Within the constraints of density functional theory, (B3LYP/6-31G(d,p) and B3LYP/6-31++G(d,p)), it is shown that 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtizane (CL-20) is unstable in the presence of an alpha-particle which transfers its charge causing the cage structure of CL-20 to be destroyed. Structural factors responsible for such a destruction are investigated. It has been found that removal of a single NO2 group from the 5- or 6-membered ring of CL-20 causes cage destruction in the dication form. Although, the carbon analog of CL-20 cage is stable in double cation form (only some distortions occur), even presence of a single nitro group on its 5- or 6- membered ring causes destruction of the carbon cage in dication form. Mono and bicentric nitrogen perturbations on the carbon cage of CL-20 (excluding the bicentric perturbation case in which nitrogens are on different pentagonal rings but located symmetrically) result in destruction on double cationic charging. Dication form of CL-20 cage (retaining cage nitrogens without nitro groups) is also unstable in double cation form.