Explosive materials have always been attracting the attention of scientists. Various explosives either in pure bulk form or as admixtures are synthesized and investigated from different points of view. However, because of dangerous character of these materials, their syntheses and properties have to be forecasted by theoretical studies. The new research trends of explosive materials generally include the designs of novel derivatives of well&ndash / known explosives to improve their detonation performances (heats of explosion, detonation velocities and detonation pressures) and thermal stabilities and decrease their sensitivities towards friction, electric spark, shock and impact either experimentally or theoretically. NTO (5&ndash / nitro&ndash / 2,4&ndash / dihydro&ndash / 3H&ndash / 1,2,4&ndash / triazol&ndash / 3&ndash / one) and PATO (3&ndash / picrylamino&ndash / 1,2,4&ndash / triazole) are very important secondary explosives that take place in the literature for many years in terms of their explosive properties. In this thesis study, new species of these explosives have been designed to enhance their detonation performances (ballistic properties) and to lower their sensitivities and reactivities computationally. Additionally, aromatic nitration reactions and their mechanisms for unprotonated and protonated PATO species have been analyzed. The ab initio quantum chemistry methods, Hartree&ndash / Fock (HF) and Density Functional Theory (DFT), have been used in the calculations with Pople basis sets. Novel NTO and PATO tautomeric species have been designed and investigated to enlighten the effects of tautomerism on their quantum chemical properties and detonation performances in the gas phase. Various aromatic nitration mechanisms (carbon and nitrogen mono&ndash / nitration mechanisms) of unprotonated tautomeric PATO species as well as PATO have been designed in gas phase and the reaction states (pre&ndash / transition states, transition states, intermediates and nitration products) have been detected belonging to these mechanisms. Nitrations in solution phase have also been analyzed. The reaction states have been detected for carbon and nitrogen mono&ndash / nitrations of protonated PATO species in the gas phase. The detonation performances of unnitrated and nitrated PATO products have been presented.