Polarizability application

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

Optimization of second-order polarizabilities applications to real molecules. 168... 

Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities. 

Macroscopic susceptibilities and molecnlar polarizabilities 155 Experimental determination of molecnlar second-order polarizabilities Optimization of second-order polarizabilities applications to real molecules a Systems and one-dimensional rr systems 168 Two-dimensional (2D) NLO-phores ID and 2D architectnre 196 Conclnsion 206 Acknowledgements 208 References 208... 

W. H. Orttung. Extension of the Kirkwood-Westheimer model of substituent effects to general shapes, charges, and polarizabilities. Application to the substituted Biocyclo[2.2.2]octanes. J. Am. Chem. Soc., /00 4369-4375 (1978). 

Consider a collection of charged particles forming an atom or molecule. A key attribute of such a body is that it is polarizable. Application of an electromagnetic field induces mulfipole moments in the system. The first few terms of the electric response, resulting in an electric dipole moment being induced, is given by the expansion... 

M. J. S. Dewar and J. J. P. Stewart, Ghent. Phys. Lett., Ill, 416 (1984). A New Procedure for Calculating Molecular Polarizabilities Applications Using MNDO. 

A precise theoretical and experimental determination of polarizability would provide an important probe of the electronic structure of clusters, as a is very sensitive to the presence of low-energy optical excitations. Accurate experimental data for a wide range of size-selected clusters are available only for sodium, potassium [104] and aluminum [105, 106]. Theoretical predictions based on DFT and realistic models do not cover even this limited sample of experimental data. The reason for this scarcity is that the evaluation of polarizability by the sum rule (46) requires the preliminary computation of S(co), which, with the exception of Ref. [101], is available only for idealized models. Two additional routes exist to the evaluation of a, in close analogy with the computation of vibrational properties static second-order perturbation theory and finite differences [107]. Again, the first approach has been used exclusively for the spherical jellium model. In this case, the equations to be solved are very similar to those introduced in Ref. [108] for the computation of atomic polarizabilities. Applications of this formalism to simple metal clusters are reported, for instance, in Ref. [109]. 

J. Applequist, J. R. Carl, and K.-K. Fung, /. Am. Chem. Soc., 94, 2952 (1972). An Atom-Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities. 

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

In many chemical applications, however, it would be more interesting to know how polarizability can stabilize a charge introduced into a molecule. Thus, rather than the global molecular property, mean molecular polarizability, a local, site-specific value for polarizability is needed. 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

This coding is performed in three steps (cf Chapter 8) First the 3D coordinates of the atoms arc calculated using the structure generator CORINA (COoRdlNAtes). Subsequently the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) is applied for calculating physicochemical properties such as charge distribution and polarizability. The 3D information and the physicochemical atomic properties are then used to code the molecule. 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

The concepts of electronegativity, hardness, and polarizability are all interrelated. For the kind of qualitative applications we will make in discussing reactivity, the concept that initial interactions between reacting molecules can be dominated by either partial electron transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is a useftxl generalization. 

Silica gel, per se, is not so frequently used in LC as the reversed phases or the bonded phases, because silica separates substances largely by polar interactions with the silanol groups on the silica surface. In contrast, the reversed and bonded phases separate material largely by interactions with the dispersive components of the solute. As the dispersive character of substances, in general, vary more subtly than does their polar character, the reversed and bonded phases are usually preferred. In addition, silica has a significant solubility in many solvents, particularly aqueous solvents and, thus, silica columns can be less stable than those packed with bonded phases. The analytical procedure can be a little more complex and costly with silica gel columns as, in general, a wider variety of more expensive solvents are required. Reversed and bonded phases utilize blended solvents such as hexane/ethanol, methanol/water or acetonitrile/water mixtures as the mobile phase and, consequently, are considerably more economical. Nevertheless, silica gel has certain areas of application for which it is particularly useful and is very effective for separating polarizable substances such as the polynuclear aromatic hydrocarbons and substances... 

The application of these methods to unsaturated hydrocarbons involves certain complications. Unsaturated hydrocarbons show an additional polarizability19 of 0.58 x 10 24 cm3 per double bond and 0.86 x 10 24 cm3 per triple bond in the molecule. Similarly the polarizability of a molecule containing a benzene ring exceeds that computed for the atoms present by about 1.28 x 10 24 cm3. These results are most readily explained on the basis that oscillations of charge from atom to atom are significant when double bonds are present. 

The extent to which anode polarization affects the catalytic properties of the Ni surface for the methane-steam reforming reaction via NEMCA is of considerable practical interest. In a recent investigation62 a 70 wt% Ni-YSZ cermet was used at temperatures 800° to 900°C with low steam to methane ratios, i.e., 0.2 to 0.35. At 900°C the anode characteristics were i<>=0.2 mA/cm2, Oa=2 and ac=1.5. Under these conditions spontaneously generated currents were of the order of 60 mA/cm2 and catalyst overpotentials were as high as 250 mV. It was found that the rate of CH4 consumption due to the reforming reaction increases with increasing catalyst potential, i.e., the reaction exhibits overall electrophobic NEMCA behaviour with a 0.13. Measured A and p values were of the order of 12 and 2 respectively.62 These results show that NEMCA can play an important role in anode performance even when the anode-solid electrolyte interface is non-polarizable (high Io values) as is the case in fuel cell applications. 

The second procedure, several aspects of which are reviewed in this paper, consists of directly computing the asymptotic value by employing newly-developed polymeric techniques which take advantage of the one-dimensional periodicity of these systems. Since the polarizability is either the linear response of the dipole moment to the field or the negative of the second-order term in the perturbation expansion of the energy as a power series in the field, several schemes can be proposed for its evaluation. Section 3 points out that several of these schemes are inconsistent with band theory summarized in Section 2. In Section 4, we present the main points of the polymeric polarization propagator approaches we have developed, and in Section 5, we describe some of their characteristics in applications to prototype systems. 

Saue, T. and Jensen, H.J.Aa. (2003) Linear response at the 4-component relativistic level Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers. Journal of Chemical Physics, 118, 522-536. 

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