The propensities for sigma hole bonding by halogen atoms bonded to central atoms below period 2 in the periodic table remain to be systematically examined. Using iodine as our reference halogen atom, a comprehensive analysis of the tendencies for halogen and other forms of significant sigma hole bonding by simple compounds of main group atoms from H to At is accomplished. An examination of the structure and bonding of complexes formed by those iodine-substituted main group compounds and sigma donating bases (ammonia and trimethylamine) is performed to probe the viability of halogen bonding by heavy main group RnM-I compounds in particular, given the historic focus on period 2. We show that propensities for halogen bonding by FnM-I systems for certain columns of the main group vary anomalously as M gets heavier due to a polarization-induced escalation of the electrostatic potential on I. In certain cases, the positive potential at the sigma hole on I is weaker than that at sigma holes on the central M or geminal R atoms. Previously unexplored cases of strong halogen bonding by the fluoroiodides of heavy group 13 atoms are identified, and prospects for other sigma hole type interactions to polarized (main group) central atoms are elucidated.