The selective binding between avian and human influenza A viral hemagglutinins (HA) subtype H3 and Neu5Acα2-3 and α2-6Gal (avian α2-3, human α2-6) is qualitatively rationalized by the fragment molecular orbital (FMO) method. We suggest a general model of analyzing protein-ligand interactions based on the electrostatic, polarization, dispersion, and desolvation components obtained from quantum-mechanical calculations at the MP2/6-31G(d) level with the polarizable continuum model of solvation. The favorable avian H3 (A/duck/Ukraine/1963)-avian α2-3 binding arises from the hydrophilic interaction between Gal-4 OH and side-chain NH(2)CO on Gln226, which is supported by the intermolecular hydrogen-bond network to the 1-COO group on Neu5Ac moiety. A substitution of Gln226Leu in the avian H3 HA1 domain increases the binding affinity to human α2-6 due to the Leu226···human α2-6 dispersion with a small entropic penalty during the complex formation. The remarkable human H3 (A/Aichi/2/1968)-human α2-6 binding is not governed by the Ser228-OH···OH-9 Neu5Ac hydrogen bond. These fragment-based chemical aspects can help design monovalent inhibitors of the influenza viral HA-sialoside binding and the simulation studies on the viral HAs-human α2-6 binding.