Nuclear tunnelling applied

The Bruno and Bialik, (1992) theory which takes into account nuclear tunneling (Section 4.2.1), was applied to an analysis of anomalous Schaad-Swain exponents in a reaction catalyzed by bovine serum amine oxidase, BSAO (Grant and Klinman, 1989). The isotope effect in this reaction is found to be markedly larger than one, expected classically. Theoretical values of H/T and D/T KIFs and its temperature dependence match Grant and Klinman s experimental data. 

In 1976 TET was first applied to H abstractions [53]. One year later Suhnel [54] used TET to explain radiationless transitions in indigoid compounds, and Phillips [55] tested the harmonic approximation used by the theory in H abstractions. CT interactions [56] and substituent effects [57] in H abstractions were also addressed, as well as H abstractions by uranyl ion [58]. Support for TET also came from the demonstration [59] that in radiationless transitions theories, some Franck-Condon factors may be expressed by a nuclear tunneling formula like the TET one. 

Later, Falk [66] used TET to explain the photoisomerization of pyrrole pigments. Markov [67] applied the theory to photoketonization of dicarbonylic compounds. Hamanoue [68] showed that TET predictions were consistent with the relative reactivity of (n, n ) and (n, Tt ) states of an-thraquinones. Following a suggestion by Isaacs [69], Okamoto [70] claimed that the increase in the KIE of the H abstraction of methanol by benzo-phenone was evidence for a nuclear tunnelling mechanism, but this claim is not entirely consistent with the predictions of Isaacs. Shizuka [71] proposed TET could be used to explain excited state proton transfers, but this may only be the case for intramolecular proton transfers or reactions in apolar solvents, otherwise the system effective reduced mass will be too high [72]. 

Meanwhile new criteria to distinguish between thermal activation and nuclear tunnelling mechanisms in the photochemistry of ketones was proposed [74]. This criteria is based on the influence of spin-orbit coupling on the crossing probability, P, at the crossing w. The experimental test of this criteria showed nuclear tunnelling is the dominant mechanism in H abstractions [75]. TET was then applied to Norrish type I reactions [76]. 

Another factor of which a nonclassical theory must take account is the quantisation of the internal modes of D and A, and the consequent relaxation of the Bom-Oppenheimer constraint that the electron must transfer within a fixed nuclear framework. In classical theory, the vibrational modes of D and A are treated as classical harmonic oscillators, but in reality their quantisation is usually significant (that is, one or more of the vibration frequencies v is sufficiently high that the classical limit hv IcT does not apply). Electron transfer then requires the overlap, not only of the electronic wavefunctions of R and P, but also of their vibrational wavefunctions. It is then possible that nuclear tunnelling may assist electron transfer. As shown in Fig. 4.12, the vibrational wave-functions of R and P extend beyond the classical parabolas and overlap to some extent. This permits nuclear tunnelling from the R to the P surface, particularly in the region just below the classical intersection point. Part of the reorganisation of D and A, required prior to ET in the classical picture, may then occur simultaneously withET, by the nuclei tunnelling short (typically < 0.1 A) distances from their R to their P positions. 

R. Atkinson and F. Houtermans apply Gamow s theory of potential barrier penetration by quantum tunnelling to suggest how stars can release nuclear energy by synthesis of hydrogen into helium by an (unspecified) cyclic process. 

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

A strict quantum mechanical calculation of a tunneling system the size of a protein quickly becomes intractably complex. Fortunately, relatively simple theory has been successful at organizing and predicting electron tunneling rates in proteins. When the donor and acceptor redox centers are well separated, non-adiabatic electron transfer theory applies Fermiis Golden Rule, in which the rate of electron transfer is proportional to two terms, one electronic. Hah, and the other nuclear, FC (Devault, 1980). 

Applying Fermiis golden rule, the rate of the electron transfer reaction is determined by the product of the probability of the nuclear transition occurring (the Franck-Condon term, FC)) and the probability of the electron tunnelling occurring ... 

W(f 77) holds all the informahon about electron tunneling, overpotential, and environmental nuclear reorganizahon. The following equations apply broadly [39-41, 60] ... 

This chapter shows the coupled thermal, hydraulic and mechanical behavior in the near field by using THAMES that is the finite element simulator originally developed by Ohnishi et al (1985). It was applied to the near field mesh shown as Figure 2. The model domain is corresponding to the shaded area shown in Figure 1. It is assumed that tunnel interval is 10 m and pit interval is 4.4 m following the Japan Nuclear Cycle Development Institute H12 report (JNC(1999)). 

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