Polarizability, and

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Doerksen R J and Thakkar A J 1999 Structures, vibrational frequencies and polarizabilities of diazaborinines, triazadiborinines, azaboroles and oxazaboroles J. Phys. C/rem. A 103 2141... 

The chirality code of a molecule is based on atomic properties and on the 3D structure. Examples of atomic properties arc partial atomic charges and polarizabilities, which are easily accessible by fast empirical methods contained in the PETRA package. Other atomic properties, calculated by other methods, can in principle be used. It is convenient, however, if the chosen atomic property discriminates as much as possible between non-equivalent atoms. 3D molecular structures are easily generated by the GORINA software package (see Section 2.13), but other sources of 3D structures can be used as well. 

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. 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

Moleeular properties sueh as dipole moment and polarizability, although in eertain fully empirieal models, bond dipoles and lone-pair eontributions have been ineorporated (although again only for eonventional ehemieal bonding situations). 

The domain is small compared to the wavelength of visible light, so Eq. (10.33) describes the scattering, provided that we can find appropriate values for the concentration and polarizability of these domains. 

Bond Energy, Polarity, and Polarizability 1.2.1. Bond Energies... 

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. 

In general, the dissection of substituertt effects need not be limited to resonance and polar components, vdiich are of special prominence in reactions of aromatic compounds.. ny type of substituent interaction with a reaction center could be characterized by a substituent constant characteristic of the particular type of interaction and a reaction parameter indicating the sensitivity of the reaction series to that particular type of interactioa For example, it has been suggested that electronegativity and polarizability can be treated as substituent effects separate from polar and resonance effects. This gives rise to the equation... 

The importance of solvent participation in the borderline mechanisms should be noted. Nucleophilic participation is minimized by high electronegativity, which reduces the Lewis basicity and polarizability of the solvent molecules. Trifluoroacetic acid and perfiuoro alcohols are among the least nucleophilic of the solvents used in solvolysis studies. These solvents are used to define the characteristics of reactions proceeding without nucleophilic solvent participation. Solvent nucleophilicity increases with the electron-donating capacity of the molecule. The order trifluoroacetic acid < trifluoroetha-nol <acetic acid < water < ethanol gives a qualitative indication of the trend in solvent nucleophilicity. More will be said about solvent nucleophilicity in Section 5.5. 

The position of aniline in the above reactivity order deserves special comment. Aniline is less basic than pyridine by a relatively small factor, 0.65 pA units, but is appreciably more polarizable it then seems likely that the inverted order of reactivity is caused by the polarizability term in accordance with Edwards equation. If this is correct, in the reactivity order piperidine > aniline > pyridine, inversion with respect to basicity appears to result from an abnormally high reactivity of aniline rather than from a particularly low reactivity of pyridine. This view differs from that based on relative steric requirements of the reagents, but other factors besides basicity and polarizability may well contribute to the quantitative experimental picture. 

The n values were high for all of the ionic liquids investigated (0.97-1.28) when compared to molecular solvents. The n values result from measuring the ability of the solvent to induce a dipole in a variety of solute species, and they will incorporate the Coulombic interactions from the ions as well as dipole-dipole and polarizability effects. This explains the consistently high values for all of the salts in the studies. The values for quaternary ammonium salts are lower than those for the monoalkylammonium salts. This probably arises from the ability of the charge center on the cation to approach the solute more closely for the monoalkylammonium salts. The values for the imidazolium salts are lower still, probably reflecting the delocalization of the charge in the cation. 

What is of primary importance chemically is not the ground state, nor the ground configuration, which is some average of valence states, of the free atom but it is the atomic response properties to perturbations by other atoms. That is governed by the energies and spatial extensions and polarizabilities of the upper core and of the compact valence orbitals ([34], p 653). 

PEO is found to be an ideal solvent for alkali-metal, alkaline-earth metal, transition-metal, lanthanide, and rare-earth metal cations. Its solvating properties parallel those of water, since water and ethers have very similar donicites and polarizabilities. Unlike water, ethers are unable to solvate the anion, which consequently plays an important role in polyether polymer-electrolyte formation. 

All the elements in a main group have in common a characteristic valence electron configuration. The electron configuration controls the valence of the element (the number of bonds that it can form) and affects its chemical and physical properties. Five atomic properties are principally responsible for the characteristic properties of each element atomic radius, ionization energy, electron affinity, electronegativity, and polarizability. All five properties are related to trends in the effective nuclear charge experienced by the valence electrons and their distance from the nucleus. 

The theoretical methods can be divided into two fundamental groups. The so-called continuum models are characterized by assuming that the medium is a structureless and polarizable dielectricum described only by macroscopic physical constants. On the other hand there are the so-called discrete models. The main advantage of... 

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