Dipole/dipolar

When the mechanism is purely dipole-dipolar (Forster mechanism), simplified eqs. (4b) and (4c) allow an estimate of the efficiency of transfer between the donor and the acceptor ... 

There are many other terms to the Hamiltonian but for spin-1/2 nuclei in liquids they can all be ignored. The dipole-dipole (dipolar or direct coupling) Hamiltonian is important in solids and partially oriented liquids, and the quadrupolar Hamiltonian is important for spins greater than 1/2. The dipolar interaction contains a multiplier of... 

Van der Waals forces are weaker than ionic interactions and include three types of interactions dipole-dipole, dipole-induced dipole and induced dipole-induced dipole. Dipolar forces can be compared to magnetic forces where a... 

On the other hand, FRET occurs when the donor (D) and the acceptor (A) lie at distances Rda>40 pm, the corresponding mechanism being dipole-dipolar (through space), as opposed to through-bond (Dexter) mechanism which operates at shorter distances (Selvin, 2000). The yield of fhe FRET fransfer is given by an equation similar to Eq. (77), Section 4.4, with Rq defined by Eq. (78) ... 

When one metal ion plays the role of a donor for sensitizing the emission of a second accepting metal ion, the characteristic lifetimes T of their excited states, which are related to their deactivation rates by em = ( em) / are affected by the intermetallic communication process (Figure 122). If the energy transfer rate is much faster than the deactivation rate of the donor ion, the situation is very simple and assuming a Forster s dipole-dipolar mechanism, the yield of the transfer is given similarly to Eq. (77) by... 

The intramolecular commimication along the Ca-axis generates two "divergent" R Cr energy transfer processes, as exemplified by the dramatic decrease in the Eu( Dq) lifetime (Table 31) which can be analyzed as follows, given the symmetry of the molecule and within the frame of the dipole-dipolar mechanism (Figure 127, bottom) ... 

Depending on the electromagnetic nature of Ti , a double-electron exchange (Dexter) mechanism or an electrostatic multipolar (Forster) mechanism have been proposed and theoretically modeled. They are sketched on Fig. 8 for the simple S - T -Ln path. Their specific dependences on the distance d separating the donor D from the acceptor A, i.e., for double-electron exchange and for dipole-dipolar processes, respectively, often limit Dexter mechanism to operate at short distance (typically 30-50 pm) at which orbital overlap is significant, while Forster mechanism may extend over much longer distances (up to 1,000 pm). 

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

At distances of a few molecular diameters, the interaction will be dominated by electric multipole interactions for dipolar molecules, such as water, the dominant tenn will be the dipole-dipole interaction ... 

The neighboring molecule B feels the dipolar electric held of A and undergoes a spon taneous adjustment m its electron positions giving it a temporary dipole moment that is complementary to that of A... 

Schematic diagram showing the development of a dipolar field and ionization on the surface of a metal filament, (a) As a neutral atom or molecule approaches the surface of the metal, the negative electrons and positive nuclei of the neutral and metal attract each other, causing dipoles to be set up in each, (b) When the neutral particle reaches the surface, it is attracted there by the dipolar field with an energy Q,. (c) If the values of 1 and <() are opposite, an electron can leave the neutral completely and produce an ion on the surface, and the heat of adsorption becomes Q,. Similarly, an ion alighting on the surface can produce a neutral, depending on the values of I and <(), On a hot filament the relative numbers of ions and neutrals that desorb are given by Equation 7.1,which includes the difference, I - <(), and the temperature, T,...

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