Ab initio calculations have been performed on a series of complexes in which (HCNH)(+) is the proton donor and CNH, NCH, FH, ClH, and FCl (molecules X and Z) are the proton acceptors in binary complexes X:HCNH+ and HCNH+:Z, and ternary complexes X:HCNH+: Z. These complexes are stabilized by C-H+center dot center dot center dot A and N-H+center dot center dot center dot A hydrogen bonds, where A is the electron-pair donor atom of molecules X and Z. Binding energies of the ternary complexes are less than the sum of the binding energies of the corresponding binary complexes. In general, as the binding energy of the binary complex increases, the diminutive cooperative effect increases. The structures of these complexes, data from the AIM analyses, and coupling constants (1)J(N-H), (1h)J(H-A), and (2h)J(N-A) for the N-H+center dot center dot center dot A hydrogen bonds, and (1)J(C-H), (1h)J(H-A), and (2h)J(C-A) for the C-H+center dot center dot center dot A hydrogen bonds provide convincing evidence of diminutive cooperative effects in these ternary complexes. In particular, the symmetric N center dot center dot center dot H+center dot center dot center dot N hydrogen bond in HCNH+: NCH looses proton-shared character in the ternary complexes X:HCNH+:NCH, while the proton-shared character of the C center dot center dot center dot H+center dot center dot center dot C hydrogen bond in HNC:HCNH+ decreases in the ternary complexes HNC:HCNH+:Z and eventually becomes a traditional hydrogen bond as the strength of the HCNH+center dot center dot center dot Z interaction increases.