Dipole modes

KEYWORDS CHIM, dipole mode, time-control function The cathode receiver with... 

Figure 1. Photoabsorption cross section for the dipole plasmon in axially deformed sodium clusters, normalized to the number of valence electrons N - The parameters of quadrupole and hexadecapole deformations are given in boxes. The experimental data [39] (triangles) are compared with SRPA results given as bars for RPA states and as the strength function (49) smoothed by the Lorentz weight with A = 0.25 eV. Contribntions to the strength function from p =0 and 1 dipole modes (the latter has twice larger strength) are exhibited by dashed curves. The bars are given in eVA. ...

The cluster s collective response is dominated by the dipole mode (Mie plasmon) and can thus be characterized by the dipole moment in real time... 

Opp is the longitudinal to longitudinal or p to p-wave" scattering cross section of an isolated scatterer. At low frequencies it is primarily associated with the monopole scattering mode. Ops is the mode conversion or longitudinal to shear wave or p to s-wave cross section. It is primarily associated with the dipole mode at low frequencies, oa is the absorption cross section which describes energy dissipation inside viscoelastic inclusions (embedded in an otherwise elastic matrix material). It is active in all modes of excitation. Combining Equation 29 and 30 yields... 

With respect to energy dissipation by solid inclusions in rigid elastic matrix materials, the situation according to Equation 29 is that in the dipole mode, is relatively small compared to ops regardless of the magnitude of the loss factor of the inclusion material. Hence, its contribution to attenuation is relatively weak. This is true regardless of whether or not the real parts of the characteristic impedances of the matrix and inclusion materials are matched. 

Thus the effective relaxation time of the dipole mode is modified to... 

The most dominant resonances appear in the dipole modes which therefore will be at the center of the discussion in the following. As argued in the previous subsection, an... 

For small isotropic nanoparticles, the LSPR can be simply described as a single dipole mode according to Mie theory. However, the reduced symmetry of anisotropic particles such as GNRs results in at least two resonance modes, a longitudinal resonance... 

On many transition metals, hydrogen adsorbs dis-sociatively, with atomic hydrogen adsorbed in high-symmetry sites. The modes perpendicular to the surface are usually dipole modes parallel, frustrated translation, modes have some impact scattering character and can be observed in off-specular... 

Interestingly, the corresponding symmetric O-C-O stretch is weak. This motion, which converts the resting form from O-C-O arrangement to an O—C-—O structure, does not lead to a change in the permanent dipole mode and is thus forbidden. You wUl learn the basis for this rnle of thnmb next year when you study spectroscopic selection rules in yom physical chemistry conrse. 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Figure Bl.25.12 illustrates the two scattering modes for a hypothetical adsorption system consisting of an atom on a metal [3]. The stretch vibration of the atom perpendicular to the surface is accompanied by a change m dipole moment the bending mode parallel to the surface is not. As explained above, the EELS spectrum of electrons scattered in the specular direction detects only the dipole-active vibration. The more isotropically scattered electrons, however, undergo impact scattering and excite both vibrational modes. Note that the comparison of EELS spectra recorded in specular and off-specular direction yields infomiation about the orientation of an adsorbed molecule.

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

Otiati titalively, we may express how sh akcahle a given normal mode will be tinder th e in fltien ce of IR ligh t, bv exam in in g th e magnitude of its induced dipoles. 

Qualitatively, the selection rule for IR absorption for a given mode is that the symmetry of qT ) " must he the same as qT ). Qiianii-talivcly, the transition dipole moment is proportion al to tlie dipole derivative with respect to a given normal mode dp/di. ... 

The result of all of the vibrational modes contributions to la (3 J-/3Ra) is a vector p-trans that is termed the vibrational "transition dipole" moment. This is a vector with components along, in principle, all three of the internal axes of the molecule. For each particular vibrational transition (i.e., each particular X and Xf) its orientation in space depends only on the orientation of the molecule it is thus said to be locked to the molecule s coordinate frame. As such, its orientation relative to the lab-fixed coordinates (which is needed to effect a derivation of rotational selection rules as was done earlier in this Chapter) can be described much as was done above for the vibrationally averaged dipole moment that arises in purely rotational transitions. There are, however, important differences in detail. In particular. 

In a symmetric top molecule such as NH3, if the transition dipole lies along the molecule s symmetry axis, only k = 0 contributes. Such vibrations preserve the molecule s symmetry relative to this symmetry axis (e.g. the totally symmetric N-H stretching mode in NH3). The additional selection rule AK = 0... 

Find the molecular model of 18 crown 6 (see Figure 16 2) on Learning By Modeling and examine its electrostatic potential map View the map in vanous modes (dots contours and as a transparent surface) Does 18 crown 6 have a dipole moment Are vicinal oxygens anti or gauche to one another"d... 

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