Intramolecular rate process: Isomerization dynamics and the transition to chaos

Leon, N. De; Berne, B. J.

doi:10.1063/1.442459

Cited by 136 publications

(43 citation statements)

References 9 publications

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“…The first illustrative example for SGOOP is a model two-state potential introduced by De Leon and Berne (48). To sample this landscape at temperature k B T = 0.1, we perform metadynamics with path CVs, a class of widely used CVs that can capture nonlocal and nonlinear fluctuations (see Supporting Information and ref.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Spectral gap optimization of order parameters for sampling complex molecular systems

Tiwary

Berne

2016

Proc. Natl. Acad. Sci. U.S.A.

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In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these lowdimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhancedsampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.collective variables | timescale separation | spectral gap | caliber | enhanced sampling W ith the advent of increasingly accurate force fields and powerful computers, molecular-dynamics (MD) simulations have become a ubiquitous tool for studying the static and dynamic properties of systems across disciplines. However, most realistic systems of interest are characterized by deep, multiple free-energy basins separated by high barriers. The timescales associated with escaping such barriers can be formidably high compared with what is accessible with straightforward MD even with the most powerful computing resources. Thus, to accurately characterize such landscapes with atomistic simulations, a large number of enhanced-sampling schemes have become popular, starting with the pioneering works of Torrie, Valleau, Bennett, and others (1-13). Many of these schemes involve probing the probability distribution along selected low-dimensional collective variables (CVs), either through a static preexisting bias or through a bias constructed on-the-fly, that enhances the sampling of hardto-access but important regions in the configuration space.The quality, reliability, and usefulness of the sampled distribution is in the end deeply dependent on the quality of the chosen CV. Specifically, one key assumption inherent in several enhanced-sampling methods is that of timescale separation (14): for efficient and accurate sampling, the chosen CV should encode all of the relevant slow dynamics in the system, and any dynamics not captured by the CV should be relatively fast. For most practical applications, there are a large number of possible CVs that could be chosen, and it is not at all obvious how to construct the best low-dimen...

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Section: Illustrative Examplesmentioning

confidence: 99%

Spectral gap optimization of order parameters for sampling complex molecular systems

Tiwary

Berne

2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

248

323

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show abstract

“…Based on a simple model representing a molecular isomerization process, an analysis of this relationship has been carried out by Berne and co-workers [25] [31] [32]. With a simple two-dimensional bound potential, De Leon and…”

Section: Numerical Simulation Of a Unimolecular Reactionmentioning

confidence: 99%

“…Berne [31] have illustrated the transition from non-RRKM to RRKM behavior as the dynamics change from regular to chaotic. Using this model potential and a stochastic scheme for coupling the two degrees of freedom [25], we study here the unimolecular decay process.…”

Section: Numerical Simulation Of a Unimolecular Reactionmentioning

confidence: 99%

“…The dissociation barrier for this potential is D = V RC (0) = 1. If we choose for the nonreactive coordinate (nRC) the same potential as De Leon and Berne [31], the Hamiltonian without coupling between the two modes becomes…”

Section: Numerical Simulation Of a Unimolecular Reactionmentioning

confidence: 99%

“…Second, to justify our choices of parameters, we briefly recall the results of Berne and co-workers [25] [31], who investigated the dynamics in a double-well potential given by Eqn. 4.1 and its mirror image.…”

Section: Numerical Simulation Of a Unimolecular Reactionmentioning

confidence: 99%

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Femtosecond Activation of Reactions: The Concepts of Nonergodic Behavior and Reduced‐Space Dynamics

Møller

Zewail

2001

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New approaches to a classical theory of unimolecular reaction rate

Rice

Zhao

1996

Int. J. Quantum Chem.

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Backgroundtudies of the rate of a unimolecular reaction S have been central to the development of our understanding of reaction dynamics for almost a century. In the early 1900s, such reactions appeared mysterious, since the source of the energy required for reaction to occur was not immediately apparent. Indeed, it took careful experimental work to demonstrate that thermal unimolecular reactions were induced by collisions and not by absorption of ambient radiation and that the observed unimolecular kinetics held in only a limited pressure range. A molecular model of the reaction dynamics was provided, in the late 1920s, by Rice, Ramsberger, and Kessel (RRK) [ 11. These investigators bypassed the very difficult analysis of the nonlinear dynamics of an excited molecule with the assumption that the intramolecular transfer of energy is very rapid on the time scale of the reaction; hence, all memory of the initial state of excitation is lost and the reaction rate depends only on the energy of the molecule. The RRK theory was recast in the 1950s by Marcus [21, who showed it was possible to take into account major elements of the state structure of the molecule imposed by quantum mechanics, while retaining the assumption that intramolecular energy transfer is complete before reaction occurs. The resultant RRKM * For Jens Peder Dahl, on the occasion of his 60th birthday.statistical theory [3] of reaction rate, by any measure, is one of the great successes of chemical physics; it is widely applicable and provides an excellent description of the experimental data in the overwhelming majority of cases. There are, however, some instances in which the statistical theory of unimolecular reaction rate gives very inaccurate predictions. In many of these instances, the failure of the RRKM theory can be traced to a breakdown of the assumption that the rate of intramolecular energy transfer is greater than the rate of reaction.Within the last decade, there has been a renaissance in the development of the classical theory of unimolecular reaction rate. In particular, the seminal work of Davis and Gray [4, 51, for model systems with 2 degrees of freedom, greatly improves our understanding of the dynamics of intramolecular energy flow and of the competition between intramolecular energy flow and the dynamical event that generates the reaction. The Davis-Gray analysis draws heavily on the properties of two-dimensional mappings in phase space, in particular, the properties of the stroboscopic representation generated when the trajectory of the system intersects the Poincar6 surface of section [6, 71. The most important elements of the theory are the calculation of the bottlenecks to intramolecular energy transfer (in a 2 degrees of freedom system, these are the canton) and the identification of the exact separatrix of the system with the transition state for the reaction. It is worth noting

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Intramolecular rate process: Isomerization dynamics and the transition to chaos

Cited by 136 publications

References 9 publications

Spectral gap optimization of order parameters for sampling complex molecular systems

Spectral gap optimization of order parameters for sampling complex molecular systems

Femtosecond Activation of Reactions: The Concepts of Nonergodic Behavior and Reduced‐Space Dynamics

New approaches to a classical theory of unimolecular reaction rate

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