Conical intersection, nonadiabatic quantum

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... 

Nonadiabatic events (transition from the excited state to the ground state at the conical intersection) pose a serious challenge because the nonadiabatic transition is rigorously quantum mechanical without a well-defined classical analog. At a simple level of theory13 (we return to a better treatment subsequently), the probability of a surface hop is given as follows ... 

In the fourth part, we study the effect of Cl on IC. It was applied to study the TtTt ->nTT transition of the pyrazine molecule. In this nonadiabatic process, the Cl of the TCK and nir PESs is believed to play a major role in the nonadiabatic fs transition. In fact, the Cl has been widely proposed to play the key factor in an IC, and quantum trajectory calculations have been used to calculate the IC rates [45]. However, this method cannot properly take into account of the initial conditions of the population and coherence of the system created by the fs pumping laser. In this chapter, we propose to develop a method to calculate the IC with conical intersections. It should be known that for the IC between Si and So in most molecules (in these cases, the energy gap between and So is of several eV), the surface crossings do not take place due to the anharmonic effect in the two PESs. Thus, the Cl should not play any role in these cases. We have proposed one method to calculate the IC rate of mt of the pyrazine molecule. The... 

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. 

When the quadratic coupling terms in Eq. (3) are included, the rotational symmetry of the potential surfaces in Eq. (4) is lost and replaced by a threefold symmetry inherent to systems with a threefold rotation axis. Consequently, j ceases to be a good quantum number and the spectra of the linear E e JT system for individual j become mixed . This inherently two-dimensional vibronic motion leads to a complicated, erratic line structure (see, for example, Ref. 21) as is typical for other, less symmetric conical intersections discussed throughout this book. The above statements about adiabatic and nonadiabatic behavior for i < 0 and E > 0, and the formation of broad quasi-resonances arising from the upper cone vibrational levels, are not affected by the inclusion of quadratic coupling terms. 

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. 

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... 

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