Rundle-Pimentel model

Taking Xep2 as a prototype for 3c/4e systems, Coulson has reexpressed the Rundle-Pimentel model in VB terms by projecting the simple MO wave function on a basis of VB structures [91], thus getting Eq. (15) below ... 

Thus, the general model for hypervalency in electron-rich systems appears to be the VB version of the Rundle—Pimentel model, coupled with the presence of a CSB feature. This latter feature imposes the cmiditions for manifestatirHi of hypervalency (1) low first and second irmization potentials for the central atom and (2) ligands that are prone to CSB in their normal-valent states (i.e., being electronegative and bearing lone pairs like F, O, etc.). Lack of any of these features explains the many exceptions to the traditional MO-based Rundle—Pimentel model, like the instability of first-row 3c/4e systems, as well as that of ArF2, H3, and so oti. 

Explanations for the existence of hypervalent species started with Pauling s proposal of d orbital hybridization [3] where, for example, a set of sp d hybrid orbitals on sulfur was put forward to account for the hexavalence of SFg. Chemical computations [4] ruled out the participation of d atomic orbitals. A later model, the Rundle-Pimentel three-center, four-electron (3c-4e) bonding model [5], does not require d orbital participation and, so, is consistent with chemical computations. Other hypervalency models include the diabatic state model of Dixon and coworkers [6] and the democracy principle of Cooper and coworkers [7]. These various models provide useful insights into some aspects of the electronic structure of hypervalent molecules, but they don t provide an overarching description of these molecules that enables connections to be drawn between hypervalency and related molecular phenomena. 

Pimentel presented a particularly simple and lucid MO model of hypervalency (building on physical concepts that were also recognized by Rundle)137 that is applicable to atoms of similar or dissimilar electronegativity. The Pimentel-Rundle model is based on a general triatomic A—B—C species in which each atom contributes only a single basis AO (/a, xb, xc) that interacts strongly with the AO on... 

The Pimentel-Rundle 3c/4e MO model can readily be generalized to hybrid orbitals (rather than pure AOs) and more general LCAO-MO mixing coefficients... 

Figure 3.84 An illustration of the Pimentel-Rundle three-center MO model of hypervalency, showing equilibrium valence AO (xa-/b-Xc) overlap patterns for (a) 2pF—2pF—2pF NAOs of the trifluoride ion, F3 and (b) 2pF—lsp—2pF NAOs of the bifluoride ion, FHF-.

Consistently with the Pimentel-Rundle 3c/4e MO model, the central atom is expected to use a single p orbital to form each cu-bonded pair (i.e., px for the cu bonds in the x direction and py for the cu bonds in the y direction), which leaves only s and pz orbitals for forming the two bonds along the z direction. As a result of the inherent symmetry of the three spatial directions and equivalence of the available orbitals for bonding in each... 

Bonding. —In the valence-bond description of XeF2, Coulson has emphasized the dominance of the canonical forms (F-Xe)+F and F (Xe-F) in the resonance hybrid. This representation accounts well for the polarity FXe F , indicated by nmr, Moss-bauer, ESCA, and thermodynamic data. It is particularly impressive that the enthalpy of sublimina-tion derived for the XeFy case, by Rice and his co-workers in 1963, on the basis of the charge distribution "FXe+F , is 13.3 kcal mol , whereas the experimental value reported in 1968 is 13.2 kcal mol . It should be recognized that the Coulson valence-bond model is not, in the final analysis, significantly different from the Rundle and Pimentel three-center molecular orbital description or the Bilham and Linnett one-electron-bond description, but it does provide for a more straightforward estimation of thermodynamic stabilities of compounds than the other approaches do. 

As an alternative tothe VSEPR approach, the following model for hypervalent molecules has been proposed (Pimentel, Rundle, Coulson, ca, 1951) ... 

The model most widely used to explain hypervalence is the three-center, four-electron (3c-4e) model of Rundle and Pimentel [5]. Coulson [31] analyzed the 3c-4e model and suggested a valence bond resonance model that shares some similarities with the MO model. Under this model, the bond is posited to arise primarily from resonance between F-X F and F X -F charge structures (with contributions from other charge configurations). Weinhold and Landis [32] incorporated natural bond orbital analysis and natural resonance theory in what is perhaps the most... 

A different bonding model that would not need to invoke d-orbitals was aheady suggested by George Pimentel and Robert Rundle [17, 18]. It involved a 3-centre 4-electron bond, and the planarity of the SO units in the sulfur oxides allows the formation of a delocalized ir-electron system, leading to m-centre-n-electron bonding. Nowadays this simple model is challenged to provide more sophisticated explanations for hypervalent molecules (e.g., [19]). 

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