Electrostatic interaction model

The results were compared to MD-simulations [317]. Whereas the scattering function of pure PEO could be well described, the dynamics of the salt-loaded samples deviates from the predictions obtained with various electrostatic interaction models. The best but still not perfect and - at least for longer times -unphysical model assumes Hookean springs between chains to simulate the Na-ion mediated transient cross-links [317]. 

In a stndy of retention of aromatic carboxylic acids under IPC conditions, linear free energy relationships were observed between the capacity factors and the extraction eqnilibrinm constants of benzoic acid and naphthalene carboxylic acid. The capacity factor of benzene polycarboxylic acids was directly related to then-association constants and qnatemary ammonium ions calculated on the basis of an electrostatic interaction model [27,28],... 

The MO explanation for the anomeric effect considers the n-a overlap between the lone-pair of Y and the vacant a orbital of the C—X bond. This stabilizing interaction is more effective when X is axial and thus the axial conformer is favoured. The electrostatic explanation invokes the destabilizing interaction between the dipole moment of the C—X bond and the dipole moment resulting from the C—Y bond and the lone-pairs of Y. Such dipole/dipole interactions are minimized when X is axial and again the axial conformer is preferred in the gas phase or in nonpolar solvents. It is not so easy to distinguish between the relative importance of each interaction. However, the observation that the axial preference is diminished by increasing solvent polarity is best explained by the electrostatic interaction model [82, 282-284], The unfavourable electrostatic dipole/dipole repulsion in the equatorial anomer decreases with increasing solvent polarity, and hence the equilibrium shifts towards the equatorial conformer in polar solvents. This solvent-dependent anomeric effect has been particularly well studied with 4,6-dimethyl-2-methoxytetrahydropyran [283, 284] and 2-methoxy-1,3 -dimethylhexahydropyrimidine [282]. 

As in the case of two interacting soft plates, when the thicknesses of the surface charge layers on soft spheres 1 and 2 are very large compared with the Debye length 1/k, the potential deep inside the surface charge layer is practically equal to the Donnan potential (Eqs. (15.51) and (15.52)), independent of the particle separation H. In contrast to the usual electrostatic interaction models assuming constant surface potential or constant surface... 

Generalized Bom (GB) approach. The most common implicit models used for small molecules are the Conductor-Like Screening Model (COSMO) [77,78], the DPCM [79], the Conductor-Like Modification to the Polarized Continuum Model (CPCM) [80,81], the Integral Equation Formalism Implementation of PCM (IEF-PCM) [82] PB models, and the GB SMx models of Cramer and Truhlar [23,83-86]. The newest Minnesota solvation models are the SMD universal Solvation Model based on solute electron density [26] and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [87-89] with semiempirical terms that account for local electrostatics [90]. Further details on these methods can be found in Chapter 11 of Reference [23]. 

Saito, T. et al.. Electrostatic interaction models for ion binding to humic substances, Colloids Surf. A, 265, 104, 2005. 

The Debye-Huckel equation (and other empirical expressions that correct measured concentrations to activities) fails to account for specific ion pairing and com-plexation in solution, which in some salt solutions may contribute more to the inequality between concentration and activity than the nonspecific electrostatic interactions modeled by the equation. Ion pairing or complexation is likely to become significant in solutions with any of the foUowing characteristics ... 

Boese and Foerster [596] found pronounced similarities in the adsorption behavior and IR spectroscopic features of isoelectronic molecules such as N2 and CO (or CO2 and N2O, vide infra). For calculations, an electrostatic interaction model was used. As mentioned above, the cations were identified as the centers of adsorption, since the main potential wells were found in front of them. Also, the geometry of the adsorption complexes was shown to be similar (cf. Fig. 34). 

An electrostatic interaction model has been presented for the calculation of the static electronic polarizability of hydrocarbons, which, contrary to previous models, can describe aliphatic, olefinic, and aromatic systems. It is based on the representation of the C and H atoms by induced electric charges and dipoles, where the actual values of the charges and dipoles are those that minimize the electrochemical energy of the molecule. The electrostatic interactions are described in terms of normalized propagators, which improves both the consistency and the numerical stability of the technique. The calibration of the model is sought by reproducing the molecular polarizabilities obtained by current density functional theory for a set of 48 reference structures. An excellent agreement with the reference data has been obtained as evidenced by the relative errors on the mean molecular polarizabilities of 0.5, 1.4, and 1.9% for alkanes, alkenes, and aromatic molecules, respectively. 

In what follows, we first discuss the basic aspects of DFT in Section 6.2 and the electrostatic interaction model for polarizability in Section 6.3. The density-based theoretical formalism for electric response of clusters and suitable coarse graining forms the subject matter of Section 6.4. Miscellaneous aspects of polarizability calculation of metal clusters are discussed in Section 6.5 which is followed by presentation of concluding remaiks in Section 6.6. 

In a simple electrostatic interaction model proposed originally by Silberstein [37] and Applequist [20], the response of an aggregate of atoms (molecule or cluster) to an external electric field can be determined through the atomic dipoles induced at each individual atom as a response to not only the external field buf also an effective field due to the other induced dipoles, which depend on the atomic polarizability parameters. The basic equation of this interaction approach to obtain the polarizability of the aggregate is given by the expression for the induced dipole p at the a-th atomic site, given by... 

The equations used in the electrostatic interaction model are however empirical or obtained through an expansion of the energy in terms of the charges and the dipoles. It is only recently that more rigorous DFT-based expressions have been obtained which are discussed in the following section. 

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