الملخص

     In this study, one of the quantum mechanics methods, the ab-initio method DFT,  was used in calculating the number of the physical variables that affect the octane number (ON). Then, these theoretically calculated variables were linked with each other as independent variables and with the octane number values ​​of gasoline derivatives, which were calculated in practice as a dependent variable. The best result obtained through these relationships was (Total Energy, HOMO, LUMO, and Torsion), where the correlation coefficient was close to the right one and the value of the standard deviation is little. Through the results of the relations, a mathematical relationship was proposed through which the ON of gasoline derivatives was theoretically calculated, there was a convergence between the practical values ​​with the theoretically calculated values, which indicated the success of the developed mathematical method.