Matrix isolation spectroscopy and spectral simulations of isotopically substituted C₆₀ molecules

Isotopically enriched (3.5% ¹³C) and depleted (0.5% ¹³C) fullerene C₆₀ molecules are isolated in parahydrogen (pH₂) solids at cryogenic temperatures and studied by high resolution (0.01-0.1 cm^-1) infrared (IR) absorption measurements. Spectra of natural isotopic abundance (1.1% ¹³C) C₆₀ molecules isolated in solid pH₂, orthodeuterium (oD₂), and Ne matrix hosts serve to identify the relatively minor spectral perturbations due to the trapping environments. Spectral features observed for the four IR-active T_1u modes of threefold degeneracy in I_h symmetry, namely, T_1u(1) at 529.77 cm^-1, T_1u(2) at 578.24 cm^-1, T_1u(3) at 1184.7 cm^-1, and T_1u(4) at 1432 cm^-1, are assigned to the superpositions of matrix perturbed vibrational-mode spectra of a number of ¹³C_n ¹²C_60-n isotopologues. New molecular orbital calculations show the symmetry lowering effects of ¹³C substitution, namely, split vibrational frequencies and modified IR intensities. IR spectral patterns calculated for the 328 distinct isotopomers of ¹³C_n ¹²C_60-n up to n = 3 are used to satisfactorily simulate most of the observed absorption features. For the T_1u(4) mode at 1432 cm^-1, the observed splitting is insensitive to the ¹³C abundance, indicating spectral perturbations due to Fermi resonance. Weak absorption features at 1545 cm^-1 are assigned to a combination of lower frequency modes. We discuss relative and absolute band strengths for the astrophysical application of estimating C₆₀ abundances in planetary nebulae.