Potential energy and dipole moment surfaces for HF@C60: Prediction of spectral and electric response properties.

We present a five-dimensional potential energy surface (PES) for the HF@C60 system computed at the DF-LMP2/cc-pVTZ level of theory. We also calculated a five-dimensional dipole moment surface (DMS) based on DFT(PBE0)/cc-pVTZ calculations. The HF and C60 molecules are considered rigid with bond length rHF = 0.9255 Å (gas phase ground rovibrational state geometry). The C60 geometry is of Ih symmetry. The ab initio points were fitted to obtain a PES in terms of bipolar spherical harmonics. The minimum of the PES corresponds to a geometry where the center of mass of HF is located 0.11 Å away from the center of the cage with an interaction energy of -6.929 kcal/mol. The DMS was also represented in terms of bipolar spherical harmonics. The PES was used to calculate the rotation-translation bound states of HF@C60, and good agreement was found relative to the available experimental data [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] except for the splitting of the first rotational excitation levels. We propose an empirical adjustment to the PES in order to account for the experimentally observed symmetry breaking. The form of that effective PES is additive. We also propose an effective Hamiltonian with an adjusted rotational constant in order to quantitatively reproduce the experimental results including the splitting of the first rotational state. We use our models to compute the molecular volume polarizability of HF confined by C60 and obtain good agreement with experiment.