Allene , symmetry

Figure 4.3 Planes and axes of symmetry in (a) H2O, (b) BF3, (c) naphthalene, (d) allene, (e) benzene and (f) [PtCU] ...

Assign the allene molecule to a point group and use the character table to form the direct products A-2 x5i,5i X 82,82 xE and E X E. Show how the symmetry species of the point group to which 1,1-dilluoroallene belongs correlate with those of allene. 

Finally, it is of interest to compare the estimates of covalency contributions for Ir(IV) hexahalides deduced by Allen et al. (11) from spectroscopic data, with those obtained by Owen and Thornley (85, 86) from ESR results. These latter authors attributed the reduction of below the free-ion value, entirely to symmetry restricted covalency, deriving the expression 0bsd = N (Cd +s , >), where the normalising constant, N , is equal to (1 —4a S + and [Pg.153]

To illustrate the importance of vicinal connectivity of conjugating units, we consider two dienes in non-vicinal relationships 1,5-hexadiene, 9, and allene, 10. As shown in Table 3.19, the direct diene conjugations are negligible in both species, on account of spatial separation in 9 and symmetry-imposed orthogonality of the two pi planes in 10. Consistently with the essential absence of conjugation, the unsaturated C—C bonds of 9 and 10 have calculated bond orders characteristic of ethylene or other unconjugated systems and the ficc NLMOs have essentially localized character ... 

As an example, which will also lead us to the concept of qualitative completeness, consider the allene skeleton, as shown in Fig. 8, and for the moment consider only achiral ligands. Besides the unit element, the symmetry group of the skeleton, "Dm, consists of the rotation operations (in permutation group notation) (12)(34), (13)(24), and (14)(23), plus the improper rotations (1)(2)(34), (12)(3)(4), (1324), and (1432). 

Problem 4-4. Construct stereographic projection diagrams for the symmetry groups of HOCl, cyclopropane, allene, and benzene. 

The number of the sp carbon atoms interposed between the two terminal sp2 carbon atoms conveniently classifies the cumulated double bond systems into two categories 1. even-numbered cumulenes of D2h symmetry (e.g. ethylene), and 2. odd-numbered cumulenes of D2d symmetry (e.g. allene). 

While the even-numbered cumulene gives (Z)-111 of C2y symmetry and ( )-112 of C2h symmetry, the odd-numbered cumulene gives two enantiomers 113 and 114 both of C2 symmetry. Bridging these two substituents A and A in 113 or 114 by a chain gives rise to a single-bridged allene of C2 symmetry whose chirality can be specified following the axial chirality rule 11 ... 

A hypothetical doubly-bridged allene 123 of D2 symmetry was first formulated in Cahn, Ingold, and Prelog s classical paper 11 > in which they summarized their novel proposal for specifying various molecular chiralities. Despite the close structural resemblance between 123 and [m.m]betweenanene, Cahn, Ingold and Prelog s rules shows that the chirality of these two classes of compounds are to be specified as axial and planar respectively. 

Did = E, 3C2,2ffrf,2S4. Allene has this symmetry, as do puckered cyclobutane and cyclooctatetraene. 

---