A search has been conducted, employing ab initio molecular orbital theory, for potential tetrel-bonded complexes between the fluorinated methanes methyl fluoride, difluoromethane and fluoroform, and the related hydrides ammonia, water, hydrogen fluoride, phosphine, hydrogen sulfide and hydrogen chloride. Eleven such complexes have been identified, six containing CH3F and five CH2F2. The complexes are typically less strongly bound than their hydrogen-bonded counterparts, and the interaction energies vary in a consistent way with the periodic trend of the electron donors. The intermolecular separations and changes of the relevant intramolecular bond lengths, the wavenumber shifts of the critical vibrational modes, and the extents of charge transfer for the atoms most closely involved in the interactions correlate, by and large, with the strengths of interaction.