Dynamic vibronic problem

Here, Q is the nuclear quadrupole moment (Fe " "), 3(Fe +) and (Fe +), 3(Fe +) are the mean values of the electric field gradients and isomeric shifts for Fe and Fe ions. The coefficients Uvn and a n are found from the solution of the dynamic vibronic problem for the arbitrary values of ct(T). The expressions for and can be obtained by means of the substitution -o- The total Mossbauer spectrum F(Q) was obtained summing the spectra yielded by different cluster vibronic states in the molecular field, taking into account their equilibrium... 

Dynamic Vibronic Problem of tbe Valence-Tautomeric Interconversion in Cobalt Compounds... 

Dynamic Vibronic Problem for a Valence Tautomeric System... 

ABBA molecules, 631-633 HCCS radical, 633-640 perturbative handling, 641-646 theoretical principles, 625-633 Hamiltonian equation, 626-628 vibronic problem, 628-631 Thouless determinantal wave function, electron nuclear dynamics (END) ... 

The formulation outlined above allows for a simple stochastic implementation of the deterministic differential equation (35). Starting with an ensemble of trajectories on a given adiabatic PES W, at each time step At we (i) compute the transition probability pk k, (h) compare it to a random number ( e [0,1], and (iii) perform a hop if pt t > C- In Ih se of a pure A -level system (i.e., in the absence of nuclear dynamics), the assumption (37) holds in general, and the stochastic modeling of Eq. (35) is exact. Considering a vibronic problem with coordinate-dependent however, it can be shown that the electronic... 

It is very likely that the metal-insulator transition, the unusual catalytic properties, the unusual degree of chemical reactivity, and perhaps even some of the ultramagnetic properties of metal clusters are all linked intimately with the dynamic, vibronic processes inherent in these systems. Consequently, the combination of pump-probe spectroscopy on the femtosecond time scale with theoretical calculations of wavepacket propagation on just this scale offers a tantalizing way to address this class of problems [5]. Here we describe the application of these methods to several kinds of metal clusters with applications to some specific, typical systems first, to the simplest examples of unperturbed dimers then, to trimers, in which internal vibrational redistribution (IVR) starts to play a central role and finally, to larger clusters, where dissociative processes become dominant. 

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]. 

On the contrary, the semiclassical approach in the problem of the optical absorption is restricted to a great extent and the adequate description of the phonon-assisted optical bands with a complicated structure caused by the dynamic JTE cannot be done in the framework of this approach [13]. An expressive example is represented by the two-humped absorption band of A —> E <8> e transition. The dip of absorption curve for A —> E <8> e transition to zero has no physical meaning because of the invalidity of the semiclassical approximation for this spectral range due to essentially quantum nature of the density of the vibronic states in the conical intersection of the adiabatic surface. This result is peculiar for the resonance (optical) phenomena in JT systems full discussion of the condition of the applicability of the adiabatic approximation is given in Ref. [13]. 

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