Dihedral axes

Z)nd groups can be difficult to identify because the dihedral axes are hard to see. 

Linear molecules fit into the above classification by using the designation for the molecular axis, implying that a rotation of any angle whatever is a symmetry operation. Thus, we have C for a molecule with no centre of inversion (examples being CO and N20) and D if there is an inversion center (examples being N2 and C02), the presence of such a center implying also that there are dihedral axes. 

Exercise 2.3-1 The projection diagram is given in Figure 2.17. The dihedral planes are rrx, crb, and rrc, where ax bisects the angle between b and c, ab bisects the angle between x and c, and rrc bisects the angle between x and b. 

Figure 2.17. Projection diagram for the point group D3d = D3(S)C, (see eq. (2.3.9)). For example, JC2b =

In the left-hand column are the direct sums of representations of C4v which yield the same character sets as the IR of Oh in column 7. The crz, ax are vertical planes in C4v because they contain the four-fold axis but are horizontal planes in Oh because they are normal to the C4 axes along z and x, respectively. The planes [Pg.363]

Table 4. Molecular structure, dihedral angle 9 between the plane of the naphthalene subunits, wavelength of maximum absorption 2n,ax and the first molecular hyperpolarizability of the naphthalene subunit calculated from HRS or EFISHG measurements (1064 nm, CHCI3).

The three marked hydrogens form an ABX system AB are the diastereotopic CH2 group (/ab = 17.7) and H is the CHBr proton (/ax = 10 hx = 1-9)- It is not normally possible to say which proton is A and which B but here with such large groups we may guess that there is one favoured conformation with one dihedral angle about 180° and one about 60°. 

In examining the conformational space of models Im, 20m and 21m, we considered only AX or AY isomers, which should be more stable than the other types (see Table 2). The conformational space was searched at the PM3 level using two parameters for the dihedral angles [C(2 )C(1 )C(6 )C(5 )] and [C(3 )C(4 )C(5 )C(6 )]. The structures obtained for the minimum-energy and transition geometries were optimized at the B3LYP/6-3 lG(d) level. 

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