Low symmetry groups

To illustrate the definitions, we consider a model case of four-membered cyclic clusters with low symmetry group C4. The idealized O framework is formed by a square of atoms A, B, C, and D. H-bonds 1 are between A and B, B and C, C and D, D and A, respectively. The only first-order invariant for such a system is simply the sum of all bond functions ... 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

FIGURE 5.8 Complex hyperfine patterns due to axes noncolinearity in a low-symmetry prosthetic group. The X-band spectrum is from 65Cu(II)-bicarbonate in human serum transferrin (a,b) experimental spectrum (c,e) simulation assuming axial symmetry (d, f) simulation assuming triclinic symmetry with the A-axes rotated with respect to the g-axes over 15° about the gz-axis and then 60° about the new y -axis. Traces b, e, and f are 5x blow-ups of traces a, c, d, respectively (Hagen 2006). (Reproduced by permisson of The Royal Society of Chemistry.)... 

On the basis of these experimental observations, the model of packing reported in Figure 2.26 (space group I4 ) has been proposed.33 153 The low symmetry of the packing comes from the fact that two of the four chains included in the tetragonal unit cell are independent, that is, are not related by... 

Figure 4.17. Two perspective views of heptahelicene corresponding to the monoclinic P2 c polymorph (Hark Beurskens, 1976). Heptahelicene belongs to the low symmetry Ci point group (only E applies).

Pyridine, symmetry group C2v, has six electrons in a system delocalized around the ring, and two lone-pair electrons in an orbital localized at the Nitrogen atom. The Is electrons, as well as the electrons in orbitals describing the a bonds, need not be considered explicitly in describing the resonance stabilization and low-lying excited states of pyridine. The simple molecular orbital description has the following characteristic assumptions ... 

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