Newton Trajectories in the Curvilinear Metric of Internal Coordinates

Quapp, Wolfgang

doi:10.1023/b:jomc.0000044524.48281.2d

Cited by 21 publications

(16 citation statements)

References 44 publications

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“…An alternative proof is given in Ref. 43. On the effective potential, V f (x), the stationary points are located at different points with respect to the unperturbed potential, V(x), where it holds ∇ x V (x) = g(x) = 0.…”

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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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 correct application of internal coordinates then also enforces the inclusion of the non-Cartesian metric of internal coordinates. 30 Often the two kinds of curves, GE and IRC, are similar, and to relate a result to one of both is useless. In contrast, if both curves are different, 21,26 especially the SD is a solution of the projector eq.…”

Section: Resultsmentioning

confidence: 99%

A comment to the nudged elastic band method

Quapp

Bofill

2010

J Comput Chem

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The minimum energy path (MEP) is an important reaction path concept of theoretical chemistry, and the nudged elastic band (NEB) method with its many facets is a central method to determine the MEP. We demonstrate in this comment that the NEB does not have to lead to a steepest descent pathway (as always assumed). In contrast, as long as it is used without spring forces, it can lead to a gradient extremal.

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“…Alternatively, one can choose a direction and perform a constrained optimization of the components of the gradient perpendicular to this direction. This is known variously as line‐then‐plane,126 reduced gradient following,127–129 and Newton trajectories 130–132. Growing string methods (GSM)131–136 are coordinate driving or reduced gradient following/Newton trajectory methods that start from both the reactant and product side.…”

Section: Special Considerations For Transition Structure Optimizationmentioning

confidence: 99%

Geometry optimization

Schlegel

2011

WIREs Comput Mol Sci

330

349

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Geometry optimization is an important part of most quantum chemical calculations. This article surveys methods for optimizing equilibrium geometries, locating transition structures, and following reaction paths. The emphasis is on optimizations using quasi‐Newton methods that rely on energy gradients, and the discussion includes Hessian updating, line searches, trust radius, and rational function optimization techniques. Single‐ended and double‐ended methods are discussed for transition state searches. Single‐ended techniques include quasi‐Newton, reduced gradient following and eigenvector following methods. Double‐ended methods include nudged elastic band, string, and growing string methods. The discussions conclude with methods for validating transition states and following steepest descent reaction paths. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 790–809 DOI: 10.1002/wcms.34 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

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Newton Trajectories in the Curvilinear Metric of Internal Coordinates

Cited by 21 publications

References 44 publications

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

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

A comment to the nudged elastic band method

Geometry optimization

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