Electrical excitation Forster energy transfer

Forster energy transfer or energy transfer at a distance occurs between two molecules, a donor (the excited fluorophore), and an acceptor (a chromophore or fluorophore). Energy is transferred by resonance, i.e., the electron of the excited molecule induces an oscillating electric field that excites the acceptor electrons. As a result of this energy transfer, the fluorescence intensity and quantum yield of the emitter will decrease. Energy transfer is described in Chapter 14. 

Dipole-dipole interaction the Forster mechanism (Figure 3.37). This is in fact the interaction of the transition moments of the excitation Q — Q and the deactivation M — M. As the excited electron of M falls to the lower orbital of M there is a change in dipole moment which produces an electric field this field is proportional to the transition moment M and to the inverse cube of the distance. An electron in the molecule Q therefore experiences a force proportional to M/r3, and as it moves towards a higher orbital it produces its own electric field which results in a force being applied on the electron in molecule M. In this way the downward motion of the electron in M and the upward motion of the electron in Q are coupled by their electric fields, the rate constant for energy transfer being... 

The Forster mechanism is also known as the coulombic mechanism or dipole-induced dipole interaction. It was first observed by Forster.14,15 Here the emission band of one molecule (donor) overlaps with the absorption band of another molecule (acceptor). In this case, a rapid energy transfer may occur without a photon emission. This mechanism involves the migration of energy by the resonant coupling of electrical dipoles from an excited molecule (donor) to an acceptor molecule. Based on the nature of interactions present between the donor and the acceptor, this process can occur over a long distances (30—100 A). The mechanism of the energy transfer by this mechanism is illustrated in Figure 11. 

The energy transfer can also proceed through an alternative mechanism, which can occur between molecular entities separated by distances considerably greater than the sum of their van der Waals radii (eg in molecular monolayers). The electron shift to less energy in AB and the increase in energy of electron in Q are coupled by their electric fields. It is described in terms of an interaction between the transition dipole moments (a dipolar mechanism, called Forster excitation transfer, Figure 4.3). 

Dexter, following the classic work by Forster, considered energy transfer between a donor (or a sensitizer) S and an acceptor (or activator) A in a solid. This process occurs if the energy difference between the ground and excited states of S and A are equal (resonance condition) and if a suitable interaction between both systems exists. The interaction may be either an exchange interaction (if we have wave function overlap) or an electric or magnetic multipolar interaction. In practice the resonance condition can be tested by considering the spectral overlap of the S emission and the A absorption spectra. The Dexter result looks as follows ... 

An approach with indirect injection of electron-hole excitations into nanocrystals by the above described noncontact nonradiative Forster-like energy transfer from a proximal quantum well that can in principle be pumped either electrically or optically, can solve the problem of pumping of nanocrystals. The result obtained by the Klimov group indicate that this energy transfer is fast enough to compete with electron-hole recombination in the quantum well, and results in... 

Let us consider the simple case of two ions, each with one excitable electronic state separated from its electronic ground state by nearly equal energy. With suitable interaction between the two electronic systems, the excitation will jump from one ion to the other before a quantum of fluorescence is emitted. The systems interact by Coulomb interactions of the Van der Waals type. Forster (1948), who first treated such a case by quantum-mechanical theory, considered the dipole-dipole interactions. He assumed that the interaction is strongest if, for both transitions, electric-dipole transitions are allowed (Forster 1960). The interaction energy (//sa) is then proportional to the inverse of the third power of the interionic distance, and the transfer probability is given by... 

---