Potential energy surfaces nonadiabatic quantum dynamics

There are many facets to a successful quantum dynamics study. Of course, if comparison with experimental results is a goal, the underlying Bom-Oppenheimer potential energy surface must be known at an appropriately high level of electronic structure theory. For nonadiabatic problems, two or more surfaces and their couplings must be determined. The present chapter, however, focuses on the quantum dynamics of the nuclei once an adequate description of the electronic structure has been achieved. 

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... 

Finally, we consider the performance of the MFT method for nonadiabatic dynamics induced by avoided crossings of the respective potential energy surfaces. We start with the discussion of the one-mode model. Model IVa, describing ultrafast intramolecular electron transfer. The comparison of the MFT method (dashed line) with the quantum-mechanical results (full line) shown in Fig. 5 demonstrates that the MFT method gives a rather good description of the short-time dynamics (up to 50 fs) for this model. For longer times, however, the dynamics is reproduced only qualitatively. Also shown is the time evolution of the diabatic electronic coherence which, too, is... 

Thus this book describes the recent theories of chemical dynamics beyond the Born-Oppenheimer framework from a fundamental perspective of quantum wavepacket dynamics. To formulate these issues on a clear theoretical basis and to develop the novel theories beyond the Born-Oppenheimer approximation, however, we should first learn a basic classical and quantum nuclear dynamics on an adiabatic (the Born-Oppenheimer) potential energy surface. So we learn much from the classic theories of nonadiabatic transition such as the Landau-Zener theory and its variants. 

In the following sections we show how the quantum-classical Liouville equation and quantum-classical expressions for reaction rates can be deduced from the full quantum expressions. The formalism is then applied to the investigation of nonadiabatic proton transfer reactions in condensed phase polar solvents. A quantum-classical Liouville-based method for calculating linear and nonlinear vibrational spectra is then described, which involves nonequilibrium dynamics on multiple adiabatic potential energy surfaces. This method is then used to investigate the linear and third-order vibrational spectroscopy of a proton stretching mode in a solvated hydrogen-bonded complex. 

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