Acetylene symmetry coordinates

For the tetraatomic system HXXH, representing both the linear acetylene and the non-linear hydrogen peroxide, we expect to be able to construct twelve symmetry coordinates. Three of them are translational, whereas two of the remaining nine in the linear conformation and three in the non-linear one are reserved for rotations. Linear tetraatomics thus have seven vibrational coordinates, motion along which changes the potential energy, whereas their nonlinear counterparts have six. Those of the linear HXXH molecule are shown in Fig. 4.4 with the subgroup into which each is taken, if only momentarily, by the displacement. 

Acetylene therefore has three nondegenerate vibrations (one has symmetry and two have symmetry), and two doubly degenerate vibrations each of 7Cu and Tig symmetry. It is now possible to form symmetry coordinates from linear combinations of the bond lengths and the bond angles <5, ... 

It may be seen from the expressions for the symmetry coordinates (Eqs. 6.86) that the qualitative normal coordinates in acetylene are those shown in Fig. 6.9. 

The coordination of oxygen to transition metal ions which occurs mostly in the side-on fashion on surfaces (Section III,A,2 and Appendix B) can be described following the model of acetylene-metal complexes (467). Both 7tu and 7tg orbitals of molecular oxygen have proper symmetry to interact with the bonding set of s, p, and d orbitals on the metal. The bonding orbitals are shown in Fig. 29. 

The crystal structures of in excess of 70 hexacarbonylalkyne-dicobalt complexes have been determined by X-ray diffraction. In all cases the basic structural features are the same and can be illustrated by the structure of [Co -FjCQCFjXCO), shown in Fig. 1,Z7 The molecule has pseudo C2v symmetry in which the two cobalt atoms and the two acetylenic carbon atoms form a quasi-tetrahedral core. The carbon-carbon bond of the alkyne is in a perpendicular orientation relative to the cobalt-cobalt bond, as opposed to the parallel orientation which is also observed in dinuclear complexes with bridging alkyne ligands. The coordination around the cobalt atoms is distorted octahedral and the two tricarbonylcobalt moieties are eclipsed. 

Symmetiy Relations. Each normal coordinate and every wavefunction involving products of the normal coordinates, must transform under the symmetry operations of the molecule as one of the symmetry species of the molecular point group. The ground-state function in Eq. (3 a) is a Gaussian exponential function that is quadratic in Q, and examination shows that this is of Xg symmetry for each normal coordinate, since it is unchanged by any of the symmetry operations. From group theory the symmetry of a product of two functions is deduced from the symmetry species for each function by a systematic procedure discussed in detail in Refs. 4, 5,7, and 9. The results for the D i, point group apphcable to acetylene can be summarized as follows ... 

One of the first and perhaps most interesting examples of a metal-assisted, symmetry-forbidden reaction was Reppe s synthesis of cyclo-octatetraene from acetylene 34). in a careful study of this system, Schrauzer proposed a concerted mechanism in which the four a bonds of the cyclo-octatetraene are essentially formed simultaneously 35). He proposed an octahedral complex (54) with four acetylene hgands fitted to adjacent ligand coordination positions, spatially defining the incipient cyclooctatetraene. 

The addition of hydrogen to olefinic or acetylenic bonds is symmetry-forbidden [87, 88]. However, the participation of a catalyst subdivides the addition of H2 to an unsaturated system into a series of successive steps which do not suffer from these symmetry restrictions. These successive steps are oxidative addition of hydrogen, insertion of the coordinated unsaturated system into a metal-hydrogen bond, and reductive elimination of the hydrogenation product. Irrespective of the individual mechanism there is overwhelming evidence from D2 addition experiments that the catalytic addition of H2 to carbon-carbon double and triple bonds is a cA-addition [20]. 

Coordination of an acetylene to a transition metal makes the acetylene stretching frequency infrared "allowed" and shifts the vibration to frequencies that are 150 to 450 cm below that of the Raman band of the free alkyne. Larger changes in the vibrational frequency wpuld be expected when the complex adopts the structure of a "metallacyclopropene" instead of a coordinated alkyne, but this prediction has not been carefully explored. Like alkene complexes, alk3me complexes can possess rotational barriers about the metal-acetylene axis, and these rotational barriers depend on the symmetry of the orbitals of the metal fragment. 

A more recent study of ethynyllithium included the effect of lithium solvation on dimerization. At the 6-3H-G level successive coordinations of water to form HCCLi(OH2), HCCLi(OH2)2, and HCCLi(OH2)3 have AE of —21, —10, and —5 kcal mol , respectively. As solvation of lithium increases, the dimerization to the corresponding solvated ethynyllithium dimer becomes less exothermic. An interesting further feature is that the dimer with two waters per lithium has D2, symmetry, with each tetracoordinated carbon associated with two terminal ethynyl carbons and two waters. With fewer waters of solvation the coordination number of the lithiums is increased by association with the r-bond of the acetylene. This feature... 

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