Displacement dipole moment

Ferroelectric fluid phases have also been observed in simulations of disk-shaped particles with embedded dipole moments along the symmetry axis [ 147,148] (see Sect. 4) and in a dipolar hard sphere model carrying two parallel dipole moments displaced equally from the sphere centre [ 149]. In the latter model antiferroelectric arrangement of the particles is, however, equally preferred at sufficiently large separations (0.3a) of the two dipole moments. 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

When you perform a single point semi-empirical or ab initio calculation, you obtain the energy and the first derivatives of the energy with respect to Cartesian displacement of the atoms. Since the wave function for the molecule is computed in the process, there are a number of other molecular properties that could be available to you. Molecular properties are basically an average over the wave function of certain operators describing the property. For example, the electronic dipole operator is basically just the operator for the position of an electron and the electronic contribution to the dipole moment is... 

As for the change of dipole moment, the change of polarizability with vibrational displacement x can be expressed as a Taylor series... 

Pyran, 2-halotetrahydro-dipole moments, 3, 628 halogen displacement reactions, 2, 64 C NMR, 3, 587 Pyran, 2-hydroxy-synthesis, 3, 741 Pyran, 3-hydroxy-synthesis, 2, 91... 

A further complication arises with Ingold s suggestion" that both the inductive and resonance effects are composed of initial state equilibrium displacements that reveal themselves in equilibrium properties like dipole moments and equilibrium constants and of time-dependent displacements produced during reaction by the approach of an attacking reagent, observed rate effects being resultants of both types of electronic effects. Hammett, however, claims that it is not necessary or possible to make this distinction. 

The change in the dipole moment with respect to a geometry displacement along a normal coordinate is approximately proportional to the intensity of an IR absorption. In the so-called double harmonic approximation (terminating the expansion at first order in the electric field and geometry), the intensity is (except for some constants)... 

Drawings using arrows help us see why acetone has a larger dipole moment than dimethyl ether. The arrows show the charge displacement for each polar bond. Experimental values for the dipole moments are butane, 0 D methyl ethyl ether, 1.12 D and acetone, 2.88 D. 

Table 1 demonstrates the distance of displacement from the center of gravity and the magnitude of the dipole moments. The dipole moments of BaTi40g were D=5.7 and D=4.1 and those of NazTigOig were D=5.3, D=5.8 and D=6.7, whereas all the moments of Ba4Tii303o was below D=5.0. It is to be noted that there is a clear difference in the dipole moment between tunnel structure titanates(D>5.0) and non-tunnel structure Ba4Tii303o (D<5.0). The ESR spectra of BaTi40g showed... 

In the quantum mechanical approach, a transition moment is introduced for characterizing the transition between an initial state and a final state (see Box 2.2). The transition moment represents the transient dipole resulting from the displacement of charges during the transition therefore, it is not strictly a dipole moment. 

It should be noted that the dipole moment of the molecule in its ground state is OF1 M vF ). In contrast, the term (Tfi M T2> is not strictly a dipole moment because there is a displacement of charges during the transition it is called transition moment Mn that characterizes the transition. 

Although the electronic structure and the electrical properties of molecules in first approximation are independent of isotope substitution, small differences do exist. These are usually due to the isotopic differences which occur on vibrational averaging. Refer to Fig. 12.1 and its caption for more detail. Vibrational amplitude effects are important when considering isotope effects on dipole moments, polarizability, NMR chemical shifts, molar volumes, and fine structure in electron spin resonance, all properties which must be averaged over vibrational motion. Any such property, P, can be expressed in terms of a Taylor series expansion over the displacements of the coordinates from their equilibrium positions,... 

An exception among organic molecules is the adsorption of thiourea since that gives no maximum on the AG° vs. plot. It was suggested " that such atypical behavior can be expected for any neutral molecule that has the normal to the surface component of the dipole moment sufficiently positive compared with the resulting dipole moment of n displaced water molecules. In the case of a TU molecule oriented with the sulfur atom toward the metal surface, the ratio of /iA// is approximately equal to 2.5 D. This value is greater than the dipole moment of water, thus fulfilling the condition of atypical behavior. The anomalous behavior of thiourea is probably due to the fact that only a few solute molecules satisfy this condition. 

The electron cloud of an ion subjected to an electric field undergoes deformations that may be translated into displacement of the baricenters of negative charges from the positions held in the absence of external perturbation, which are normally coincident with the centers of nuclear charges (positive). The noncoincidence of the two centers causes a dipole moment, determined by the product of the displaced charge (Z ) and the displacement d. The displacement is also proportional to the intensity of the electrical field (F). The proportionality factor (a) is known as ionic polarizability ... 

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