The radial potential energy is calculated ab initio at the explicitly correlated level of theory CCSD(T)(F12c)/cc-pVTZ-F12 for the five axially symmetric, halogen-bonded complexes BClF (B=N-2, CO, PH3, HCN, and NH3) as a function of the intermolecular distance r. The PE curves are fitted by the Hulburt-Hirschfelder analytical function under the assumption of a pseudo-diatomic model. The spectroscopic constants omega sigma and omega sigma x sigma , and alpha sigma of the intermolecular stretching mode upsilon sigma are calculated by two closely related approaches. The first involves derivatives of a polynomial fitted to the ab initio calculated points near to r(e) and evaluated at r=r(e). The second uses the constants of the fitted H-H function. Both procedures are tested on (ClF)-Cl-35 by fitting (a) its RKR-type function and (b) the CCSD(T)(F12c)/cc-pVTZ-F12 version. The complexes OC....ClF and H3P....ClF behave differently from the other three. A point of inflection/secondary minimum with a shortened r(C...Cl) and an increased r(Cl-F) detected for B=CO, suggests a second isomer with a significant contribution from the valence-bond structure OC+Cl...F-. The shape of the ab initio calculated function for H3P...ClF is different from those involving B=N-2, HCN, or NH3, a difference attributed to H3PCl+...F(-)character. The ab initio generated curve for H3P...ClF is, nevertheless, satisfactorily fitted by the three-parameter H-H function.