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Gray TH, Yong EH. An effective one-dimensional approach to calculating mean first passage time in multi-dimensional potentials. J Chem Phys 2021; 154:084103. [PMID: 33639738 DOI: 10.1063/5.0040071] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermally activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape-or the mean first-passage time (MFPT)-is important. Unlike in one dimension, there is no general, exact formula for the MFPT. However, Langer's formula, a multi-dimensional generalization of Kramers's one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers's and Langer's formulas are related to one another by the potential of mean force (PMF): when calculated along a particular direction (the unstable mode at the saddle point) and substituted into Kramers's formula, the result is Langer's formula. We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, although discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point.
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Affiliation(s)
- Thomas H Gray
- Department of Chemical Engineering and Biotechnology, West Cambridge Site, University of Cambridge, Philippa Fawcett Drive, CB3 0AS Cambridge, United Kingdom
| | - Ee Hou Yong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
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2
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Sheong FK, Zhang JX, Lin Z. Principal interacting spin orbital: understanding the fragment interactions in open-shell systems. Phys Chem Chem Phys 2020; 22:10076-10086. [PMID: 32342069 DOI: 10.1039/d0cp00127a] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Due to the recent rise in the interest and research efforts on first-row transition metal catalysis and other radical-related reactions, open-shell systems play a much more important role in modern chemistry. However, the development of bonding analysis tools for open-shell systems is still lagging behind. In this work, we present the principal interacting spin orbital (PISO) analysis, which is an analysis framework developed based on our previously reported principal interacting orbital (PIO) analysis. We will demonstrate the power of our framework to analyse different kinds of open-shell systems, ranging from simple organic radicals to much more complicated coordination complexes, from which we can see how different kinds of odd-electron bonds could be identified. We will also illustrate its advantage when used in the analysis of chemical reactions, through which we can observe subtle patterns that could be helpful for tuning or rational design of related reactions.
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Affiliation(s)
- Fu Kit Sheong
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People's Republic of China.
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Zhu L, Sheong FK, Cao S, Liu S, Unarta IC, Huang X. TAPS: A traveling-salesman based automated path searching method for functional conformational changes of biological macromolecules. J Chem Phys 2019; 150:124105. [DOI: 10.1063/1.5082633] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Lizhe Zhu
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, China
| | - Fu Kit Sheong
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Siqin Cao
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Song Liu
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Ilona C. Unarta
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Bioengineering Program, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
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McGibbon RT, Husic BE, Pande VS. Identification of simple reaction coordinates from complex dynamics. J Chem Phys 2017; 146:044109. [PMID: 28147508 PMCID: PMC5272828 DOI: 10.1063/1.4974306] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2016] [Accepted: 01/05/2017] [Indexed: 11/14/2022] Open
Abstract
Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems, as a maximally predictive one-dimensional projection. We then show that this criterion is uniquely satisfied by a dominant eigenfunction of an integral operator associated with the ensemble dynamics. We present a new sparse estimator for these eigenfunctions which can search through a large candidate pool of structural order parameters and build simple, interpretable approximations that employ only a small number of these order parameters. Example applications with a small molecule's rotational dynamics and simulations of protein conformational change and folding show that this approach can filter through statistical noise to identify simple reaction coordinates from complex dynamics.
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Affiliation(s)
- Robert T McGibbon
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Brooke E Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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Bofill JM, Quapp W, Caballero M. The Variational Structure of Gradient Extremals. J Chem Theory Comput 2012; 8:927-35. [DOI: 10.1021/ct200805d] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Josep Maria Bofill
- Institut de Química Teòrica
i Computacional, Universitat de Barcelona (IQTCUB), C/Martí i Franquès, 1, 08028 Barcelona, Catalunya,
Spain
| | - Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, PF 100920, D-04009 Leipzig,
Germany
| | - Marc Caballero
- Institut de Química Teòrica
i Computacional, Universitat de Barcelona (IQTCUB), C/Martí i Franquès, 1, 08028 Barcelona, Catalunya,
Spain
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Crehuet R, Bofill JM. The reaction path intrinsic reaction coordinate method and the Hamilton-Jacobi theory. J Chem Phys 2007; 122:234105. [PMID: 16008428 DOI: 10.1063/1.1927521] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The definition and location of an intrinsic reaction coordinate path is of crucial importance in many areas of theoretical chemistry. Differential equations used to define the path hitherto are complemented in this study with a variational principle of Fermat type, as Fukui [Int. J. Quantum Chem., Quantum Chem. Symp. 15, 633 (1981)] reported in a more general form some time ago. This definition is more suitable for problems where initial and final points are given. The variational definition can naturally be recast into a Hamilton-Jacobi equation. The character of the variational solution is studied via the Weierstrass necessary and sufficient conditions. The characterization of the local minima character of the intrinsic reaction coordinate is proved. Such result leads to a numerical algorithm to find intrinsic reaction coordinate paths based on the successive minimizations of the Weierstrass E-function evaluated on a guess curve connecting the initial and final points of the desired path.
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Affiliation(s)
- Ramon Crehuet
- Departament de Química Orgànica Biològica, Institut de Investigacions Químiques i Ambientals de Barcelona, IIQAB-CSIC, Jordi Girona 18, 08034 Barcelona, Catalonia, Spain.
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Affiliation(s)
- Grigory A. Natanson
- a Department of Chemistry , and the James Franck Institute, The University of Chicago , Chicago , Illinois , 60637 , U.S.A
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Fukui K. Grenzorbitale - ihre Bedeutung bei chemischen Reaktionen (Nobel-Vortrag). Angew Chem Int Ed Engl 2006. [DOI: 10.1002/ange.19820941105] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Ziegler T, Autschbach J. Theoretical methods of potential use for studies of inorganic reaction mechanisms. Chem Rev 2005; 105:2695-722. [PMID: 15941226 DOI: 10.1021/cr0307188] [Citation(s) in RCA: 367] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Tom Ziegler
- Department of Chemistry, University of Calgary, Canada.
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Kelly E, Seth M, Ziegler T. Calculation of Free Energy Profiles for Elementary Bimolecular Reactions by ab Initio Molecular Dynamics: Sampling Methods and Thermostat Considerations. J Phys Chem A 2004. [DOI: 10.1021/jp036007v] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Evan Kelly
- Department of Chemistry, University of Calgary, 2500 University Drive, Calgary, Alberta, Canada T2N 1N4
| | - Michael Seth
- Department of Chemistry, University of Calgary, 2500 University Drive, Calgary, Alberta, Canada T2N 1N4
| | - Tom Ziegler
- Department of Chemistry, University of Calgary, 2500 University Drive, Calgary, Alberta, Canada T2N 1N4
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Michalak A, Ziegler T. First-Principle Molecular Dynamic Simulations along the Intrinsic Reaction Paths. J Phys Chem A 2001. [DOI: 10.1021/jp0041297] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Artur Michalak
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta, Canada T2N 1N4, and Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland
| | - Tom Ziegler
- Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta, Canada T2N 1N4, and Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland
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Taketsugu T, Gordon MS. Dynamic reaction path analysis based on an intrinsic reaction coordinate. J Chem Phys 1995. [DOI: 10.1063/1.470704] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chapuisat X, Nauts A. Overall rotation along a reaction path. Mol Phys 1994. [DOI: 10.1080/00268979400100804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Xavier Chapuisat
- a Laboratoire de Chimie Théorique (CNRS, URA 506) , Faculté des Sciences, Université de Paris-Sud , Bátiment 490, 91405 , Orsay Cédex , France
- b Unité Fyam , Université Catholique de Louvain, Département de Physique , Chemin du cyclotron, 2, 1348 , Louvain-la-Neuve , Belgium
| | - André Nauts
- a Laboratoire de Chimie Théorique (CNRS, URA 506) , Faculté des Sciences, Université de Paris-Sud , Bátiment 490, 91405 , Orsay Cédex , France
- b Unité Fyam , Université Catholique de Louvain, Département de Physique , Chemin du cyclotron, 2, 1348 , Louvain-la-Neuve , Belgium
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Tsuda M, Oikawa S, Nagayama K. On the primary process in plasma-chemical and photochemical vapor deposition from silane: An ab initio study of unimolecular decomposition of SiH4 in the lowest triplet state. Chem Phys Lett 1985. [DOI: 10.1016/0009-2614(85)85340-9] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Tapia O, Andrés J. A simple protocol to help calculate saddle points. Transition-state structures for the Meyer—Schuster reaction in non-aqueous media: An ab initio MO study. Chem Phys Lett 1984. [DOI: 10.1016/0009-2614(84)80346-2] [Citation(s) in RCA: 70] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Directed graphs of structurally stable potential energy surfaces representing a-priori reaction pathways. Theor Chem Acc 1984. [DOI: 10.1007/bf00551331] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems. ACTA ACUST UNITED AC 1984. [DOI: 10.1007/bf00549673] [Citation(s) in RCA: 76] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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B�lint I, B�n MI. Search for saddle points of energy hypersurfaces using a multi-dimensional space of ?guiding? coordinates. ACTA ACUST UNITED AC 1983. [DOI: 10.1007/bf00569250] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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