To gain new insight into the nature of hypervalency, we have characterized the bonding across the entire SFn sequence (n = 1-6) with high-level quantum chemical theory (multireference configuration interaction and coupled cluster calculations using correlation consistent basis sets). In contrast to most previous studies, this work examined both the stable equilibrium structures and the process of SFn-F bond formation. We conclude that two different types of bonding can occur in these species: normal polar covalent bonding and a new type that we call recoupled pair bonding. The two bonding processes can be seen in diatomic SF, where hypervalent behavior first occurs. In the covalently bonded (2)Pi ground state, the bond is formed by straightforward singlet coupling of electrons in the singly occupied S 3p and F 2p orbitals. But there is also a low-lying (4)Sigma(-) excited state where the S 3p(2) pair of electrons must first be decoupled so that one of the electrons can singlet couple with the electron in the F 2p orbital, hence the term recoupled pair bonding. Energy is required to decouple the electron pair, but the bond energy of SF((4)Sigma(-)) is still a substantial fraction (about 40%) of the bond energy of SF((2)Pi). Recoupled pair bonding is the basis for hypervalent behavior: for example, the three unpaired electrons of SF((4)Sigma(-)) are available for further bond formation, and their spatial orientations clearly anticipate the structure of SF4. The new model of hypervalent bonding introduced in this work accounts for the observed trends in the structures of SFn molecules and the variations in the (SFn-F bond fort-nation. We conclude) bond energies. The model also predicts the existence of low-lying excited states in some SF,, species and provides explanations for their energetic separations and orderings.