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Nagahata Y, Hernandez R, Komatsuzaki T. Phase space geometry of isolated to condensed chemical reactions. J Chem Phys 2021; 155:210901. [PMID: 34879678 DOI: 10.1063/5.0059618] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.
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Affiliation(s)
- Yutaka Nagahata
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Tamiki Komatsuzaki
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0 020, Japan
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Nagahata Y, Borondo F, Benito RM, Hernandez R. Identifying reaction pathways in phase space via asymptotic trajectories. Phys Chem Chem Phys 2020; 22:10087-10105. [PMID: 32342955 DOI: 10.1039/c9cp06610a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this paper, we revisit the concepts of the reactivity map and the reactivity bands as an alternative to the use of perturbation theory for the determination of the phase space geometry of chemical reactions. We introduce a reformulated metric, called the asymptotic trajectory indicator, and an efficient algorithm to obtain reactivity boundaries. We demonstrate that this method has sufficient accuracy to reproduce phase space structures such as turnstiles for a 1D model of the isomerization of ketene in an external field. The asymptotic trajectory indicator can be applied to higher dimensional systems coupled to Langevin baths as we demonstrate for a 3D model of the isomerization of ketene.
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Affiliation(s)
- Yutaka Nagahata
- Department of Chemistry, Johns Hopkins University, Baltimore, MD 21218, USA.
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Pradhan R, Lourderaj U. Can reactions follow non-traditional second-order saddle pathways avoiding transition states? Phys Chem Chem Phys 2019; 21:12837-12842. [PMID: 31166331 DOI: 10.1039/c9cp02431j] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We report here an ab initio (CASSCF/6-31+G*) trajectory simulation study on the mechanisms of the denitrogenation of 1-pyrazoline and its subsituted analogue that reveals reaction pathways via a high energy second-order saddle (SOS) region. This mechanism involves the molecule adopting a five-membered planar structure contrary to the traditional boat-like transition state. The SOS offers a trifurcation point where a pathway branches into three, different from the single pathway associated with a transitions state. We observe that the molecules following the SOS path exhibit distinctive dynamical features and form products with high translational energies and low rotational energies compared to those following the traditional pathways. In addition, the SOS pathway provides an alternative mechanism for the formation of stereo-selective products. Interestingly, although the reaction proceeds via a trimethylene diradical intermediate, the simulations show that the product cyclopropane is formed with a major single inversion of the configuration consistent with experimental observations. They also reveal mechanisms that do not follow the minimum energy paths and exhibit non-statistical dissociation dynamics.
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Affiliation(s)
- Renuka Pradhan
- National Institute of Science Education and Research (NISER), Bhubaneswar, HBNI, P.O. Jatni, Khurda, Odisha, India.
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Mauguière FA, Collins P, Kramer ZC, Carpenter BK, Ezra GS, Farantos SC, Wiggins S. Roaming: A Phase Space Perspective. Annu Rev Phys Chem 2017; 68:499-524. [DOI: 10.1146/annurev-physchem-052516-050613] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Peter Collins
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom;, ,
| | - Zeb C. Kramer
- Department of Chemistry and Biochemistry, La Salle University, Philadelphia, Pennsylvania 19141
| | - Barry K. Carpenter
- School of Chemistry, Cardiff University, Cardiff CF10 3AT, United Kingdom
| | - Gregory S. Ezra
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853
| | - Stavros C. Farantos
- Department of Chemistry, University of Crete, Heraklion 700 13, Greece
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, Heraklion 711 10, Greece
| | - Stephen Wiggins
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom;, ,
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Nagahata Y, Maeda S, Teramoto H, Horiyama T, Taketsugu T, Komatsuzaki T. Deciphering Time Scale Hierarchy in Reaction Networks. J Phys Chem B 2015; 120:1961-71. [DOI: 10.1021/acs.jpcb.5b09941] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yutaka Nagahata
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
| | - Satoshi Maeda
- Department
of Chemistry, Faculty of Science, Hokkaido University, Kita 10,
Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| | - Hiroshi Teramoto
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
- Molecule
and Life Nonlinear Sciences Laboratory, Research Institute for Electronic
Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
| | - Takashi Horiyama
- Graduate
School of Science and Engineering, Saitama University, Shimo-Ookubo
255, Sakura-ku, Saitama 338-8570, Japan
| | - Tetsuya Taketsugu
- Department
of Chemistry, Faculty of Science, Hokkaido University, Kita 10,
Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| | - Tamiki Komatsuzaki
- Graduate
School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0812, Japan
- Molecule
and Life Nonlinear Sciences Laboratory, Research Institute for Electronic
Science, Hokkaido University, Kita 20, Nishi 10, Kita-ku, Sapporo 001-0020, Japan
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Nagahata Y, Teramoto H, Li CB, Kawai S, Komatsuzaki T. Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042923. [PMID: 24229265 DOI: 10.1103/physreve.88.042923] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2013] [Indexed: 06/02/2023]
Abstract
Reactivity boundaries that divide the origin and destination of trajectories are of crucial importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index 1 saddles [Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the reactivity boundary and propose a more general definition that can involve a single reaction associated with a bottleneck composed of higher-index saddles and/or several saddle points with different indices, where the normal form theory, based on expansion around a single stationary point, does not work. We numerically demonstrate the reactivity boundary by using a reduced model system of the H(5)(+) cation where the proton exchange reaction takes place through a bottleneck composed of two index 2 saddle points and two index 1 saddle points. The cross section of the reactivity boundary in the reactant region of the phase space reveals which initial conditions are effective in making the reaction happen and thus sheds light on the reaction mechanism.
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Affiliation(s)
- Yutaka Nagahata
- Graduate School of Life Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan
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