Local pairing of electrons

Heterocyclic ligands such as pyridine (py), V-methylimidazole (Meim), benzotriazole (btaH) and related molecules are good ligands due to the presence of at least one nitrogen ring atom with a localized pair of electrons. When this nitrogen bears a substituent, such as in pyrrole, the coordinating possibilities are reduced or absent. 

It is shown in this chapter that, while the Lewis model of the electron pair does not correspond to the existence of spatially localized pairs of electrons, it does find a more abstract but no less real physical expression in the topological properties of the Laplacian of the charge density, the quantity V p(r) as defined in eqn (2.3) (Bader and Ess6n 1984 Bader et al. 1984). The... 

The spherical surface, on which the electron pairs are assumed to be localized in Gillespie s model, is identified with the sphere of maximum charge concentration in the VSCC of the central A atom, and the localized pairs of electrons are identified with the local concentrations of electronic charge present on the sphere of maximum charge concentration. 

There is partial localization of the valence density in methane. The condensation into four partially localized pairs of electrons arranged along four tetrahedral axes is a result of the combined effects of the ligand field and the Pauli exclusion principle described above. Most important is that this partial localization of the pair density is reflected in the properties of the VSCC of the carbon atom which undergoes a corresponding condensation into four local concentrations of electronic charge. These properties of the pair density are not just the result of the tetrahedral symmetry of the ligand field in methane because, as we will now see, the Fermi hole exhibits the same behaviour in the ammonia molecule. 

A more fundamental criticism of VSEPR as an explanatory model is that it relies upon a consideration of localized pairs of electrons having opposite spins. However, as already mentioned in our discussion of p(r), localized... 

However, if one solves self-consistently for the best orbitals of that molecule, the best VB-type wavefunction will correspond to perfectly localized pairs of electrons in the plane of the molecule, which can be clearly identified with the C-C and C-H bonds, and six mono-occupied degenerate orbitals in the plane perpendicular to the molecule (tc orbitals), each one localized at one of the carbon atoms. For the allyl radical, the same situation is observed, with the three tt electrons localized each on a carbon atom. These results clearly indicate that a much deeper analysis of this concept is required. 

Work by Frost and co-workers in the mid 1960s abandoned the idea of AO-based functions to arrive at an even more compact basis set. They suggested the use of s-type Gaussians that were not fixed at the atomic centers, but could float in space so as to optimally represent each localized pair of electrons. Because only one function was needed for each pair of electrons, the basis sets used in floating spherical Gaussian (FSGO) scheme were often referred to as subminimal. Extensions of Frost s idea to ellipsoidal Gaussians of the form... 

---