Induced polarization charges

Figure 18. The centers of mass of the induced electronic charge (xe), and induced polarization charge (x,) as a function of the amount of induced surface charge, in units of 10-3 e/(a.u.)3. The black filled circles show the calculated values of xe, and the solid black line is a quadratic fit to these values. The open circles indicate the calculated center of mass of the xs (equal to the edge position of an equivalent, classical uniform dielectric), and the line labeled Exp. dielectric edge indicates where they would need to be in order to reproduce the experimental compact capacity. The line labeled Shifted Oxygen dist. is the position of the oxygen surface layer as a function of charge, shifted downward by 2.4 a.u. From Ref. 52, by permission.

The parts that are related to the polarization interactions between the quantum mechanical subsystem and the induced polarization charges in the classical subsystem. These terms contain the operators T, A1, A,J. 

Generalized Reaction Fields from Surface Charge Densities Rather than centering attention on the charges or distributed multipoles, at various positions inside the solute cavity, that induce the reaction field, one can instead focus on the cavity surface. In particular, the effect of the reaction field may be modeled by an appropriately distributed set of induced polarization charges (virtual charges) on the surface S of the dielectric, as already mentioned. The virtual charge density, a(r), for each location r on S is... 

Directing the orientation of an anisotropic dielectric object in an electric field relies on the coupling of the electric field to induced polarization charges, whose distribution depends on the orientation of the object. When an external electric field is applied to a dielectric material by means of a constant potential difference across external electrodes, the electrostatic contribution to the free energy of the system [E] is given by... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

The induction (polarization) forces arise from the effeet of a moment in a polar molecule inducing a charge separation in an adjaeent molecule. The average potential energy funetions are... 

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. 

Ferenczy GG, Reynolds CA (2001) Modeling polarization through induced atomic charges. J Phys Chem A 105(51) 11470-11479... 

In this case, the agreement of the values calculated by the two methods is good, but it is not always so. One reason is that the simple vector approach ignores the effects of unshared pairs of electrons. Also, highly polar bonds can induce additional charge separation in bonds that might not otherwise... 

Klinke, C. Chen, J. Afzali, A. Avouris, P. 2005. Charge transfer induced polarity switching in carbon nanotube transistors. Nano Lett. 5 555-558. 

In the case of charged molecules, an additional friction force should be introduced as a result of the induced polarization of the surrounding solvent molecules. 

A dipole-induced dipole force is similar to that of an ion-induced dipole force. In this case, however, the charge on a polar molecule is responsible for inducing the charge on the non-polar molecule. Non-polar gases such as oxygen and nitrogen dissolve, sparingly, in water because of dipole-induced dipole forces. 

Figure 1.26 Induced polarization effects arising from a cationic vacancy in a crystal (negative net charge). Arrows mark induced dipoles at various lattice positions. From Lasaga (1981c). Reprinted with permission of The Mineralogical Society of America.

Subtracting a charge in a given lattice position also contributes to the defect energy with an induced polarization term whose significance was described in section 1.19 ... 

The dipole moments are generally affected by intermolecular electrostatic interactions. In a crystal, molecules tend to line up such that opposite charges are proximal, in order to maximize the electrostatic attractions. Induced polarization therefore tends to enhance the electrostatic moments. 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

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