Based on detailed, high level ab initio calculations on a number of halogenated compounds of second row, late p-block elements, the SF(n), ClF(n), PFn, SCl(n), and SF(n)Cl families, we found that a new type of bond--the recoupled pair bond--accounts for the ability of these elements to form hypervalent, or hypercoordinated, compounds. Hypervalent molecules are formed when it is energetically favorable for the electrons in a lone pair orbital to be recoupled, allowing each of the electrons to form chemical bonds with ligands. In this paper, we characterize the structures and energies of the ground and low-lying excited states of the ClF(n)(+) (n = 1-6) ions, using high level ab initio methods [MRCI, CCSD(T)/RCCSD(T)] with large correlation consistent basis sets. We computed a number of quantities, including ClF(n)(+) structures, bond dissociation energies, and ClF(n) ionization energies and compared our results with the available experimental data. Both the bond dissociation energies and the ionization energies oscillate, variations that are readily explained using the recoupled pair bonding model. Comparisons are drawn between the ClF(n)(+) cations and their counterparts in the isoelectronic SF(n) series, which possess many similarities. We found two significant differences between the ClF(n)(+) and the SF(n) series: (i) the bond dissociation energies of ClF(n)(+) are much weaker than those of the corresponding SF(n) species, and (ii) there is no stable (3)A2 state in ClF2(+) corresponding to the stable state found in SF2. An examination of the Mulliken populations at the HF/AVTZ level for ClF(n)(+) and SF(n) species predicts that the F atom in the axial (recoupled pair bonding) position is more highly charged than the F atom in the equatorial (covalent bonding) position; there is also less charge transfer to the F atoms in ClF(n)(+) than in SF(n). The positive charge on Cl(+) makes it more difficult for an F atom to attract electrons from Cl(+) than from S and correspondingly less favorable to recouple the electrons in the lone pair orbitals in the ClF(n)(+) species.