Vibrational Assignment of All 46 Fundamentals of C₆₀ and C₆₀⁶: Scaled Quantum Mechanical Results Performed in Redundant Internal Coordinates and Compared to Experiments

Traditional vibrational assignment in terms of bond stretching, angle bending, and torsion is not possible in fullerenes due to the very large number of coupled internal coordinates. Large scale density functional calculations of the vibrational properties of C₆₀ and C₆₀^6- have been carried out with Becke3LYP and BeckeLYP exchange-correlation functionals in the pursuit of obtaining a reliable set of 174 normal modes (46 fundamental frequencies) and understanding the effect of charge transfer (doping) on the vibrational modes. The calculations involve scaling of the force field in redundant internal coordinates as proposed by Pulay et al. The scaled quantum mechanical (SQM) calculations yield excellent agreement with experiment for the 14 allowed frequencies. This provides the basis for an accurate assignment of all nonallowed fundamentals and the reassignment of the observed overtone and combination bands of the high-resolution Raman (Wang et al., 1993) and IR (Martin et al. 1994) spectra. The calculated intensity ratios for the four IR active bands agree with experiment. The large IR intensity enhancements observed for C₆₀^6- relative to C₆₀ are explained by the enhancement of certain components of the atomic polar tensor that is partially due to bond equalization in the charged fullerene. This enhancement appears to be largely a molecular rather then a solid state effect.