ab initio Calculations of Changes in Sulfur’s Orbital Energies and Sizes with Oxidation State as a Means of Explaining Hypervalency

The energetics and orbital sizes of sulfur’s valence 3d and fluorine’s valence 2p orbitals were measured using a closed active space self-consistent field calculation to determine the degree of possible bonding available to sulfur’s 3d. It was determined that for orbital energies, the cc-pVXZ and aug sets converged hyperbolically onto a single energy value as X increased and that for both fluorine and sulfur orbital energies scaled down linearly with oxidation state. This resulted in a 0.47 hartree difference between the sulfur 3d and fluorine 2p orbitals at S0.6+ and F-0.1, far exceeding the energy gap between 3p and 2p and thereby suggesting that pure 3d’s small energetic overlap with 2p may likely exclude it from bonding. However, the basis sets did not scale down hyperbolically to a single orbital size with increasing X and did not show a linear decrease in size with oxidation state. The calculated difference in orbital size between the sulfur 3d and fluorine 2p was only 0.4 bohr, which is similar to the differences in size between 3s and 2p and 3p and 2p, suggestive of the fact that 3d is not diffuse and can geometrically overlap with fluorine’s 2p only slightly worse than the 3p. This work establishes that geometric arguments against participation of 3d orbitals in hypercovalent bonding are lacking, but that the energetic argument still holds merit and can be used to catalyze further research into SFx molecules to see whether these trends hold