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Hexadecapole moment

The multipole moment of rank n is sometimes called the 2"-pole moment. The first non-zero multipole moment of a molecule is origin independent but the higher-order ones depend on the choice of origin. Quadnipole moments are difficult to measure and experimental data are scarce [17, 18 and 19]. The octopole and hexadecapole moments have been measured only for a few highly syimnetric molecules whose lower multipole moments vanish. Ab initio calculations are probably the most reliable way to obtain quadnipole and higher multipole moments [20, 21 and 22]. [Pg.188]

Many molecules, such as carbon monoxide, have unique dipole moments. Molecules with a center of inversion, such as carbon dioxide, will have a dipole moment that is zero by symmetry and a unique quadrupole moment. Molecules of Td symmetry, such as methane, have a zero dipole and quadrupole moment and a unique octupole moment. Likewise, molecules of octahedral symmetry will have a unique hexadecapole moment. [Pg.110]

Once an approximation to the wavefunction of a molecule has been found, it can be used to calculate the probable result of many physical measurements and hence to predict properties such as a molecular hexadecapole moment or the electric field gradient at a quadrupolar nucleus. For many workers in the field, this is the primary objective for performing quantum-mechanical calculations. But from... [Pg.103]

Hexadecapole moment (Debye-Ang 3) XXXX= -1574.8336 YYYY= -1160.7386 ZZZZ=... [Pg.183]

Although the spherical form of the multipole expansion is definitely superior if the orientational dependence of the electrostatic, induction, or dispersion energies is of interest, the Cartesian form171-174 may be useful. Mutual transformations between the spherical and Cartesian forms of the multipole moment and (hyper)polarizability tensors have been derived by Gray and Lo175. The symmetry-adaptation of the Cartesian tensors of quadrupole, octupole, and hexadecapole moments to all 51 point groups can be found in Ref. (176) while the symmetry-adaptation of the Cartesian tensors of multipole (hyper)polarizabilities to simple point groups has been considered in Refs. (172-175). [Pg.44]

For SFe, the measurements of Rosenberg and Bimbaum give a very small value of B, comparable to those obtained from atomic gas mixtures. By neglecting possible contributions from dipoles caused by overlap forces, and attributing all of to the effects of the hexadecapole moment, Rosenberg and Bimbaum calculate an upper limit of + 17 x 10 Cm for [Pg.52]

Obviously, for spherical symmetry, the hexadecapole moment vanishes. In the tetrahedral and octahedral cases, it reduces to one component... [Pg.118]

Molecules of still higher, e.g. octahedral, symmetry possess a Oowest) hexadecapole moment the electric fields of these hexadecapoles now induce a dipole moment in neighbouring molecules. Here, too, 9 0, and... [Pg.170]

The non-zero tensor components of multipole moments have been determined specifically for the tetrahedraland octahedral symmetries, beside the axial symmetry for which we have the general formula (40a). Lately, Kielich and Zawodny, resorting to methods of group theory, have calculated and tabulated all non-zero and independent tensor components of electric dipole, quadrupole, octupole, and hexadecapole moments for 51 point groups (Tables 4—7). [Pg.322]

The preceding considerations lead to the condusion that, whereas numerical determinations of electric dipoles require, in accordance with equation (241a), the investigation of substances in the absence of molecular correlations, the quadrupole, octupole, and hexadecapole moments are accessible to determination only if at least pairwise radial correlations are present in the non-dipolar medium. Numerical values of electric moments of higher order are determined by the method of measuring second dielectric virial coeffidents worked out and successfully applied by Cole et al. It has yielded quadrupole, octupole, and hexadecapole moments in good numerical agreement with the values obtained by other methods (see Section 2). [Pg.372]

It is worth noting that the four-fold symmetry of hexadecapole moment is revealed only at the synchronous pumping and, what is important, at time moments when the hexadecapole moment is precisely aligned with one of its symmetry axis along the linear polarization of the field and the atomic coherence p 2, 2 in the M-system has its maximal value. The periodic change of the optical properties of atomic medium modulates the angle of tight polarization that leads to the FM NMOR resonances. If the time-dependent optical rotation is measured at the first harmonic of (.lm, a resonance is seen when Qm = k Ql which allows one to separate the NFS produced by different atomic PM. Indeed, in the experiment the in-phase and quadrature amplitudes of optical rotation,... [Pg.97]

To describe the hexadecapole resonances, a more complicated theory is needed, because the presence of the hexadecapole moment requires ground-state angular momentum > 2 and second-order interactions with the light. [Pg.102]

Fig. 11. The charge distribution of the dxy dx -y component of the Ai Ti cobalt(III) transition with the correlation produced of the induced dipole in the ligands, Bj, A2, Ciand C2 (solid arrows), and the corresponding dipole aligiunent in the ligands, B2, Aj, A2, and Ci (broken arrows) due to the field of the hexadecapole moment of the dyz dy component... Fig. 11. The charge distribution of the dxy dx -y component of the Ai Ti cobalt(III) transition with the correlation produced of the induced dipole in the ligands, Bj, A2, Ciand C2 (solid arrows), and the corresponding dipole aligiunent in the ligands, B2, Aj, A2, and Ci (broken arrows) due to the field of the hexadecapole moment of the dyz dy component...
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... [Pg.74]


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See also in sourсe #XX -- [ Pg.126 ]




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