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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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Angulo G, Jedrak J, Ochab-Marcinek A, Pasitsuparoad P, Radzewicz C, Wnuk P, Rosspeintner A. How good is the generalized Langevin equation to describe the dynamics of photo-induced electron transfer in fluid solution? J Chem Phys 2017; 146:244505. [DOI: 10.1063/1.4990044] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Gonzalo Angulo
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Jakub Jedrak
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Anna Ochab-Marcinek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Pakorn Pasitsuparoad
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Czesław Radzewicz
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
| | - Paweł Wnuk
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Am Coulombwall 1, D-85748 Garching, Germany
| | - Arnulf Rosspeintner
- Department of Physical Chemistry, University of Geneva, Quai Ernest-Ansermet 30, CH-1211 Geneva, Switzerland
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Kawai S, Miyazaki Y. Recovering hidden dynamical modes from the generalized Langevin equation. J Chem Phys 2016; 145:094102. [PMID: 27608984 DOI: 10.1063/1.4962065] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.
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Affiliation(s)
- Shinnosuke Kawai
- Department of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan
| | - Yusuke Miyazaki
- Department of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan
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Alaghemandi M, Green JR. Reactive symbol sequences for a model of hydrogen combustion. Phys Chem Chem Phys 2016; 18:2810-7. [PMID: 26729563 DOI: 10.1039/c5cp05125h] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Transient, macroscopic states of chemical disequilibrium are born out of the microscopic dynamics of molecules. As a reaction mixture evolves, the temporal patterns of chemical species encodes some of this dynamical information, while their statistics are a manifestation of the bulk kinetics. Here, we define a chemically-informed symbolic dynamics as a coarse-grained representation of classical molecular dynamics, and analyze the sequences of chemical species for a model of hydrogen combustion. We use reactive molecular dynamics simulations to generate the sequences and derive probability distributions for sequence observables: the reaction time scales and the chain length - the total number of reactions between initiation of a reactant and termination at products. The time scales and likelihood of the sequences depend strongly on the chain length, temperature, and density. Temperature suppresses the uncertainty in chain length for hydrogen sequences, but enhances the uncertainty in oxygen sequence chain lengths. This method of analyzing a surrogate chemical symbolic dynamics reduces the complexity of the chemistry from the atomistic to the molecular level and has the potential for extension to more complicated reaction systems.
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Affiliation(s)
- Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125, USA.
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125, USA. and Department of Physics, University of Massachusetts Boston, Boston, MA 02125, USA
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Kawai S. On the environmental modes for the generalized Langevin equation. J Chem Phys 2015; 143:094101. [DOI: 10.1063/1.4929710] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shinnosuke Kawai
- Department of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529, 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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Popov AV, Hernandez R. Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032145. [PMID: 24125251 DOI: 10.1103/physreve.88.032145] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2013] [Indexed: 06/02/2023]
Abstract
Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.
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Affiliation(s)
- Alexander V Popov
- Center for Computational and Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA
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Nagahata Y, Teramoto H, Li CB, Kawai S, Komatsuzaki T. Reactivity boundaries to separate the fate of a chemical reaction associated with an index-two saddle. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062817. [PMID: 23848739 DOI: 10.1103/physreve.87.062817] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2012] [Revised: 05/27/2013] [Indexed: 06/02/2023]
Abstract
Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one.
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Affiliation(s)
- Yutaka Nagahata
- Graduate School of Life Science, Hokkaido University, Kita 10 Nishi 8, Sapporo 060-0810, Japan.
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Inertial likelihood maximization for reaction coordinates with high transmission coefficients. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.10.051] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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