Ab initio calculations are used to compare the abilities of the aromatic groups of the Phe, Tyr, Trp, and His amino acids (modeled respectively by benzene, phenol, indole, and imidazole) to form H-bonds of three different types. Strongest of all are the conventional H-bonds (e.g., OH..O and OH..N). His forms the strongest such H-bond, followed by Tyr, and then by Trp. Whereas OH..phi bonds formed by the approach of a proton donor to the pi electron cloud above the aromatic system are somewhat weaker, they nonetheless represent an important class of stabilizing interactions. The strengths of H-bonds in this category follow the trend Trp > His > Tyr similar to Phe. CH..O interactions are weaker still, and only those involving His and Trp are strong enough to make significant contributions to protein structure. A protonated residue such as HisH(+) makes for a very powerful proton donor, such that even its CH..O H-bonds are stronger than the conventional H-bonds formed by neutral groups.