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Dalton BA, Kiefer H, Netz RR. The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media. Nat Commun 2024; 15:3761. [PMID: 38704367 PMCID: PMC11069540 DOI: 10.1038/s41467-024-48016-7] [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: 09/22/2023] [Accepted: 04/18/2024] [Indexed: 05/06/2024] Open
Abstract
Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.
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Affiliation(s)
| | - Henrik Kiefer
- Freie Universität Berlin, Fachbereich Physik, Berlin, Germany
| | - Roland R Netz
- Freie Universität Berlin, Fachbereich Physik, Berlin, Germany.
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2
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Pollak E. A personal perspective of the present status and future challenges facing thermal reaction rate theory. J Chem Phys 2024; 160:150902. [PMID: 38639316 DOI: 10.1063/5.0199557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 03/06/2024] [Indexed: 04/20/2024] Open
Abstract
Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
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Pollak E, Miret-Artés S. Recent Developments in Kramers' Theory of Reaction Rates. Chemphyschem 2023; 24:e202300272. [PMID: 37537153 DOI: 10.1002/cphc.202300272] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Revised: 05/26/2023] [Indexed: 08/05/2023]
Abstract
In this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100, Rehovoth, Israel
| | - Salvador Miret-Artés
- Instituto de Física Fundamental, Consejo, Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain
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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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Rondin L, Gieseler J, Ricci F, Quidant R, Dellago C, Novotny L. Direct measurement of Kramers turnover with a levitated nanoparticle. NATURE NANOTECHNOLOGY 2017; 12:1130-1133. [PMID: 29209016 DOI: 10.1038/nnano.2017.198] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Accepted: 08/23/2017] [Indexed: 05/22/2023]
Abstract
Understanding the thermally activated escape from a metastable state is at the heart of important phenomena such as the folding dynamics of proteins, the kinetics of chemical reactions or the stability of mechanical systems. In 1940, Kramers calculated escape rates both in the high damping and low damping regimes, and suggested that the rate must have a maximum for intermediate damping. This phenomenon, today known as the Kramers turnover, has triggered important theoretical and numerical studies. However, as yet, there is no direct and quantitative experimental verification of this turnover. Using a nanoparticle trapped in a bistable optical potential, we experimentally measure the nanoparticle's transition rates for variable damping and directly resolve the Kramers turnover. Our measurements are in agreement with an analytical model that is free of adjustable parameters. The levitated nanoparticle presented here is a versatile experimental platform for studying and simulating a wide range of stochastic processes and testing theoretical models and predictions.
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Affiliation(s)
- Loïc Rondin
- ETH Zürich, Photonics Laboratory, 8093 Zürich, Switzerland
| | - Jan Gieseler
- ETH Zürich, Photonics Laboratory, 8093 Zürich, Switzerland
| | - Francesco Ricci
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Romain Quidant
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Wien, Austria
- Erwin Schrödinger International Institute for Mathematics and Physics, University of Vienna, Boltzmanngasse 9, 1090 Wien, Austria
| | - Lukas Novotny
- ETH Zürich, Photonics Laboratory, 8093 Zürich, Switzerland
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Chakraborty A. Buckled nano rod – a two state system and quantum effects on its dynamics using system plus reservoir model. Mol Phys 2011. [DOI: 10.1080/00268976.2010.533207] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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7
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Time-Dependent Transition State Theory. ADVANCES IN CHEMICAL PHYSICS 2008. [DOI: 10.1002/9780470371572.ch4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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8
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Pomyalov A, Tannor DJ. The non-Markovian quantum master equation in the collective-mode representation: Application to barrier crossing in the intermediate friction regime. J Chem Phys 2005; 123:204111. [PMID: 16351244 DOI: 10.1063/1.2121649] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.
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Affiliation(s)
- Anna Pomyalov
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 76100 Israel
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Hershkovits E, Hernandez R. Chemical reaction dynamics within anisotropic solvents in time-dependent fields. J Chem Phys 2005; 122:14509. [PMID: 15638676 DOI: 10.1063/1.1829252] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.
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Affiliation(s)
- Eli Hershkovits
- Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332-0400, USA
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Guantes R, Vega JL, Miret-Artes S, Pollak E. Hamiltonian theory for vibrational line shapes of atoms adsorbed on surfaces. J Chem Phys 2004; 120:10768-79. [PMID: 15268103 DOI: 10.1063/1.1737299] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
The vibrational motions of atomic adsorbates on surfaces can be probed by helium atom scattering. The experimental observable is the dynamic structure factor, which shows an inelastic peak around the vibrational frequency of the isolated adsorbates known as the frustrated translational or T-mode peak. In this paper we develop a theory for the line shape of this peak, as well as for its temperature-dependent shift and broadening, based on a Hamiltonian equivalent of the generalized Langevin equation. The theory can be used to infer physical parameters of the adatom-surface interaction, such as the friction coefficient, the barrier height to diffusion, and the anharmonicity parameter. Numerical simulations are used to ascertain the range of validity of the theory, which is also generalized to describe multidimensional systems and to include quantum corrections. We compare the theoretical predictions for the shift and broadening with experimental results for the Na/Cu(001) system, showing quantitative agreement within experimental resolution.
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Affiliation(s)
- R Guantes
- Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain
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Guantes R, Vega JL, Miret-Artés S, Pollak E. Kramers’ turnover theory for diffusion of Na atoms on a Cu(001) surface measured by He scattering. J Chem Phys 2003. [DOI: 10.1063/1.1587687] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Hershkovitz E, Wiesenfeld L. Multidimensional reactive rate calculations in dissipative chaotic systems. J Chem Phys 2000. [DOI: 10.1063/1.1288686] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Reaction rates in condensed phases. Perspective on “Brownian motion in a field of force and the diffusion model of chemical reactions”. Theor Chem Acc 2000. [DOI: 10.1007/978-3-662-10421-7_12] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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16
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Reigada R, Romero AH, Lindenberg K, Sancho JM. On the generalized Kramers problem with oscillatory memory friction. J Chem Phys 1999. [DOI: 10.1063/1.479347] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gershinsky G, Berne BJ. The dependence of the rate constant for isomerization on the competition between intramolecular vibrational relaxation and energy transfer to the bath: A stochastic model. J Chem Phys 1999. [DOI: 10.1063/1.478148] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Caratti G, Ferrando R, Spadacini R, Tommei G. The Kramers problem in 2D-coupled periodic potentials. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00126-8] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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19
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Reese SK, Tucker SC. Curvilinear-path based theory of the energy transfer limited rate of a two-dimensional solute in a dissipative bath. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00129-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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20
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Drozdov A, Brey J. On the role of the energy loss in turnover theories of activated rate processes. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00059-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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21
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Hershkovitz E. A fourth-order numerical integrator for stochastic Langevin equations. J Chem Phys 1998. [DOI: 10.1063/1.476380] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Berezhkovskii AM, Zitserman VY, Sheu SY, Yang DY, Kuo J, Lin SH. Kramers theory of chemical reactions in a slowly adjusting environment. J Chem Phys 1997. [DOI: 10.1063/1.474218] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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