Use and abuse of the distinguished-coordinate method for transition-state structure searching

Williams, Ian H.; Maggiora, Gerald M.

doi:10.1016/0166-1280(82)80095-x

Cited by 86 publications

(79 citation statements)

References 28 publications

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“…It was proposed to choose a driving coordinate along a valley, to go a step in this direction, and to perform an energy optimization of the residual coordinates [3].…”

Section: Rgf Newton Trajectoriesmentioning

confidence: 99%

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Reaction channels of the potential energy surface: application of Newton trajectories

Hirsch

Quapp

2004

Journal of Molecular Structure: THEOCHEM

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The reaction path is an important concept of theoretical chemistry. We employ the definition of the Newton trajectory (NT). An NT follows a curve where the gradient is always a pointer to a fixed direction. Usually, a whole family of NTs connects two adjacent stationary points of an index difference of one. We will name such a family a reaction channel. The border between two reaction channels is formed by singular NTs which cross valley-ridge inflection (VRI) points. Examples are given with the Müller -Brown potential, and the potential energy surfaces of water and formaldehyde. q

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“…It was proposed to choose a driving coordinate along a valley, to go a step in this direction, and to perform an energy optimization of the residual coordinates [3].…”

Section: Rgf Newton Trajectoriesmentioning

confidence: 99%

“…Any parameterization s of the RP xðsÞ ¼ ðx 1 ðsÞ; …; x n ðsÞÞ T is called reaction coordinate. We use here the distinguished or driven coordinate method [3,4] in the modern form of RGF [5,6], also called Newton trajectory (NT).…”

Section: Introductionmentioning

confidence: 99%

Reaction channels of the potential energy surface: application of Newton trajectories

Hirsch

Quapp

2004

Journal of Molecular Structure: THEOCHEM

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“…4 Recently, the method was transformed into a new mathematical form to RGF. 6,7,20 The concept is that a selected gradient direction is fixed along the curve x(s) g͑x͑s͒͒/͉g͑x͑s͉͒͒ ϭ r,…”

Section: Rgf Curvesmentioning

confidence: 99%

“…This curve is not a model for a minimum energy reaction path. The turning point case 4,17,21 divides RGFs into those which can serve as loose RPs, and others: if the RGF does not contain a TP at the pathway from minimum up to the SP, it may be used as an RP model. 22 (However, in any case, an RGF curve may serve for a predynamical trajectory of a reaction.…”

Section: Rgf Curvesmentioning

confidence: 99%

“…How a reaction path ascends to the SP is an uncertainty of the RP definition. We use here the intrinsic reaction coordinate (IRC), 3 the distinguished or driven coordinate method 4,5 in the modern form of reduced gradient following (RGF), 6,7 and the gradient extremal (GE). 8 We insist that the search for an appropriate MEP is not necessarily equivalent to the finding of the steepest descent (SD) pathway from the SP.…”

Section: Introductionmentioning

confidence: 99%

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Reaction pathways and projection operators: Application to string methods

Quapp

2004

J Comput Chem

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Abstract:The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of diverse projection operators for the intrinsic reaction coordinate (IRC), for the following of the reduced gradient (RGF) or Newton trajectory (NT), and for the Gradient Extremal (GE). We describe different numerical schemes for the definitions in the context of string methods. It comes out that Newton trajectories are the best ansatz for a string method.

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Searching for saddle points of potential energy surfaces by following a reduced gradient

et al. 1998

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The old coordinate driving procedure to find transition structures in chemical systems is revisited. The well‐known gradient criterion, ∇E(x)=0, which defines the stationary points of the potential energy surface (PES), is reduced by one equation corresponding to one search direction. In this manner, abstract curves can be defined connecting stationary points of the PES. Starting at a given minimum, one follows a well‐selected coordinate to reach the saddle of interest. Usually, but not necessarily, this coordinate will be related to the reaction progress. The method, called reduced gradient following (RGF), locally has an explicit analytical definition. We present a predictor–corrector method for tracing such curves. RGF uses the gradient and the Hessian matrix or updates of the latter at every curve point. For the purpose of testing a whole surface, the six‐dimensional PES of formaldehyde, H2CO, was explored by RGF using the restricted Hartree–Fock (RHF) method and the STO‐3G basis set. Forty‐nine minima and saddle points of different indices were found. At least seven stationary points representing bonded structures were detected in addition to those located using another search algorithm on the same level of theory. Further examples are the localization of the saddle for the HCN⇌CNH isomerization (used for steplength tests) and for the ring closure of azidoazomethine to 1H‐tetrazole. The results show that following the reduced gradient may represent a serious alternative to other methods used to locate saddle points in quantum chemistry. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1087–1100, 1998

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Use and abuse of the distinguished-coordinate method for transition-state structure searching

Cited by 86 publications

References 28 publications

Reaction channels of the potential energy surface: application of Newton trajectories

Reaction channels of the potential energy surface: application of Newton trajectories

Reaction pathways and projection operators: Application to string methods

Searching for saddle points of potential energy surfaces by following a reduced gradient

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