Metal-ligand nonbonded models

The success of the ligand-ligand repulsion model prompted its adoption as an element of a molecular mechanics program. In the resulting approach the valence angles around the metal ion are modeled solely by nonbonded interactions, using the usual van der Waals potential (for example, Eq. 2.9 kg = 0 in Eq. 2.7 Urey-Bradley approach)136. 6 Again, the fact that the electronic effects responsible for the directionality of bonds are not explicitly modeled here may seem questionable but extensive tests have shown the model to be reliable 371. An explanation for this apparent contra-... 

The s and f block elements present a particular challenge in the molecular mechanics field because the metal-ligand interactions in both cases are principally electrostatic. Thus, the most appropriate way to model the M-L bonds is with a combination of electrostatic and van der Waals nonbonded interactions. Indeed, most reported studies of modeling alkali metal, alkaline earth metal and rare earth complexes have used such an approach. 

If we directly apply the CSED model to determine the nonbonding orbitals, we will see that the dxz and dy orbitals (the e/ set) are available but did not contribute to the metal-ligand bonding in the pentagonal bipyramid geometry. We can therefore declare that these two orbitals should each be filled with two electrons, consistent with the valency counting picmre that the metal center should have a d configuration. 

In nonbonded methods, the metal ion is not formally connected to the ligand donor atoms and the metal-dependent interactions present in bonded methods are not included. There are no explicit M-L bonds, M-L-X and L-M-L angles, or M-L-X-X and L-M-L-X torsional interactions. Instead the metal-ligand complex is modeled with a collection of pairwise electrostatic and van der Waals interactions between the metal and all ligand atoms, i.e., with M-L and M-X interactions. 

As idealized computational models of metal hypovalency, let us therefore consider the early second-series transition-metal hydrides YH3, ZrH4, and NbfL (avoiding both the complications of lone-pair-bearing ligands and those associated with the lanthanide series). Figure 4.54 shows optimized structures of these species, and Table 4.33 summarizes the bonding (omh) and nonbonding (nM ) orbitals and occupancies at the metal center. 

The molecular orbital model can also be applied to complexes of the d-block elements. In octahedral complexes the d-orbitals of the metal are not degenerate, as they are in the free metal, because of the interaction between the ligand and metal orbitals. The five d-orbitals are split into three t2g (nonbonding) and two e (antibonding) MOs that is ... 

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