A method for finding the ridge between saddle points applied to rare event rate estimates

Maronsson, Jón Bergmann; Jónsson, Hannes; Vegge, Tejs

doi:10.1039/c2cp23421a

Cited by 9 publications

(5 citation statements)

References 25 publications

(28 reference statements)

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“…( 7) numerically. In a different setting, the corrections to TST rates that are due to rank-2 saddles were recently estimated by Maronsson et al [40], who calculated the energy ridge that connects the rank-1 saddle to the rank-2 saddles. In contrast to ours, their method takes account of the precise shape of the potential along the ridge.…”

Section: B Calculation Of the Reaction Ratementioning

confidence: 99%

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

2012

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We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the "activated complex" that mediates the collapse of the condensate. For a certain value of the s-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetrybreaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows to smoothly pass the bifurcation.

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Section: B Calculation Of the Reaction Ratementioning

confidence: 99%

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

2012

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“…For cases where a suitable distinguished coordinate can be found that leads to a SPP that smoothly connects the first-and second-order saddle points, we expect that the SPP will serve as a useful starting point for a fully, variationally optimized, global dividing surface. We note that Maronsson et al 33 have recently reported a rigorous algorithm for following ridges between two first-order saddle points. These ridges can be considered as an analogue of the IRC, just as the distinguished coordinate SPP is the analogue of the MEP.…”

Section: Introductionmentioning

confidence: 97%

Separability of Tight and Roaming Pathways to Molecular Decomposition

2012

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Recent studies have questioned the separability of the tight and roaming mechanisms to molecular decomposition. We explore this issue for a variety of reactions including MgH(2) → Mg + H(2), NCN → CNN, H(2)CO → H(2) + CO, CH(3)CHO → CH(4) + CO, and HNNOH → N(2) + H(2)O. Our analysis focuses on the role of second-order saddle points in defining global dividing surfaces that encompass both tight and roaming first-order saddle points. The second-order saddle points define an energetic criterion for separability of the two mechanisms. Furthermore, plots of the differential contribution to the reactive flux along paths connecting the first- and second-order saddle points provide a dynamic criterion for separability. The minimum in the differential reactive flux in the neighborhood of the second-order saddle point plays the role of a mechanism divider, with the presence of a strong minimum indicating that the roaming and tight mechanisms are dynamically distinct. We show that the mechanism divider is often, but not always, associated with a second-order saddle point. For the formaldehyde and acetaldehyde reactions, we find that the minimum energy geometry on a conical intersection is associated with the mechanism divider for the tight and roaming processes. For HNNOH, we again find that the roaming and tight processes are dynamically separable but we find no intrinsic feature of the potential energy surface associated with the mechanism divider. Overall, our calculations suggest that roaming and tight mechanisms are generally separable over broad ranges of energy covering most kinetically relevant regimes.

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“…A recent paper of Maronsson et al (118) provides an algorithm for finding an index-two saddle point on a (1D) ridge connecting two index-one saddle points. Note that this algorithm does not prove that the existence of two index-one saddles implies that there is a ridge connecting them that contains an index-two saddle.…”

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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A method for finding the ridge between saddle points applied to rare event rate estimates

Cited by 9 publications

References 25 publications

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

Separability of Tight and Roaming Pathways to Molecular Decomposition

Roaming: A Phase Space Perspective

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