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

Abstract

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, Ag(1) breathing mode instead of previously alleged quadrupolar modes. Although the effect of centrifugal distortion on the Ag(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 Ag(1), and therefore, the NTE is not observed in 13C NMR shielding and isotope shifts.