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.