The energy gap defined as the energy difference between the HOMO and the LUMO states for all structures were summarized in table 1. It is clearly seen that the pristine adamantane has a wide band gap ranging from 5.7 to 9.2 eV depending on the exchange-correlation functional and basis sets used. These results suggested that the pristine adamantane is categorized as an insulator [12]. Substituting the tertiary hydrogen atoms of adamantane with Li and Na atoms significantly changes in the energy gaps, especially for one Li/Na substitution [13].