Quantum fluctuations of a fullerene cage modulate its internal magnetic environment

To investigate the effect of quantum fluctuations on the magnetic environment inside a C₆₀ fullerene cage, we have calculated the nuclear magnetic shielding constant of protons in H₂@C₆₀ and HD@C₆₀ systems by on-the-fly ab initio path integral simulation, including both thermal and nuclear quantum effects. The most dominant upfield from an isolated hydrogen molecule occurs due to the diamagnetic current of the C₆₀ cage, which is partly cancelled by the paramagnetic current, where the paramagnetic contribution is enlarged by the zero-point vibrational fluctuation of the C₆₀ carbon backbone structure via a widely distributed HOMO-LUMO gap. This quantum modulation mechanism of the nuclear magnetic shielding constant is newly proposed. Because this quantum effect is independent of the difference between H₂ and HD, the H₂/HD isotope shift occurs in spite of the C₆₀ cage. The nuclear magnetic constants computed for H₂@C₆₀ and HD@C₆₀ are 32.047 and 32.081 ppm, respectively, which are in reasonable agreement with the corresponding values of 32.19 and 32.23 ppm estimated from the experimental values of the chemical shifts.