Local energy decomposition analysis and molecular properties of encapsulated methane in fullerene (CH₄@C₆₀)

Methane has been successfully encapsulated within cages of C₆₀ fullerene, which is an appropriate model system to study confinement effects. Its chemistry and physics are also relevant for theoretical model descriptions. Here we provide insights into intermolecular interactions and predicted spectroscopic responses of the CH₄@C₆₀ complex and compared them with results from other methods and with data from the literature. Local energy decomposition analysis (LED) within the domain-based local pair natural orbital coupled cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) framework was used, and an efficient protocol for studies of endohedral complexes of fullerenes is proposed. This approach allowed us to assess energies in relation to electronic and geometric preparation, electrostatics, exchange, and London dispersion for the CH₄@C₆₀ endohedral complex. The calculated stabilization energy of CH₄ inside the C₆₀ fullerene was -13.5 kcal mol^-1 and its magnitude was significantly larger than the latent heat of evaporation of CH₄. Evaluation of vibrational frequencies and polarizabilities of the CH₄@C₆₀ complex revealed that the infrared (IR) and Raman bands of the endohedral CH₄ were essentially "silent" due to the dielectric screening effect of C₆₀, which acted as a molecular Faraday cage. Absorption spectra in the UV-vis domain and ionization potentials of C₆₀ and CH₄@C₆₀ were predicted. They were almost identical. The calculated ¹H/¹³C NMR shifts and spin-spin coupling constants were in very good agreement with experimental data. In addition, reference DLPNO-CCSD(T) interaction energies for complexes with noble gases (Ng@C₆₀; Ng = He, Ne, Ar, Kr) were calculated. The values were compared with those derived from supramolecular MP2/SCS-MP2 calculations and estimates with London-type formulas by Pyykkö and coworkers [Phys. Chem. Chem. Phys., 2010, 12, 6187-6203], and with values derived from DFT-based symmetry-adapted perturbation theory (DFT-SAPT) by Hesselmann & Korona [Phys. Chem. Chem. Phys., 2011, 13, 732-743]. Selected points at the potential energy surface of the endohedral He₂@C₆₀ trimer were considered. In contrast to previous theoretical attempts with the DFT/MP2/SCS-MP2/DFT-SAPT methods, our calculations at the DLPNO-CCSD(T) level of theory predicted the He₂@C₆₀ trimer to be thermodynamically stable, which is in agreement with experimental observations.