Theoretical Study of Methane Storage in Cu₂₄(m-BDC)₂₄

Calculations on the Cu₂₄(m-BDC)₂₄ (m-BDC = 1,3-benzenedicarboxylate) polyoxometalate (POM) cage with 0, 12, 24, and 40 methane molecules inside were made using the M06 exchange/correlation functional. During filling of the cage with 40 CH₄ molecules, the 12 strongest binding CH₄ molecules are those to the coordination unsaturated sites (CUS) to the inwardly directed Cu(+2) centers via agostic interactions. The next 12 CH₄ molecules are less tightly bound followed by the next 16 CH₄ molecules with average binding energies of 8.27, 7.88, and 7.36 kcal/mol per CH₄, respectively. A section of the Cu₂₄(m-BDC)₂₄ cage was taken with the formula Cu₄(m-BDC)(BC)₆ (BC = benezenecarboxylate) in order to estimate zero-point, thermal, and entropy corrections of the larger cage. Estimating free energies at 1 bar, the Cu₂₄(m-BDC)₂₄ POM is predicted to lose 16, 12, and 12 CH₄ molecules at 67, 123, and 171 °C, respectively. The 40CH₄@Cu₂₄(m-BDC)₂₄ cage, which is isostructural to the main cavity of HKUST-1 with 40 CH₄ molecules inside, is predicted to have a loading of 224 cm³(STP) cm^-3 at 1 bar.