Ab initio calculations at the MP2/6-31G* level have shown that variously substituted di- and trifluorobenzenes form non-covalent complexes with benzene that adopt either aromatic-aromatic or H-F binding, the choice being determined by the pattern of fluorination. The binding energies of these structures are from 3.4 to 4.5 kcal mol(-1). This range is large enough to account for observed variations in the binding affinity of a library of fluoroaromatic inhibitors of carbonic anhydrase. This enzyme has an aromatic amino acid at a central position in the active site. The diverse modes of binding of the dimers also suggest that aggregates of fluorobenzenes might adopt specified 3-dimensional shapes in the solid state.