Induced electric dipole

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

In much the same way as Stevens operators, the summation in Equation 1.15 is limited to well-defined values for f-electrons, the restriction k <7 holds, while q is limited to those values consistent with the point symmetry of the site. Finally, the even part k = 0, 2,4,6) is responsible for the CF splitting, while the odd part k = 1,3, 5,7) is responsible for the intensity of induced electric dipole transitions in optical spectroscopy [5b, 26]. 

The interaction between permanent or induced electric dipoles with an applied electric field is called polarization, which is the induced dipole moment per unit volume. Polarization causes positive charge to accumulate on the bottom surface next to the... 

We can examine how induced polarization behaves as a function of an applied electric field, ( , by considering the induced electric dipole moment (cf. Section 6.1.2.2), as a Taylor series expansion in... 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

The selection rules for the Raman spectrum turn out to depend not on the matrix elements of the electric dipole moment, but on the matrix elements of the molecular polarizability, which we now define. The application of an electric field E to a molecule gives rise to an induced electric dipole moment djnd (which is in addition to the permanent dipole moment d). If E= "> 1 + yl+ >zk, then the induced dipole moment has the components... 

In inelastic Raman scattering a photon loses (or gains) one quantum of rotational or vibrational energy to (or from) the molecule. The process involves the electric field of the radiation inducing an electric dipole in the molecule and so depends on the polarizability tensor of the molecule. (A (second-order) tensor is a physical quantity with nine components.) The induced electric dipole D is proportional to the electric field E ... 

It is found experimentally that the intensity of both the magnetic dipole and vibronically induced electric dipole allowed transitions are principally determined by the orbital character of the electronic states. That is, transitions that are forbidden in the orbital basis but allowed in the spin-orbit basis in Table 1, are likely to be weak. 

An alternative way of calculating the static polarizability is to evaluate the induced electric dipole moment by applying an external electric field in the SCF calculations, as described in section III. Variation of the induced dipole moment as a function of the applied electric field in the SCF calculations for Ceo is shown in Fig. 21 for the Hedin-Lundquvist exchange-correlation potential and an extended basis set. The calculations were performed using an electric field of strength up to 0.032 a.u. corresponding to 0.16-10 Vm . ... 

Linear Dipolar Electric Polarization. Even atoms and microsystems with symmetrically distributed charges are known to exhibit polarization under the influence of an external electric field or the internal (molecular) electric field of a neighbour. Such a system is said to become endowed with an induced electric dipole (or higher multipoles). In many a case it sufiSces to assume that the induced dipole moment p E) is proportional to the field strength inducing it ... 

Fluctuations of the Molecular Fields. The second right-hand term of Kerr s constant (191), in the case of dipolar molecules, leads directly to the result (178). We shall now show that this part of the Kerr constant is non-zero even in liquids composed of non-dipolar molecules. This is due to the circumstance that in dense media, even if no external field is applied, intense molecular fields fluctuating in time and space have to be considered locally. The molecular fields Fm induce electric dipoles in the molecules in such regions, giving rise in the medium to the non-zero total dipole moment A/q occurring in the second part of the constant (191). In fact, we have in a linear approximation ... 

Judd (13) has shown that the oscillator strength of an induced electric dipole transition may be related to the energy of the transition (v, in cm. ") and the square of the matrix elements of the unit tensor operators connecting the initial and final states via three phenomenological parameters T (A = 2, 4, and 6) according to Equation 2. 

The induced electric dipole moment P responsible for the Raman signal can be related to the electric field E of the incident radiation by the power series... 

Atom-Atom Interactions. - The methods applied, usually to interactions in the inert gases, are a natural extension of diatomic molecule calculations. From the interaction potentials observable quantities, especially the virial coefficients can be calculated. Maroulis et al.31 have applied the ab initio finite field method to calculate the interaction polarizability of two xenon atoms. A sequence of new basis sets for Xe, especially designed for interaction studies have been employed. It has been verified that values obtained from a standard DFT method are qualitatively correct in describing the interaction polarizability curves. Haskopoulos et al.32 have applied similar methods to calculate the interaction polarizability of the Kr-Xe pair. The second virial coefficients of neon gas have been computed by Hattig et al.,33 using an accurate CCSD(T) potential for the Ne-Ne van der Waals potential and interaction-induced electric dipole polarizabilities and hyperpolarizabilities also obtained by CCSD calculations. The refractivity, electric-field induced SHG coefficients and the virial coefficients were evaluated. The authors claim that the results are expected to be more reliable than current experimental data. 

Lifetimes of emitting states of Fe, Co, and Ni atoms isolated in Ar and Kr matrices lie in the reuige 150-1250 jis. The role of the matrix euid the possibilities of magnetic dipole or vibrationally induced electric dipole mechanisms for emission have been discussed. Ligauid field excitation of [Fe(CNCH,),] in acetonitrile solution induces consecutive photosubstitution processes involving formation of the monosolvated intermediate [Fe(CNCH,) s(NCCH,) which subsequently gives... 

Sum-frequency generation (SFG) at second-order and the nonlinear Raman spectroscopy BioCARS at fourth-order can also probe chiral molecules. They have no analog in linear optics. We show that both are only symmetry allowed in a fluid, if the fluid is chiral. However, in contrast to optical activity phenomena, these processes arise entirely from induced electric-dipoles (without magnetic or quadrupolar transitions) and they are not circular differential. All laser beams can be linearly polarized and no polarization modulation is required as the detection of a sum-frequency (yiz. five-wave mixing) photon is in itself a measure of the solution s chirality. Since an achiral solvent can not contribute to the signal, these techniques are sensitive, background-free probes of molecular chirality. The SFG... 

In the ligand polarization mechanism for optical activity, the potential of the electric hexadecapole component, Hxy(x>-y>), produces a determinate correlation of the induced electric dipole moment in each ligand group which does not lie in an octahedral symmetry plane of the [Co Ng] chromophore (Fig. 8). The resultant first-order electric dipole transition moment has a non-vanishing component collinear with the zero-order magnetic moment of the dxy dxj yj transition in chiral complexes, and the scalar product of these two moments affords the z-component of the rotational strength, RJg, of the Aj -> Ti octahedral excitation. 

The dynamic coupling between the electric hexadecapole moment of a d—d transition in the metal ion and an induced electric dipole in each ligand is forbidden in a four-coordinate complex containing a tetrahedral chromophore, although the mechanism becomes formally allowed on reduction to D2(i or lower chromophoric symmetry. In tetrahedral complexes the dynamic coupling between a d—d quadrupolar... 

The energy-dependent — r r polarization propagator is thus the dynamic polarizability tensor, i.e. the induced electric dipole moment in units of an external electric field. 

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