Local polarizability

Since hardness and the shear modulus are usually proportional, the factors that determine the shear moduli need to be understood. The shear moduli are functions of the local polarizability and this depends on the valence electron density, as well as the energy needed to promote a valence electron to its first excited state. The latter depends on the strength of the chemical bond between two atoms. This will be discussed in more detail in Chapter 3. 

Role of DFT Descriptors in the (Evaluation of) Dispersion Interaction From Local Polarizability to Local Softness... 

Both correlations indicate that polarizability at local level can be used to quantify the dispersion energy. In the next section, we take a further step within direction, moving to an atoms-in-molecules level, thereby linking local polarizability to local softness. 

As a further step currently under investigation, the relationship between local polarizability and local softness is studied with the aim to substitute atom-in-molecule polarizabilities by atom-condensed softness values. In this way, conceptual DFT could be exploited in a computational strategy, an ansatz rarely used until now, the best known example being the electronegativity equalization method [101]. 

In addition to its role with regard to chemical reactivity, 7(r) is also linked to atomic shell structure and electronegativity, local temperature (or kinetic energy), radical characterization, bond strain and local polarizability. For a recent overall review, see Politzer and Murray. ... 

Just as it is useful to have a local ionization energy, so would it be desirable, in the context of reactive behavior, to have a local polarizability, a(r). Reflecting the discussion earlier in this section, we have suggested that 7s(r) be viewed as an inverse measure of as(r) we focus upon the surface local ionization energy and surface local polarizability because the outermost electrons are expected to make the greatest contributions to a. The volume dependence that is so important on a macroscopic scale should not be a factor on the local level, which considers only infinitesimal volume elements dr. We have presented evidence in support of the concept expressed by equation 14 ... 

Some idea of the relative polarizabilities of various portions of the molecules in Table 8 can be obtained by looking at the group values in Table 7. However, a more detailed picture is provided by the variation of the local ionization energy 7s(r) over the molecular surface, if it is accepted that this is an inverse measure of local polarizability (equation 14). 

We have approached these multi-faceted systems by looking in particular at two local molecular properties the electrostatic potential, P(r) and Vs(r). and the local ionization energy, /s(r). In terms of these, we have addressed hydrogen bonding, lone pair-lone pair repulsion, conformer and isomer stability, acidity/basicity and local polarizability. We have sought to show how theoretical and computational analyses can complement experimental studies in characterizing and predicting molecular behavior. ... 

As noted in Chapter 2, computation of charge-charge (or dipole-dipole) terms is a particularly efficient means to evaluate electrostatic interactions because it is pairwise additive. However, a more realistic picture of an actual physical system is one that takes into account the polarization of the system. Thus, different regions in a simulation (e.g., different functional groups, or different atoms) will be characterized by different local polarizabilities, and the local charge moments, by adjusting in an iterative fashion to their mutual interactions, introduce many-body effects into a simulation. 

Although only a1 and e are used as additional descriptors so far, some others might be useful in the future. One of the most apparent is the local electronic polarizability of the molecule in the vicinity of a surface segment i, which we may represent by a local refractive index n,. Such local polarizability or local refractive index would allow for a refinement of the electrostatic misfit term, which presently only takes into account an average electronic polarizability of organic molecules. It is also likely that the local electronic polarizability is of importance to the strength of hydrogen bonds, which so far in COSMO-RS are only a function of polarity. Finally, from a physical perspective, the vdW interactions should be a function of the local polarizability as well. 

Unfortunately, the rigorous evaluation of a reasonable measure of local polarizability would take an extreme amount of additional computation time in the DFT/COSMO calculations. An approximate, but very fast quantum chemical calculation method for the local polarizability has recently been suggested by Politzer, Jin, and Murray [95]. The variations of the local polarizability on the surface of acetic acid are visualized in Fig. 7.1 according to this method. Its use for the improvement of COSMO-RS is just being tested. 

Fig. 7.1. Approximate local polarizability visualized on the surface of acetic acid [95]. (Courtesy of P. Politzer and P. Jin.)...

On the other hand, there are several clear perspectives for future improvements and extensions of COSMO-RS. One of the most obvious perspectives is the improvement of the underlying quantum chemical methods. While density functional theory appears to have reached its limit regarding the quality of the electrostatics, and hence of the COSMO polarization charge densities, there will be an increase in the availability of higher correlated ab initio methods like coupled cluster calculations at affordable computational cost. Quantum chemical calculation of local polarizability and eventually of suitable descriptors for dispersion forces should provide additional information about the strength of local surface interactions and can be used to improve the various surface interaction functionals. At the other end, the quantum chemical COSMO calculations for larger biomolecules and enzymes, which have just become available at reasonable... 

The significance of l(r) extends well beyond the prediction of reactivity toward electrophiles. It correlates with the shell structures of atoms57 and their electronegativities,58 indicates bond strain,59 and is related to local temperature60 and local polarizability.61,62 For a recent review, see Politzer and Murray.63... 

Jin P, Murray JS, Politzer P (2004) Local ionization energy and local polarizability. Int. J. Quantum Chem. 96 394-401... 

Here we note that only a single polarizability or susceptibility exists for any system. The reconstruction from local contributions is in fact an abstraction, the result of which depends on the detail wanted macroscopic with local susceptibilities or microscopic with local polarizabilities and—more importantly—on the partitioning of such properties. However, experimental chemists are used to such procedures from well-chosen series of compounds they derive bond energies as local contributions to heats of formation and ionic radii from crystal structures. Theoretical chemists obtain atomic charges from, e.g., a Mulliken analysis of their wave functions. We are able, following similar reasoning, to construct molecular polarizabilities from atomic ones [38,60], although there is formally no connection between them. In an opposite direction we can decompose a molecular polarizability into a many-center... 

The average local ionization energy 7(r) has many interesting and significant aspects and applications. It is related to local temperature and atomic shell structure, it is linked to electronegativity and shows promise as a measure of local polarizability. It permits the characterization of bonds and radical sites, and - in conjunction with volume -the prediction of molecular and group polarizabilities. Finally, it is an effective guide to reactivity towards electrophiles, especially when complemented by the electrostatic potential. All of these areas continue to be studied. 

Diffuse dispersive attractions and hydrophobic effects One may easily imagine that many different, inhomogeneous electric fields are present in supramolecular assemblies. These fields induce new electric fields, which may also be decomposed into electrostatic multipoles (for instance, dipole moments may be induced depending on the strength of the inducing permanent field and the (local) polarizability of the system, which is the material specific quantity). Interactions based on these effects are usually denoted van der Waals interactions. But note that the induced fields themselves will induce new polarization effects and so on. 

As the next step, using a generalized version of Little s original propxal, we have to take into account that the atomic cores of the TCNQ molecules (containing besides the nuclei and the Is electrons also the valence shell electrons in the PFP approximation) provide a localized polarizable "side chain" electron system which may substantially reduce through its screening the repulsion between the Jtf -electrons. For the description of these electrons we applied LCAO molecular orbitals localized each on... 

The As atom has been found to induce a HAE on a Trp residue of Eco RI methyltransferase (Table II). The perturbing group is (CH3)2 As (III) that is produced, for example, by reduction of cacodylic acid with mercaptides. Like CH3Hg+, it binds to accessible Cys residues. The use of mutant enzymes has shown that the perturbed residue is Trp-225, and that the perturbing As binds with high affinity to Cys-223, thus revealing the proximity of the side chains of these residues in the methylase structure. In addition to the HAE, which is T -specific, reducing its lifetime to around 25 msec, a phosphorescence red shift of 9.8 nm also is induced. This may reflect an increase in local polarizability from introduction of the As atom. 

We have seen that the physical reason why the superposition approximation fails is the induced tilting of neighboring colloids. More generally, any finite particle in contact with the membrane will induce extra membrane deformations if the membrane in its vicinity is perturbed. This is simply a polarization effect Any incoming field interacts with the boundary conditions imposed by the particle and these then create new outgoing fields. Superposition of fields would work for point particles, but these do not capture the polarization effects, unless we equip them with the requisite polarizabilities. But this of course we can do. We can write a new Hamiltonian of interacting point particles, where each of them has the same polarizabilities as the actual finite size particles of the situation we actually wish to describe. This works by adding terms to the Hamiltonian that are localized at the position of the particle and that couple to the field in the same way that a local polarizability would. For instance, if a particle at the position r has a dipole... 

Van Nhu, N. Nowak, G. Svejda, P. Excess Gibbs energies of some liquid mixtures with polar components, effects of local polarizability Ben Bunsen-Ges. Phys. Chem. 1988,92,1537-1543... 

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