How does a reaction path branching take place? A classification of bifurcation events

Quapp, Wolfgang

doi:10.1016/s0022-2860(03)00742-7

Cited by 26 publications

(55 citation statements)

References 34 publications

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“…Even though the reaction rates are beyond the scope of this paper, we would like to highlight Quapp's work 56 where he addresses the case in which two reactions have the same saddle point. The branching of the path may occur in the presence of a ridge bifurcation in the potential energy surface.…”

Section: Discussionmentioning

confidence: 99%

Migration mechanisms and diffusion barriers of carbon and native point defects in GaN

2016

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Carbon related defects are readily incorporated in GaN due to its abundance during growth both with MBE and MOCVD techniques. Employing first-principles calculations, we compute the migration barriers of carbon interstitials and we discuss possible relevant mechanisms of diffusion in the wurtzite GaN crystal. In addition, we calculate the migration barriers for the diffusion of the native defects of the crystal, i.e., gallium and nitrogen interstitials and vacancies. The Minimum Energy Path (MEP) and the migration barriers of these defects are obtained using the Nudged Elastic Band (NEB) method with the climbing image modification (CI-NEB). In addition, the Dimer method is used to independently determine the results. The results yield a quantitative description of carbon diffusion in GaN allowing for the determination of the most preferable migration paths.

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Section: Discussionmentioning

confidence: 99%

Migration mechanisms and diffusion barriers of carbon and native point defects in GaN

2016

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“…An often used RP model is the distinguished coordinate [1]. It was later generalized as the distinguished coordinate path (DCP) [2,3,4] and was finally refined as Newton trajectory (NT) [3,4,5,6,7,8,9,10]. For this type of RP holds that at every point of the curve the gradient of the PES points into the same direction, a direction of a prescribed search vector.…”

Section: Introductionmentioning

confidence: 99%

A contribution to a theory of mechanochemical pathways by means of Newton trajectories

2016

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The reaction path is a central subject in theoretical chemistry. It is a pathway imagined on the potential energy surface (PES). It provides a one-dimensional description of a chemical reaction in an N −dimensional configuration space. Additionally, one can apply mechanical stress in a defined direction to the molecule and generate an effective PES. Changes for minima and saddle points by the stress are described by Newton trajectories on the original PES. The barrier of a reaction fully breaks down for the maximal value of the norm of the gradient of the PES along a pulling Newton trajectory. This point is named barrier breakdown point (BBP). We discuss topologically different, 2-dimensional examples for this model to understand and classify the mechanochemistry of molecules.

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“…Thus, in each point of this path, the gradient has the same direction. A curve with this feature is known as Newton trajectory (NT) [44][45][46][47][48][49][50][51] or more recently as the curve of the force displaced stationary points (FDSPs). 38,39 It is known that every NT satisfies the Branin equation, 38,52,53…”

Section: Introductionmentioning

confidence: 99%

An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis

Bofill

Ribas‐Ariño

García

et al. 2017

The Journal of Chemical Physics

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The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.

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How does a reaction path branching take place? A classification of bifurcation events

Cited by 26 publications

References 34 publications

Migration mechanisms and diffusion barriers of carbon and native point defects in GaN

Migration mechanisms and diffusion barriers of carbon and native point defects in GaN

A contribution to a theory of mechanochemical pathways by means of Newton trajectories

An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis

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