Conical intersection, nonadiabatic quantum dynamics

Thoss M, MUler WH, Stock G (2000) Semiclassical description of nonadiabatic quantum dynamics AppUcation to the Si - S conical intersection in pyrazine. J Chem Phys 112 10282-10292... 

Assmann M, Worth GA, Gonzflez L (2012) 9D nonadiabatic quantum dynamics through a four-state conical intersection investigating the homolysis of the 0-0 bond in anthracene-9,10-endoperoxide. J Chem Phys 137 22A524... 

As a last example of a molecular system exhibiting nonadiabatic dynamics caused by a conical intersection, we consider a model that recently has been proposed by Seidner and Domcke to describe ultrafast cis-trans isomerization processes in unsaturated hydrocarbons [172]. Photochemical reactions of this type are known to involve large-amplitode motion on coupled potential-energy surfaces [169], thus representing another stringent test for a mixed quantum-classical description that is complementary to Models 1 and II. A number of theoretical investigations, including quantum wave-packet studies [163, 164, 172], time-resolved pump-probe spectra [164, 181], and various mixed... 

Basic questions are analyzed, as is the case for the photochemistry of formaldehyde. Contrary to previous results, direct quantum dynamics simulations showed that the H2 + CO H + HCO branching ratio in the Si/Sq nonadiabatic photodissociation of formaldehyde is controlled by the direction and size of the mean momentum of the wavepacket when it crosses the seam of conical intersection. In practice, if the wavepacket falls down from the barrier to the conical intersection with no initial momentum the system leads to H2 + CO, while an extra momentum toward products favors... 

The examples collected for this survey of femtosecond nonadiabatic dynamics at conical intersections illustrate the interesting interplay of coherent vibrational motion, vibrational energy relaxation and electronic transitions within a fully microscopic quantum mechanical description. It is remarkable that irreversible population and phase relaxation processes are so clearly developed in systems with just three or four nuclear degrees of freedom. 

The goal of this review is to critically compare — from both a concep-tional and a practical point of view — various MQC strategies to describe non-Born-Oppenheimer dynamics. Owing to personal preferences, we will focus on the modeling of ultrafast bound-state processes following photoexcitation such as internal-conversion and nonadiabatic photoisomerization. To this end, Sec. 2 introduces three model problems Model I represents a three-mode description of the Si — S2 conical intersection in pyrazine. Model II accounts for the ultrafast C B X internal-conversion process in the benzene cation, and Model III represents a three-mode description of ultrafast photoisomerization triggered by a conical intersection. Allowing for exact quantum-mechanical reference calculations, all models have been used as benchmark problems to study approximate descriptions. 

As explained in the Introduction, one needs to distinguish the following kinds of surface hopping (SH) methods (i) Semiclassical theories based on a connection ansatz of the WKB wave function, " (ii) stochastic implementations of a given deterministic multistate differential equation, e.g. the quantum-classical Liouville equation, and (iii) quasiclassical models such as the well-known SH schemes of Tully and others. " In this chapter, we focus on the latter type of SH method, which has turned out to be the most popular approach to describe nonadiabatic dynamics at conical intersections. 

The mapping procedure introduced in Sec. 6 results in a quantum-mechanical Hamiltonian with a well-defined classical limit, and therefore extends the applicability of the established semiclassical approaches to nonadiabatic dynamics. The thus obtained semiclassical version of the mapping approach, as well as the equivalent formulation that is obtained by requantizing the classical electron analog model of Meyer and Miller, have been applied to a variety of systems with nonadiabatic dynamics in the recent years. It appears that this approach is so far the only fully semiclassical method that allows a numerical treatment of truly multidimensional nonadiabatic dynamics at conical intersections. 

Koppel H, Schubert B, Lischka H (2008) Conical intersections and strong nonadiabatic coupling effects in singlet-excited acetylene an ab initio quantum dynamical study. Chem Phys 343 319... 

The topography of the cone affects the system s dynamics. Simple classic arguments can rationalize the way topography affects a trajectory Vertical cones facilitate transitions from the upper surface to the lower surface whereas tilted cones are less efficient. Actual quantum mechanical calculations have confirmed these generalizations. " The efficacy of a conical intersection in promoting a nonadiabatic transition reflects the topography in the vicinity of a conical intersection. ... 

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