Cyclic systems involving d orbitals

The incorporation of the d orbitals complicates the group theoretic procedure to some extent. Table 7.1.7 gives some useful steps in the derivation of the linear combinations of six atomic orbitals. With the results in Table 7.1.7, the linear combination of the atomic orbitals can be readily derived  

Since the first expression is the difference of the last two expressions, we can select the first expression as well as the sum of the last two  

Labeling of the N 2p orbitals and P 3d orbitals taking part in the 7t bonding of (NPX2)3- Note that only the signed lobes above the molecular plane are shown. Also, a mismatch, in this case occurring between orbitals a and/, is inevitable. 

It is not difficult to show that, when we form the 2x2 secular determinants with E symmetry, the first component of (7.1.58) interacts with the second component of (7.1.60). Analogously, the second component of (7.1.58) interacts 

4 Linear combinations of ligand orbitals for AL4 molecules with Tj symmetry 

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