Electron confinement meet electron delocalization: non-additivity and finite-size effects in the polarizabilities and dispersion coefficients of the fullerenes

Abstract

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (α with = 1, 2, 3) for the C₆₀–C₈₄ fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. By comparing against classical models of the fullerenes as conducting spherical shells (or solid spheres) of uniform electron density, a detailed critical analysis of the derived effective scaling laws (α₁ ∼ N^1.2, α₂ ∼ N^2.0, α₃ ∼ N^2.7) demonstrates that 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 frequency-dependent polarizabilities were obtained by inputting the α series into the hollow sphere model (within the modified single frequency approximation), and used to compute the molecular dispersion coefficients (C_n with n = 6, 8, 9, 10) needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems. Using first-order perturbation theory in conjunction with >140 000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions to α₁ in C₆₀ and C₇₀, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.