Electronic Structure of Buckminsterfullerene C₆₀ and Absorption Spectra of the Cu₄²⁺@C₆₀ and Ag₄²⁺@ C₆₀ Clusters

Abstract

This work systematically examines the structural, vibrational, and electronic characteristics of buckminsterfullerene C₆₀ and its metal-encapsulated derivatives, Ag₄²⁺@C₆₀ and Cu₄²⁺@C₆₀, employing density Functional Theory (DFT) in conjunction with Time-Dependent DFT (TD-DFT). The C₆₀ molecule is most stable in the icosahedral I_h point group. Due to this high symmetry, only four vibrational modes (all T_1u) are infrared active, with calculated frequencies of 537, 574, 1193, and 1483 cm^-1. Electronic analysis indicates the lowest energy electron transitions form HOMO to LUMO as well as LUMO+1 create fifteen excited states which are 3-,3-,4- and 5-fold degeneracy, and the addition of a single electron to C₆₀ induces a symmetry descent from I_h → T → C_i. Subsequent optimization of the metal-doped clusters reveals structural bonding between the carbon cage and the metal atoms. While Ag₄²⁺ resides at the cage center, the Cu₄²⁺ cluster adopts an off-center position. Crucially, metal encapsulation dramatically alters the optical properties. While pure C₆₀ exhibits forbidden transitions in the UV-Vis region, the doped clusters display distinct absorption bands - specifically 224, 264, and 355 nm for Ag₄²⁺@C₆₀, and 250, 327, and 346 nm for Cu₄²⁺@C₆₀. These spectral shifts are ascribed to the participation of the transition-metal s and d orbitals in the fullerene π → π* electronic transitions.