Spin systems, nonadiabatic quantum dynamics

Second, the mapping approach to nonadiabatic quantum dynamics is reviewed in Sections VI-VII. Based on an exact quantum-mechanical formulation, this approach allows us in several aspects to go beyond the scope of standard mixed quantum-classical methods. In particular, we study the classical phase space of a nonadiabatic system (including the discussion of vibronic periodic orbits) and the semiclassical description of nonadiabatic quantum mechanics via initial-value representations of the semiclassical propagator. The semiclassical spin-coherent state method and its close relation to the mapping approach is discussed in Section IX. Section X summarizes our results and concludes with some general remarks. 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

Considerable work has already been carried out using ab initio calculations to predict the photodissociation dynamics of gas-phase metal carbonyls (45). This is a fertile area for computational work, given the extensive experimental results available, which include the use of ultrafast methods to characterize the short time behavior in photoexcited states. There is considerable evidence that surface crossings, especially of a spin-forbidden nature, play a considerable part in the dynamics. Much of the theoretical work so far has focused on reduced-dimensionality models of the PESs, which have been used in quantum mechanical smdies of the nonadiabatic nuclear dynamics, in which spin-forbidden transitions are frequently observed (45). Here, too, the potential benefits to be derived from a proper understanding of the spin-state chemistry are considerable, due to the importance of light-induced processes in organometallic and bioinorganic systems. 

Decoherence is an essential concept appearing in a system in which a quantum subsystem contacts classical subsystem(s) in one way or another. As is widely recognized, the SET cannot describe this dynamics since there is no mechanism in it to switch off the electronic coherence along the nuclear path. The decoherence problem is critically important not only in our nonadiabatic dynamics but in other contemporary science such as spin-Boson dynamics in quantum computation theory and more extensively a quantum theory in open (dissipative) systems [147]. The decoherence problem is also critical to chaos induced by nonadiabatic djmamics [136, 137,182, 453, 454]. Therefore, in the rest of this section, we pay deeper attention to the aspect of the effect of electronic state decoherence strongly coupled with the relevant nuclear motion. A review about the notion of decoherence related to quantum mechanical measmement theory is found in the papers by Rossky et al. [53]. 

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