On the Higher-Order Static Polarizabilities and Dispersion Coefficients of the Fullerenes: An Ab Initio Study
<div>In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (<i>i.e.</i>, dipole, quadrupole, and octupole ) for the C<sub>60</sub>-C<sub>84</sub> 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 <i>and</i> 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. </div><div>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 C<sub>60</sub> and C<sub>70</sub>, thereby enabling direct comparison between theory and experiment for these quintessential nanostructures.</div>
