Vibrational spectra of La@C₆₀ and Ce@C₆₀ endohedral fullerenes: Influence of spin state multiplicity

Endohedral fullerenes with paramagnetic encapsulated atoms are new magnetic materials of interest for numerous applications from medicine to quantum computers. An important phenomenon with endohedral fullerenes is the appearance of new vibrational frequencies not associated with empty fullerenes. The vibrational spectra of the lanthanide endohedral fullerenes La@C₆₀ and Ce@C₆₀ in various spin states are calculated using the density functional method. Most of the spectral lines lie in the 300-1600 cm^-1range, and their intensities change dramatically depending on the molecule's symmetry and spin state, which are determined by the encapsulated lanthanide atom. The average frequency shift of the carbon cage vibrations caused by spin transition is only 5 cm^-1. The calculated frequencies of the coupled "metal-carbon cage" vibrations of the lanthanide endohedral fullerenes La@C₆₀ and Ce@C₆₀ in various spin states lie in the 10-170 cm^-1range. The computational results for both the frequencies and intensities of the metal-cage modes depend considerably on the spin state. The changes in these vibrational modes are due to the changes in the molecular symmetry and the metal-carbon bond lengths. Such dependence can be used as a basis for controlling the spin state of metallofullerenes by measuring the vibration frequencies in the far-infrared zone, which could be important for nanoelectronics and quantum informatics.