Electrostatic contributions frequency

The original formal theory is expressed in terms of quanttun electrodynamics with the continuum mediwn characterized by its spectnun of complex dielectric frequencies. A more recent formulation, derived from this theory, is based on the extension of the reaction field concept to a dipole subject to fluctuations exclusively electric in origin. Another procedme has been formulated starting, as for the repulsion contribution, from the theory of intermolecular forces. Following the scheme commonly exploited to derive the electrostatic contribution to the interaction energy, the molecule B is substituted by a continuum medium, the solvent S, described by a surface charge density as induced by the solute transition densities of M (the equivalent of A) and spreading on the cavity surface. 

The simplest van der Waals forces involving free charge carriers occur where only a single substance has the free charges and no other substance in the system being considered can make an electrostatic contribution. For example, an electrolyte sphere coated with a nonpolar hydrocarbon near a pure water aerosol particle is such a system. In this case, the two-particle interaction force can be computed by use of local dielectric permeabilities whenever the charge carrier s plasma frequency is less than the lowest absorption frequency of the system [e.g., in (5.38)]. 

At r = 300 K, fcr 3 X lO J, which is an order of magnitude less that the dispersion contribution. The actual difference between the two terms (dispersion and electrostatic) will be reduced by mathematical cancellations in the second (dispersion) term in Equation (4.47), but only rarely will the electrostatic contribution constitute the dominant factor in the total interaction. The presence of imaginary frequencies in the second term may cause some problems in terms of physical concepts of the processes involved however, their use is actually a result of mathematical manipulations (i.e., tricks) that disappear as one works through the complete calculation. 

Next we have calculated the frequencies and the intensities of the dimer vibrational transitions in the range of the 1/3 vibrations of SFe and SiF4 and the 1/4 vibration of SiH4. The force fields used for the monomers are given in Ref. 8. We have analyzed the various contributions to the splitting and shifts of the monomer frequencies, and we have investigated the orientational dependence of each contribution, as well as the orientational dependence of the dimer transition strengths. From the results in Table 2 we conclude that the electrostatic contributions are dominant in all cases. As explained in Section 2, the electrostatic dipole-dipole shifts (indicated in parentheses) are —2A, — A, A and 2A, for all dimers, independent of the monomer orientations. Also the dipole-induced dipole shifts have constant ratios —4 — 1 — 1 —4, independent of the monomer orientations. 

They showed that in various halogenated solvents, contributions from dispersion, electrostatic and induction all lowered the CN stretching frequency, while only repulsion raised it. In this study, which yielded good agreement between theory and experiment, CN stretching frequencies were measured over pressures of 1-10,000 atm (Figure 16). 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

First, diatomic molecules are usually adsorbed on cations (some exceptions to this empirical rule are mentioned in the case studies). The type of interaction and the resulting vibrational perturbation (purely electrostatic or with some orbital overlap contribution) depend on the charge carried by the cation and by the anions in nearest-neighbor positions and on the electronic structure of the cation (with or without d electrons). As a typical example of the effect of a purely electrostatic perturbation on the stretching mode of a diatomic molecule, we mention the classic case of CO adsorbed on Na+ exposed on NaCl (100) (Fig. 2), in which it is clearly shown that the frequency of adsorbed CO is distinctly blue shifted with respect to that of CO gas (2143 cm-1) (48). More general considerations concerning the role of the electrostatic field in perturbing the adsorbed molecules are discussed elsewhere (12-15, 21-23). 

The calculated frequencies are in satisfactory agreement with the experimental values for the (0112) and (1120) faces. This result again indicates that the Cr3+ CO bond is mainly electrostatic in nature (even if a minor contribution of chemical overlap forces is present). 

Across real surfaces and interfaces, the dielectric response varies smoothly with location. For a planar interface normal to a direction z, we can speak of a continuously changing s(z). More pertinent to the interaction of bodies in solutions, solutes will distribute nonuniformly in the vicinity of a material interface. If that interface is charged and the medium is a salt solution, then positive and negative ions will be pushed and pulled into the different distributions of an electrostatic double layer. We know that solutes visibly change the index of refraction that determines the optical-frequency contribution to the charge-fluctuation force. The nonuniform distribution of solutes thereby creates a non-uniform e(z) near the interfaces of a solution with suspended colloids or macromolecules. Conversely, the distribution of solutes can be expected to be perturbed by the very charge-fluctuation forces that they perturb through an e(z).5... 

This response is that of a permanent dipole that is partly oriented by a weak electrostatic field. "Weak" means that the energy put into orientation is much less than thermal energy the field gently perturbs otherwise random orientation. This response is slow x is so large that the contribution to forces from dipole orientation "counts" only in the n = 0 limit of low frequency. 

V is the vibrational frequency in the gas phase, v is the frequency in the solvent of relative permittivity Sr, and C is a constant depending upon the molecular dimensions and electrical properties of the vibrating solute dipole. The electrostatic model leading to Eq. (6-8) assumes that only the electronic contribution to the solvent polarization can follow the vibrational frequencies of the solute ca. 10 " s ). Since molecular dipole relaxations are characterized by much lower frequencies (10 to 10 s ), dipole orientation cannot be involved in the vibrational interaction, and Eq. (6-8) may be written in the following modified form [158, 168] ... 

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