Symmetry labels

Their symmetry labels can be obtained by vector coupling (see Appendix G) the spin and orbital angular momenta of the two subsystems. The orbital angular momentum coupling... 

For the ease given above, one finds n(ai) =1, n(a2) = 1, and n(e) =1 so within the eonfiguration e there is one Ai wavefunetion, one A2 wavefunetion and a pair of E wavefunetions (where the symmetry labels now refer to the symmetries of the determinental wavefunetions). This analysis tells one how many different wavefunetions of various spatial symmetries are eontained in a eonfiguration in whieh degenerate orbitals are fraetionally oeeupied. Considerations of spin symmetry and the eonstruetion of proper determinental wavefunetions, as developed earlier in this Seetion, still need to be applied to eaeh spatial symmetry ease. 

Recall that the symmetry labels e and o refer to the symmetries of the orbitals under reflection through the one Cy plane that is preserved throughout the proposed disrotatory closing. Low-energy configurations (assuming one is interested in the thermal or low-lying photochemically excited-state reactivity of this system) for the reactant molecule and their overall space and spin symmetry are as follows ... 

The C2H2CI2 molecule has a ah plane of symmetry (plane of molecule), a C2 axis ( to plane), and inversion symmetry, this results in C2h symmetry. Using C2h symmetry labels... 

Combine POs with the same symmetry label(s) to form approximate MOs. From each couple, an in-phase and an out-of-phase combination must again be obtained. POs whose symmetry is such that they cannot mix, will remain as non-bonding orbitals. The in-phase combination will have a lower energy than the out-of-phase one. 

Figure 8a shows how the SACs for the 02 group can be formed, with their symmetry labels. Again, two sp hybrids have been constructed first. Figure 8b shows the MOs of... 

FIGURE 8. (a) Symmetry-adapted combinations of sp hybrids and of p orbitals on the oxygens of an OXO group. Symmetry labels are with respect to the 0X0 plane and to the plane perpendicular to it. (b) Combinations of these SACs with two sp hybrids and two p orbitals on sulphur to give the MOs of S02. 

Assignments for [2Fe-2S]-CyS4 clusters were taken from Han et al. (128), those for oxidized Rieske clusters from Kuila et al. (67). Symmetry labels refer to idealized cluster cores. 

Figure 4. Schematic of torsional energy levels in Si electronic state of phenylsilane and Do electronic state of phenylsilane+. The torsional state symmetry labels arise under the molecular symmetry group G12.

Fig. 7. Approach of two triatomic fragments, a) Relevant planes of symmetry labels such as AA, SS, AS refer to symmetry or antisymmetry with respect to planes 1 and 2 respectively, b) Level diagram for the least-motion approach of two methylenes, c) Level diagram for the least-motion cis dimerization of HNO.

Each bond NBO is identified by the usual diatomic symmetry label (a, n, or 6) to indicate its angular symmetry about the W—W axis. 

Although the classification of metal-metal bonds into distinct a, n, and 5 types is reasonably clear in HW=WH (C2h), such diatomic symmetry labels may become... 

Fig. 4. Pi group orbital interactions in the cis and trans forms of the difluoroethylene dication. The symmetry labels are assigned with respect to a mirror plane (cis isomer) or a rotational axis (trans isomer)...

---