The effect of substituents on the stabilities of cumulenes-ketenes, allenes, diazomethanes and isocyanates and related systems-alkynes, nitriles and nitrile oxides is studied using the density functional theory (B3LYP, SVWN and BP86) and ab initio (HF, MP2) calculations at the 6-31G* basis set level. Using isodesmic reactions, correlation between stabilization energies of cumulenes and substituent group electronegativities (c BE) is established and the results from DFT and MP2 methods are compared with the earlier HF calculations. Calculations revealed that the density functional methods can be used to study the effect of substituents on the stabilities of cumulenes. It is observed that the cumulenes are stabilized by electropositive substituent groups from s -electron donation and p -electron withdrawal and are destabilized by electronegative substituent groups from n-p donation. The calculated geometries of the cumulenes are compared with the available experimental data.High level ab initio and density functional theory calculations have been used to study the energetics of low-barrier hydrogen bond (LBHB) systems. Using substituted formic acid-formate anion complexes as model LBHB systems, hydrogen bond strength is correlated to the pKa mismatch between the hydrogen bond donor and the hydrogen bond acceptor. LBHB model systems are characterized by the 1H-NMR chemical shift calculations. A linear correlation between the calculated hydrogen bond strength and the predicted 1H-NMR chemical shift was established. It is concluded that the pKa matching within the enzyme active site of the two species involved in the LBHB is important to maximizing catalytic stabilization.