Clusters symmetry orbitals

Reduced species of the type [Os6(CO)2i] have not yet been characterized crystallographically, but evidence to support the existence of the orbital described above is provided by X-ray and ESR studies of the related species [Fe3Pt3(CO)ij]"" (n = 1, 2). The a2 symmetry orbital is fully occupied in the dianion of this mixed-metal cluster, which is easily oxidized to the paramagnetic species [Fe3Pt3(CO)i5] [Eq. (35)] 283). 

Figure 3. As in Figure 1, for the lowest energy broken symmetry state of the doubly-reduced ZnFeg cluster. Valence orbitals are numbered within each symmetry and have been placed in three columns depicting the location of their primary charge distribution. Vertical bars indicate occupied orbitals. 

We used the C24 model cluster, which consists of seven carbon hexagons, to represent the graphite plane (Fig. 1 (a)). To perform the ground state calculations, we classified the carbon atoms into three types, and performed the calculations under symmetry. To avoid model cluster termination effects, we treated the electronic structure of the inner carbon atoms as that of graphite. When we performed Slater s transition state calculations, however, we took four types of carbon atom into account. This was because one of the inner carbon atoms, in which the Is electron transits to an unoccupied level, should be distinguished from the other inner carbon atoms. Further we didn t use any symmetry orbitals for the transition state calculations. 

For a basis set of (re) atomic orbitals which are singly noded in the plane perpendicular to the radial vector (see Fig. 16b), the required Harmonics are the Vector Surface Harmonics146). The two p11 (or d") atomic orbitals at each cluster vertex (i) behave as a pair of orthogonal unit vectors which are tangential to the surface of the sphere, jrf and jif are defined as Jt-symmetry orbitals on the ith cluster atom, pointing in the direction of increasing 0 and cj> respectively, as shown in Fig. 18. At the poles of the cluster sphere these vectors may be related to Cartesian vectors as follows ... 

Since the number of bonding molecular orbitals is determined by the cluster symmetry, the same polyhedron can serve as the basis for the structures of an ample range of isoelectronic species as neutral carboranes with formula C2B -2H or the naked clusters as Ge that will be dealt with in Chapter 4. 

For example, the three NH bonding and three NH antibonding orbitals in NH3, when symmetry adapted within the C3V point group, cluster into ai and e mos as shown in the Figure below. The N-atom localized non-bonding lone pair orbital and the N-atom Is core orbital also belong to ai symmetry. 

In a second example, the three CH bonds, three CH antibonds, CO bond and antibond, and three 0-atom non-bonding orbitals of the methoxy radical H3C-O also cluster into ai and e orbitals as shown below. In these cases, point group symmetry allows one to identify degeneracies that may not have been apparent from the structure of the orbital interactions alone. 

---