Theoretical calculations in the gas phase on a series of intermolecular complexes formed between 1-methylimidazole (1-MeIm) and four carboxylic acids R-COOH, where R = CF3, CHCl2, C(CH3)Cl-2, and CH2Cl, have been carried out. Results from NMR and FTIR spectroscopy, in previous experimental studies, have been used by Frey and co-workers, trying to characterize the hydrogen bond between those carboxylic acids and 1-methylimidazole in aprotic organic solvents. Our energetic results for the proton transfer through the hydrogen bond indicate that only one of the carboxylic acids is able to form a low-barrier hydrogen bond (LBHB) with 1-MeIm in gas phase. However, there is not equalization between the pK(a)s of R-COOH and 1-MeImH(+) (the conjugate acid of 1-MeIm). We suggest that, for short hydrogen bonds, a requirement for forming a LBHB is energy degeneration (or nearly degeneration) of the two minima in a double-well hydrogen bond. This energy degeneration in the double well is determined by a thermodynamic cycle where the pK(a) difference of the conjugate acids of the interacting groups is one of the factors taken into account. We have also shown that a delocalized LBHB is not necessarily stronger than a localized hydrogen bond. Along with the thermodynamic results, an analysis of the electronic wave function at several stationary points of the different complexes is presented.