Dipole vectors

At the linear level, the microscopic induced dipole vector on a single molecule in the local Cartesian... 

This is, for instance, the case of the a and 5 forms of PVDF (also called form II and form lip, that is form II polarized), both contain chains with a TG+TG" conformation and have an orthorhombic unit cell with substantially identical dimensions [30, 31]. Detailed X-ray diffraction analyses have shown that the two chains in the unit cells are with the dipole vectors pointing in opposite directions in the a form, while they are in the same direction in the 8 form [32],... 

It is important to notice that the work function, , of a given solid surface changes significantly with chemisorption. Thus oxygen chemisorption on transition metal surfaces causes up to 1 eV increase in while alkali chemisorption on transition metal surfaces causes up to 3 eV decrease in . In general electronegative, i.e. electron acceptor adsorbates cause an increase in 0 while electropositive, i.e. electron donor adsorbates cause a decrease in 0. Note that in the former case the dipole vector P formed by the adsorbate and the surface points to the vacuum while in the latter case P points to the surface (Fig. 4.20). 

The dependence of cross-correlated relaxation on the projection angle between the two dipole vectors can be exploited to determine local conformations in ribose rings. 

Equations (7.6) and (7.7) provide a means of determining excited dipole moments together with dipole vector angles, but they are valid only if (i) the dipole moments in the FC and relaxed states are identical, (ii) the cavity radius remains unchanged upon excitation, (iii) the solvent shifts are measured in solvents of the same refractive index but of different dielectric constants. 

Orientation a. The molecule is lined up with the dipole moment vector either parallel or antiparallel to the z-axis. The molecule is rotated about the dipole vector. The molecule is rotated about the z-axis. 

Orientation b. The molecule is aligned with the dipole vector along the x-axis, and the molecule in the xz-plane. The dipole vector is then rotated about the z-axis in the xy-plane. 

Table 3. Transition Dipole Vector Coupllng-Oxyhemocyanln...

In the system of quantum dipoles, dipole and momentum variables have to be replaced by the quantum operators, and quantum statistical mechanics has to be applied. Now, the kinetic energy given by Eq. 9 does affect the thermal average of quantity that depends on dipole variables, due to non-commutivity of dipole and momentiun operators. According to the Pl-QMC method, a quantum system of N dipoles can be approximated by P coupled classical subsystems of N dipoles, where P is the Trotter munber and this approximation becomes exact in the limit P oo. Each quantiun dipole vector is replaced by a cychc chain of P classical dipole vectors, or beads , i.e., - fii -I-. .., iii p, = Hi,I. This classical system of N coupled chains... 

To include the effects of collisions on the rotational motion part of any of the above C(t) functions, one must introduce a model for how such collisions change the dipole-related vectors that enter into C(t). The most elementary model used to address collisions applies to gaseous samples which are assumed to undergo unhindered rotational motion until struck by another molecule at which time a randomizing "kick" is applied to the dipole vector and after which the molecule returns to its unhindered rotational movement. 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

An important signature of the dynamics of water molecules is the reorientation of its dipole vector that can be probed by dielectric and NMR measurements. We have calculated the single molecule dipole-dipole time correlation function (TCF), defined as,... 

Thus, if van der Waals forces are responsible for the stability of the caffeine-pyrogallol complex we would expect the molecules to be oriented as in V. Bearing in mind, however, the uncertainty as to the exact orientation of caffeine s dipole vector, the superposition of molecular planes might in the final analysis not be so different from I. In that case one would have to look to other evidence to establish whether or not charge transfer forces were involved. 

Because the components (X,Y,Z) of the dipole vector in C2V transformas (AuB Bj the transition Aj — A2 is orbitally forbidden. The transition — 3A2 is both orbitally forbidden and spin-forbidden. Although the transitions are theoretically forbidden, they are both observed but with small intensities. The xAj — aAi transition is found between 4000 and 3000 A, and 1A1 —- rAz is found between 3700 and 2300 A. We shall not discuss the mechanisms that make these transitions slightly allowed. The Aj — 1A2 transition, with a maximum around 3000 A, is a trademark of the carbonylgroup. 

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