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Journal ArticleDOI

The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models

15 Sep 1980-Journal of Chemical Physics (American Institute of Physics)-Vol. 73, Iss: 6, pp 2715-2732
TL;DR: In this paper, the stable states picture (SSP) was used to derive the time correlation function (tcf) for the rate constant κ for a wide variety of gas and solution phase reaction models.
Abstract: The time correlation function (tcf) formulas for rate constants κ derived via the stable states picture (SSP) of chemical reactions are applied to a wide variety (a–d) of gas and solution phase reactionmodels. (a) For gas phase bimolecular reactions, we show that the flux tcf governing κ corresponds to standard numerical trajectory calculation methods. Alternate formulas for κ are derived which focus on saddle point surfaces, thus increasing computational efficiency. Advantages of the SSP formulas for κ are discussed. (b) For gas phase unimolecular reactions, simple results for κ are found in both the strong and weak coupling collision limits; the often ignored role of product stabilization is exposed for reversible isomerizations. The SSP results correct some standard weak coupling rate constant results by as much as 50%. (c) For barrier crossing reactions in solution, we evaluate κ for a generalized (non‐Markovian) Langevin description of the dynamics. For several realistic models of time dependent friction, κ differs dramatically from the popular Kramers constant friction predictions; this has important implications for the validity of transition state theory. (d) For solutionreactions heavily influenced by spatial diffusion, we show that the SSP isolates short range reaction dynamics of interest and includes important barrier region effects in structural isomerizations often missed in standard descriptions.
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TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

5,180 citations

Journal ArticleDOI
TL;DR: In this article, the authors present an overview of the current status of transition-state theory and its generalizations, including recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, progress in the theory and application of transitionstate theory to condensed-phase reactions, and insight into the relation of transition state theory to accurate quantum dynamics.
Abstract: We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.

1,919 citations

Journal ArticleDOI
15 Oct 2010-Science
TL;DR: Simulation of the folding of a WW domain showed a well-defined folding pathway and simulation of the dynamics of bovine pancreatic trypsin inhibitor showed interconversion between distinct conformational states.
Abstract: Molecular dynamics (MD) simulations are widely used to study protein motions at an atomic level of detail, but they have been limited to time scales shorter than those of many biologically critical conformational changes. We examined two fundamental processes in protein dynamics—protein folding and conformational change within the folded state—by means of extremely long all-atom MD simulations conducted on a special-purpose machine. Equilibrium simulations of a WW protein domain captured multiple folding and unfolding events that consistently follow a well-defined folding pathway; separate simulations of the protein’s constituent substructures shed light on possible determinants of this pathway. A 1-millisecond simulation of the folded protein BPTI reveals a small number of structurally distinct conformational states whose reversible interconversion is slower than local relaxations within those states by a factor of more than 1000.

1,650 citations


Cites methods from "The stable states picture of chemic..."

  • ...4d of the paper, with the Stable States Picture (SSP) algorithm (42)....

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1,365 citations

References
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Journal ArticleDOI
TL;DR: In this article, a particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.

7,289 citations

Book
01 Jan 1941

3,988 citations

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01 Jan 1974

1,460 citations

Book
01 Jan 1973

1,163 citations

BookDOI
01 Jan 1976
TL;DR: In this paper, the potential energy surfaces and their effect on collision processes are discussed. But the authors focus on the nonadiabatic processes in collision theory and not on the classical trajectories of trajectories.
Abstract: 1. Classical Trajectory Methods in Molecular Collisions.- 2. Features of Potential Energy Surfaces and Their Effect on Collisions.- 3. Dynamics of Unimolecular Reactions.- 4. Semiclassical Methods in Molecular Collision Theory.- 5. Nonadiabatic Processes in Molecular Collisions.- 6. Statistical Approximations in Collision Theory.- 7. Thermodynamic Approach to Collision Processes.- Author Index.

1,002 citations