Ab initio methods are used to discover the effects of formaldehyde substituents on potential hypersurfaces for proton transfer in the equilibrium complex (ABCO-H-OCXH)(+) in which A, B, and X are electron-releasing or -withdrawing groups. The potential profiles span the full range from symmetric double well, asymmetric double well, to single well, depending on the substituents. A symmetric double well corresponds to a complex with two equivalent subunits such as (FCHO-H-OCHF)(+), whereas in (HFCO-H-OCH2)(+) only one minimum structure is obtained in the entire potential surface. When the protonation energies of the two subunits are not greatly different an asymmetric double well might form. A ratio omega to represent the extent of the difference of protonation energies between the two subunits in the complex was introduced to illustrate the formation of an asymmetric double well for calculated several complexes. To determine which conformation of the two wells has lower energy, the magnitude of the addition of binding energy of the conformation and the protonation energy of the subunit nearer the central proton is a crucial factor, The bigger is the magnitude of the conformation, the deeper is the well. A deeper right well in either the trans or cis conformer of (CH3FCHO-H-OCH2)(+) can be clarified easily with this magnitude as a parameter. It would be puzzling if only one term of energy (either binding energy of the conformation of two wells or protonation energy of the two subunits) were used, The difference of the magnitudes in two wells represents the potential gap between the two wells. The geometries of complexes varied from the parent complex (H2CO-H-OCH2)(+) are discussed briefly based on the direction of the dipole moment in the substituted subunits. The thermodynamic properties Delta H degrees, Delta S degrees, and Delta G degrees of the association reaction ABCOH(+) + HXCO --> (ABCO-H-OCXH)(+) at several temperatures are evaluated according to standard thermodynamic formulae that incorporate the vibrational frequencies of the various species.