Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates

Martens, Craig C.

doi:10.1063/1.1436116

Cited by 28 publications

(18 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with a characteristic correlation time τ and a damping strengh γ 0 , the GLE (1) can be replaced by a system of differential equations on a finite dimensional extended phase space [31][32][33][34]…”

mentioning

confidence: 99%

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces

et al. 2016

View full text Add to dashboard Cite

The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing-free dividing surface. We show here that it is possible to define such optimal dividing surface in systems with non-Markovian friction. However, a more direct approach to rate calculation is based on invariant manifolds and avoids the use of a dividing surface altogether, Using that method we obtain an explicit expression for the rate of crossing an anharmonic potential barrier. The excellent performance of our method is illustrated with an application to a realistic model for LiNC LiCN isomerization.

show abstract

mentioning

confidence: 99%

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces

et al. 2016

View full text Add to dashboard Cite

show abstract

“…The dynamics around the saddle point is recently investigated extensively in terms of nonlinear dynamics [26][27][28][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], in the context of transition state (TS) theory [29,30] in molecular science. Among them, particularly relevant to the present work is the finding of the "tube" [26] structures in phase space to conduct the reacting trajectories from the reactant to the product across an index-one saddle.…”

Section: Pechukas and Pollakmentioning

confidence: 99%

“…Those studies were mostly done on two degrees of freedom (DoFs) systems. The problem one of high dimension in the region of index-one saddles was later overcome [26][27][28][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Reactivity boundaries to separate the fate of a chemical reaction associated with an index-two saddle

Nagahata

Teramoto

et al. 2013

Phys. Rev. E

View full text Add to dashboard Cite

Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one. Saddle points and the dynamics in their vicinities play crucial roles in chemical reactions. A saddle point on a multidimensional potential energy surface is defined as a stationary point at which the Hessian matrix does not have zero eigenvalues and, at least, one of the eigenvalues is negative. Saddle points are classified by the number of the negative eigenvalues, and a saddle that has n negative eigenvalues is called an index-n saddle. An index-one saddle on a potential surface has especially long been considered to make a bottleneck for reactions [1][2][3], the sole unstable direction corresponding to the "reaction coordinate." This is because index-one saddles are considered to be the lowest energy stationary point connecting two potential minima, of which one corresponds to the reactant and the other to the product, and the system must traverse the index-one saddle from the reactant to the product [4][5][6][7].To estimate reaction rate constants across the saddles, transition state theory was proposed [1][2][3], by envisaging the existence of a nonrecrossing dividing surface [i.e., transition state (TS)] in the region of an index-one saddle. Recent studies of nonlinear dynamics in the vicinity of index-one saddles have revealed the firm theoretical ground for the robust existence of the no-return TS in the phase space [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] (see also Refs. [25,26], and references therein). and systems with rovibrational couplings [18,19] and showed the robust existence of reaction boundaries even while a no-return TS ceases to exist [13].For complex molecular systems, the potential energy surface becomes more complicated, and transitions from a potential basin to another involve not only index-one saddles but also higher index saddles [28][29][30]. For example, it was shown in a computer simulation of an inert gas cluster containing seven atoms that transitions from a solid-like phase to a liquid-like phase occur mostly through index-two saddles rather than through index-one saddle with the increase of kinetic temperature [29]. This indicates that the more rugged a ...

show abstract

“…In Ref. [5], Pollak describes the connection between infinite dimensional Hamiltonian systems and reduced stochastic descriptions, such as the generalized Langevin equation (see also [6]). In classical mechanics, an alternative view of the dynamics of a system is given by considering statistical distributions in the system's configuration or phase space, consistent with constraints on the system.…”

Section: Introductionmentioning

confidence: 99%

Solving evolution equations using interacting trajectory ensembles

et al. 2010

Self Cite

View full text Add to dashboard Cite

Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates

Abstract: A refined ring polymer molecular dynamics theory of chemical reaction rates A theory for nonisothermal unimolecular reaction rates

Cited by 28 publications

References 41 publications

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces

Reactivity boundaries to separate the fate of a chemical reaction associated with an index-two saddle

Solving evolution equations using interacting trajectory ensembles

Contact Info

Product

Resources

About