The natural product argadin is a cyclopentapeptide chitinase inhibitor that binds to chitinase B (ChiB) from the pathogenic bacteria Serratia marcescens. N(ω)-Acetyl-L-arginine and L-aminoadipic acid of argadin form intramolecular ionic hydrogen bonds in the aromatic hydrophobic pocket of ChiB. We performed ab initio molecular orbital and density functional theory calculations to elucidate the role of this intramolecular hydrogen bonding on intermolecular interactions between argadin and ChiB. We found that argadin accrues large stabilization energies from the van der Waals dispersion interactions, such as CH-π, π-π, and π-lone pair interactions, in the aromatic hydrophobic pocket of ChiB, although intramolecular hydrogen bonding within argadin might result in loss of entropy. The intramolecular ionic hydrogen bonding formation canceled local molecular charges and provided good van der Waals interactions with surrounding aromatic residues.