Nonadiabatic Theories

Seidner L, Stock G and Domcke W 1995 Nonperturbative approach to femtosecond spectroscopy - general theory and application to multidimensional nonadiabatic photoisomerization processes J. Chem. Phys. 103 4002... 

Kolos W and Wolniewicz L 1963 Nonadiabatic theory for diatomic molecules and its application to the hydrogen molecule Rev. Mod. Phys. 35 473-83... 

Yarkony D R 1995 Electronic structure aspects of nonadiabatic processes in polyatomic systems Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 642-721... 

Sun X, Wang H B and Miller W H 1998 Semiclassical theory of electronically nonadiabatic dynamics Results of a linearized approximation to the initial value representation J. Chem. Phys. 109 7064... 

Hammes-Schiffer S and Tully J C 1995 Nonadiabatic transition state theory and multiple potential energy surfaces molecular dynamics of infrequent events J. Chem. Phys. 103 8528... 

Zhu C and Nakamura H 1994 Theory of nonadiabatic transition for general curved potentials I. J. Chem. Phys. 101 10 630... 

Obviously, the BO or the adiabatic states only serve as a basis, albeit a useful basis if they are determined accurately, for such evolving states, and one may ask whether another, less costly, basis could be Just as useful. The electron nuclear dynamics (END) theory [1-4] treats the simultaneous dynamics of electrons and nuclei and may be characterized as a time-dependent, fully nonadiabatic approach to direct dynamics. The END equations that approximate the time-dependent Schrddinger equation are derived by employing the time-dependent variational principle (TDVP). 

B. H. Lengsfield and D. R. Yarkony, Nonadiabatic Interactions Between Potential Energy Surfaces Theory and Applications, in State-Selected and State to State Ion-Molecule Reaction Dynamics Part 2 Theory, M. Baer and C.-Y. Ng, eds., John Wiley Sons, Inc., New York, 1992, Vol, 82, pp. 1-71. 

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... 

Now we make the usual assumption in nonadiabatic transition theory that non-adiabaticity is essential only in the vicinity of the crossing point where e(Qc) = 0- Therefore, if the trajectory does not cross the dividing surface Q = Qc, its contribution to the path integral is to a good accuracy described by adiabatic approximation, i.e., e = ad Hence the real part of partition function, Zq is the same as in the adiabatic approximation. Then the rate constant may be written as... 

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. 

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. 

For example, the ZN theory, which overcomes all the defects of the Landau-Zener-Stueckelberg theory, can be incorporated into various simulation methods in order to clarify the mechanisms of dynamics in realistic molecular systems. Since the nonadiabatic coupling is a vector and thus we can always determine the relevant one-dimensional (ID) direction of the transition in multidimensional space, the 1D ZN theory can be usefully utilized. Furthermore, the comprehension of reaction mechanisms can be deepened, since the formulas are given in simple analytical expressions. Since it is not feasible to treat realistic large systems fully quantum mechanically, it would be appropriate to incorporate the ZN theory into some kind of semiclassical methods. The promising semiclassical methods are (1) the initial value... 

The ZN formulas can also be utihzed to formulate a theory for the direct evaluation of thermal rate constant of electronically nonadiabatic chemical reactions based on the idea of transition state theory [27]. This formulation can be further utilized to formulate a theory of electron transfer and an improvement of the celebrated Marcus formula can be done [28]. 

As discussed by Miller and co-workers [52,53], it is worthwhile to develop theories that enable us to evaluate thermal reaction rate constants directly and not to rely on the calculations of the most detailed scattering matrix or the state-to-state reaction probabihty. Here, our formulation of the nonadiabatic transition state theory is briefly described for the simplest case in which the transition state is created by potential surface crossing [27]. 

Figure 10. Arrhenius plot of the thermal rate constants for the 2D model system. Circles-full quantum results. Thick solid (dashed) curve present nonadiabatic transition state theory by using the seam surface [the minimum energy crossing point (MECP)] approximation. Thin solid and dashed curves are the same as the thick ones except that the classical partition functions are used. Taken from Ref. [27].

The nonadiabatic transition state theory given in the Section II.C, namely, Eq. (17), can be applied to the electron-transfer problem [28]. Since the electron transfer theory should be formulated in the free energy space, we introduce the... 

The electron transfer discussed above corresponds to the so-called normal case in which the NT type of nonadiabatic transition plays the essential role. There is another important case called inverted case, in which the LZ type of nonadiabatic transition plays a role. Since the ZN theory can describe this type of transition also, the corresponding electron-transfer theory can be formulated [114]. On the other hand, the realistic electron transfer occurs in solution and... 

Note again that the parameters of the optimal laser pulses can be estimated from the ZN theory of nonadiabatic transition regardless of the dimensionality of the system. 

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