Resonance energy transfer ͑RET͒ is the principal mechanism for the intermolecular or intramolecular redistribution of electronic energy following molecular excitation. In terms of fundamental quantum interactions, the process is properly described in terms of a virtual photon transit between the pre-excited donor and a lower energy ͑usually ground-state͒ acceptor. The detailed quantum amplitude for RET is calculated by molecular quantum electrodynamical techniques with the observable, the transfer rate, derived via application of the Fermi golden rule. In the treatment reported here, recently devised state-sequence techniques and a novel calculational protocol is applied to RET and shown to circumvent problems associated with the usual method. The second-rank tensor describing virtual photon behavior evolves from a Green's function solution to the Helmholtz equation, and special functions are employed to realize the coupling tensor. The method is used to derive a new result for energy transfer systems sensitive to both magnetic-and electric-dipole transitions. The ensuing result is compared to that of pure electric-dipoleelectric-dipole coupling and is analyzed with regard to acceptable transfer separations. Systems are proposed where the electric-dipole-magnetic-dipole term is the leading contribution to the overall rate.

Fundamental theory is developed for three-body resonance energy transfer in the condensed phase, involving two donors and a single acceptor. This energy pooling mechanism is responsible for recent experimental observations on trichromophore molecules and other moieties, manifest for example in the photochemistry of organo dyes and rare-earth ion doped crystals. A full quantum electrodynamical (QED) treatment of this pooling is developed and formulated with the aid of a novel diagrammatic method, which proves to have several advantages over Feynman diagram methods. Following derivation of the rate of energy pooling for an isolated group of chromophores, the electronic influences of the medium across which the energy migrates are embedded in the theory and duly discussed. Energetic constraints on the acceptor molecule are elucidated and shown to account for a variety of postulated mechanisms: the geometry of the three-center system is itself shown to exercise considerable control over the dominant mechanism. By extension, the theory is amenable to the study of more complex energy transfer arrangements, such as those observed in dendrimer chemistry and the light-harvesting photochemistry of the photosynthetic unit.

The process of laser-assisted resonance-energy transfer ͑LARET͒ is described and analyzed within the framework of molecular quantum electrodynamics. LARET is a higher-order perturbative contribution to the familiar spontaneous dipole-dipole mechanism for resonance-energy transfer, in which an auxiliary laser field is applied specifically to stimulate the energy transfer. The frequency of the auxiliary beam is chosen to be off-resonant with any molecular transition frequencies in order to eliminate direct photoabsorption by the interacting molecules. Here consideration is given to the general case where the energy exchange takes place between two uncorrelated molecular species, as for example in a molecular fluid, or a system in which the molecules are randomly oriented. In the ensuing calculations it is necessary to implement phase-weighted averaging in tandem with standard isotropic averaging procedures. Results are discussed in terms of a laser intensity-dependent mechanism for energy transfer. Identifying the applied field regime where LARET should prove experimentally significant, transfer rate increases of up to 30% are predicted on reasonable estimates of the molecular parameters. Possible detection techniques are discussed and analyzed with reference to illustrative models.

A quantum electrodynamical calculation is presented that focuses individually on the two quantum pathways or time orderings for resonance energy transfer. Conventional mathematical procedures necessitate summing the quantum pathway amplitudes at an early stage in the calculations. Here it is shown, by the adoption of a different strategy that allows deferral of the amplitude summation, that it is possible to elicit key information regarding the relative significance of the two pathways and their distinct distance dependences. A special function integration method delivers equations that also afford new insights into the behavior of virtual photons. It is explicitly demonstrated that both time-ordered pathways are effective at short distances, while in the far field the dissipation of virtual traits favors one pathway. Hitherto unknown features are exhibited in the oblique asymptotic behavior of the time-ordered contributions and their quantum interference. Consistency with the rate equations of resonance energy transfer is demonstrated and results are presented graphically.

Three-center energy transfer affords the basic mechanism for a variety of multiphoton processes identified within materials doped with rare earths. Addressing the theory using quantum electrodynamics, general results are obtained for systems in which the fundamental photophysics engages three ions. Distinct cooperative and accretive mechanistic pathways are identified and the theory is formulated to elicit their role and features in energy transfer phenomena of pooling upconversion, sensitization, and downconversion or quantum cutting. It is shown that although the two mechanisms play significant roles in pooling and cutting, only the accretive mechanism is responsible for sensitization processes. Both mechanisms are shown to invoke Raman selection rules, which govern transitions of the mediator ions in the accretive mechanisms and transitions of the acceptor ions in the cooperative mechanisms. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structural effects. Attention is drawn to a general implication of implementing a multipolar description for the optical properties of doped solid-state ionic materials