Symmetry-allowed interactions

Figure 12.7. Orbital interactions in the Cope rearrangement (a) symmetry-allowed interactions of the g and orbitals (b) effect of X (or C ) and Z (or C ) substituents in the 3-position (c) effect of Z substituents at the 1-position.

The Ms = 0 component of a triplet has X symmetry, Sz transforms like S7w and singlets are totally symmetric, resulting again in a symmetry-allowed interaction. 

Turn on symmetry allowed interactions between the Bloch functions at each k point (repulsion and mixing between associated bands) to generate the final COs. In the general case, the shapes of the resulting bands will reflect characteristics of the specific compound. 

High resolution spectroscopic measurements in the gas phase yield the most detailed structural information possible. For example, measurements of weakly-bound complexes in the far-IR [24, 25] and IR [26, 27] have provided the most exact information on their structure and steady-state dynamics. Of course, a much higher level of theory must be used than was presented in section Bl.2.2.1. Quite often the modes are so strongly coupled that all vibrational degrees of freedom must be treated simultaneously. Coriolis coupling and symmetry-allowed interactions among bands, i.e. Fermi resonances, are also quite significant, and must be treated explicitly. Direct measurement of the low frequency van der... 

Lor the trigonal bipyramid there are four symmetry-allowed interactions shown in 17.32-17.35. Three involve interaction with the c" orbitals and one interaction with the e orbitals. 17.34 and 17.35 are equivalent by symmetry. Since the e orbitals are hybridized away from the ligands as described above, the 7r-iype overlap of a ligand orbital with c in 17.32 is significantly larger than any of the other interac-... 

Wigner-Eckart theorem, a transition dipole between two b2 orbitals must transform as the direct product b2 b2 = a hence, only the x - component will be dipole-allowed. In a perturbative approach, which takes into account the symmetry-allowed interaction between the metal and ligand orbitals, one has ... 

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