Density Functional Theory (DFT) has been used to calculate the energies of over 30 different structures with the general formula (AlOMe)(n). (AlMe3)(m) where n ranges from 6 to 13 and m ranges between 1 and 4, depending upon the structure of the parent (AlOMe)(n) cage. The way in which TMA (trimethylaluminum) bonds to MAO (methylaluminoxane) has been determined as well as the location of the acidic sites present in MAO caged structures. Topological arguments have been used to show chat TMA does not bind to MAO cages where n = 12 or n greater than or equal to 14. The ADF energies in conjunction with frequency calculations based on molecular mechanics have been used to estimate the finite temperature enthalpies, entropies, and free energies of the TMA containing MAO structures. Using the Gibbs free energies found for pure MAO structures calculated in a previous work, in conjunction with the free energies of TMA containing MAO structures obtained in the present study, it was possible to determine the percent abundance of each TMA containing MAO within the temperature range of 198.15 K-598.15 K. We have found that very little TMA is actually bound to MAO. The Me/Al ratio on the MAO cages is determined as being approximately 1.00, 1.01, 1.02, and 1.03 at 198, 298, 398, and 598 K, respectively. Moreover, the percentage of Al found as TMA has been calculated as being 0.21%, 0.62%, 1.05%, and 1.76% and the average unit formulas of (AlOMe)(18.08). (TMA)(0.04), (AlOMe)(17.04). (TMA)0.11, (AlOMe)(15.72). (TMA)(0.17), and (AlOMe)(14.62). (TMA)(0.26) have been determined at the aforementioned temperatures.