Allene, point group

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. 

The point group of allene is D2d = E 2Sa C2 2C2 2aa (see Problem 2.3). Choose a right-handed system of axes so that the vertical OZ axis points along the principal axis of symmetry. 

The point groups V d have, in addition to the axes defining Vn, n diagonal planes Od which bisect the angles between successive twofold axes. The ad and C2 axes imply that there is also an S2n and, if n is odd, a center of symmetry Molecules of T>2d symmetry have the shape of two equivalent halves twisted b 90°, for example, allene and spiran shown here ... 

Identify the symmetry point groups of formaldehyde [C2v, ammonia [C3J, phenol [CJ, gyloxal C2h and allene [D2hl-... 

J. W. Yao, J. C. Cole, E. Pidcock, F. H. Allen, J. A. K. Howard and W. D. S. Motherwell, CSDSymmetry the definitive database of point-group and space-group symmetry relationships in small-molecule crystal structures, Acta Cryst., B58, 640-646 (2002). 

Fig. 3.14 Dimethyl substituted allene occurs in two chiral forms, which are the mirror image of each other, and cannot be superimposed the point group of each form is Cz...

Allene (H2C=C=CH2) is an interesting species as the first member of the cumulene series and as a representative of the less common point group D2d- In the D2d point group the degeneracy of electronic states is not lifted, as is usually the case, by degenerate modes of E symmetry, but by nondegenerate modes of and B2 symmetry. This so called E x B Jahn-Teller effect is described by the Hamiltonian of Eqs. (13)-(15), where the modes of B2 sjmimetry (< 5, 7 in allene) possess non-vanishing intra-... 

The symmetry elements of the point groups (a) >3, (b) D2d and (c) Dgh- (a) A twisted form of ethane, neither perfectly staggered nor eclipsed, viewed along the C3 axis, (b) Allene, where the planes xz and yz are planes and the C 2 axes lie at 45° to the x and y axes in the xy plane, (c) Benzene. Note that the Cg axis includes C3, C2, Sg and S3 axes. Also shown are the three axes (one of which lies along x) and the three C axes (one of which lies along y). The xy plane is CTh and there are vertical mirror planes including each C 2 and C axis the center of the molecule is an inversion center, i. 

Determine the point groups of the following molecules, (a) Hydrogen peroxide, H2O2 (It is not planar.) (b) Allene, CH2=C=CH2 (c) o-alanine (Its absolute stereochemistry can be found in any good organic or biochemistry textbook.) (d) i-alanine, and compare with part c above. 

Figure 21 An allene molecule belonging to the point group D2d-...

The photoelectron and optical spectra of allene (1,2-propadiene) have been of considerable Aeoietical and experimental interest because a significant portion of Aese spectra is not only quite conq)lex but also raAer peculiar. The molecular point group of allene in Ae ground state is D2d, wiA Ae self-consistent field (SCF) approximation described by Ae orbital occupation a hi2a Qb2Aa bile, RenK)val of an electron from Ae highest occupied nK)lecular orbital 2n (or 2e) of... 

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