Five structurally similar —ONO₂ and —N₃ derivatives of pentaerythritol, including tetraazido pentaerythritol (TAPE), pentaerythritol triazido nitrate (PTAN), pentaerythritol diazido dinitrate (PDADN), pentaerythritol azido trinitrate (PATN), and pentaerythritol tetranitrate (PETN) were studied by the B3LYP/6-31G ^* method. The molecular geometric configurations were optimized and vibration analyses were performed. Their densities, heats of formation, thermodynamic functions, detonation performances and specific impulses were estimated. The bond dissociation energy (E_BD) of the possible trigger bond and the activation energy (E_a) of the hydrogen transfer reaction were computed. The results show that in comparison with PTAN, PDADN, PATN and PETN, TAPE has the maximum heat of formation among five derivatives and specific impulse level approaching that of PETN. The detonation performance and stability of PATN are close to those of PETN, and better than that of other derivatives, including PDADN. The pyrolysis of TAPE with —N₃ is initiated from the transfer of H to —N₃ which leads to the elimination of N₂ and has an E_a of 130.57 kJ·mol^-1. The pyrolysis of other derivatives containing —ONO₂ is started from the rupture of the O—NO₂ bond with an E_BD of 130.91~137.45 kJ·mol^-1. These energy values satisfy the stability requirements for the energetic compounds.