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The nature of the H-bonds between the human protein HLA-DR1 (DRB*0101) and the hemagglutinin peptide HA306-318 has been studied using the Quantum Theory of Atoms in Molecules for the first time. We have found four H-bond groups: one conventional CO··HN bond group and three nonconventional CO··HC, π··HC involving aromatic rings and HN··HC aliphatic groups. The calculated electron density at the determined H-bond critical points suggests the follow protein pocket binding trend: P1 (2,311) >> P9 (1.109) > P4 (0.950) > P6 (0.553) > P7 (0.213) which agrees and reveal the nature of experimental findings, showing that P1 produces by a long way the strongest binding of the HLA-DR1 human protein molecule with the peptide backbone as consequence of the vast number of H-bonds in the P1 area and at the same time the largest specific binding of the peptide Tyr308 residue with aromatic residues located at the binding groove floor. The present results suggest the topological analysis of the electronic density as a valuable tool that allows a non-arbitrary partition of the pockets binding energy via the calculated electron density at the determined critical points.