Tunneling radiationless

Next, let the focus be on one of the chosen ions, say, Fe3, and its hydration sheath (somewhat distorted by adsorption in the double layer). The energy levels in this ion at 300 K are predominantly in the ground state. Because the tunneling of the electron to the ion is taken to occur from the Fermi level of the metal and to be radiationless, the energy states in the ion are the ones of interest for electron transfer. This means that the electrons will be likely to find a home only in electronic states of the hydrated Fe3 ion, well above the ground state. 

However, and this was the essence of Levich s view, any given ion would suffer fluctuations in its electrostatic interactions—brief moments in which the ion s energy would be made more positive, less stable—and thus bring the energy levels of an ion adsorbed at an electrode into the range of the Fermi energy of electrons in the metal so that radiationless electron tunneling for electrons could occur. 

Totally deuterated aromatic hydrocarbons yield measured phosphorescence lifetimes greater than their protonated analogs.182 This behavior is ascribed to the closer spacing of vibrational levels in deuterated compounds with a consequent decrease in probability for nonradiative T -> S0 transitions. Quantum mechanical tunnelling may also contribute to the rate of the radiationless process with the normal compounds. 

Discussing theoretical approaches, it is also necessary to note the application [54] of the radiationless theory to describe the tunneling of hydrogen atoms in condensed media. 

Electron transfer from the excited states of Fe(II) to the H30 f cation in aqueous solutions of H2S04 which results in the formation of Fe(III) and of H atoms has been studied by Korolev and Bazhin [36, 37]. The quantum yield of the formation of Fe(III) in 5.5 M H2S04 at 77 K has been found to be only two times smaller than at room temperature. Photo-oxidation of Fe(II) is also observed at 4.2 K. The actual very weak dependence of the efficiency of Fe(II) photo-oxidation on temperature points to the tunneling mechanism of this process [36, 37]. Bazhin and Korolev [38], have made a detailed theoretical analysis in terms of the theory of radiationless transitions of the mechanism of electron transfer from the excited ions Fe(II) to H30 1 in solutions. In this work a simple way is suggested for an a priori estimation of the maximum possible distance, RmSiX, of tunneling between a donor and an acceptor in solid matrices. This method is based on taking into account the dependence... 

Fig. 1.2. Schematic illustration of electronic (a) and vibrational (b) predissociation. In the first case, the molecule undergoes a radiationless transition (rt) from the binding to the repulsive state and subsequently decays. In the second case, the photon creates a quasi-bound state in the potential well which decays either by tunneling (tn) or by internal energy redistribution (IVR).

Chapter 3 describes radiationless transitions in the tunneling electron transfers in multi-electron systems. The following are examined within the framework of electron Green s function approach the dependence on distance, the influence of crystalline media, and the effect of intermediate particles on the tunneling transfer. It is demonstrated that the Born-Oppenheimer approximation for the wave function is invalid for longdistance tunneling. 

Processes at electrodes are radiationless. Therefore energy levels at the Fermi level in the metal must be matched with suitable vacant (LUMO) or occupied (HOMO) orbitals in the reactant, depending on the direction of charge transfer, for significant rates of charge transfer to occur (Fig. 1). Normally an applied, or spontaneously generated, potential is required to modify the electron work function to some value eV to achieve this condition of balance (Fig. 1) required for facile electron transfer to take place at the potential V, usually by tunneling. 

This review shows how the photochemistry of ketones can be rationalized through a single model, the Tunnel Effect Theory (TET), which treats reactions of ketones as radiationless transitions from reactant to product potential energy curves (PEC). Two critical approximations are involved in the development of this theory (i) the representation of reactants and products as diatomic harmonic oscillators of appropriate reduced masses and force constants (ii) the definition of a unidimensional reaction coordinate (RC) as the sum of the reactant and product bond distensions to the transition state. Within these approximations, TET is used to calculate the reactivity parameters of the most important photoreactions of ketones, using only a partially adjustable parameter, whose physical meaning is well understood and which admits only predictable variations. 

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. 

Although not directly related to TET, Scaiano [63] had also obtained linear Arrhenius plots in the 227-313 K range and KIE of 3 for 2 -methylacetophenone photoenolization, and concluded that thermal activation was dominant for this reaction. However, it was later shown that tunnelling was the dominant mechanism for this and other related reactions [64], which clearly show nonlinear Arrhenius plots at lower temperatures and a KIE of 150 at 180K. Marcantonatos exciplex mechanism was also shown to be inconsistent with experimental data on uranyl ion quenching and the role of radiationless transitions was emphasized [65]. 

The near identity of the geometry in the E and A2 states means that the weak coupling limit of radiationless transition theory, in which represents a tunnelling rate, is applicable [15]. In this theory three parameters are important, the E — A2 energy gap (A ), the energy of the high-frequency... 

A recent tunneling effect model for radiationless transitions (198) has been applied to benzene and other aromatic hydrocarbons. The CH stretching vibrations are considered as dominant for the non-radiatlve process. Rate constants for the radiationless process Sg calculated by theory are of the same order of magni-... 

Deuteratlon of 2 -OH reduces rip (Table 5). If no Impurity effects are Involved, this would indicate that either the rate of S S is reduced or that radiationless deactivation is enhanced, the latter effect differing from the usual effect of deuteratlon. No measureable activation energy is needed to pass from S to S, since rip at 7°K is decreased only by about 35 percent both in the H and the D product. Proton tunneling is, therefore, proposed as the mechanism for Interconversion. 

In the quantum-mechanical theories the intersection of the potential energy surfaces is deemphasized and the electron transfer is treated as a radiationless transition between the reactant and product state. Time dependent perturbation theory is used and the restrictions on the nuclear configurations for electron transfer are measured by the square of the overlap of the vibrational wave functions of the reactants and products, i.e. by the Franck-Condon factors for the transition. Classical and quantum mechanical description converge at higher temperature96. At lower temperature the latter theory predicts higher rates than the former as nuclear tunneling is taken into account. 

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