Molecular Orbitals for n Bonding in AB Molecules

This means that SALCs of , Tu and T2 symmetries can be constructed from the eight n orbitals of the B atoms. But, n MOs can be formed only if there are appropriate AOs on atom A with which they can interact. (Strictly speaking, a SALC on the B atoms alone is also a MO, but it is a nonbonding one.) Inspection of the Td character table shows that the following AOs are available. 

This result has two important consequences. First, it is impossible to form a complete set of k bonds (i.e., two to each B atom), because there are no orbitals on atom A of T, symmetry (assuming, as always, that we consider only s-, / -, and d-type orbitals). Second, the n bonding will not be entirely independent of the a bonding, since 7 MOs are required for both. There are two sets of T2 type AOs and thus it is possible to have both a and n MOs of T2 symmetry. In the general case, there will be both p and d orbital contributions to both, although in specific cases it is possible that little mixing will occur. 

Octahedral AB6. As before, we employ a set of vectors (Fig. 8.12) representing n orbitals on the B atoms to determine the representation corresponding to a Complete set (12) of A—B n bonds. We obtain the following results  

We now examine the right side of the Oh character table to see what AOs on A are available to match these requirements. Within an j, p, d manifold, there are none for Tlg or Tltl. For T2k and Tiu we have, respectively (drt., dx=, dy.) and (pSJ pt pzj. If we look back at our previous treatment of a bonding in octahedral AB6 we find that the Tu, set was also needed there. In view of the need for strong a bonds and the fact that the set of p orbitals is very well shaped to form a bonds, this is normally their primary role. We are then left with only the type of A—B n bonding. 

When these two sets of Tu orbitals are combined with positive overlap (as 

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