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The valence shell electron pair repulsion (VSEPR) model-also known as the Gillespie-Nyholm rules-has for many years provided a useful basis for understanding and rationalizing molecular geometry, and because of its simplicity it has gained widespread acceptance as a pedagogical tool. In its original formulation the model was based on the concept that the valence shell electron pairs behave as if they repel each other and thus keep as far apart as possible. But in recent years more emphasis has been placed on the space occupied by a valence shell electron pair, called the domain of the electron pair, and on the relative sizes and shapes of these domains. This reformulated version of the model is simpler to apply, and it shows more clearly that the Pauli principle provides the physical basis of the model. Moreover, Bader and his co-workers' analysis of the electron density distribution of many covalent molecules have shown that the local concentrations of electron density (charge concentrations) in the valence shells of the atoms in a molecule have the same relative locations and sizes as have been assumed for the electron pair domains in the VSEPR model, thus providing further support for the model. This increased understanding of the model has inspired efforts to examine the electron density distribution in molecules that have long been regarded as exceptions to the VSEPR model to try to understand these exceptions better. This work has shown that it is often important to consider not only the relative locations and sizes, but also the shapes, of both bonding and lone pair domains in accounting for the details of molecular geometry. It has also been shown that a basic assumption of the VSEPR model, namely that the core of an atom underlying its valence shell is spherical and has no influence on the geometry of a molecule, is normally valid for the nonmetals but often not valid for the metals, including the transition metals. The cores of polarizable metal atoms may be nonspherical because they include nonbonding electrons or because they are distorted by the ligands, and these nonspherical cores may have an important influence on the geometry of a molecule.

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The bonding in a large number of hypervalent molecules of P, As, S, Se, Te, Cl, and Br with the ligands F, Cl, O, CH(3), and CH(2) has been studied using the topological analysis of the electron localization function ELF. This function partitions the electron density of a molecule into core and valence basins and further classifies valence basins according to the number of core basins with which they have a contact. The number and geometry of these basins is generally in accord with the VSEPR model. The population of each basin can be obtained by integration, and so, the total population of the valence shell of an atom can be obtained as the sum of the populations of all the valence basins which share a boundary with its core basin. It was found that the population of the V(A, X) disynaptic basin corresponding to the bond, where A is the central atom and X the ligand, varies with the electronegativity of the ligand from approximately 2.0 for a weakly electronegative ligand such as CH(3) to less than 1.0 for a ligand such as F. We find that the total population of the valence shell of a hypervalent atom may vary from close to 10 for a period 15 element and close to 12 for a group 16 element to considerably less than 8 for an electronegative ligand such as F. For example, the phosphorus atom in PF(5) has a population of 5.37 electrons in its valence shell, whereas the arsenic atom in AsMe5 has a population of 9.68 electrons in its valence shell. By definition, hypervalent atoms do not obey the Lewis octet rule. They may or may not obey a modified octet rule that has taken the place of the Lewis octet rule in many recent discussions and according to which an atom in a molecule always has fewer than 8 electrons in its valence shell. We show that the bonds in hypervalent molecules are very similar to those in corresponding nonhypervalent (Lewis octet) molecules. They are all polar bonds ranging from weakly to strongly polar depending on the electronegativity of the ligands. The term hypervalent therefore has little significance except to indicate that an atom in a molecule is forming more than four electron pair bonds.

Studies of the Laplacian of the calculated electron density (V^) for the fluorides of Mg, Ca, Sr, and Ba, for the hydrides of Ca, Sr, and Ba, and for Ca(CH3)2 were undertaken in order to understand why these molecules with the exception of Mgp2 have a bent rather than a linear geometry. A linear geometry is expected on the basis of the simple ionic model or the VSEPR model and is observed for BeF2 and Mgp2. The Laplacian distribution for the metal atom in each of the remaining molecules shows that the outer shell of its core is perturbed by the polarizing field of the ligands and is distorted in a manner corresponding to the presence of four approximately tetrahedrally localized concentrations of electronic charge. The angular shapes of these molecules can be understood in terms of the interaction between the distorted core and the ligands. In contrast, the distortion of the magnesium core in Mgp2 exhibits only two charge concentrations, one associated with each Mg-F bond, so that no deviation from the linear geometry is expected or found. This paper helps to establish the generality of the formation of localized concentrations of electronic charge in positions that are spatially opposed to the attached ligands, in the outer shell of the core of an element with accessible (nl)d orbitals, where n is the valence shell. The distortions of the cores of the heavier alkaline earth elements that are revealed by the Laplacian of the electron density have the same form as that proposed some years ago in an extension of the VSEPR model to account for the angular shape of these molecules. main group elements, for which the VSEPR model is very successful. It was pointed out some time ago, however, that