Testing the concept of hypervalency: charge density analysis of K2SO4

One of the most basic concepts in chemical bonding theory is the octet rule, which was introduced by Lewis in 1916, but later challenged by Pauling to explain the bonding of third-row elements. In the third row, the central atom was assumed to exceed the octet by employing d orbitals in double bonding leading to hypervalency. Ever since, polyoxoanions such as SO(4)(2-), PO(4)(3-), and ClO(4)(-) have been paradigmatic examples for the concept of hypervalency in which the double bonds resonate among the oxygen atoms. Here, we examine S-O bonding by investigating the charge density of the sulfate group, SO(4)(2-), within a crystalline environment based both on experimental and theoretical methods. K(2)SO(4) is a high symmetry inorganic solid, where the crystals are strongly affected by extinction effects. Therefore, high quality, very low temperature single crystal X-ray diffraction data were collected using a small crystal (∼30 μm) and a high-energy (30 keV) synchrotron beam. The experimental charge density was determined by multipole modeling, whereas a theoretical density was obtained from periodic ab initio DFT calculations. The chemical bonding was jointly analyzed within the framework of the Quantum Theory of Atoms In Molecules only using quantities derived from an experimental observable (the charge density). The combined evidence suggests a bonding situation where the S-O interactions can be characterized as highly polarized, covalent bonds, with the "single bond" description significantly prevailing over the "double bond" picture. Thus, the study rules out the hypervalent description of the sulfur atom in the sulfate group.