Density polarizable

As the formation of a covalent bond between two atoms implies a (dipolar) deformation of the density, polarizability and reactivity must be related. Indeed, Nagle demonstrated an empirical relation between the atomic polarizabilities (response to a field) and the scales of electronegativities (reactivity) [36]. More... 

The scope of the quantum chemistry is manifold. It provides numerical solutions obtained by the use of equations of the quantum mechanical theory. It enables to calculate bond and dissociation energies, characteristics of spectral transitions, force constants, electron and spin densities, polarizabilities. The properties referring to atoms, molecules and other systems can be theoretically determined without knowledge of empirical data of these systems (ab initio level). 

Table 1. Ionic Radii, hydration numbers, softness parameters a, surface charge densities, polarizabilities, free energies AG° enthalpies AH° and entropies A S° of hydration of metal cations from groups Za o,nd II ...

The reactivity indices method is based on the assumption of a direct correlation between the activation free energy of a process and some intrinsic parameters, called reactivity indices, related to the electronic properties of the heteroaromatic species involved in the process itself. Some indices, such as charge density, frontier electron density, polarizability, or free valence, pertain to electronic properties of the unperturbed neutral substrate, which is considered in an isolated state. Other indices, such as the localization energy, are related to the stability of the transitional or intermediate state of the substitution process, e.g., the n or a complex in electrophilic substitution reactions (Fig. 1). 

Atomic Densities, Polarizabilities, and Natural Orbitals Derived from Generalized Sturmian Calculations... 

Fig. 11.5 Experimental density/polarizability plot for solid hydrogen (T=80 to 90 K), from polarizability data (O) and H2/dieimond RI matching ( ). Near-linetirity of the curve indicates the constancy of the A factor. (Adapted from [29] with permission of the American Physical Society (Copyright 1998) and Lawrence Livermore national Laboratory)...

The indices described above are most appropriate for indicating the relative ease of reaction in the early stages. By the time the reactants have reached the transition state, the substrate is quite far from its starting condition, so charge densities, polarizabilities, free valences calculated from the wavefunction of the unperturbed molecule may no... 

The currently described knowledge about localized charge entrapment and polarization associated with the skin of both the liquid and the solid specimen provides an electronic mechanism for the 4S. According to the BOLS-NEP notation, the small fluidic drop can be viewed as a liquid core covered with a solid-like, densely charged, and elastic sheet with pinned dipoles. The energy density, charge density, polarizability, and the trap depth are bond order dependence. 

Mineva T, Russo N and Sicilia E 1998 Solvation effects on reaction profiles by the polarizable continuum model coupled with Gaussian density functional method J. Oomp. Ohem. 19 290-9... 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

The larger the box (moleeule), the more polarizable the eleetron density. 

Many molecular properties can be related directly to the wave function or total electron density. Some examples are dipole moments, polarizability, the electrostatic potential, and charges on atoms. 

This modification of the charge interaction is responsible for shifts in the electron density as permitted by the polarizability of the molecule. 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

In the next section we shall pursue the scattering by fluctuations in density. In the case of solutions of small molecules, it is the fluctuations in the solute concentration that plays the equivalent role, so we shall eventually replace 6p by 6c2. First, however, we must describe the polarizability of a density fluctuation and evaluate 6p itself. 

This is opposite from the order in solution as revealed by the pK data in water and DMSO shown in Table 4.14. These changes in relative acidity can again be traced to solvation effects. In the gas phase, any substituent effect can be analyzed directly in terms of its stabilizing or destabilizing effect on the anion. Replacement of hydrogen by alkyl substituents normally increases electron density at the site of substitution, but this effect cannot be the dominant one, because it would lead to an ordering of gas-phase acidity opposite to that observed. The dominant effect is believed to be polarizability. The methyl... 

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