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## Transition state theory in liquids beyond planar dividing surfaces

### Citations

855 |
Understanding Molecular Simulation: From Algorithms to Applications
- Frenkel, Smit
- 2001
(Show Context)
Citation Context ...ce, the stable and unstable manifolds do not intersect in the four-dimensional phase space.) 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 calculate the TS trajectory. =-=[75, 84, 85]-=-. Instead, they must be described in atomistic detail iftheir effects ontheeffective freeenergies (that is, thetime-independent properties) andthe solvent response (that is, the non-equilibrium or tim... |

649 |
Random Dynamical Systems.
- Arnold
- 1998
(Show Context)
Citation Context ...s plausible to expect that they should have the desired properties.[78] This can indeed be shown to be true. A thorough discussion of the underlying theory of random dynamical systems is contained in =-=[96]-=-. The practical advantages of our proposed approaches are not merely numerical. Our construction shows how rate-determining phase space structures (like the “superhighways” for mass transport in the s... |

258 | Persistence and smoothness of invariant manifolds for flows - FENICHEL - 1971 |

91 | Asymptotic stability with rate conditions, - Fenichel - 1974 |

83 |
Hydrophobicity at small and large length scales.
- Lum, Chandler, et al.
- 1999
(Show Context)
Citation Context ...ce, the stable and unstable manifolds do not intersect in the four-dimensional phase space.) 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 calculate the TS trajectory. =-=[75, 84, 85]-=-. Instead, they must be described in atomistic detail iftheir effects ontheeffective freeenergies (that is, thetime-independent properties) andthe solvent response (that is, the non-equilibrium or tim... |

66 |
Nonlinear generalized Langevin equations.
- Zwanzig
- 1973
(Show Context)
Citation Context ...ollak[68, 69] showed that thesame rate expression can be obtained from TST if the Langevin equation is recast as a Hamiltonian system in whichthesubsystem iscoupledtoaninfinitesetofharmonicoscillators=-=[52,70]-=-andadividing surface issought inthe full space of the extended Hamiltonian. (It is worthwhile to point out that such a linearized approximation for the effect of solvation is not without error. Recent... |

54 | Statistical mechanics of assemblies of coupled oscillators - Ford, Kac, et al. - 1965 |

52 |
Influence of Dissipation on Quantum Tunneling in Macroscopic Systems.
- Caldeira, Leggett
- 1981
(Show Context)
Citation Context ...ollak[68, 69] showed that thesame rate expression can be obtained from TST if the Langevin equation is recast as a Hamiltonian system in whichthesubsystem iscoupledtoaninfinitesetofharmonicoscillators=-=[52,70]-=-andadividing surface issought inthe full space of the extended Hamiltonian. (It is worthwhile to point out that such a linearized approximation for the effect of solvation is not without error. Recent... |

46 | collective motion, and Brownian motion,” Prog - Mori, “Transport - 1965 |

43 |
Statistical mechanics of isomerization dynamics in liquids and the transition state.
- Chandler
- 1978
(Show Context)
Citation Context ...ription of the multi-dimensional geometry of the molecular reaction. This is a difficult problem even when it is appropriateto assume that classical mechanics is sufficient[1], and that a rate exists.=-=[2]-=- If it is appropriate, then such a formalism is applicable well beyond chemistry because processes in many other fields are also determined by rare events—that is, those that go through bottlenecks al... |

40 | Memory effects in irreversible thermodynamics. - Zwanzig - 1961 |

23 | Current status of transition-state theory - Truhlar, Hase, et al. - 1983 |

21 |
Transport in 3D volume-preserving flows
- MACKAY
- 1994
(Show Context)
Citation Context ...that approach the barrier in the interior of the stable manifolds, which are cylinders in phase space. They form the reaction tubes described in [90–92]. It has been realized only relatively recently =-=[4, 31, 35, 36, 38]-=- that the phase space picture ofnon-recrossingTST, butnottheconfigurationspacepicture, canbegeneralizedtosystems with many degrees of freedom. This approach provides a higher-dimensional analog of the... |

20 |
Statistical theory of the decay of metastable states
- Langer
- 1969
(Show Context)
Citation Context ...) or activated complex. Intuitively, the crossing of the TS is the rate-determining step. The rate is calculated by obtaining the flux through this transition state divided by the reactant population.=-=[10, 15, 16]-=- The calculation of the instantaneous flux through the transition state side-steps the need to calculate the dynamics at any time, let alone long times. Meanwhile, there is no longer a question of ide... |

19 |
The stable states picture of chemical reactions ii. rate constants for condensed and gas phase reaction models.
- Grote, Hynes
- 1980
(Show Context)
Citation Context ...wed that they could obtain a more accurate rate formula than that afforded by the naive TST theory—obtained in the frame of the reaction path—by extending the reactive flux calculation tolonger times.=-=[67]-=- However, Pollak[68, 69] showed that thesame rate expression can be obtained from TST if the Langevin equation is recast as a Hamiltonian system in whichthesubsystem iscoupledtoaninfinitesetofharmonic... |

16 |
The transition state method,
- Wigner
- 1938
(Show Context)
Citation Context ...the trajectories can be shown to be strictly “non-recrossing” through the dividing surface, then the TST rate is exact.[17] That is, as one reduces the number of recrossings, the TST rate is improved.=-=[1, 18]-=- This is the basis of variational transition state theory.[11, 19–26] Ideally, one aims to construct a dividing surface that rigorously admits no recrossing trajectories. In two dimensional systems, t... |

16 | Transition path sampling: throwing ropes over mountains in the dark
- Bolhuis
(Show Context)
Citation Context ... to excellent estimates of the rate in various solvated reactions.[11, 19–26] Acompletely different approach is taken by the Monte-Carlo-based transition pathensemble scheme of Chandler and coworkers.=-=[75]-=- It bypasses the identification of a TS structure and focuses on the calculation of the entire long-time transition paths from the reactant to the product region instead. They avoid calculating non-re... |

15 | Reaction rate theory: what it was, where is it today, and where is it going - Pollak, Talkner |

15 | Variational transition state theory - Truhlar - 1984 |

15 |
The geometry of reaction dynamics, Nonlinearity 15
- Uzer, Jaffé, et al.
- 2002
(Show Context)
Citation Context ...he transition state can then be identified with a normally hyperbolic invariant manifold (NHIM), while the stable and unstable manifolds of the NHIM channel the reaction towards and away from the TS. =-=[31]-=- A critical result from the mathematical (nonlinear dynamics) community is the proof [32–36] that these manifolds persist under small perturbations of the Hamiltonian, so that they will survive if anh... |

13 |
Calculation of the Rate of Elementary Association Reactions
- Wigner
- 1937
(Show Context)
Citation Context ...es requires a long-time description of the multi-dimensional geometry of the molecular reaction. This is a difficult problem even when it is appropriateto assume that classical mechanics is sufficient=-=[1]-=-, and that a rate exists.[2] If it is appropriate, then such a formalism is applicable well beyond chemistry because processes in many other fields are also determined by rare events—that is, those th... |

13 |
Flux over a saddle Phys
- MacKay
- 1990
(Show Context)
Citation Context ...ined as an integral over the NHIM alone, without any reference to a dividing surface at all [43]. In two degrees of freedom, the flux is given by the action integral along the Liapunov periodic orbit =-=[86, 95]-=-. The dividing surface itself, which has traditionally been at the heart of TST, thereby loses some of its importance (though it is still useful in many computational schemes). The NHIM and its invari... |

12 |
Direct construction of a dividing surface of minimal flux for multi-degree-of-freedom systems that cannot be recrossed
- Waalkens, Wiggins
- 2004
(Show Context)
Citation Context ...ssing-free, and all of these will yield the same reactive flux. Indeed, the flux across the TS can be determined as an integral over the NHIM alone, without any reference to a dividing surface at all =-=[43]-=-. In two degrees of freedom, the flux is given by the action integral along the Liapunov periodic orbit [86, 95]. The dividing surface itself, which has traditionally been at the heart of TST, thereby... |

10 |
Statistical theory of asteroid escape rates
- Jaffé, Ross, et al.
(Show Context)
Citation Context ...—that is, those that go through bottlenecks along the reaction path. For example, the ionization of atoms,[3] the rearrangement of clusters,[4] conductance through microjunctions,[5] asteroid capture,=-=[6]-=- and even phase transitions in cosmology[7] all involve rare events traversing through bottlenecks. The beauty of Transition State Theory (TST)[8–14] lies partly in that it addresses both the question... |

10 | Classical and modern methods in reaction rate theory - Berne, Borkovec, et al. - 1988 |

10 |
2000] Transition state theory without time-reversal symmetry: chaotic ionization of the hydrogen atom
- Jaffé, Farrelly, et al.
(Show Context)
Citation Context ... a recrossing-free dividing surface in phase space. Once a phase space view has been adopted, TST can be applied to systems without time-reversal invariance, e.g., in the presence of a magnetic field =-=[3, 87]-=-. In addition to a dividing surface, the phase space picture of TST contains the stable and unstable manifolds of the Liapunov periodic orbit. These are surfaces that contain all those trajectories th... |

9 |
Variational Theory of Reaction Rates
- Keck
- 1967
(Show Context)
Citation Context ...ier can be approximated as parabolic. In order to do this more generally, many have resorted to the use of a variational transition state theory in the infinite-dimensional phase space following Keck.=-=[19]-=- These nonplanar dividing surfaces have been shown to lead to excellent estimates of the rate in various solvated reactions.[11, 19–26] Acompletely different approach is taken by the Monte-Carlo-based... |

9 |
Transition states, trapped trajectories, and classical bound states embedded in the continuum
- Pechukas, Pollak
- 1978
(Show Context)
Citation Context ...um effects) [17]. For systems with two degrees of freedom, it was realized in the 70s that an ideal recrossing-free dividing surface is provided by an unstable periodic orbit close to the barrier top =-=[17, 21, 86]-=- that is often called the Liapunov orbit. Although the initial formulations of TST relied on dividing surfaces restricted to the configuration space, it is 4115 116 117 118 119 120 121 122 123 124 12... |

8 |
Regularity in chaotic reaction paths
- Komatsuzaki, Berry
- 1999
(Show Context)
Citation Context ...sses in many other fields are also determined by rare events—that is, those that go through bottlenecks along the reaction path. For example, the ionization of atoms,[3] the rearrangement of clusters,=-=[4]-=- conductance through microjunctions,[5] asteroid capture,[6] and even phase transitions in cosmology[7] all involve rare events traversing through bottlenecks. The beauty of Transition State Theory (T... |

6 |
Transition state theory for ballistic electrons
- Eckhardt
- 1995
(Show Context)
Citation Context ...rmined by rare events—that is, those that go through bottlenecks along the reaction path. For example, the ionization of atoms,[3] the rearrangement of clusters,[4] conductance through microjunctions,=-=[5]-=- asteroid capture,[6] and even phase transitions in cosmology[7] all involve rare events traversing through bottlenecks. The beauty of Transition State Theory (TST)[8–14] lies partly in that it addres... |

6 |
Homoclinic chaos in the dynamics of a general bianchi type-ix model
- Oliveira, Almeida, et al.
(Show Context)
Citation Context ... along the reaction path. For example, the ionization of atoms,[3] the rearrangement of clusters,[4] conductance through microjunctions,[5] asteroid capture,[6] and even phase transitions in cosmology=-=[7]-=- all involve rare events traversing through bottlenecks. The beauty of Transition State Theory (TST)[8–14] lies partly in that it addresses both the question of time and geometry in a single step. The... |

6 |
Classical transition state theory: a lower bound to the reaction probability
- Pollak, Child, et al.
- 1980
(Show Context)
Citation Context ...um effects) [17]. For systems with two degrees of freedom, it was realized in the 70s that an ideal recrossing-free dividing surface is provided by an unstable periodic orbit close to the barrier top =-=[17, 21, 86]-=- that is often called the Liapunov orbit. Although the initial formulations of TST relied on dividing surfaces restricted to the configuration space, it is 4115 116 117 118 119 120 121 122 123 124 12... |

6 |
Impenetrable barriers in phase-space
- Wiesenfeld, Uzer
(Show Context)
Citation Context ...o-called Normally Hyperbolic Invariant Manifold (NHIM) which act like scissors cutting the phase space into the hypervolumes of those initial conditions which lead to reactions and those which do not.=-=[31, 39, 40]-=- Once these manifolds are calculated, large-scale simulations of reactivity are no longer needed. Instead, one only needs to check on which side of these manifolds (known as “separatrices”) the initia... |

6 | S 2002 Chemical reactions dynamics: many-body chaos and regularity - Komatsuzaki, Berry |

6 |
Theory of activated rate processes: A new derivation of Kramers’ expression
- Pollak
- 1986
(Show Context)
Citation Context ...obtain a more accurate rate formula than that afforded by the naive TST theory—obtained in the frame of the reaction path—by extending the reactive flux calculation tolonger times.[67] However, Pollak=-=[68, 69]-=- showed that thesame rate expression can be obtained from TST if the Langevin equation is recast as a Hamiltonian system in whichthesubsystem iscoupledtoaninfinitesetofharmonicoscillators[52,70]andadi... |

6 |
Classical mechanics of a collinear exchange reaction: A direct evaluation of the reaction probability and product distribution,
- Pollak, Child
- 1980
(Show Context)
Citation Context .... Trajectories on the invariant manifolds neither cross the barrier nor return into the well from which they originate. The importance of the trapped trajectories was realized by Pollak and coworkers =-=[86, 88, 89]-=-: Being neither reactive nor non-reactive, these trajectories form the natural boundaries between reactive and non-reactive regions in phase space. Reactive trajectories are those that approach the ba... |

5 |
Classical transition state theory is exact if the transition state is unique
- Pechukas, Pollak
- 1979
(Show Context)
Citation Context ...ts recross the identified transition state (dividing) surface. Indeed, if all of the trajectories can be shown to be strictly “non-recrossing” through the dividing surface, then the TST rate is exact.=-=[17]-=- That is, as one reduces the number of recrossings, the TST rate is improved.[1, 18] This is the basis of variational transition state theory.[11, 19–26] Ideally, one aims to construct a dividing surf... |

5 | Variational transition-state theory for reaction rates in dissipative systems - Pollak, Tucker, et al. - 1990 |

5 |
Theory of classical diffusion jumps in solids. Phys
- Toller, Jacucci, et al.
- 1985
(Show Context)
Citation Context ...that approach the barrier in the interior of the stable manifolds, which are cylinders in phase space. They form the reaction tubes described in [90–92]. It has been realized only relatively recently =-=[4, 31, 35, 36, 38]-=- that the phase space picture ofnon-recrossingTST, butnottheconfigurationspacepicture, canbegeneralizedtosystems with many degrees of freedom. This approach provides a higher-dimensional analog of the... |

5 | Dynamical hierarchy in transition states: Why and how does a system climb over the mountain - Komatsuzaki, Berry |

4 |
Talkner P, Borkovec M. Reaction rate theory; fifty years after Kramers. Rev Mod Phys
- Hänggi
- 1990
(Show Context)
Citation Context ...) or activated complex. Intuitively, the crossing of the TS is the rate-determining step. The rate is calculated by obtaining the flux through this transition state divided by the reactant population.=-=[10, 15, 16]-=- The calculation of the instantaneous flux through the transition state side-steps the need to calculate the dynamics at any time, let alone long times. Meanwhile, there is no longer a question of ide... |

4 | Variational transition state theory for reactions in condensed phases - Pollak - 1991 |

4 | Variational transition state theory in condensed phases - Tucker - 1995 |

4 |
Unified statistical model for “complex” and “direct” reaction mechanisms: A test on the collinear H +H2 exchange reaction
- Pollak, Pechukas
- 1979
(Show Context)
Citation Context ..., 19–26] Ideally, one aims to construct a dividing surface that rigorously admits no recrossing trajectories. In two dimensional systems, this is precisely what was accomplished by Pechukas and Pollak=-=[27, 28]-=- in identifying dividing surfaces as periodic orbits that are strictly non-recrossing.[27–30] Analogous structures in higher-dimensional systems can be described explicitly if the transition is mediat... |

4 | Theory of activated rate processes: position dependent friction - Carmeli, Nitzan - 1983 |

4 | Generalized Langevin dynamics simulations with arbitrary time-dependent memory kernels - Berkowitz, Morgan, et al. - 1983 |

4 | Variational transition state theory for dissipative systems - Pollak - 1992 |

3 | Chemical reaction dynamics in solution, Annu - Hynes - 1985 |

3 |
Periodic orbits and the theory of reactive scattering
- Pollak
- 1985
(Show Context)
Citation Context ..., 19–26] Ideally, one aims to construct a dividing surface that rigorously admits no recrossing trajectories. In two dimensional systems, this is precisely what was accomplished by Pechukas and Pollak=-=[27, 28]-=- in identifying dividing surfaces as periodic orbits that are strictly non-recrossing.[27–30] Analogous structures in higher-dimensional systems can be described explicitly if the transition is mediat... |

3 |
Semiclassical transition state theory. A new perspective.
- Hernandez, Miller
- 1993
(Show Context)
Citation Context ...the expansion of the potential at the col of the potential energy surface— of a conservative system was originally exploited to construct highly accurate semiclassical transition state theory (SCTST).=-=[37, 38, 45]-=- In order to extend such an SCTST to a dissipated system, one could couple the reactive system to a Langevin bath. The latter in turn would then be rewritten into the Zwanzig Hamitonian—viz, the finit... |

3 |
A combined use of perturbation theory and diagonalization: application to bound energy levels and semiclassical rate theory
- Hernandez
- 1994
(Show Context)
Citation Context ...that approach the barrier in the interior of the stable manifolds, which are cylinders in phase space. They form the reaction tubes described in [90–92]. It has been realized only relatively recently =-=[4, 31, 35, 36, 38]-=- that the phase space picture ofnon-recrossingTST, butnottheconfigurationspacepicture, canbegeneralizedtosystems with many degrees of freedom. This approach provides a higher-dimensional analog of the... |

3 |
A new look at the transition state: Wigner’s dynamical perspective revisited
- Jaffé, Kawai, et al.
- 2005
(Show Context)
Citation Context ...o-called Normally Hyperbolic Invariant Manifold (NHIM) which act like scissors cutting the phase space into the hypervolumes of those initial conditions which lead to reactions and those which do not.=-=[31, 39, 40]-=- Once these manifolds are calculated, large-scale simulations of reactivity are no longer needed. Instead, one only needs to check on which side of these manifolds (known as “separatrices”) the initia... |

3 | Regularity in Chaotic Transitions on Two-Basin Landscapes - Komatsuzaki, Berry |

3 | Ab Initio calculation of anharmonic constants for a transition state, with application to semiclassical transition state tunneling probabilities.
- Miller, Hernandez, et al.
- 1990
(Show Context)
Citation Context ...the expansion of the potential at the col of the potential energy surface— of a conservative system was originally exploited to construct highly accurate semiclassical transition state theory (SCTST).=-=[37, 38, 45]-=- In order to extend such an SCTST to a dissipated system, one could couple the reactive system to a Langevin bath. The latter in turn would then be rewritten into the Zwanzig Hamitonian—viz, the finit... |

3 | On the generalized Langevin equation: classical and quantum - Cortes, West, et al. - 1985 |

3 |
Transition-state recrossing dynamics in activated rate processes, Phys
- Pollak, Talkner
- 1995
(Show Context)
Citation Context ...neralized Langevin equations. [49– 65] For example, within the time scale of a chemical reaction event, fluctuations of the environment will almost inevitably cause recrossings of the dividing surface=-=[66]-=-, so that a naive TST ratecalculation would yield a poorestimate of the rate. Indeed, GroteandHynes showed that they could obtain a more accurate rate formula than that afforded by the naive TST theor... |

3 |
Stochastic transition states: reaction geometry amidst noise
- Bartsch, Uzer, et al.
- 2005
(Show Context)
Citation Context ...static dividing surface does in conventional TST. In addition, the TS trajectory possesses stable and unstable invariant manifolds. For systems with harmonic barriers, we described these manifolds in =-=[76, 77]-=- using an explicit solution of the equations of motion, through which they can be identified easily. In anharmonic systems, a more qualitative approach to characterizing invariant manifolds is require... |

3 |
Identifying reactive trajectories using a moving transition state
- Bartsch, Uzer, et al.
- 2006
(Show Context)
Citation Context ...e sufficiently weak, one can regard these sets as small deformations of the invariant manifolds in the harmonic system, and it appears plausible to expect that they should have the desired properties.=-=[78]-=- This can indeed be shown to be true. A thorough discussion of the underlying theory of random dynamical systems is contained in [96]. The practical advantages of our proposed approaches are not merel... |

3 | Transition state theory for laser-driven reactions - Kawai, Bandrauk, et al. |

3 |
Macroscopic theory of activated decay of metastable states
- Graham
- 1990
(Show Context)
Citation Context ... reaction and the solvent is linear within the Langevin representation, the solvent is uncoupled to the reacting subsystem. Such decoupling leads to a tremendous simplification, as observed by Graham =-=[82]-=- and Martens [83]. In our previous work, we followed this further by constructing a dividing surface in a time-dependent frame in which the trajectories are strictly non-recrossing, albeit by construc... |

3 |
Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates
- Martens
- 2002
(Show Context)
Citation Context ... solvent is linear within the Langevin representation, the solvent is uncoupled to the reacting subsystem. Such decoupling leads to a tremendous simplification, as observed by Graham [82] and Martens =-=[83]-=-. In our previous work, we followed this further by constructing a dividing surface in a time-dependent frame in which the trajectories are strictly non-recrossing, albeit by constructing such a surfa... |

3 | Geometry and dynamics of stable and unstable cylinders in Hamiltonian systems - Almeida, Leon, et al. - 1990 |

3 | Local regularity and non-recrossing path in transition state – a new strategy in chemical reaction theories - Komatsuzaki, Berry - 2000 |

3 | Regularity in chaotic reaction paths III: Ar6 local invariances at the reaction bottleneck - Komatsuzaki, Berry - 2001 |

2 |
Activated rate processes: Generalization of the Kramers-Grote-Hynes and Langer theories
- Berezhkovskii, Pollak, et al.
- 1992
(Show Context)
Citation Context ...) or activated complex. Intuitively, the crossing of the TS is the rate-determining step. The rate is calculated by obtaining the flux through this transition state divided by the reactant population.=-=[10, 15, 16]-=- The calculation of the instantaneous flux through the transition state side-steps the need to calculate the dynamics at any time, let alone long times. Meanwhile, there is no longer a question of ide... |

2 | Variational transition state theory for activated rate processes - Pollak - 1990 |

2 | Numerical methods for locating stable periodic orbits embedded in a largely chaotic system - Marcinek, Pollak - 1994 |

2 | Ab initio prediction of fundamental, overtone and combination band infrared intensities - Jr, Willetts, et al. - 1990 |

2 | The prediction of spectroscopic properties from quartic corrected force fields - Green, Jayatilaka, et al. - 1990 |

2 | Langevin equations with multiplicative noise: theory and applications to physical processes - Lindenberg, Shuler, et al. - 1983 |

2 | Molecular dynamics of a model SN2 reaction in - Gertner, Bergsma, et al. - 1987 |

2 | Possible thermodynamic law violations and astrophysical issues for secular acceleration of electrodynamic particles in the vacuum, Phys - Cole - 1995 |

2 |
The transition state in a noisy environment
- BARTSCH, HERNANDEZ, et al.
- 2005
(Show Context)
Citation Context ...static dividing surface does in conventional TST. In addition, the TS trajectory possesses stable and unstable invariant manifolds. For systems with harmonic barriers, we described these manifolds in =-=[76, 77]-=- using an explicit solution of the equations of motion, through which they can be identified easily. In anharmonic systems, a more qualitative approach to characterizing invariant manifolds is require... |

2 |
Definability of no-return transition states in the high-energy regime above the reaction threshold
- Li, Shoujiguchi, et al.
- 2006
(Show Context)
Citation Context ...e complex than what was described above [21, 27]. One might expect that a higher-dimensional NHIM can also bifurcate at high energies, and indeed evidence for such bifurcations has recently been seen =-=[93, 94]-=-. For applications to specific systems, it is essential that we can calculate the NHIM and its associated invariant manifolds, for which we have so far only invoked existence theorems. Such calculatio... |

2 |
Bifurcation of no-return transition states in manybody chemical reactions
- Li, Toda, et al.
(Show Context)
Citation Context ...e complex than what was described above [21, 27]. One might expect that a higher-dimensional NHIM can also bifurcate at high energies, and indeed evidence for such bifurcations has recently been seen =-=[93, 94]-=-. For applications to specific systems, it is essential that we can calculate the NHIM and its associated invariant manifolds, for which we have so far only invoked existence theorems. Such calculatio... |

2 | Regularity in chaotic reaction paths. II. Ar6. Energy dependence and visualization of the reaction bottleneck - Komatsuzaki, Berry - 1999 |

1 | Dynamics ofMolecules and Chemical Reactions - Pollak, rateprocesses, et al. - 1996 |

1 | Phasespaceconduits for reactionin multidimensional systems: HCN isomerization in three dimensions - Waalkens, Burbanks, et al. - 2004 |

1 | CumulativereactionprobabilitiesforH+H2 → H2 +H from a knowledge of the anharmonic force - Cohen, Hernandez - 1992 |

1 | A generalizedLangevin equation approachto molecular collision dynamics - Schatz - 1978 |

1 | Generalized Langevin theory for many-body problems in chemical dynamics: General formulation and the equivalent harmonic chain representation - Adelman - 1979 |

1 | A reference trajectory approach to Langevin equations in gas phase collision dynamics - Schatz - 1980 |

1 | Chemical reaction dynamics in liquid solutions - Adelman - 1983 |

1 | Comparison of rate theories for generalized Langevin dynamics - Tucker, Tuckerman, et al. - 1991 |

1 | Uses and abuses ofthe Langevinequation for chemicalreactionsin condensed phases - Oppenheim, Orsky - 1991 |

1 |
Theory ofactivated rate processesfor arbitraryfrequency dependent friction: Solution of the turnover problem
- Pollak, Grabert, et al.
- 1989
(Show Context)
Citation Context ...obtain a more accurate rate formula than that afforded by the naive TST theory—obtained in the frame of the reaction path—by extending the reactive flux calculation tolonger times.[67] However, Pollak=-=[68, 69]-=- showed that thesame rate expression can be obtained from TST if the Langevin equation is recast as a Hamiltonian system in whichthesubsystem iscoupledtoaninfinitesetofharmonicoscillators[52,70]andadi... |

1 | Hamiltonian theory of stochastic acceleration - Makhnovskii, Pollak - 2006 |

1 | The momentum and velocity autocorrelation functions of a diatomic molecule are not necessarily proportional to each other - Moix, Hernandez, et al. |

1 | Transition-state theory rate calculations with a recrossing-free moving dividing surface
- Bartsch, Uzer, et al.
(Show Context)
Citation Context ...ving TS obtained from 4.9 is a good approximation to the moving TS for the exact dynamics leading to high accuracy in assigning which trajectories are reactive. Two additional computer-enabled methods=-=[80]-=- for transition state theory (TST) rate calculations have also been developed by us to take advantage of these notions of the moving dividing surface and the associated moving separatrices: One is bas... |

1 |
Time-dependent transition state theory
- Bartsch, Moix, et al.
- 2008
(Show Context)
Citation Context ...e non-recrossing TST of isolated systems to such driven (or timedependent) Hamiltonians, then onecan presumably also address reactions in solutions. Such a generalization has indeed been accomplished.=-=[79, 81]-=- In the limit that the interaction between the reaction and the solvent is linear within the Langevin representation, the solvent is uncoupled to the reacting subsystem. Such decoupling leads to a tre... |

1 | Cylindrical manifolds in phasespace asmediatorsof chemical reaction dynamics and kinetics. II. Numerical considerations and applications to models with two degrees of freedom - Leon, Mehta, et al. - 1991 |

1 | Atomic clusters: Powerful tools to probe complex dynamics - Berry |

1 |
E.Pollak,reduced-dimensional semiclassical reaction rate theory for dissipative systems
- Hernandez
(Show Context)
Citation Context ...theactions connected to quantum numbers using theBohr-Sommerfeldquantization rules asdoneinthesmall-dimensional case.[37, 38, 45] To our knowledge, this has yet to be published in the open literature.=-=[103]-=- Equally interesting would be the generalization of such a procedure using the moving TST discussed here. However it is not clear how one would identify the requisite good action angle-variables neede... |

1 |
Solvent-induced acceleration in an activated molecular reaction
- García-Müller, Hernandez, et al.
- 2008
(Show Context)
Citation Context ...reactions, and its parameterization was used as the basis for our earlier work in which the solvent is represented by implicit and stochastic forces.[78] The former reaction has recently been modeled =-=[104]-=- in argon baths using full molecular dynamics simulations under high temperature conditions. The 12415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 ... |