Static dielectric response of icosahedral fullerenes from C60 to C2160 by an all electron density functional theory

The static dielectric response of C60, C180, C240, C540, C720, C960, C1500, and C2160 fullerenes is characterized by an all-electron density-functional method. First, the screened polarizabilities of C60, C180, C240, and C540, are determined by the finite-field method using Gaussian basis set containing 35 basis functions per atom. In the second set of calculations, the unscreened polarizabilities are calculated for fullerenes C60 through C2160 from the self-consistent Kohn-Sham orbitals and eigen-values using the sum-over-states method. The approximate screened polarizabilities, obtained by applying a correction determined within linear response theory show excellent agreement with the finite-field polarizabilities. The static dipole polarizability per atom in C2160 is (4 Angstrom^3) three times larger than that in C60 (1.344 Angstrom^3). Our results reduce the uncertainty in various theoretical models used previously to describe the dielectric response of fullerenes and show that quantum size effects in polarizability are significantly smaller than previously thought.