Vibrational polarization

Here the indices X, V, Z indicate vibration polarizations, other designations being the same as in expressions (3.2.6). Finally, the Davydov splitting of spectral lines obtained as... 

Ultrafast vibrational spectroscopy offers a variety of techniques for unraveling the microsopic dynamics of hydrogen bonds occurring in the femto- to picosecond time domain. In particular, different vibrational couplings can be separated in nonlinear experiments by measuring vibrational dynamics in real-time. Both coherent vibrational polarizations and processes of population and energy relaxation have been studied for a number of hydrogen bonded systems in liquids [1],... 

Comments on NLO and Electrooptic Coefficients. Typically, the Pockels effect is observed at relatively low frequencies (up to gigahertz) so that slower nonlinear polarization mechanisms, such as vibrational polarizations, can effectively contribute to the "r" coefficients. The tensor used traditionally by theorists to characterize the second-order nonlinear optical response is xijk Experimentalists use the coefficient dijk to describe second-order NLO effects. Usually the two are simply related by equation 31 (16) ... 

This scattering process is due to the interaction of electrons with the electric field induced by the lattice vibration polarization (polar longitudinal-optical phonons) occurring in polar semiconductors with partially ionic bonding. According to Devlin [55], the optical Hall mobility can be calculated by... 

The intensification of the band identified by Moncuit aig a u for the free ion (situated at 2,800 A for the platinocyanides and at 2,400 A for the palladocyanides) when working on thin polycrystalline sheets can easily be explained by the preferential orientation of the crystals on the quartz plate. It must be remembered that this band related to incident vibrations polarized perpendicular to planar groups no longer appears clearly at this energy for the complexes with alkali-metal and alkaline-earth cations. 

The polarization P of a molecule has three frequency components v and v v and the vibrational polarization emits light with its frequency. Therefore in general light scattering experiments, scattered light with these frequencies can be observed. In contrast a Raman spectrum can be measured only in the case where there are changes in molecular polarizability in the various vibrational modes, since Eq. (4.16) is expected to hold at dA/dQ 0 (Raman active). 

Equation (4.1.15) implies that at any point in the medium there are two linear vibrations polarized along the local principal axes. The polarization directions of these two vibrations rotate with the principal axes as they travel along the axis of twist and the phase difference between them is the same as that in the untwisted medium. This result was first derived by Mauguin and is sometimes referred to as the adiabatic approximation. It is this property that is made use of in the twisted nematic device discussed in 3.4.2. 

A dipolar process is described in terms of three quantities the orientation polarization, the vibrational polarization, and the relaxation time. The first of the three is expressed as A =85-8oc, where is as defined earlier, and is the limiting high-frequency permittivity. The vibrational polarization is expressed as A8vib=eoo- op. where op is the refractive index of the material, usually at the... 

Contribution from vibrational polarization in a material is given by the following ... 

Of course, the equilibrium configurations of the molecule with and without an electric field differ. In a simple case, say the HCl molecule, the HCl distance increases. It has to increase since the cathode pulls the hydrogen atom and repels the chlorine atom, while the anode does the opposite. In more complex cases, like a flexible molecule, the field may change its conformation. This means that the polarizability results both from the electron cloud deformation and the displacement of the nuclei. It mrns out that the latter effect (called vibrational polarization) is of great importance. ... 

Momany s idea has led to a new definition of atomic charges. It would be possible to write volumes about atomic charges (AC), a concept that has no a precise definition in QM formalism, but is of extreme utility in practical applications. Many definitions of AC are based on manipulations of the molecular wave function, as, for example, the famous Mulliken charges. Other definitions are based on different analyses of the QM definition of the charge density, as for example Bader s charges.There are also charges derived from other theoretical approaches, such as the electronegativity equalization, or from experimental values, such as from the vibrational polar tensors. 

The symmetric rotor fine structure for a totally symmetric vibration (polarized) should be similar in the Raman effect to the parallel ( ) infrared band of the same type of molecule, except that 0 and S branches occur and that the Q branch is very strong. The nontotally symmetric and degenerate modes in the Raman spectrum should have a fine structure resembling that of a perpendicular ( L) infrared band, since changes in K occur. 

Pr is a matrix of dipole moment derivatives widi respect to internal coordinates. Vx is called vibrational polar tensor matrix. B and L are defined by relations (2.4) and (2.12). 

Px is a sum of two terms — vibrational polar tensor (PgBg) and rotational polar tensor (PpP). The rotational polar tensor is evaluated using an equilibrium dipole moment value of -1.87 D [34]. The PsBs and PpP matrices are given below. 

Coordinate definitions, Lg and P matrices for H2O used in evaluating the atomic polar tensor elements are as given in section 3.3. With the aid of relation (4.14) die Pg matrix is transformed into vibrational polar tensor, while the rotational polar tensor is calculated using a permanent dipole moment value of-1.85 D [34]. The two submatrices obtained are as follows (in units of D A l) ... 

In general matrix formulation the vibrational polar tensor of a molecule is given by... 

The expression Pg Bg - Rg Bg appearing in the right-hand side of Eq. (5.8) represents a vibrational polar tensor corrected for contributions arising from the compensatoiy molecular rotation accompanying some vibrational modes. This relation was used in section 4.4 to obtain rotation-free atomic polar tensor Px(v) [Eq. (4.143)]. As already mentioned, in contrast to the usual atomic polar tensors Px, the rotation-free tensor Px(v) refers to a molecule-fixed Cartesian system. Because of the presence of the term Rg Bg, the elements of Px(v) will be the same for all isotopes of the molecule with identical symmetry. 

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