Electric dipole moment induced

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... 

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... 

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 . ... 

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... 

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 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. 

Following the approach of electromagnetism, we characterize the linear response of the medium to the electromagnetic field by a freqnency-dependent dielectric constant e. The induced electric dipole moment is equal to this dielectric constant mnltiplied by the value of the electric field of the irradiating electromagnetic wave, s is a complex quantity, having the form, with F = — 1... 

Metallomesogens have been studied for their potential as nonlinear optical (NLO) materials. Such materials could find applications in the domains of opto-electronics and photonics.Nonlinearity of the optical properties means that when a molecule is placed in an intense light beam, there is no linear relationship between the induced electric dipole moment and the applied electric field, the induced dipole moment is given by Equation 2.3. 

The summation runs over repeated indices, i i is the /th component of the induced electric dipole moment and Ei are components of the applied electromagnetic field. The coefficients Oij, / ijk and yijki are... 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

An objection to taking (13.140) as the dipole moment is that we considered only the first-order energy correction. If we had included in (13.139), the comparison with (13.136) would not have given (13.140) as the dipole moment. Actually, (13.140) is the dipole moment of the system in the absence of an applied electric field and is the permanent electric dipole moment. Application of the field distorts the wave function from giving rise to an induced electric dipole moment in addition to the permanent dipole moment. The induced dipole moment corresponds to the energy correction FP. (For the details, see Merzbacher, Section 17.4.) The induced dipole moment /tj d is related to the applied electric field E by... 

The bulk polarization can be related to the induced electric dipole moments of the constituent molecules through... 

The force can be deduced from the potential energy of the induced electric dipole moment in the inducing fields themselves. Thus the induced dipole moment o is associated with a potential... 

Now introduce (4.6) for the bulk polarization, with the induced electric dipole moment written in terms of the polarizability ... 

Since P represents the induced electric dipole moment per unit volume and M represents the induced magnetic dipole moment per unit volume, in homogeneous isotropic media these quantities may therefore be expressed as... 

The Mcroaeopic polarization I (t) ia ordinarily taken to be for a sum of classical permanent and induced electric dipole moments of molecules or constituent segments as in polymers for example. This approximation is justified quantum... 

A. Baranowska, B. Fernandez, A. Rizzo, B. Jansik, The CO-Ne van der Waals complex ab initio intermolecular potential energy, interaction induced electric dipole moment and polarizability surfaces, and second viral coefficients. Phys. Chem. Chem. Phys. 11, 9871... 

For the dynamics simulation, we again used our approach [80] for the coupled electron and nuclear quantum dynamics. We followed the time-dependent expectation value of the induced electric dipole moment nit) = which is related to the time-dependent electron density ptot r,t R t)) of Eq. (8.12) through n(t)) = (ptotir,l R(l)) fi (ptot(r,t, R(t )r) with the dipole operator. 

Baranowska et reported a high-level investigation of the potential energy surface (PES) of the Ne-CO interaction. The calculations were performed at the CCSD(T) level of theory with the d-aug-cc-pVTZ basis set supplemented with 3s3p2dlflg midbond functions. The minimum of the PES corresponds to a nearly T-shaped structure with the Ne atom located at a distance of 3.383 A from CO and an angle of 79.4°. The interaction-induced electric dipole moment and polarizability was determined at the CCSD/d-aug-cc-pVTZ-33211 level of theory. In addition, the authors determined the dielectric and refractivity virial coeflicients and the pressure virial coeflicients of the CO-Ne complex. 

When light is incident on a polymer sample the sample is subg ed to an alternating electric field with frequencies in the ran 10 to 10 Hertz. In response to this field the electrons in the sample move with a periodic motion and become themselves a source of secondary dipole radiation. Hence the induced electric dipole moment, Pj, in the i direction (i = x, y, z) may be expanded in terms of the electric field by the equation ... 

The induced electric dipole moment p of individual atoms and molecules can be written in terms of the local electric field F and the polarizabilities, similar to Eq. (6) ... 

The linear response function describing the first-order induced electric dipole moment due to an oscillating and spatially uniform electric field is related to the frequency-dependent electric... 

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