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

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (alpha with = 1, 2, 3) for the C-60-C-84 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 (alpha(1) similar to N-1.2, alpha(2) similar to N-2.0, alpha(3) similar to 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 alpha 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 alpha(1) in C-60 and C-70, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.

Automated summary

This study utilized finite-field derivative techniques and density functional theory to compute static isotropic polarizability series for fullerenes, analyzing the unique electron structure effects on quantum mechanical responses. The results demonstrate the limits and enhancements in response to electric field perturbations due to the quasi-spherical cage-like structures and encapsulated void spaces of finite-sized fullerenes. Additionally, the study computed frequency-dependent polarizabilities and molecular dispersion coefficients to describe the non-trivial van der Waals interactions in fullerene-based systems.