Electrostatic interaction model induced dipole

Image-charge models. These models take into account the discreteness of surface charges, which induces orientation in the adjacent water dipoles [574-577]. Dipoles due to zwit-terionic surface groups, for example, phospholipid headgroups [578], have been also taken into consideration in models of the electrostatic interaction between planar dipole lattices [579-583]. 

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 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... 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

Here, a. and a L are the polarizabilities of the diatom parallel and perpendicular to the internuclear separation, R12. The electrostatic theory accounts for the distortions of the local field by the proximity of a point dipole (the polarized collisional partner) and suggests that the anisotropy is given by ft Rn) 6intermolecular interactions). This is the so-called dipole-induced dipole (DID) model, which approximates the induced anisotropy of such diatoms often fairly well. It gives rise to pressure-induced depolarization of scattered light, and to depolarized, collision-induced Raman spectra in general. 

Yonker and co-workers (60) used near-and mid-IR spectroscopy to study supercritical C02 and binary supercritical fluid systems composed of C02/H20, Kr/H20, and Xe/H20. The C02 results are consistent with increased intermolecular interaction between C02 molecules with increasing density. This parallels previous results using UV-Vis solvatochromism (21-28,32). For an ideal gas/water system an Onsanger electrostatic model (dipole-induced-dipole) sufficed to describe the spectral shifts. In contrast, the C(VH20 system exhibited density-dependent changes in specific intermolecular interactions. 

To further illustrate the importance of coupling the electrostatic and short-ranged repulsion interactions, we consider the example of a dimer of polarizable rare gas atoms, as presented by Jordan et al. In the absence of an external electric field, a PPD model predicts that no induced dipoles exist (see Eq. [12]). But the shell model correctly predicts that the rare gas atoms polarize each other when displaced away from the minimum-energy (force-free) configuration. The dimer will have a positive quadrupole moment at large separations, due to the attraction of each electron cloud for the opposite nucleus, and a negative quadrupole at small separations, due to the exchange-correlation repulsion of the electron clouds. This result is in accord with ab initio quantum calculations on the system, and these calculations can even be used to help parameterize the model. ... 

In the Debye-Hilckel model the interactions contributing to the potential energy, 0, are long range coulombic interactions between the ions. However, because of the versatility of the computer simulation calculations, the statistical mechanical description of an electrolyte solution could include all conceivable electrostatic interactions such as the ion-ion, ion-dipole and dipole-dipole, dipole-quadrupole and quadrupole-quadrupole as weU as induced dipole interactions between the ions, and between the ions and the solvent and between solvent molecules. The total potential energy, 0, fed into the calculations which ultimately lead to g( (ri2) could be made up of contributions such as these and those given in Sections... 

Attempts to represent the three-body interactions for water in terms of an analytic function fitted to ab initio results date back to the work of dementi and Corongiu [191] and Niesar et al. [67]. These authors used about 200 three-body energies computed at the Hartree-Fock level and fitted them to parametrize a simple polarization model in which induced dipoles were generated on each molecule by the electrostatic field of other molecules. Thus, the induction effects were distorted in order to describe the exchange effects. The three-body potentials obtained in this way and their many-body polarization extensions have been used in simulations of liquid water. We know now that the two-body potentials used in that work were insufficiently accurate for a meaningful evaluation of the role of three-body effects. 

The boundary element method of Rashin is similar in spirit to the polarisable continuum model, but the surface of the cavity is taken to be the molecular surface of the solute [Rashin and Namboodiri 1987 Rashin 1990]. This cavity surface is divided into small boimdary elements. The solute is modelled as a set of atoms with point polarisabilities. The electric field induces a dipole proportional to its polarisability. The electric field at an atom has contributions from dipoles on other atoms in the molecule, from polarisation charges on the boundary, and (where appropriate) from the charges of electrolytes in the solution. The charge density is assumed to be constant within each boundary element but is not reduced to a single point as in the PCM model. A set of linear equations can be set up to describe the electrostatic interactions within the system. The solutions to these equations give the boimdary element charge distribution and the induced dipoles, from which thermodynamic quantities can be determined. 

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