Nonadiabatic tunneling theory

The problem of nonadiabatic tunneling in the Landau-Zener approximation has been solved by Ovchinnikova [1965]. For further refinements of the theory beyond this approximation see Laing et al. [1977], Holstein [1978], Coveney et al. [1985], Nakamura [1987]. The nonadiabatic transition probability for a more general case of dissipative tunneling is derived in appendix B. We quote here only the result for the dissipationless case obtained in the Landau-Zener limit. When < F (Xe), the total transition probability is the product of the adiabatic tunneling rate, calculated in the previous sections, and the Landau-Zener-Stueckelberg-like factor... 

C. Zhu and H. Nakamura, Theory of nonadiabatic transition for general two-state curve crossing problems. I Nonadiabatic tunneling case, J. Chem. Phys. 101 10630 (1994). 

For the nonadiabatic ET reactions, the upper adiabatic PES cannot be neglected. However, recent work shows that such reactions themselves may still be described by the adiabatic Hamiltonian eqn (12.24), although the nonadiabatic tunneling elfects should be properly incorporated. The mechanism is from the surface hopping proposed by Tully and Preston. One, therefore, may extend the quantum Kramers theory to the ET process. To do so, we make the normal mode analysis in the vicinity of the barrier of the potential in eqn (12.24). The standard procedure reads ... 

The theoretical treatments of nonadiabatic transitions and the formulation of hydrogen atom or proton tunnelling, as particular cases of such transitions, motivated various theoretical developments of CPET. In the simplest case, when only one initial and one final vibrational states are involved in the reaction, the CPET rate has been written in a form similar to that given by the nonadiabatic ET theory ... 

Multidimensional theory is not yet available, unformnately, not only for the nonadiabatic tunneling problem but also for general nonadiabatic transition problems. For practical applications, the Zhu-Nakamura formulas for transition amplitude including phases can be incorporated into classical or semiclassical propagation... 

Thebook reviews low-dimensional theories and clarifies their insufficiency conceptually and numerically. It also examines the phenomenon of nonadiabatic tunneling, which is common in molecular systems. The book describes applications to real polyatomic molecules, such as vinyl radicals and malonaldehyde, demonstrating the high efficiency and accuracy of the method. It discusses tunneling in chemical reactions, including theories for direct evaluation of reaction rate constants for both electronically adiabatic and nonadiabatic chemical reactions. In the final chapter, the authors touch on future perspectives. 

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

In 1989, Borgis and Hynes proposed a theory for nonadiabatic proton transfer that includes all the parameters contained with the DKL model. In addition, they addressed the important issue of low-frequency vibrations serving as promoting modes in proton tunneling [11]. For nonadiabatic proton transfer, the distance dependence of the tunneling coupling, C(Q), has the analytical form [13]... 

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