Quantum chemical calculations were performed in order to clarify the chemical properties for having the cetane number increase effect and the relationship between the chemical structure of the cetane improvers and their effects. The density functional theory (DFT) calculation, including the B3LYP calculation coupled to a 6-31+G(d) basis set, was used to estimate the thermochemical properties of the chemical compounds. First, the bond-dissociation energy of various cetane improvers and compounds having no cetane number increase effects were calculated to estimate the threshold value of the bond-dissociation energy necessary to have the cetane number increase effect. The result suggests that the 190-210 kJ/mol of the bond-dissociation energy could be the threshold value of the bond-dissociation energy necessary to have the cetane number increase effect. Next, the reaction Gibbs free energies by oxygen addition reactions (-DeltaG) of various alkyl radicals that were produced from the thermal decomposition of the cetane improvers were calculated. The relationship between the reaction Gibbs free energy for the O-2 addition reaction and cetane number increase by cetane improvers from which these alkyl radicals were produced were investigated. As a result, there is a positive correlation between -DeltaG and the cetane number improvement when comparing the radicals with the same molecular skeletons.