Noble gas endohedral fullerenes, Ng@C60 (Ng=Ar, Kr): a particular benchmark for assessing the account of non-covalent interactions by density functional theory calculations

This work is dedicated to a special test, checking the capability of density functional theory computations in the account of long-range effects. The particular case of endohedral noble gas atoms in C-60 fullerene puts several methodological challenges, such as the numeric problem in the balance of covalent versus non-covalent interactions. We designed a procedure based on the shifts of vibrational frequencies in C-60 versus Ng@C-60 couples. The energy scale of the investigated vibrations is comparable to that of the extracted van der Waals interaction parameters, achieving then a well-tempered description. A phenomenological model, based on transparent analytical formulas of the totally symmetric modes, is outlined and used to assess the computational results on series of functionals belonging to different classes (genuine forms, long-range corrected and with empiric dispersion ingredients). While the vast majority of the tested functionals undergo failures, good results are obtained for some long-range-corrected functionals (LC-BLYP and LC-wPBE), which follow the Tsuneda and Hirao's scheme, provided that richer basis sets (with diffuse components) are used. Successes are obtained also for the Grimme B97D functional, when coupled with the D2 and D3 dispersion scheme, the results being rather independent from the basis set, as expected from the empirical nature of this type of amendment.