1
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Anderson MC, Dodin A, Fay TP, Limmer DT. Coherent control from quantum commitment probabilities. J Chem Phys 2024; 161:024115. [PMID: 38995082 DOI: 10.1063/5.0213444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2024] [Accepted: 06/24/2024] [Indexed: 07/13/2024] Open
Abstract
We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail.
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Affiliation(s)
- Michelle C Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Amro Dodin
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Thomas P Fay
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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2
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Pandey P, Keshavamurthy S. Dynamic matching ‐ revisiting the Carpenter model. J PHYS ORG CHEM 2022. [DOI: 10.1002/poc.4404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Priyanka Pandey
- Department of Chemistry Indian Institute of Technology Kanpur Uttar Pradesh India
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3
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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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4
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Naik S, Wiggins S. Detecting reactive islands in a system-bath model of isomerization. Phys Chem Chem Phys 2020; 22:17890-17912. [PMID: 32478352 DOI: 10.1039/d0cp01362e] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this article, we study the conformational isomerization in a solvent using a system-bath model where the phase space structures relevant for the reaction dynamics are revealed. These phase space structures are an integral part of understanding the reaction mechanism, that is the pathways that reactive trajectories undertake, in the presence of a solvent. Our approach involves detecting the analogs of the reactive islands first discussed in the works by Davis, Marston, De Leon, Berne and coauthors in the system-bath model using Lagrangian descriptors. We first present the structure of the reactive islands for the two degrees of freedom system modelling isomerization in the absence of the bath using direct computation of cylindrical (tube) manifolds and verify the Lagrangian descriptor method for detecting the reactive islands. The hierarchy of the reactive islands as indicated in the recent work by Patra and Keshavamurthy is shown to be related to the temporal features in committor probabilities. Next, we investigate the influence of the solvent on the reactive islands that we previously revealed for the two degrees of freedom system and discuss the use of the Lagrangian descriptor in the high-dimensional phase space of the system-bath model.
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Affiliation(s)
- Shibabrat Naik
- School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK.
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5
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Naik S, Wiggins S. Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential. Phys Rev E 2019; 100:022204. [PMID: 31574621 DOI: 10.1103/physreve.100.022204] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2019] [Indexed: 11/07/2022]
Abstract
We present a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include a normally hyperbolic invariant manifold and its stable and unstable manifolds, which act as codimension-1 barriers to phase space transport. In this article, finding the invariant manifolds in high-dimensional phase space will constitute identifying coordinates on these invariant manifolds. The method of Lagrangian descriptor is demonstrated by applying to classical two and three degrees of freedom Hamiltonian systems which have implications for myriad applications in chemistry, engineering, and physics.
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Affiliation(s)
- Shibabrat Naik
- School of Mathematics, University of Bristol, University Walk, Clifton BS8 1TW, Bristol, United Kingdom
| | - Stephen Wiggins
- School of Mathematics, University of Bristol, University Walk, Clifton BS8 1TW, Bristol, United Kingdom
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6
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Paul S, Nair NN, Vashisth H. Phase space and collective variable based simulation methods for studies of rare events. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1634268] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Sanjib Paul
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
| | - Nisanth N. Nair
- Department of Chemistry, Indian Institute of Technology, Kanpur, India
| | - Harish Vashisth
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
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7
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Leitner DM, Yamato T. MAPPING ENERGY TRANSPORT NETWORKS IN PROTEINS. REVIEWS IN COMPUTATIONAL CHEMISTRY 2018. [DOI: 10.1002/9781119518068.ch2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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8
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Leitner DM. Molecules and the Eigenstate Thermalization Hypothesis. ENTROPY 2018; 20:e20090673. [PMID: 33265762 PMCID: PMC7513195 DOI: 10.3390/e20090673] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 09/02/2018] [Accepted: 09/03/2018] [Indexed: 11/18/2022]
Abstract
We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.
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Affiliation(s)
- David M Leitner
- Department of Chemistry, University of Nevada, Reno, NV 89557, USA
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Patra S, Keshavamurthy S. Detecting reactive islands using Lagrangian descriptors and the relevance to transition path sampling. Phys Chem Chem Phys 2018; 20:4970-4981. [PMID: 29387842 DOI: 10.1039/c7cp05912d] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.
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Affiliation(s)
- Sarbani Patra
- Department of Chemistry, Indian Institute of Technology, Kanpur, U.P. 208 016, India.
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Feldmaier M, Junginger A, Main J, Wunner G, Hernandez R. Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.09.008] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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11
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Revuelta F, Craven GT, Bartsch T, Borondo F, Benito RM, Hernandez R. Transition state theory for activated systems with driven anharmonic barriers. J Chem Phys 2017; 147:074104. [DOI: 10.1063/1.4997571] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- F. Revuelta
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
- Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain
| | - Galen T. Craven
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104,
USA
| | - Thomas Bartsch
- Centre for Nonlinear Mathematics and Applications, Department of Mathematical Sciences, Loughborough University, Loughborough
LE11 3TU, United Kingdom
| | - F. Borondo
- Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain
- Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
| | - R. M. Benito
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, 28040 Madrid, Spain
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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12
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Junginger A, Duvenbeck L, Feldmaier M, Main J, Wunner G, Hernandez R. Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins. J Chem Phys 2017; 147:064101. [DOI: 10.1063/1.4997379] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrej Junginger
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Lennart Duvenbeck
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Feldmaier
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Günter Wunner
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Craven GT, Junginger A, Hernandez R. Lagrangian descriptors of driven chemical reaction manifolds. Phys Rev E 2017; 96:022222. [PMID: 28950601 DOI: 10.1103/physreve.96.022222] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Indexed: 06/07/2023]
Abstract
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
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Affiliation(s)
- Galen T Craven
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Andrej Junginger
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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14
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Junginger A, Craven GT, Bartsch T, Revuelta F, Borondo F, Benito RM, Hernandez R. Transition state geometry of driven chemical reactions on time-dependent double-well potentials. Phys Chem Chem Phys 2016; 18:30270-30281. [DOI: 10.1039/c6cp02519f] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The minimum contour in the forward Lagrangian descriptor overlaps the invariant manifold (in green) dividing reactant and product regions.
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Affiliation(s)
- Andrej Junginger
- Center for Computational Molecular Science and Technology
- School of Chemistry and Biochemistry
- Georgia Institute of Technology
- Atlanta
- USA
| | - Galen T. Craven
- Center for Computational Molecular Science and Technology
- School of Chemistry and Biochemistry
- Georgia Institute of Technology
- Atlanta
- USA
| | - Thomas Bartsch
- Department of Mathematical Sciences
- Loughborough University
- Loughborough LE11 3TU
- UK
| | - F. Revuelta
- Grupo de Sistemas Complejos
- Escuela Técnica Superior de Ingeniería Agronómica
- Alimentaria y de Biosistemas
- Universidad Politécnica de Madrid
- Madrid
| | - F. Borondo
- Instituto de Ciencias Matemáticas (ICMAT)
- Cantoblanco
- Spain
- Departamento de Química
- Universidad Autónoma de Madrid
| | - R. M. Benito
- Grupo de Sistemas Complejos
- Escuela Técnica Superior de Ingeniería Agronómica
- Alimentaria y de Biosistemas
- Universidad Politécnica de Madrid
- Madrid
| | - Rigoberto Hernandez
- Center for Computational Molecular Science and Technology
- School of Chemistry and Biochemistry
- Georgia Institute of Technology
- Atlanta
- USA
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15
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Craven GT, Hernandez R. Deconstructing field-induced ketene isomerization through Lagrangian descriptors. Phys Chem Chem Phys 2016; 18:4008-18. [DOI: 10.1039/c5cp06624g] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Phase space contours (shown in color) constructed using the method of Lagrangian descriptors resolve the separatrices governing state transitions on the reaction-path potential energy surface (shown in white) for field-induced ketene isomerization.
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Affiliation(s)
- Galen T. Craven
- Center for Computational Molecular Science and Technology
- School of Chemistry and Biochemistry
- Georgia Institute of Technology
- Atlanta
- USA
| | - Rigoberto Hernandez
- Center for Computational Molecular Science and Technology
- School of Chemistry and Biochemistry
- Georgia Institute of Technology
- Atlanta
- USA
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16
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Leitner DM, Pandey HD. Asymmetric energy flow in liquid alkylbenzenes: A computational study. J Chem Phys 2015; 143:144301. [DOI: 10.1063/1.4932227] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David M. Leitner
- Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557, USA
- Freiburg Institute for Advanced Studies (FRIAS), Freiburg, Germany
| | - Hari Datt Pandey
- Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557, USA
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