On the Higher-Order Static Polarizabilities and Dispersion Coefficients of the Fullerenes: An Ab Initio Study

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (i.e., dipole, quadrupole, and octupole ) for the C₆₀-C₈₄ fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. Critical analysis of the derived effective scaling laws provides new insight into how the electronic structure of finite-sized fullerenes---a unique dichotomy of electron confinement and delocalization effects due to their quasi-spherical cage-like structures and encapsulated void spaces---simultaneously limits and enhances their quantum mechanical response to electric field perturbations. Corresponding molecular dispersion coefficients needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems were obtained by inputting the polarizabilities into the hollow sphere model within the modified single-frequency approximation.

Using first-order perturbation theory in conjunction with >140,000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions (zpvc) to the dipole polarizability in C₆₀ and C₇₀, thereby enabling direct comparison between theory and experiment for these quintessential nanostructures.