The structure, energetics, vibrations, and barrier to internal rotation around the N...H-O hydrogen bond of the binary pyridine-formic acid complex are calculated using one properly selected hybrid density functional theory procedure. The calculations demonstrate that the most stable isomer of the complex has a strong N... H-O hydrogen-bonding interaction, whose strength is enhanced by the presence of an agostic interaction between the carbonylic oxygen and the a hydrogen of the pyridine. Rotation around N...H-O, which prevents such an agostic interaction to occur, results in a decrease of the bonding energy of the complex from 11.1 kcal/mol to 6.43 kcal/mol. Additionally, a normal-mode analysis of the vibrations of the two most stable complexes characterized has been carried out and compared with the experimental vibrational frequencies of the pyridine-acetic acid complex. Furthermore, the effect of the specific solvation by one more formic acid molecule and one methanol molecule has also been considered. Both solvents enhance substantially the strength of the N...H-O hydrogen bond as shown by the decrease of the N-H distance and the appreciable red shift of the O-H vibrational mode upon solvation.