Vibrational motion, electrical

Just as the electrical behaviour of a real diatomic molecule is not accurately harmonic, neither is its mechanical behaviour. The potential function, vibrational energy levels and wave functions shown in Figure f.i3 were derived by assuming that vibrational motion obeys Hooke s law, as expressed by Equation (1.63), but this assumption is reasonable only... 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

Abstract 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. 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. 

In this way one obtains the mean value of P averaged over vibrational motion in terms of mean displacements, mean square displacements, and so on. This approach has been long used to discuss isotope effects on electrical properties of molecules. 

A dipole exists when the centers of positive and negative charge do not coincide. When exposed to an electric field, these oppositely charged centers will move in opposite directions either toward each other or away from each other. In infrared radiation, the direction of the electric field oscillates, causing the positive and negative centers within polar bonds to move toward each other and then away from each other. Thus, when exposed to infrared radiation, the polar bonds within a compound stretch and contract in a vibrating motion. 

Bishop s attention turned to accurate calculations of electrical and magnetic properties, especially those of importance in nonlinear optics. Since most experiments in this field measure ratios, not absolute values, it is necessary to have a calculated value. Universally, Bishop s helium nonlinear optical properties are used. In the same field, he was the first to seriously investigate the effects of electric fields on vibrational motions, with a much-quoted paper.65 His theory and formulation has now been added to two widely used computational packages HONDO and SPECTROS. He has also derived a rigorous formula to account for the frequency dependence (dispersion) in nonlinear optical properties.66 He used this theory to demonstrate that the anomalous dispersion in neon, found experimentally, is an artifact of the measurements. 

The Raman effect can be seen, from a classical point of view, as the result of the modulation due to vibrational motions in the electric field-induced oscillating dipole moment. Such a modulation has the frequency of molecular vibrations, whereas the dipole moment oscillations have the frequency of the external electric field. Thus, the dynamic aspects of Raman scattering are to be described in terms of two time scales. One is connected to the vibrational motions of the nuclei, the other to the oscillation of the radiation electric field (which gives rise to oscillations in the solute electronic density). In the presence of a solvent medium, both the mentioned time scales give rise to nonequilibrium effects in the solvent response, being much faster than the time scale of the solvent inertial response. 

High-frequency vibrating motion similar to that produced by the Hummer electric, or the Leahy No-Blind screen. 

As the vibrational motion is oscillatory, this creates a fluctuating electric field that may interact with the electric part of the electromagnetic radia-... 

The colloid vibration potential (difference) E or CVP is the a.c. potential difference measured between two Identical relaxed electrodes, placed in the dispersion if the latter Is subjected to an (ultra)sonlc field. CVP Is a particular case of the more general phenomenon, ultrasonic vibration potential (UVP), applying to any system, whether or not colloids are present. This field sets the particles into a vibrating motion, as a result of which the centres of particle charge and countercharge are periodically displaced with respect to each other. This phenomenon is the a.c. equivalent of that observed in the Dorn effect. Counterpart to this is the electrokinetic sonic amplitude, ESA, the amplitude of the (ultra)sonlc field created by an a.c, electric field in a dispersion. 

As Werner and Meyer [91] and Adamowicz and Bartlett [70] have clearly explained, molecular electrical properties have another contribution from vibrational motion. Recall that each electrical property is strictly defined as a derivative of the molecular state energy with respect to elements of V. 

In this analysis and in that of the next section, the vibrational motion effects presume a field source that is rotating with the molecule, such as when the electrical perturbation is due to a weakly complexed partner molecule. A freely rotating molecule in a laboratory-fixed field source, however, is different, and then evaluations of electrical properties should account for rotational state dependence as well [114, 115]. 

The results we have obtained provide a reinterpretation of IR absorption along the following lines the IR radiation is a dynamic electric field which causes oscillations in the electronic cloud. The perturbed electrons, in turn, induce an additional dynamic electric field at the nuclei via a feedback effect. The latter are hence acted upon by the effective electric field (145), that is, by a frequency-dependent Lorentz force that is responsible for changes of nuclear vibrational motion. Accordingly, the electron distribution of a molecule plays a fundamental role in determining the general features of nuclear vibrations and the magnitude of IR parameters. 

Fig. 20. Photostimulated vibrational motion of a rod shaped polyacrylamide gel having 3.1 mol% triphenylmethane leucocyanide groups under an alternating electric field ( + 0.8 v/cm, 0.5 Hz) in water in the preseiK of4x lO MNaCl...

Electronic motion with a typical frequency of 3 x 10 s" (i>= 10 cm ) is much faster than vibrational motion with a typical frequency of 3 x 10 s (v = 10 cm" ). As a result of this, the electric vector of light of frequencies appropriate for electronic excitation oscillates far too fast for the nuclei to follow it faithfully, so the wave function for the nuclear motion is still nearly the same immediately after the transition as before. The vibrational level of the excited state whose vibrational wave function is the most similar to this one has the largest transition moment and yields the most intense transition (is the easiest to reach). As the overlap of the vibrational wave function of a selected vibrational level of the excited state with the vibrational wave function of the initial state decreases, the transition moment into it decreases cf. Equation (1.36). Absorption intensity is proportional to the square of the overlap of the two nuclear wave functions, and drops to zero if they are orthogonal. This statement is known as the Franck-Condon principle (Franck, 1926 Condon, 1928 cf. also Schwartz, 1973) ... 

To conduct an electric current, a substance must satisfy two conditions. First, the substance must contain charged particles. Second, those particles must be free to move. Because ionic compounds are composed of charged particles, you might expect that they could be good conductors. While particles in a solid have some vibrational motion, they remain in fixed locations, as shown by the model in Figure 11a. Therefore, ionic solids, such as salts, generally are not conductors of electric current because the ions cannot move. 

We are interested here in the linear and nonlinear optical properties that determine the response of a chemical system to spatially uniform electric fields. The vibrational contribution to this response, which arises from vibronic coupling, can often be as important as tlie pure electronic contribution or even more important [1-14]. In addition, it is often inadequate in this context to treat the effect of vibrational motions at tlie harmonic level of approximation. The purpose of this review, then, is to show how the vibrational contribution to linear and nonlinear optical properties can be evaluated with both harmonic and anharmonic effects included. 

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