Classical electron analog model

On a purely classical level, it has been shown that the mapping formalism recovers the classical electron analog model of Meyer and Miller [89]. The Langer-hke modifications [101] that were empirically introduced in this model could be identified as a zero-point energy term that accounts for quantum fluctuations in the electronic DoF [102, 103]. This in practice quite important... 

Considering the semiclassical description of nonadiabatic dynamics, only the mapping approach [99, 100] and the equivalent formulation that is obtained by requantizing the classical electron analog model of Meyer and Miller [112] appear to be amenable to a numerical treatment via an initial-value representation [114, 116, 117, 121, 122]. Other semiclassical formulations such as Pechukas path-integral formulation [45] and the various connection... 

Particle-In-A-Box Model Classic mathematical analogy of the motion of an electron in an atomic orbital, subject to certain conditions, such as the requirement to have specific values at the limiting boundaries of the box. 

ReUance on simple classical electron coimting rules corresponds to an approximate description of the clamped cycle in terms of its annulene perimeter, and this is clearly insufficient. We can propose three perturbed perimeter models, whereby the simple perimeter annulene analogy is considered as the zeroth-order solution (Model 0) in a perturbative treatment. Model I includes the non-perimeter bonds perturbatively. Model II includes the perimeter heteroatoms perturbatively. Model III includes both (see Scheme 5). By means of these pictorial perturbative models (I, II and III) it is shown below that, when first-order corrections to the angular momentum character and orbital energies of the perimeter annulene (Model 0) are taken into account, it is possible, within the ipsocentric model, to give a unified rationalisation for the survival of the original ring current in XHXH clamped monocycles, and its extinction in HC = CH-clamped monocycles, even at the simple Hiickel level of theory. 

Next we model the laser-driven electron dynamics quantum mechanically to reveal analogies and differences to the simple classical model. In view of the SPODS mechanism, which is based on resonant interactions, we consider only two quantum states at hrst, the ground state and the resonantly excited state. Eor this purpose, we briehy recapitulate the relevant equations for a two-state system driven on... 

Let us consider a one-dimensional model system with coordinate R as illustrated in Figure 13.1. Vq(R) and Vi(R) are the potentials in the ground and in the excited electronic states and >i(R) represents the initial wavefunction. In analogy to Equation (6.3), the classical absorption cross section may be approximately written as... 

---