Energy spectrum transfer

It is relevant to note at this point that, because the metal ions are isoelcctronic, the spectra of low-spin Fe complexes might be expected to be similar to those of low-spin Co ". However, Fe" requires a much stronger crystal field to effect spin-pairing and the ligands which provide such a field also give rise to low-energy charge-transfer bands which almost always obscure the d-d bands. Nevertheless, the spectrum of the pale-yellow [Fe(CN)f,] shows a shoulder at... 

The energy spectrum of the dodecaborides (YB,2, YbB,2, LuBj2> computed by the MO-linear combination of atomic orbitals (LCAO) method shows that the direction of the electron transfer is uncertain". ... 

Let us consider a cathode electron transfer process at metal electrode. The role of the electron donor is played here by the metal electrode. The specific feature of this donor consists of the fact that its electron energy spectrum is practically continuous... 

An increase in sensitivity and reliability of chip analysis can also be achieved by using fluorescence resonance energy transfer (FRET). For this purpose both the probe and the target are labeled with a fluorophor. When the emission spectrum of the donor, e.g. Cy5, overlaps with the absorption spectrum of the acceptor, e.g. Cy5.5, and the donor and the acceptor are at a certain distance from each other, energy is transferred from the donor to the acceptor on excitation of the donor fluorophor. 

The theory of electron-transfer reactions presented in Chapter 6 was mainly based on classical statistical mechanics. While this treatment is reasonable for the reorganization of the outer sphere, the inner-sphere modes must strictly be treated by quantum mechanics. It is well known from infrared spectroscopy that molecular vibrational modes possess a discrete energy spectrum, and that at room temperature the spacing of these levels is usually larger than the thermal energy kT. Therefore we will reconsider electron-transfer reactions from a quantum-mechanical viewpoint that was first advanced by Levich and Dogonadze [1]. In this course we will rederive several of, the results of Chapter 6, show under which conditions they are valid, and obtain generalizations that account for the quantum nature of the inner-sphere modes. By necessity this chapter contains more mathematics than the others, but the calculations axe not particularly difficult. Readers who are not interested in the mathematical details can turn to the summary presented in Section 6. 

In order to understand the role of spectral energy transfer in determining the turbulent energy spectrum at high Reynolds numbers, it is useful to introduce the spectral energy transfer rate Tu(jc,t) defined by... 

As discussed in Section 2.1, in high-Reynolds-number turbulent flows the scalar dissipation rate is equal to the rate of energy transfer through the inertial range of the turbulence energy spectrum. The usual modeling approach is thus to use a transport equation for the transfer rate instead of the detailed balance equation for the dissipation rate derived from (1.27). Nevertheless, in order to understand better the small-scale physical phenomena that determine e, we will derive its transport equation starting from (2.99). 

In principle, the forward and backward transfer rates can be computed directly from DNS (see Appendix A). However, they are more easily computed by assuming idealized forms for the scalar energy spectrum (Fox 1995). In the general formulation (Fox 1999), they include both a forward cascade (a) and backscatter (/() ... 

Radiation quality is defined by the nature, charge, and energy spectrum of the particles and can be characterized by the linear energy transfer (LET) or, alternatively, by the micro-dosimetric spectra at the point of interest under the actual irradiation conditions. 

It is clear that the analysis outlined is only the first step in developing a satisfactory theory of photochemical reactions. For example, the energy spectrum studied is not typical of all photodecomposable molecules, it is possible that direct photoexcitation of the bond that breaks is most important in some reactions, and that intramolecular energy transfer is important in others, etc. Much more work will be required before we have complete understanding of even the simplest photodissociation reactions. 

The long lifetime of lower excited states favors the efficient transfer of electron excitation energy from molecules of the solvent to molecules of the solute, provided the emission spectrum of the donor overlaps the absorption spectrum of the acceptor. The mechanism of the nonradiative transfer of electron excitation energy was found by Forster and Dexter39-40. The distance over which the energy is transferred may be as large as 20-30 A. The migration of electron excitation also occurs in... 

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