Quantum-mechanical treatment of thermal effects on the structure and 13C NMR shielding of buckminsterfullerene C60

Abstract

We investigate thermal effects on the structure and ¹³C nuclear magnetic resonance (NMR) shielding of buckminsterfullerene, C₆₀, using a quantum-mechanical treatment of thermal rovibrational motion at the density functional theory (DFT) level. Volumes calculated from the temperature-dependent effective geometries confirm that C₆₀ fullerene indeed experiences negative thermal expansion (NTE). However, the NTE is much smaller and occurs at temperatures higher than previously predicted by classical MD simulations, above T = 100 K. The normal mode analysis of the contributions to the effective geometry reveals that the NTE is caused by a single low-frequency, fully symmetric, A_g(1) breathing mode instead of previously alleged quadrupolar modes. Although the effect of centrifugal distortion on the A_g(1) mode monotonically increases the volume of C₆₀ at finite temperatures, the NTE is caused by the negative anharmonic vibrational correction that activates above T = 100 K and reaches a minimum around T = 320 K. The validity of the current rovibrational approach is further confirmed by good agreement with the experimental results of temperature dependence of ¹³C NMR shielding as well as its secondary isotope shifts. For them, the harmonic vibrational correction is the main contribution and also plays a dominant role in thermal effects,whereas the effective geometry contributionis smaller. The temperature dependence of the harmonic vibrational correction is due to several low-frequency normal modes different from A_g(1), and therefore, the NTE is not observed in ¹³C NMR shielding and isotope shifts.