We report the results of extensive ab initio HF and post-HF (as well as DFT) studies of the "magic number" metallocarbohedrene ("metcar") clusters Ti8C12 and Mo8C12 in various electronic states of T-d symmetry and the Jahn-Teller-distorted D-2d, C-3nu, and C-1 symmetries. An essential feature of the present work is that it is a systematic study employing a hierarchy of theoretical methods to explore the effect of refining the treatment of electron correlation in determining the geometry and electronic ground state of these species. For Ti8C12, we show using relatively high-level theories such as MP2, MP4, and QCISD that the Aufbau principle for the occupation of the molecular orbitals is obeyed, resulting in a Jahn-Teller distortion of the proposed T-d symmetry. These higher-level calculations identify a D-2d structure close to T-d symmetry for the electronic ground state and allow some of its chemical properties to be explored with confidence using a lower level of theory. The reactivity of Ti8C12 toward H2O, CO, and Cl is also investigated. It is found that Ti8C12 can act as a Lewis acid to accept lone pairs of electrons from H2O (Lewis base) and that it can also be oxidized by Cl atoms through electron donation from C-2 units in Ti8C12 to the Cl mediated by a Ti d(Z)(2) orbital. Thus, a relationship among structure, electronic properties, and reactivity is established. For Mo8C12, we find that the T-d structure is not subject to a Jahn-Teller effect, and it is a true minimum at the HF level; B3LYP DFT calculations prefer a lower-symmetry (near-D-2) structure. The results of ab initio and DFT methods are compared.