Theoretical Study of the Binding Energy of a Methane Molecule in a (H₂O)₂₀ Dodecahedral Cage

The interaction energy of a methane molecule encapsulated in a dodecahedral water cage is calculated using the MP2, MP2C, various dispersion-corrected DFT, and diffusion Monte Carlo (DMC) methods. The MP2, MP2C, and DMC methods give binding energies of -5.04, -4.60, and -5.3 ± 0.5 kcal/mol, respectively. In addition, the two- and three-body contributions are evaluated using the DFT, MP2, and CCSD(T) methods. All of the DFT methods considered appreciably overestimate the magnitude of the three-body contribution to the interaction energy. The two- and three-body energies are further analyzed by use of symmetry-adapted perturbation theory (SAPT) which allows decomposition into electrostatics, exchange, induction, and dispersion contributions. The SAPT calculations reveal that the induction, dispersion, and exchange three-body contributions to the methane-cage binding energy are all sizable, with the net three-body contribution to the binding energy being about 1 kcal/mol.

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