Polarizability polarization contributions

For an interface between two phases with no common charged or polarizable components, contributions of the two phases to certain properties are easily distinguished theoretically. The charge density and electrical polarization at any point in the interface are each sums of two contributions which can be assigned to the two phases. The overall electroneutrality of a planar interface may be written... 

The terms polarizability constant and dielectric constant can be utilized interchangeably in the qualitative discussion of the magnitude of the dielectric constant. The k values obtained utilizing dc and low-frequency measurements are a summation of electronic E, atomic A, dipole P0, and interfacial /, polarizations. Only the contribution by electronic polarizations is evident at high frequencies. The variation of dielectric constant with frequency for a material having interfacial, dipole, atomic, and electronic polarization contributions is shown in Figure 6.1. 

Like alkanes, alkenes are relatively nonpolar. They are insoluble in water but soluble in nonpolar solvents such as hexane, gasoline, halogenated solvents, and ethers. Alkenes tend to be slightly more polar than alkanes, however, for two reasons The more weakly held electrons in the pi bond are more polarizable (contributing to instantaneous dipole moments), and the vinylic bonds tend to be slightly polar (contributing to a permanent dipole moment). 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

The polarization contribution Ep itself could be calculated from F and the polarizability a of the adsorbate, using ... 

The contribution p is due to the polarization of the molecules by electric fields on the adsorbent surface, eg, electric fields between positively charged cations and the negatively charged framework of a zeolite adsorbent. The attractive interaction between the induced dipole and the electric field is called the polarization contribution. Its magnitude is dependent upon the polarizability a of the molecule and the strength of the electric field F of the adsorbent (4) P = —l/2aF2. 

The atomic polarizability as may be taken as a fixed parameter, but the total electric field on atom s, Ej, must be computed at every step. This is a quite computer demanding calculation, hence the solvent polarization contribution is often discarded. 

Veldhuizen and de Leeuw (1996) used the OPLS parameters for methanol and both a nonpolarizable and a polarizable model for carbon tetrachloride for MD simulations over a wide range of compositions. The polarization contribution was found to be very important for the proper description of mixture properties, such as the heat of mixing. A recent study by Gonzalez et at (1999) of ethanol with MD simulations using the OPLS potential concluded that a nonpolarizable model for ethanol is sufficient to describe most static and dynamic properties of liquid ethanol. They also suggested that polarizabilities be introduced as atomic properties instead of the commonly approach of using a single molecular polarizability. 

It is interesting to note that formula (64) is applicable to two cylindrically symmetric particles, such as between two nanotubes [43, 61], if fhe applied field is the only source of radiation. If fhis is fhe case, only the principal axis (diagonal elements) of the polarizability tensors contribute, corresponding to the component aligned in the same direction as the laser polarization. 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

Fig. 9 Plot of the regressions between the quadrupole moments and molecular polarizabilities to a the electrostatic contribution, b polarization contribution and c van der Waals contribution of the total interaction energy calculated with MlPp for the compounds interacting with chloride at the minimum, d Plot of the regression between the quadrupole moments to the interaction energy at the MP2/6-31++G level of theory for the compounds interacting with chloride at the minimum. From reference [31]...

State-specific response of the polarizable environment, calculated by Eq. 5.15, is several times smaller than the indirect polarization shift, or 0.01-0.02 eV in absolute values. Thus, polarization correction provides only a minor contribution to the solvatochromic shift in pNA-water complexes. However, when the ground (reference) state and excited state signiflcantly differ in character, such as the case in EOM-IP methods, direct polarization contribution might become veiy significant. An overall role of polarization is expected to increase in larger clusters and bulk systems, where the many-body effects become prominent. 

Numerous polarizable water models have recently been developed [75-82]. At least three types of polarizable models have been used for supercritical water PPC [83], a polarizable TIP-type model [84], and a few variations of SPC-type models with either point or smeared electrostatic charges [78,85,86]. With a few exceptions [87-89] the polarizable models are typically built upon successful non-polarizable counterparts, by scaling the Coulombic charges to match the gas-phase dipole moment, and by including either a polarizable point charge or point dipole to account for the many-body polarization contributions. Moreover, sometimes the permanent dipole moment is set larger than the gas-phase value of 1.85D in order to obtain better agreement with experimental data at ambient conditions [78,82]. 

At optical fiequOTcies, only the electronic polarization contributes to the molecular polarizability, which is small, and the electric field is usually low. De Jeu and Bordewijk experimraitally showed that (1) (2cx + e//)/3p is a constant through the nematic and isotropic phases [25,26], where / is the mass draisily, (2) the dielectric anisotropy Ae = c//-ex is directly proportional... 

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

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