2011
DOI: 10.1007/s10910-011-9827-2
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Non-adiabatic transitions near avoided crossings: theory and numerics

Abstract: We present a review of rigorous mathematical results about nonadiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.

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Cited by 11 publications
(8 citation statements)
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“…then one has to expect that the coupling εF 12 (x * )η is either singular or approximately of the order one with respect to ε, and one obtains leading order non-adiabatic transitions between the eigenspaces. These transitions, which are ubiquituous for polyatomic molecules and explain spectacular chemical reactions as for example the first step of vision (the cis-trans isomerization of retinal in rhodopsin), have been discussed for the propagation of Hagedorn wave packets through actual crossings by Hagedorn (1994) and through avoided crossings in (Hagedorn 1998a, Hagedorn and Joye 1999a, Bourquin, Gradinaru and Hagedorn 2012. With respect to general initial data, the propagation of expectation values through conical intersections has been carried out in (Fermanian-Kammerer and Gérard 2002, Lasser and Teufel 2005, Fermanian Kammerer and Lasser 2008, while avoided crossings have been considered in (Fermanian Kammerer and Lasser 2017).…”
Section: More On Adiabatic Decouplingmentioning
confidence: 99%
“…then one has to expect that the coupling εF 12 (x * )η is either singular or approximately of the order one with respect to ε, and one obtains leading order non-adiabatic transitions between the eigenspaces. These transitions, which are ubiquituous for polyatomic molecules and explain spectacular chemical reactions as for example the first step of vision (the cis-trans isomerization of retinal in rhodopsin), have been discussed for the propagation of Hagedorn wave packets through actual crossings by Hagedorn (1994) and through avoided crossings in (Hagedorn 1998a, Hagedorn and Joye 1999a, Bourquin, Gradinaru and Hagedorn 2012. With respect to general initial data, the propagation of expectation values through conical intersections has been carried out in (Fermanian-Kammerer and Gérard 2002, Lasser and Teufel 2005, Fermanian Kammerer and Lasser 2008, while avoided crossings have been considered in (Fermanian Kammerer and Lasser 2017).…”
Section: More On Adiabatic Decouplingmentioning
confidence: 99%
“…then we have to expect that the coupling εF 12 (x * )η is either singular or approximately of order one with respect to ε, and we obtain leading-order non-adiabatic transitions between the eigenspaces. These transitions, which are ubiquitous for polyatomic molecules and explain spectacular chemical reactions, for example the first step of vision (the cis-trans isomerization of rhodopsin), were discussed for the propagation of Hagedorn wave packets through actual crossings by Hagedorn (1994) and through avoided crossings in Hagedorn (1998a), Hagedorn and Joye (1999a) and Bourquin, Gradinaru and Hagedorn (2012). With respect to general initial data, the propagation of expectation values through conical intersections was carried out in Fermanian-Kammerer and Gérard (2002), Lasser and Teufel (2005) and Fermanian Kammerer and , while avoided crossings were considered in Fermanian Kammerer and Lasser (2017).…”
Section: Systems Of Semiclassical Schrödinger Equationsmentioning
confidence: 99%
“…27. In the method proposed there one common set of parameters {q, p, Q, P, S}, propagated according to one, guiding, PES was used for the wave packets on all surfaces.…”
Section: Photodissociation Of Ibrmentioning
confidence: 99%