We find for distinct classes of halogen bonded complexes (MF3-X...Y) that the ab initio BSSE-corrected binding energies (Delta E) and enthalpies (Delta H) are predicted by functions of the form y = A/r(n) + C. Here X is a halogen atom, Y is a base, r is the X...Y separation, and A, n, and C are constants. The actual value of n (5.5 < n < 7.0 for Delta E) for each class is determined evidently by the availability of the lone pairs on the base and is insensitive to M such that all of the complexes of a given base fall on the same curve for y versus r. Remarkably, several bases show the same behavior in some cases such that just three curves account for 55 MF3I...Y complexes of 11 bases, where M = C, Si, Ge, Sn, and Pb. Two additional bases, THF and NF3, which form especially strong and weak complexes, respectively, are in classes by themselves. Anomalous modes of halogen bonding are identified; in particular, furan forms sigma-hole complexes via carbons 2 and 3 (through the pi system) in the ring in preference to the oxygen site. These results are in line with experimental observations for furan-dihalogen complexes, and several other small MF3I...Y pairs are proposed in this work for experimental interrogation. Instead of halogen bonding, CF4 tends to form weak sigma-hole bonds to bases via the polarized central carbon atom, and new examples of such pro-dative interactions to carbon in CF4 are identified in this work. We find that GeF3I and SnF3I form I...Y halogen bonds of comparable energies to those formed by the smaller and better studied CF3I. PbF3I forms the strongest halogen bond regardless of the identity of the base; SiF3I consistently forms the weakest link.