We report density functional theory calculations at the B3LYP/D95(d,p) level on the hydrogen- bonding complexes of tetraazaanthracenedione, 1, with N-(pyridin-2-yl)urea, 2H, or N-(6-aminopyridin-2-yl)urea, 2N. The interaction energy of the 1-2H complex exceeds that of 1-2N, despite the fact that 1-2N contains a strong N-H center dot center dot center dot O interaction in place of a weak C-H center dot center dot center dot O interaction in 1-2H. We show that the 1-2N interaction is weaker than the sum of the four normal individual H-bonding interactions because the steric constraints of the complex prevent the H-bonding donors and acceptors from optimally approaching each other to form the two central H-bonds. This steric phenomenon, which we call attractive strain, is likely present to some extent in most H-bonding systems that contain more than two H-bonds between rigid monomers. Attractive strain is unusually important in 1-2N. Attractive strain can be conceived of as an enthalpic cost for the entropic benefits of freezing the dihedral angles of the multiple H-bond donors and acceptors by designing rigid systems.