Transition state determination by the X-method

Mezey, Paul G.; Peterson, Michael R.; Csizmadia, Imre G.

doi:10.1139/v77-407

Cited by 17 publications

(3 citation statements)

References 6 publications

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“…13 Fitting of (x, y ) sets to E ( X , y ) according to eq. (6) using the data in Table I11 gives Since the reaction path is the line bisecting the angle formed by these level lines13 (Fig.…”

Section: Resultsmentioning

confidence: 99%

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A MINDO/3 study of the hetero‐Diels–Alder reaction

1984

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The transition states involved in the hetero-Diels-Alder reactions of acrylaldehyde-ethylene and butadiene-formaldehyde systems were characterized using an efficient method of locating a saddle point on the energy surface of two coordinates calculated with MIND0/3 method. It has been shown that parallel transition and rotation of the conjugate coordinate frame lead to the reaction and orthogonal coordinate system on the hyperbolic paraboloid energy surface. It was concluded that the method we adopted is similar to the "X-method" but is much simpler to apply to real reaction systems.The Diels-Alder reaction has been a subject of numerous experimental and theoretical investigations. Theoretically various MO approaches, such as intermolecular orbital (IMO), perturbation molecular orbital (PMO), and frontier molecular orbital (FMO) methods, have been applied in rationalizing regio-and stereo-selectivities, as well as in elucidating reactivity and mechanism of the Diels-Alder reactions.'P2 Theoretical characterization of the transition state (TS) has been hampered, however, due to the multicenter nature of the reaction, for which more than one independent reaction coordinates3 are normally required. In the Diels-Alder addition of butadiene and ethylene, the symmetry of the molecules involved suggests, and indeed was found,4 that the distances between the corresponding terminal carbons of the two molecules remain equal during the reaction; for this case the reaction coordinate can be reduced to one. Burke, Leroy, and Sana4 reported the results of the ab initio MO calculations on the potential energy hypersurface of the super-system formed in the cycloaddition of ethylene to butadiene using the distance between reacting terminal carbons of the two molecules as the reaction coordinate. Their conclusion of symmetrical bond formation at the TS has, however, been questioned by Dewar, Olivella, and Rzepa, who have claimed that their MIND0/3 calculations predict the unsymmetrical ~tructure.~In a hetero-Diels-Alder reaction involving addition of a molecule with a terminal hetero atom, *Determination of reactivity by MO theory (Part 31). the two reaction centers become asymmetric, and hence it is convenient to adopt two independent reaction coordinates in locating the saddle point.In this work we report on the characterization of the transition state involved in the heteroDiels-Alder addition of acrylaldehyde-ethylene and butadiene-formaldehyde using an efficient method of locating a saddle point on the energy surface of the two coordinates. METHODIf we let denote a set of molecular coordinates and E the potential energy, then E ( X , y ) of eq. ( 1 ) defines a constrained minimum energy surface with respect to the two coordinates, x and y in so f a r as the molecular system is constrained to achieve an energy minimum6 regarding the remaining n -2 coordinates. Above the two dimensional plane (x, y ) , E ( X , y ) forms an energy surface, lines connecting equal values of E( x , y ) forming contours.The problem of finding a sadd...

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Section: Resultsmentioning

confidence: 99%

“…This is really the condition that the saddle point can be located, since otherwise the two level lines are either imaginary or coalesce to a single line. 13 Fitting of (x, y ) sets to E ( X , y ) according to eq. (6) using the data in Table I11 gives Substitution of these into eq.…”

Section: _ --mentioning

confidence: 99%

A MINDO/3 study of the hetero‐Diels–Alder reaction

1984

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“…Figure 14 shows the pseudo-convexity boundary on the MB potential. At the StPs of index one the boundary forms an "X" which was proposed for a leading line to find such SPs [1,27].…”

Section: Pseudo-convexity Indexmentioning

confidence: 99%

Reaction Pathways and Convexity of the Potential Energy Surface: Application of Newton Trajectories

Hirsch

Quapp

2004

Journal of Mathematical Chemistry

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The reaction path is an important concept of theoretical chemistry. We employ the definitions of the intrinsic reaction coordinate (IRC), the gradient extremal (GE), and the Newton trajectory (NT). The usual imagination in chemistry is that a minimum energy path is in a convex region of the potential energy surface. We describe different schemes of convexity to handle the situation. It comes out that NTs are the best ansatz for the problem: NTs, which monotonically increase (or monotonically decrease), are automatically strictly pseudo-convex throughout, and they go throughout along a valley between minimum and saddle point.

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Reaktionswege auf mehrdimensionalen Energiehyperflächen

Müller

1980

Angewandte Chemie

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Die theoretische Erorterung einer chemischen Reaktion erfordert detaillierte Kenntnis der potentiellen Energie eines molekularen Systems. Als erstes mussen Reaktionswege minimaler Energie auf der im allgemeinen vieldimensionalen Molekulpotentialflache berechnet werden. Bereits bei diesem ersten Schritt stoBt man auf Probleme, die erst in den letzten Jahren befriedigend gelost worden sind. Anhand eines zweiparametrigen Modellpotentials werden die Schwierigkeiten und ihre Uberwindung durch mehrere Verfahren erlautert. Drei chemische Beispiele illustrieren Notwendigkeit und Nutzen, aber auch derzeitige Moglichkeiten und Grenzen von solchen theoretischen Behandlungen.

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Transition state determination by the X-method

Cited by 17 publications

References 6 publications

A MINDO/3 study of the hetero‐Diels–Alder reaction

A MINDO/3 study of the hetero‐Diels–Alder reaction

Reaction Pathways and Convexity of the Potential Energy Surface: Application of Newton Trajectories

Reaktionswege auf mehrdimensionalen Energiehyperflächen

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