Strategies, studying quantum

The capability to understand chemical reactions on the atomic scale and subsequently to design control strategies will be illustrated for pho-toinduced reactions via conical intersections. The ultrafast photochemical ring opening of cyclohexadiene, which occurs within 200 fs in gas as well as in condensed phase, is taken as an example. This reaction has been studied quantum chemically, by resonance-Raman spectroscopy and by femtosecond spectroscopy offering already a wealth of information. After photoexcitation to the S2 state, the molecule decays within a few femtoseconds to the S state, from where the relaxation to the ground state is mediated by at least two conical intersections. 

Summary Two strategies can be used to study highly reactive species. One is kinetic stabilization by bulky groups. The other is the direct observation of the parent species under extreme conditions (matrix isolation techniques). The latter method has the advantage that the observed spectra can be correlated with the results of quantum chemical calculations. 

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

These results suggest a computational strategy for the study of reactions in condensed phases. One starts from some realistic intermolecular potentials and performs a molecular-dynamics-Kramers-Grote-Hynes scheme that consists of the following steps.First, we fix the proton at the transition state and run a MD simulation. The friction kernel y(t) is calculated and along with Eqs. (7,8) enables the calculation of the Grote-Hynes rate. This scheme has also been used as a means of obtaining input for quantum calculations as well. ... 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

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