Molecular tweezers are simple molecular receptors that can be characterized by the presence of two flat pincers separated by a more or less rigid tether. They have the ability to form complexes with a substrate molecule by gripping the substrate between the tips of the tweezers in a similar manner to that of mechanical tweezers. Klärner et al. synthesized one of the structurally simplest molecular tweezers, which is reported to bind electrodeficient aromatic and aliphatic substrates as well as organic cations. Complexes between these molecular tweezers and electron-rich aromatic, aliphatic, or anionic substrates have not been observed. Inspired by several recent reports that describe the interaction of hexafluorobenzene with electron-rich sites of molecules, we conducted a theoretical study to show the possibility of building molecular tweezers, based on those synthesized by Klärner, which were able to bind to anions and thus increase their potential as molecular receptors. We characterized complexes formed between several fluorinated derivatives of simple tweezers and an iodine anion, and analyzed the nature of the intermolecular interactions as well as the energetics for the process of complexation. The stabilization trend reflected by the energetic results when fluorine substituents were added to benzene rings confirms our hypothesis about the possibility of obtaining neutral tweezers composed of aromatic rings that can bind anions.