de Physique et Chimie Théoriques LPCT UMR 7019-CNRS, Université de Lorraine, Vandœuvre-lés-Nancy, France
| | - Tomáš Bučko
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Ilkovičova 6, SK-84215, Bratislava, Slovakia
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84236, Bratislava, Slovakia
| | - Michael Badawi
- Laboratoire de Physique et Chimie Théoriques LPCT UMR 7019-CNRS, Université de Lorraine, Vandœuvre-lés-Nancy, France
- Laboratoire Lorrain de Chimie Moléculaire L2CM UMR 7053-CNRS, Université de Lorraine, Metz, France
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2
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Wang JN, Xue Y, Li P, Pan X, Wang M, Shao Y, Mo Y, Mei Y. Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls. J Phys Chem Lett 2023; 14:4866-4875. [PMID: 37196031 PMCID: PMC10840091 DOI: 10.1021/acs.jpclett.3c00671] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.
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Affiliation(s)
- Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Pengfei Li
- Single Particle, LLC, San Diego 92127, California, United States
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman 73019, Oklahoma, United States
| | - Meiting Wang
- School of Medical Engineering, Xinxiang Medical University, Xinxiang 453003, Henan, China
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman 73019, Oklahoma, United States
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, Shanxi, China
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3
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Berger F, Rybicki M, Sauer J. Molecular Dynamics with Chemical Accuracy─Alkane Adsorption in Acidic Zeolites. ACS Catal 2023. [DOI: 10.1021/acscatal.2c05493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- Fabian Berger
- Institut für Chemie, Humboldt-Universität zu Berlin, D-10099Berlin, Germany
| | - Marcin Rybicki
- Institut für Chemie, Humboldt-Universität zu Berlin, D-10099Berlin, Germany
| | - Joachim Sauer
- Institut für Chemie, Humboldt-Universität zu Berlin, D-10099Berlin, Germany
- Department of Physical and Macromolecular Chemistry & Charles University Center of Advanced Materials, Charles University, Hlavova 8, 128 43Prague 2, Czech Republic
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4
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Giese TJ, Zeng J, York DM. Multireference Generalization of the Weighted Thermodynamic Perturbation Method. J Phys Chem A 2022; 126:8519-8533. [PMID: 36301936 PMCID: PMC9771595 DOI: 10.1021/acs.jpca.2c06201] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.
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Affiliation(s)
- Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Jinzhe Zeng
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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5
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Bassman Oftelie L, Klymko K, Liu D, Tubman NM, de Jong WA. Computing Free Energies with Fluctuation Relations on Quantum Computers. PHYSICAL REVIEW LETTERS 2022; 129:130603. [PMID: 36206437 DOI: 10.1103/physrevlett.129.130603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 01/07/2022] [Accepted: 08/05/2022] [Indexed: 06/16/2023]
Abstract
As a central thermodynamic property, free energy enables the calculation of virtually any equilibrium property of a physical system, allowing for the construction of phase diagrams and predictions about transport, chemical reactions, and biological processes. Thus, methods for efficiently computing free energies, which in general is a difficult problem, are of great interest to broad areas of physics and the natural sciences. The majority of techniques for computing free energies target classical systems, leaving the computation of free energies in quantum systems less explored. Recently developed fluctuation relations enable the computation of free energy differences in quantum systems from an ensemble of dynamic simulations. While performing such simulations is exponentially hard on classical computers, quantum computers can efficiently simulate the dynamics of quantum systems. Here, we present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. We discuss under which conditions our approximation becomes exact, and under which conditions it serves as a strict upper bound. Furthermore, we successfully demonstrate a proof of concept of our algorithm using the transverse field Ising model on a real quantum processor. As quantum hardware continues to improve, we anticipate that our algorithm will enable computation of free energy differences for a wide range of quantum systems useful across the natural sciences.
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Affiliation(s)
| | | | - Diyi Liu
- School of Mathematics, University of Minnesota, Minnesota 55455, USA
| | - Norm M Tubman
- NASA Ames Research Center, Mountain View, California 94035, USA
| | - Wibe A de Jong
- Lawrence Berkeley National Lab, Berkeley, California 94720
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6
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De Wispelaere K, Plessow PN, Studt F. Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5. ACS PHYSICAL CHEMISTRY AU 2022; 2:399-406. [PMID: 36855690 PMCID: PMC9955322 DOI: 10.1021/acsphyschemau.2c00020] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.
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Affiliation(s)
- Kristof De Wispelaere
- Center
for Molecular Modeling, Ghent University, Technologiepark 46, B-9052 Ghent, Belgium,
| | - Philipp N. Plessow
- Institute
of Catalysis Research and Technology, Karlsruhe
Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany,
| | - Felix Studt
- Institute
of Catalysis Research and Technology, Karlsruhe
Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany,Institute
for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany,
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7
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Raucci U, Rizzi V, Parrinello M. Discover, Sample, and Refine: Exploring Chemistry with Enhanced Sampling Techniques. J Phys Chem Lett 2022; 13:1424-1430. [PMID: 35119863 DOI: 10.1021/acs.jpclett.1c03993] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Over the last few decades, enhanced sampling methods have been continuously improved. Here, we exploit this progress and propose a modular workflow for blind reaction discovery and determination of reaction paths. In a three-step strategy, at first we use a collective variable derived from spectral graph theory in conjunction with the explore variant of the on-the-fly probability enhanced sampling method to drive reaction discovery runs. Once different chemical products are determined, we construct an ad-hoc neural network-based collective variable to improve sampling, and finally we refine the results using the free energy perturbation theory and a more accurate Hamiltonian. We apply this strategy to both intramolecular and intermolecular reactions. Our workflow requires minimal user input and extends the power of ab initio molecular dynamics to explore and characterize the reaction space.
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Affiliation(s)
- Umberto Raucci
- Italian Institute of Technology, Via E. Melen 83, 16152, Genova, Italy
| | - Valerio Rizzi
- Italian Institute of Technology, Via E. Melen 83, 16152, Genova, Italy
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8
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Xue Y, Wang JN, Hu W, Zheng J, Li Y, Pan X, Mo Y, Shao Y, Wang L, Mei Y. Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential. J Phys Chem A 2021; 125:10677-10685. [PMID: 34894680 PMCID: PMC9108008 DOI: 10.1021/acs.jpca.1c07727] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
Path integral molecular dynamics (PIMD) is becoming a routinely applied method for incorporating the nuclear quantum effect in computer simulations. However, direct PIMD simulations at an ab initio level of theory are formidably expensive. Using the protonated 1,8-bis(dimethylamino)naphthalene molecule as an example, we show in this work that the computational expense for the intramolecular proton transfer between the two nitrogen atoms can be remarkably reduced by implementing the idea of reference-potential methods. The simulation time can be easily extended to a scale of nanoseconds while maintaining the accuracy on an ab initio level of theory for thermodynamic properties. In addition, postprocessing can be carried out in parallel on massive computer nodes. A 545-fold reduction in the total CPU time can be achieved in this way as compared to a direct PIMD simulation at the same ab initio level of theory.
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Affiliation(s)
- Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Yongle Li
- Department of Physics, International Center of Quantum and Molecular Structure, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China,NYU–ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Lu Wang
- Department of Chemistry and Chemical Biology, Institute for Quantitative Biomedicine, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China,NYU–ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China,Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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9
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Rizzi A, Carloni P, Parrinello M. Targeted Free Energy Perturbation Revisited: Accurate Free Energies from Mapped Reference Potentials. J Phys Chem Lett 2021; 12:9449-9454. [PMID: 34555284 DOI: 10.1021/acs.jpclett.1c02135] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential. The convergence is accelerated by a mapping function that increases the overlap between the target and the reference distributions. Building on recent work, we show that this map can be learned with a normalizing flow neural network, without requiring simulations with the expensive target potential but only a small number of single-point calculations, and, crucially, avoiding the systematic error that was found previously. We validate the method by numerically evaluating the free energy difference in a system with a double-well potential and by describing the free energy landscape of a simple chemical reaction in the gas phase.
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Affiliation(s)
- Andrea Rizzi
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, Jülich 52428, Germany
- Atomistic Simulations, Italian Institute of Technology, Via Morego 30, Genova 16163, Italy
| | - Paolo Carloni
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, Jülich 52428, Germany
- Molecular Neuroscience and Neuroimaging (INM-11), Forschungszentrum Jülich GmbH, Jülich 52428, Germany
- Department of Physics and Universitätsklinikum, RWTH Aachen University, Aachen 52074, Germany
| | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, Via Morego 30, Genova 16163, Italy
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10
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Wang JN, Liu W, Li P, Mo Y, Hu W, Zheng J, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 4. Adaptive QM/MM. J Chem Theory Comput 2021; 17:1318-1325. [PMID: 33593057 PMCID: PMC8335528 DOI: 10.1021/acs.jctc.0c01149] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Although quantum mechanical/molecular mechanics (QM/MM) methods are now routinely applied to the studies of chemical reactions in condensed phases and enzymatic reactions, they may experience technical difficulties when the reactive region is varying over time. For instance, when the solvent molecules are directly participating in the reaction, the exchange of water molecules between the QM and MM regions may occur on a time scale comparable to the reaction time. To cope with this situation, several adaptive QM/MM schemes have been proposed. However, these methods either add significantly to the computational cost or introduce artificial restraints to the system. In this work, we developed a novel adaptive QM/MM scheme and applied it to the study of a nucleophilic addition reaction. In this scheme, the configuration sampling was performed with a small QM region (without solvent molecules), and the thermodynamic properties under another potential energy function with a larger QM region (with a certain number of solvent molecules and/or different levels of QM theory) are computed via extrapolation using the reference-potential method. Our simulation results show that this adaptive QM/MM scheme is numerically stable, at least for the case studied in this work. Furthermore, this method also offers an inexpensive way to examine the convergence of the QM/MM calculation with respect to the size of the QM region.
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Affiliation(s)
- Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Wei Liu
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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11
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12
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Hu W, Li P, Wang JN, Xue Y, Mo Y, Zheng J, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States. J Chem Theory Comput 2020; 16:6814-6822. [PMID: 32975951 PMCID: PMC7658029 DOI: 10.1021/acs.jctc.0c00794] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of the free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events, and some low-energy conformations may get oversampled in simulations of a finite length. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.
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Affiliation(s)
- Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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13
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Bučko T, Gešvandtnerová M, Rocca D. Ab Initio Calculations of Free Energy of Activation at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning. J Chem Theory Comput 2020; 16:6049-6060. [DOI: 10.1021/acs.jctc.0c00486] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tomáš Bučko
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Ilkovičova 6, SK-84215 Bratislava, Slovakia
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84236 Bratislava, Slovakia
| | - Monika Gešvandtnerová
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava, Ilkovičova 6, SK-84215 Bratislava, Slovakia
| | - Dario Rocca
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
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14
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Pan X, Li P, Ho J, Pu J, Mei Y, Shao Y. Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanical accuracy via a semi-empirical reference potential. II. Recalibrating semi-empirical parameters with force matching. Phys Chem Chem Phys 2019; 21:20595-20605. [PMID: 31508625 PMCID: PMC6761017 DOI: 10.1039/c9cp02593f] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
An efficient and accurate reference potential simulation protocol is proposed for producing ab initio quantum mechanical/molecular mechanical (AI-QM/MM) quality free energy profiles for chemical reactions in a solvent or macromolecular environment. This protocol involves three stages: (a) using force matching to recalibrate a semi-empirical quantum mechanical (SE-QM) Hamiltonian for the specific reaction under study; (b) employing the recalibrated SE-QM Hamiltonian (in combination with molecular mechanical force fields) as the reference potential to drive umbrella samplings along the reaction pathway; and (c) computing AI-QM/MM energy values for collected configurations from the sampling and performing weighted thermodynamic perturbation to acquire an AI-QM/MM corrected reaction free energy profile. For three model reactions (identity SN2 reaction, Menshutkin reaction, and glycine proton transfer reaction) in aqueous solution and one enzyme reaction (Claisen arrangement in chorismate mutase), our simulations using recalibrated PM3 SE-QM Hamiltonians well reproduced QM/MM free energy profiles at the B3LYP/6-31G* level of theory all within 1 kcal mol-1 with a 20 to 45 fold reduction in the computer time.
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Affiliation(s)
- Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, 101 Stephenson Pkwy, Norman, OK 73019, USA.
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China.
| | - Junming Ho
- School of Chemistry, University of New South Wales, Sydney, NSW 2052, Australia
| | - Jingzhi Pu
- Department of Chemistry and Chemical Biology, Indiana University-Purdue University Indianapolis, 402 N Blackford St, LD326, Indianapolis, IN 46202, USA.
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University, Shanghai 200062, China. and NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, 101 Stephenson Pkwy, Norman, OK 73019, USA.
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Danese M, Bon M, Piccini G, Passerone D. The reaction mechanism of the azide–alkyne Huisgen cycloaddition. Phys Chem Chem Phys 2019; 21:19281-19287. [DOI: 10.1039/c9cp02386k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By means of computational methods to sample reaction free energies, this paper provides novel insights into the Huisgen cycloaddition mechanism.
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Affiliation(s)
- Martina Danese
- Empa, Swiss Federal Laboratories for Materials Science and Technology
- Dübendorf
- Switzerland
| | - Marta Bon
- Empa, Swiss Federal Laboratories for Materials Science and Technology
- Dübendorf
- Switzerland
| | | | - Daniele Passerone
- Empa, Swiss Federal Laboratories for Materials Science and Technology
- Dübendorf
- Switzerland
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