Dipole polarizability model

Interesting properties of the induced dipole polarizable model can be derived by simple mathematical manipulation. A particularly important one relates the minimum of the energy with converged values of the induced dipole. By combining Eqs. (9-9) and (9-10), the induction energy can be rewritten as... 

The most popular way of introducing MM polarization is the isotropic dipole polarizability model in which each MM atom, m, is assigned an isotropic dipole polarizability, am- This means that it is possible to induce a dipole on each atom, limt whose magnitude is proportional to the size of the electric field at the atom, Em ... 

The dipole polarizability model can be readily adapted for use with QM/MM hybrid potentials. The major hurdle in doing so arises because the electric field at an MM atom will depend not only on the charge distribution of the MM atoms but also on that of the QM atoms as well. This means that both the induced dipoles on the MM atoms and the wavefunction of the atoms in the QM region must be determined self-consistently. In practice, this is achieved by an iterative procedure in which the MM dipoles and QM wavefunction are obtained at each cycle and the process repeated until convergence. 

This dipole polarizability model has been implemented for use in hybrid potentials by a number of groups. Both Warshel and Levitt [15] and Singh and... 

The dipole polarizability model is not the only way in which polarization effects can be included in an MM force field. An alternative, although less widely used, scheme is based upon the concept of electronegativity equalization [38, 39]. In the most common version of the method it is supposed that the electrostatic energy of a MM system, Ee ec, can be written as ... 

The static electric dipole polarizability a of the model system investigated is therefore... 

For a given a the force constant ko can be chosen in a way that the displacement d of the Drude particle remains much smaller than the interatomic distance. This guarantees that the resulting induced dipole jl, is almost equivalent to a point dipole. In the Drude polarizable model the only relevant parameter is the combination q /ko which defines the atomic polarizability, a. It is... 

Results of parameter optimization and MD simulations of small model compounds have been published, including alcohols [63], alkanes [63], aromatic [64] and heteroaromatic [209] compounds and liquid amides [65], Studies of ions in aqueous solution were also performed [61, 88] and results from an MD simulation on a DPPC lipid monolayer have been reported (Harder, MacKerell, Roux, submitted). Notable from the monolayer study was the reproduction of the dipole potential across the monolayer, a value that cannot be reproduced using non-polarizable models. This exciting, unforeseen observation points to the types of results that may be obtained from polarizable macromolecular force fields that are not accessible to the present additive models. 

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

To answer this question, let us first consider a neutral molecule that is usually said to be polar if it possesses a dipole moment (the term dipolar would be more appropriate)1 . In solution, the solute-solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole m = E induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole-dipole, solute dipole-solvent polarizability, solute polarizability-solvent dipole, polarizability-polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

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. 

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