Dipole polarizability/polarization

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. 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

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-... 

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

Any molecule has an infinity of excited orbitals in the continuum above the first ionization energy. The electric dipole polarizability is connected partly with a few of these continuum orbitals and partly with the valence orbitals (7). If the simultaneous formation of empty orbitals of X, but with the continuum, it is reasonable to think of M being polarized by X. The population of the continuum orbitals of X is expected to be the more... 

Ion-induced dipole-a polar solid and polarizable adsorbate. 

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. 

Benzophenone (see Figure 7-5) is another example of the importance of the solute polarization. This molecule is more polarizable than acetone. Benzophenone has polarizable tt clouds in the rings and larger dipole polarizability estimated as 144 eaft [125], compared to 43 eal [126] for acetone. 

This polarization has two components the induced polarization P (due to movement of the centers of charge, or to the static electric dipole polarizability a of molecules) and the dipole polarization Pjt (due to the orientation of the permanent dipoles m in the applied electric field E) ... 

One feature of the semiempirical models is that because the polarization is described by a set of coefficients that have a normalization condition, for example, Eq. [69], there will be no polarization catastrophe like there can be with dipole polarizable or fluctuating charge models. With a finite basis set, the polarization response is limited and can become only as large as the state with the largest dipole moment. 

The linear and non-linear polarizabilities of a molecule in solution differ from those of the isolated molecule in the gas phase since the molecular properties are modified by solute-solvent interactions. Some of these interactions are present even in the absence of externally applied static or optical fields. For molecules with a non-zero dipole moment fj in the electronic ground state the dominant interaction is usually due to the reaction field contribution The molecular dipole moment polarizes the solvent environment and thus generates a polarization field which interacts with the solute. This field is given by (88) (Boettcher, 1973 Wortmann and Bishop, 1998). 

The occurrence of Raman scattering is connected to the change in polarizability during the transition of the molecule from one vibrational state to the other. Circular polarization ROA arises from interference of the electric dipole electric dipole polarizability tensor with the electric dipole - magnetic dipole and the electric dipole electric quadrupole optical activity tensors. Due to limited space, no rigorous derivation of the theory will be given here, but only the most important results shall be shown. 

Ah initio and experimental Raman optical activity in (+)-(/ )-Methyloxirane were reported by Bose et al. (1990). The measured spectra include depolarized, polarized, and magic angle Raman and ROA spectra. Magic angle (i.e. transmission axis of the analyser set at 35.26 ° to the vertical) ROA spectra contain only contributions arizing from the electric dipole magnetic dipole polarizability. All three kinds of spectra were calculated with two basis sets and compared to experiments. All spectral features could be reproduced correctly in sign but only moderately in intensity. 

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