Dipole contribution

The experimental data and arguments by Trassatti [25] show that at the PZC, the water dipole contribution to the potential drop across the interface is relatively small, varying from about 0 V for An to about 0.2 V for In and Cd. For transition metals, values as high as 0.4 V are suggested. The basic idea of water clusters on the electrode surface dissociating as the electric field is increased has also been supported by in situ Fourier transfomr infrared (FTIR) studies [26], and this model also underlies more recent statistical mechanical studies [27]. 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

The numbers of IR- and Raman-active modes are 4 (4tiJ and 10 (2ag + 8hg), respectively. On the other hand, hyper-Raman-active modes are all of the modes with u symmetry, including the silent modes. Compared with the theoretically calculated result, the expected modes are clearly seen in the spectmm. (The appearance of Raman-active modes is due to magnetic dipole contributions.)... 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization Ps 2a)) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor co, m) is large enough to dwarf the contribution from higher... 

If the electric dipole contribution dominates in the total SH response, the macroscopic response can be related to the presence of optically nonlinear active compounds at the interface. In this case, the susceptibility tensor is the sum of the contribution of each single molecule, all of them coherently radiating. For a collection of compounds, it yields ... 

That way, the Distributed Electrostatic Moments based on the ELF Partition (DE-MEP) allows computing of local moments located at non-atomic centres such as lone pairs, a bonds and n systems. Local dipole contributions have been shown to be useful to rationalize inductive polarization effects and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a n character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. 

Table 6-4. Local dipole contributions and magnitude of the first and second moments of some basins of typical basins involved in the main chain...

Theoretical calculations on the dithiazolyl radical 4 (R=CF3) have recently shown that n -n dimerisation was unfavourable but association of two such dimers via electrostatic interactions generated a thermodynamically stable tetramer consistent with single crystal X-ray studies. Thus while the value of [AE-P ] may favour (or disfavour) dimer formation, the van der Waals, dipole contributions and electrostatic interactions to the lattice enthalpy should not be underestimated in assessing the thermodynamic stability or instability of these... 

Note that two distinct types of interactions (ion-quadrupole and dipole-dipole) contribute to an overall R 3 dependence, and the number of distinct multipole types having similar R n dependences continues to increase with increasing n. For uncharged systems, the dipole-dipole interaction (5.23d) is expected to dominate, with an angular term that favors parallel alignment of the two dipoles. 

Nonlinear Optical Activity and Magnetic Dipole Contributions... 

However, the components of the yj2) e, e tensor are chiral (i.e., only present in a chiral isotropic medium), whereas the components of the tensors y 2) and y(2) meeare achiral (i.e., present in any isotropic medium, chiral or achiral). Hence, only the electric dipole response of chiral isotropic materials is related to chirality. The experimental work on chiral polymers described in Section 4 showed that large magnetic contributions to the nonlinearity are due to chirality. However, such contributions will therefore not survive in chiral isotropic media. In this respect, the electric dipole contributions associated with chirality may prove more interesting for applications. 

The intimate relationship between double layer emersion and parameters fundamental to electrochemical interfaces is shown. The surface dipole layer (xs) of 80SS sat. KC1 electrolyte is measured as the difference in outer potentials of an emersed oxide-coated Au electrode and the electrolyte. The value of +0.050 V compares favorably with previous determinations of g. Emersion of Au is discussed in terms of UHV work function measurements and the relationship between emersed electrodes and absolute half-cell potentials. Results show that either the accepted work function value of Hg in N2 is off by 0.4 eV, or the dipole contribution to the double layer (perhaps the "jellium" surface dipole layer of noble metal electrodes) changes by 0.4 V between solution and UHV. 

We see that the electric dipole allowed transitions are, in general, much more intense than the magnetic dipole allowed transitions. In fact, the magnetic dipole contribution to an optical transition of a center dominated by an electric dipole character is usually completely masked by the much more intense J electric dipole transitions. 

As the electron approaches the molecule, an electric field is established that is described in terms of a Coulomb potential, (()(-. It is assumed that when the Coulomb potential reaches the electron transition energy (the ionization potential, Eq) the orbital electron involved in the transition absorbs energy from the field, the efficiency of the ionization depending on the transition probability, F, .. When the electron-induced dipole contribution is neglected, a cross section, which will be an underestimate, can be calculated from the interparticle separation when (()(- = Eq. In order to deduce the maximum ionization cross section, a., the transition probability P,. must be taken into account ... 

Thus, if Pi is known, then the measurement of 77 provides the extreme narrowing conditions, the heteronuclear NOE reaches a maximum value (minimum for 71 < 0) and can be used to determine the dipole-dipole contribution to the total relaxation rate ... 

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