Saddle points of index 2 on potential energy surfaces and their role in theoretical reactivity investigations

Heidrich, Dietmar; Quapp, Wolfgang

doi:10.1007/bf00532206

Cited by 57 publications

(50 citation statements)

References 18 publications

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“…Harding et al (39) have proposed that index-two (second-order) saddles (as well as conical intersections) might be of key significance in distinguishing between different dissociation mechanisms, because, according to the Murrell-Laidler theorem (57,114,115), an index-two saddle can be found between two index-one saddles defining nominally distinct DS. (We note that use of the term "theorem" in relation to the Murrell-Laidler work has no strict mathematical justification and that the notion of "between two points" in high dimensions requires a careful explanation.…”

Section: The Roaming Saddle and Its Role In Roamingmentioning

confidence: 99%

Roaming: A Phase Space Perspective

Mauguière

Collins

Kramer

et al. 2017

Annu. Rev. Phys. Chem.

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In this review we discuss the recently described roaming mechanism for chemical reactions from the point of view of nonlinear dynamical systems in phase space. The recognition of the roaming phenomenon shows the need for further developments in our fundamental understanding of basic reaction dynamics, as is made clear by considering some questions that cut across most studies of roaming: Is the dynamics statistical? Can transition state theory be applied to estimate roaming reaction rates? What role do saddle points on the potential energy surface play in explaining the behavior of roaming trajectories? How do we construct a dividing surface that is appropriate for describing the transformation from reactants to products for roaming trajectories? How should we define the roaming region? We show that the phase space perspective on reaction dynamics provides the setting in which these questions can be properly framed and answered. We illustrate these ideas by considering photodissociation of formaldehyde. The phase-space formulation allows an unambiguous description of all possible reactive events, which also allows us to uncover the phase space mechanism that explains which trajectories roam, as opposed to evolving toward a different reactive event.

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Section: The Roaming Saddle and Its Role In Roamingmentioning

confidence: 99%

Roaming: A Phase Space Perspective

Mauguière

Collins

Kramer

et al. 2017

Annu. Rev. Phys. Chem.

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“…[22][23][24][25]. More recently, index two [26][27][28] and higher index 29 saddles have been studied (see also Refs. [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Mauguière

Collins

Kramer

et al. 2016

The Journal of Chemical Physics

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We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories. C 2016 AIP Publishing LLC.[http://dx

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“…The negative second derivative corresponds to an unbound vibrational mode with a negative force constant and an imaginary frequency. A second‐order transition state has two unbound normal vibrational modes with two imaginary frequencies 1–3.…”

Section: Introductionmentioning

confidence: 99%

Internal‐rotation and inversion potential energy surfaces for methylamine and methylphosphine

Kim

Zeroka

2007

Int J of Quantum Chemistry

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Using the HF, MP2, and DFT methods with a 6-311G** basis set, we examine the internal-rotation and inversion of the amino and phosphino groups in methylamine and methylphosphine. The resulting energy surfaces are reported as a function of rotation and inversion descriptors. Both surfaces are characterized by several special points: three minimum energy states, three first-order internal-rotation transition states, six first-order inversion transition states, and six second-order inversion transition states. The MP2 method gave better agreement with experiment. For methylamine, the MP2 energy barrier for internal-rotation is 8.73 kJ/mol; for firstorder inversion it is 22.80 kJ/mol and for second-order inversion it is 22.41 kJ/mol. For methylphosphine, the MP2 energy barriers are 7.53, 149.88, and 149.65 kJ/mol, respectively. The energy barriers include ZPE correction contributions. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem 108: 974 -982, 2008

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Saddle points of index 2 on potential energy surfaces and their role in theoretical reactivity investigations

Cited by 57 publications

References 18 publications

Roaming: A Phase Space Perspective

Roaming: A Phase Space Perspective

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

Internal‐rotation and inversion potential energy surfaces for methylamine and methylphosphine

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