Mechanical dipole

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

Figure 9.6 Energy diagrams for tensors x(2) e, x(2) eOT and jO-),mee por (2). ) input photons (frequency to) are annihilated and output photon (frequency 2co) is created through electric dipole interactions. For x(2) ", one input photon at frequency to is annihilated by a magnetic interaction whereas other interactions occur through electric dipole mechanism. On the other hand, for X(2 ) " output photon is generated through magnetic interaction.

Figure 23. Two principal mechanisms of excitation energy transfer (EET). (a) The Forster dipole-dipole mechanism, in which the active electrons, one and two, remain, respectively, on D and A throughout the process, (b) In the (Dexter) exchange mechanism, electrons one and two exchange locations.

Understand that both mechanisms for singlet-singlet energy transfer require an overlap between the florescence spectrum of the donor and the absorption spectrum of the acceptor. In addition, understand that a favourable orientation of donor and acceptor is necessary for the dipole mechanism. 

Understand that triplet-triplet energy transfer by the dipole mechanism is forbidden, but that the application of the Wigner spin rule shows that it can occur by the exchange mechanism. 

Dexter s formulation of exchange energy transfer (very weak coupling) In contrast to the inverse sixth power dependence on distance for the dipole-dipole mechanism, an exponential dependence is to be expected from the exchange mechanism. The rate constant for transfer can be written as... 

In the case of E, transitions, that is, those ocurring through the electric dipole mechanism, k=, and for an T /electron system with k= 1, in atomic units (which are used throughout, except in the figures, where the energy values are given in cm ). 

In solution, dipole-dipole interactions constitute a relaxation mechanism, and the dipolar relaxation which is the basis for the well-known nuclear Overhauser effect (NOE), mostly used in the homonuclear H, H case. The 2D HOESY method between H and Li has been used to obtain structural information of many organolithium systems in solution and this field was reviewed in 1995. Li is commonly used as the relaxation is dominated by the dipole-dipole mechanism and the relaxation time is relatively long. Knowledge of the proximity of the lithium cation relative to protons in the substrate is used to derive information about the structure and aggregation of organolithium systems in solution. In a few cases quantitative investigations have been made °. An average error of the lithium position of ca 0.2 A was reported. 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

Figure 4.18 Concentration depolarization by dipole-dipole mechanism. Arrows indicate the vector directions.

The rate constant for long range transfer by dipole-dipole mechanism is given by... 

Short range transfer by exchange mechanism occurs when donor and aceer. electronic wavefunctions spatially overlap. The rate follows diflusion-contro",. kinetics if donor and acceptor energy levels are in near resonance. Transit forbidden by dipole-dipole mechanism may occur by exchange mechanism, e.g... 

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