Molecular Orbitals in Complexes

The 4s orbital on the metal has a positive sign that is invariant in all directions. The combination of ligand orbitals, which are referred to as symmetry adjusted linear combinations (SALC) or ligand group 

Because the px orbital is positive in the direction toward ligand 1 and negative in the direction toward ligand 3, the appropriate combination of ligand orbitals will be 

In a similar way, we obtain the wave functions for combinations of ligand group orbitals with the py and pz orbitals from the metal ion. They can be written as 

Note that the three wave functions arising from the p py, and pz orbitals are identical except for the directional character as indicated by the subscripts. Therefore, they must represent a triply degenerate set (the t2g set, which will be apparent later). 

the combination of wave functions making up the first molecular orbital will be 

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The three LGOs of r1u symmetry that will overlap with the metal p orbitals are constructed in a similar manner, as shown in Fig. 11.19. Since the metal crbkals cannot participate in a-overlap, they are considered nonbonding molecular orbitals in complexes where there is no possibility for it bonding. In cases where there are ligand orbtals of appropriate symmetry available, the orbitals will be involved m n bonds. 

When computing UV visible spectra, you should do a Cl singles calculation, RHFor L H F ealcu lation s arc sufficient to reproduce the proper order of molecular orbitals in most complexes. 

We are now ready to apply the ideas in the preceding three sections to the construction of molecular orbitals in octahedral complexes. 

In the usual formulation of the extended Hiickel method, the elements of the hamiltonian matrix are computed according to a simple set of arithmetic rules, and do not depend on the molecular orbitals. In this way, there is no need for the iterations required by more sophisticated methods, and in practice the results may be obtained nowadays in a question of seconds for any reasonably sized complex. 

The simplest and most widely-employed method is the so-called configuration interaction singles or CIS method. This involves singleelectron promotions only (from occupied molecular orbitals in the reference wavefunction to unoccupied molecular orbitals). Because there are relatively few of these, CIS is in fact practical for molecules of moderate complexity. As noted previously, single-electron promotions do not lead to improvement in either the ground-state wavefunction or energy over the corresponding Hartree-Fock... 

The crucial molecular orbital in these molecules appears to be one of Bau symmetry, which is an in-plane o- -orbital and is strongly antibonding between the metals. The electron population of this orbital is (B3u)2, (B iu) and (fl3u)° when n is 0, +1, and +2, respectively, in the complexes above. Removal of electrons from this antibonding orbital... 

Molecular orbitals in heteronudear diatomic molecules. 167-175 in homonudear diatomic molecules, 160-166 of metallocenes. 670-673 in octahedral complexes, 414-418... 

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