Short Strong Hydrogen Bonds (SSHBs) play an important role in many fields of physics, chemistry and biology. Since it is known that SSHBs exist in many biological systems, the role of hydrogen bonding motifs has been particularly interesting in enzyme catalysis, bio-metabolism, protein folding and proton transport phenomena. To explore the characteristic features of neutral, anionic and cationic hydrogen bonds, we have carried out theoretical studies of diverse homogeneous and heterogeneous hydrogen bonded dimers including water, peroxides, alcohols, ethers, aldehydes, ketones, carboxylic acids, anhydrides, and nitriles. Geometry optimization and harmonic frequency calculations are performed at the levels of Density Functional Theory (DFT) and Møller-Plesset second order perturbation (MP2) theory. First principles Car-Parrinello molecular dynamics (CPMD) simulations are performed to obtain IR spectra derived from velocity- and dipole-autocorrelation functions. We find that the hydrogen bond energy is roughly inversely proportional to the fourth power of the r(O/N-H) distance. Namely, the polarization of the proton accepting O/N atom by the proton-donating H atom reflects most of the binding energy in these diverse cation/anion/neutral hydrogen bonds. The present study gives deeper insight into the nature of hydrogen-bonded dimers including SSHBs.