Perspective on “The transition state method”

Garrett, Bruce C.

doi:10.1007/978-3-662-10421-7_10

Cited by 10 publications

(11 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the prefactor τ 0 is related to the effective timescale of the motion along the reaction coordinate1234. Equation (2) shows that for Δ P <Δ P crit , the trapping time is described by the Bell–Evans model and log( τ / τ 0 ) is a first-degree polynomial in Δ P (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Theoretical efforts to describe such reactions led to the development of TST in the second half of the 1930s, notably by Eyring, Polanyi, Evans and Wigner123. TST for elementary chemical reactions assumes, as Wigner summarized it, statistical mechanics, classical motion of atomic nuclei, adiabatically changing electronic states and what has become known as TST's fundamental assumption, fundamental dynamical assumption or no-recrossing assumption.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

et al. 2016

View full text Add to dashboard Cite

Transition state theory (TST) provides a simple interpretation of many thermally activated processes. It applies successfully on timescales and length scales that differ several orders of magnitude: to chemical reactions, breaking of chemical bonds, unfolding of proteins and RNA structures and polymers crossing entropic barriers. Here we apply TST to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field. Reaction pathways are effectively one dimensional and so long that they are observable in a microscope. Reaction rates are so slow that transitions are recorded on video. We find sharp transition states that are independent of the applied force, similar to chemical bond rupture, as well as transition states that change location on the reaction pathway with the strength of the applied force. The states of equilibrium and transition are separated by micrometres as compared with angstroms/nanometres for chemical bonds.

show abstract

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

et al. 2016

View full text Add to dashboard Cite

show abstract

“…8 TST assumes that the molecules that cross the dividing surface, which is located at the transition state (the bottleneck for reaction), never return to reactants. 9 In the canonical version of VTST, this approximation is smothered by allowing the dividing surface to move along a given path. The location of the dividing surface is the one that maximizes the free energy.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Isotope Effects in Multipath VTST: Application to a Hydrogen Abstraction Reaction

et al. 2015

View full text Add to dashboard Cite

In this work we apply multipath canonical variational transition state theory with small-tunneling corrections (MP-CVT/SCT) to the hydrogen abstraction reaction from ethanol by atomic hydrogen in aqueous solution at room temperature. This reaction presents two transition states which can interconvert by internal rotations about single bonds and another two transition states that are non-interconvertible enantiomers to the former structures. The study also includes another three reactions with isotopically substituted species for which there are experimental values of thermal rate constants and kinetic isotope effects (KIEs). The agreement between the MP-CVT/SCT thermal rate constants and the experimental data is good. The KIEs obtained by the MP-CVT/SCT methodology are factorized in terms of individual transition state contributions to facilitate the analysis. It was found that the percentage contribution of each transition state to the total KIE is independent of the isotopic substitution.

show abstract

“…Computing chemical reaction rates is based on the fundamental framework of transition state theory as formulated in phase space by Polanyi, Evans, Wigner, Eyring [11,12,21,48]). Further research has shown that constructing a locally recrosssing free, minimal flux orientable surface called a dividing surface (DS) is the phase space structure that provides the correct estimate for reaction rates.…”

Section: Introductionmentioning

confidence: 99%

Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors

Naik

García-Garrido

Wiggins

2019

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in multi-stable mechanical systems, and reaction rates in chemical reaction dynamics. Thus, methods that can reveal their geometry in high dimensional phase space (4 or more dimensions) need to be benchmarked by comparing with known results. In this study we assess the capability of one such method called Lagrangian descriptor for revealing the types of high dimensional phase space structures associated with index-1 saddle in Hamiltonian systems. The Lagrangian descriptor based approach is applied to two and three degree-of-freedom quadratic Hamiltonian systems where the high dimensional phase space structures are known, that is as closed-form analytical expressions. This leads to a direct comparison of features in the Lagrangian descriptor plots and the phase space structures' intersection with an isoenergetic two-dimensional surface, and hence provides a validation of the approach.

show abstract

Perspective on “The transition state method”

Cited by 10 publications

References 56 publications

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

Kinetic Isotope Effects in Multipath VTST: Application to a Hydrogen Abstraction Reaction

Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors

Contact Info

Product

Resources

About