Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior

Manthe, Uwe; Köppel, Horst

doi:10.1063/1.459094

Cited by 172 publications

(130 citation statements)

References 36 publications

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“…The CI between the first two 2 A 0 states of the NO 2 molecule is known to lead to an extremely complex absorption spectra, [35][36][37] and has been the subject of numerous studies of nonadiabatic dynamics. [38][39][40][41][42][43][44] For C 2v geometries the two surfaces ( 2 A 1 and 2 B 2 ) intersect at a bond angle that depends on the bond length and form a one-dimensional CI seam. 39 The seam is located close to the bottom of the excited state and is readily accessible by a vibrational wavepacket launched onto the excited electronic surface from the Franck-Condon region of the ground state.…”

Section: Introductionmentioning

confidence: 99%

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

Arasaki

Wang

McKoy

et al. 2011

Phys. Chem. Chem. Phys.

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We have previously shown how femtosecond angle-and energy-resolved photoelectron spectroscopy can be used to monitor quantum wavepacket bifurcation at an avoided crossing or conical intersection and also how a symmetry-allowed conical intersection can be effectively morphed into an avoided crossing by photo-induced symmetry breaking. The latter result suggests that varying the parameters of a laser to modify a conical intersection might control the rate of passage of wavepackets through such regions, providing a gating process for different chemical products. In this paper, we show with full quantum mechanical calculations that such optical control of conical intersections can actually be monitored in real time with femtosecond angle-and energy-resolved photoelectron spectroscopy. In turn, this suggests that one can optimally control the gating process at a conical intersection by monitoring the photoelectron velocity map images, which should provide far more efficient and rapid optimal control than measuring the ratio of products. To demonstrate the sensitivity of time-resolved photoelectron spectra for detecting the consequences of such optical control, as well as for monitoring how the wavepacket bifurcation is affected by the control, we report results for quantum wavepackets going through the region of the symmetry-allowed conical intersection between the first two 2 A 0 states of NO 2 that is transformed to an avoided crossing. Geometry-and energy-dependent photoionization matrix elements are explicitly incorporated in these studies. Time-resolved photoelectron angular distributions and photoelectron images are seen to systematically reflect the effects of the control pulse.

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Section: Introductionmentioning

confidence: 99%

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

Arasaki

Wang

McKoy

et al. 2011

Phys. Chem. Chem. Phys.

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show abstract

“…This is an inter-esting effect, likely to be due to oscillations in the asymptotic probability which arise from the Hamiltonian part of the rate equation (57) . (We call attention to the discussion in section VI of [32], concerning the discrepancy of about the same magnitude and sense between their classical and computed asymptotic probabilities.) Trivially, the other diagonal matrix (ρ 22 ) tends to a value that is lower than its asymptotic value, since the two diagonal matrix elements add up to unity.…”

Section: A Lindblad-type Formalism For CImentioning

confidence: 99%

“…Ultimately, for "long" times of the order of picoseconds, the probability will tend to some asymptotic limit (say, P 1,∞ ) between 0 and 1. (Figures 1-4, in [32]. Actually, in any individual run it will slightly oscillate about the asymptotic probability.)…”

Section: A Simplified Formalism For CImentioning

confidence: 99%

“…(Following the notation of [32], we shall here denote these by Q 1 and Q c , the former being a "tuning" and the latter the "coupling" mode coordinate. They are actually two linearly independent combinations of the nuclear coordinates.)…”

Section: Descent Across a Conical Intersectionmentioning

confidence: 99%

“…Temporarily simplifying the situation of [32] to the case where there is only one tuning mode Q 1 , as well as the coupling mode Q c , we have for the two coordinates the following harmonic oscillator Hamiltonian:…”

Section: A Simplified Formalism For CImentioning

confidence: 99%

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A “square-root” method for the density matrix and its applications to Lindblad operators

Yahalom

Englman

2006

Physica A: Statistical Mechanics and its Applications

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The evolution of open systems, subject to both Hamiltonian and dissipative forces, is studied by writing the nm element of the time (t) dependent density matrix in the formThe so called "square root factors", the γ(t)'s, are non-square matrices and are averaged over A systems (α) of the ensemble. This square-root description is exact. Evolution equations are then postulated for the γ(t) factors, such as to reduce to the Lindblad-type evolution equations for the diagonal terms in the density matrix. For the off-diagonal terms they differ from the Lindblad-equations. The "square root factors" γ(t) are not unique and the equations for the γ(t)'s depend on the specific representation chosen. Two criteria can be suggested for fixing the choice of γ(t)'s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the γ(t) formalism and the Lindblad-equations. When the method is tested on cases which have been previously treated by other methods, our results agree with them. Examples chosen are (i) molecular systems, such that are either periodically driven 1 near level degeneracies, for which we calculate the decoherence occurring in multiple Landau-Zener transition, or else when undergoing descent around conical intersections in the potential surfaces, (ii) formal dissipative systems with Lindblad-type operators representing either a non-Markovian process or a two-state system coupled to bosons.Attractive features of the present factorization method are complete positivity, the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process.

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Valenzbindungsdiagramme – eine Hilfe zum Verständnis chemischer Reaktivität

Shaik

Shurki

1999

Angewandte Chemie

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Eine einheitliche Beschreibung chemischer Reaktivität ermöglichen Valenzbindungsdiagramme, wie sie im Bild schematisch für einen einfachen Fall (nur Reaktant‐ und Produktzustände müssen betrachtet werden) und ein komplexeres System (ein Zwischenzustand spielt ebenfalls eine wichtige Rolle) gezeigt sind (RC = Reaktionskoordinate). Ihre Anwendung wird an Reaktivitäts‐ und mechanistischen Problemen der organischen und metallorganischen Chemie demonstriert: In‐situ‐DNA‐Reparatur, C‐F‐ und C‐H‐Aktivierung, SRN2c‐Mechanismus, schrittweise vs. konzertierte Cycloaddition und vieles mehr.

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Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior

Cited by 172 publications

References 36 publications

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

A “square-root” method for the density matrix and its applications to Lindblad operators

Valenzbindungsdiagramme – eine Hilfe zum Verständnis chemischer Reaktivität

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