Energy transfer Coulombic

For many energy transfer processes, the interaction takes place when the partners are separated by more than the sum of the gas-kinetic collision radii. For example, energy transfer between excited singlet states of hydrocarbons occurs as fast as spontaneous decay at concentrations in benzene corresponding to a distance, r, between exchanging molecules of about 5 nm, or about 10 times the collision diameter. The measured rate constants for transfer of excitation in the hydrocarbons also seem greatly to exceed the diffusion-limited rate, and do not depend on solvent viscosity. 

The Forster equation for the first-order rate constant, ke, for energy transfer by the inductive-resonance mechanism can be written in simplified form 

The exchange interaction requires collision between the partners because it involves orbital overlap, as is the case for any chemical reaction. It can be visualized (figure 4) as an exchange of two electrons which can only take place when there is simultaneous and favorable overlap of the appropriate 

As A and B approach each other in solution, long-range Coulombic forces perturb their electronic clouds. The electrostatic potential can be replaced by a multiple expansion, the first term of which (i.e., the dipole-dipole interaction term) is the most important. The electronic coupling matrix can then be expressed by 

The distance between A and B at which energy transfer to B and internal deactivation of A are equally probable is known as the critical transfer distance R. Under such conditions kgjdip) = 1/x ) substituting k f (dip) with 1/t into equation 10 gives the following expression for 

Introduction of reasonable numerical values into this equation leads to the expectation that k idip) can be much larger than the diffusion rate, so that energy transfer by dipole-dipole interaction can be significant even at distances considerably larger than molecular diameters. The Coulombic mechanism, in fact, does not involve formation of an encounter complex and its selection rules are the same as those for the corresponding electric dipole transitions in the isolated molecular partners. In particular, no change in spin in either partner is allowed. Thus processes (12) and (13) are fast. 

The efficiency of energy transfer (equation 16), however, can be high also 

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LONG-RANGE DIPOLE-DIPOLE (COULOMBIC) ENERGY TRANSFER... 

Coulombic energy transfer is a consequence of mutual electrostatic repulsion between the electrons of the donor and acceptor molecules. As D relaxes to D, the transition dipole thus created interacts by Coulombic (electrostatic) repulsion with the transition dipole created by the simultaneous electronic excitation of A to A (Figure 6.9). 

Figure 6.9 Electron movements occurring in long-range Coulombic energy transfer. Note that the electrons initially on D remain on D and electrons initially on A remain on A. This energy transfer does not require physical contact between the donor and acceptor...

Coulombic energy transfer is sometimes called resonance energy transfer because the energies of the coupled transitions are identical, or in other words, in resonance (Figure 6.10). 

A detailed theory of energy transfer by the Coulombic mechanism was developed by Forster, so the process is often referred to as Forster resonance energy transfer (FRET). According to the Forster theory, the probability of Coulombic energy transfer falls off inversely with the sixth power of the distance between the donor and the acceptor. For... 

Rapid multistep Coulombic energy transfer takes place as the excitation energy is transferred between the antenna chromophores and the special pair of bacteriochlorophyll molecules (P) in the reaction centre. 

Energy transfer is considered as a type of dynamic quenching. In general, dynamic quenching can be described with three different processes electron transfer, electron exchange, and Forster or coulombic energy transfer (Figure 14.3). 

In metal complexes, the only excited state of appreciable lifetime is generally the lowest, spin-forbidden excited state [33], so that Coulombic energy transfer is only expected to take place in then presence of very strong spin-orbit coupling (e.g., when 5d metal complexes are involved). 

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