Oscillator strength acceptors

All of the examples of singlet energy transfer we have considered take place via the long-range resonance mechanism. When the oscillator strength of the acceptor is very small (for example, n-> n transitions) so that the Fdrster critical distance R0 approaches or is less than the collision diameter of the donor-acceptor pair, then all evidence indicates that the transfer takes place at a diffusion-controlled rate. Consequently, the transfer mechanism should involve exchange as well as Coulomb interaction. Good examples of this type of transfer have been provided by Dubois and co-workers.(47-49)... 

In Eq. (4.5) the donor emission spectrum/ and the acceptor absorption spectrum eA are separately normalized to unity, so that the transfer rate is independent of the oscillator strength of either transition. Unfortunately, the constants W and L are not easily determined by experiment. Nevertheless, an exponential dependence on the distance is expected. It should be noted that this type of transfer involves extensive orbital overlap and is guided by Wigner s (1927) spin rule. 

When located at opposite ends (or at conjugated positions) in a molecular system, a donor and an acceptor do more than simply add up their separate effects. A cooperative phenomenon shows up, involving the entire disubstituted molecule, known as charge transfer (C.T.). Such compounds are colored (from pale yellow to red, absorption from 3,000 to 5,000 A) and show high U.V. absorption oscillator strength. "Figure 2 helps understand the enhancement of optical nonlinearity in such a system. 

Equation (4.79) shows that Ro, and consequently the transfer rate, is independent of the donor oscillator strength but depends on the acceptor oscillator strength and on the spectral overlap. Therefore, provided that the acceptor transition is allowed (spin conservation) and its absorption spectrum overlaps the donor fluorescence spectrum, the following types of energy transfer are possible ... 

In this expansion the dipole-dipole term is the most prominent if donor-acceptor distance R is not too small. The dipole-dipole term represents the interaction between the transition dipole moments Md and MA of donor and acceptor molecules, respectively. The square of these transition dipoles is proportional to the oscillator strengths fy> and fA for radiative transitions in the individual donor and acceptor molecules (equation 3.73). Higher order terms such as electric dipole-electric quadrupole, electric-dipole-magnetic dipole, become important at close approach and may be effective in crystals and highly ordered array of chromophores. 

The unique electronic structure of these (L-A3)MoO(dithiolene) complexes arises from two basic factors. The first is the strong axial a- and Ji-donor properties of the terminal oxo ligand, which dominates the ligand field and predetermines the energy of the Mo-based dxz, dyz, and dzi acceptor orbitals. The second is the equatorial dithiolene sulfur donors, from which the low-energy LMCT transitions arise. Dithiolene covalency contributions to the electroactive C, or redox, orbital can be directly probed via the relative oscillator strengths of the / —> ixy and /fp —> (/", transitions (see above). These three wave functions may be expanded in terms of Mo- and dithiolene sulfur-based functions ... 

For weak coupling cases, Hush showed that the intensity of an intervalence transition was related to the extent of coupling between donor and acceptor. The derivation (11) begins by considering the theoretical expression for oscillator strength,... 

In this case f) and the emission spectrum of donor and absorption spectrum of acceptor, respectively, are both normalized to unity, so that the rate constant for energy transfer, k, is independent of the oscillator strength of both transitions (contrast to Forster mechanism). 

In equation 12, W is the energy of the optical transition, /is the oscillator strength, and g is the difference between ground-state and excited-state dipole moments. Increases in the electron-donating ability of the donor substituent and the electronegativity of the acceptor should increase both A Xg g and/to a point that should have a favorable impact on p. Beyond that point, further increases in polarity will result in decreases in both F and A Xgg, and P will become smaller. 

These wavefunctions account for the attractive force between A and D leading to the formation of an EDA complex, for its increased polar character and also for the existence of charge-transfer absorption that is often observed when EDA complexes form. Low-lying excited states of A or D+ must be included in the wave function to describe additional charge-transfer bands. These bands appear in addition to the absorption bands of the molecules A and D they are usually broad and of low oscillator strengths because there is little overlap between the HOMO of the donor and the LUMO of the acceptor (Section 4.4, Equation 4.20). Many examples of the formation of EDA complexes between, for example, tetracyanoethylene and aromatic hydrocarbons are known. The... 

Since the first energy level calculations of the EM centres in silicon and germanium [28,34], many calculations have been undertaken to explain quantitatively the absorption and photoluminescence (PL) spectra associated with these centres in many semiconductors. The first part of this chapter is devoted to the presentation of the energy level calculations of EM donors and it is followed by the results of the calculations for EM acceptors. The modification to EMA, which is independent of the chemical nature of the centres, is also discussed. The chapter concludes with results of calculations of the oscillator strength (OS) for transitions between the ground states and the acceptor or donor states. 

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