Quantum hydrodynamic model for the enhanced moments of inertia of molecules in helium nanodroplets: Application to SF6

The increase in moment of inertia, ΔI, of SF6 in helium nanodroplets is calculated using the quantum hydrodynamic approach [Callegari et al., Phys. Rev. Lett. 83, 5058 (1999); 84, 1848 (2000)], which we extend here to an explicit three-dimensional treatment. Three plausible helium densities are reconstructed by interpolation of previously published “density cuts” in terms of an expansion into cubic harmonics (several interpolation strategies are presented). This allows us to predict a value of ΔI that ranges from as low as 30 u⋅Å2 to as high as 318 u⋅Å2. The lower limit reproduces the prediction of Kwon et al. [J. Chem. Phys. 113, 6469 (2000)], who use the same hydrodynamic model and an unpublished density based upon a Path Integral Monte Carlo calculation. These values can be compared with the experimentally measured ΔI (310±10 u⋅Å2) for large (N⩾103 He atoms), and with Fixed Node, Diffusion Monte Carlo calculations by Lee, Farrelly, and Whaley [Phys. Rev. Lett. 83, 3812 (1999)], which found ΔI=290–305 u⋅Å2 for N=8–20 helium atoms. The present results show that the value of ΔI obtained from the hydrodynamic model is quite sensitive to physically reasonable variations in the helium density; therefore one has to be careful as to which density to use. Because the model is based upon the assumption that the helium is in the ground “quasienergy” state of the helium-molecule time-dependent potential, we propose that calculations should be done using densities calculated at 0 K rather than at finite temperature. We have extended our original algorithm to also handle irregular boundaries. We find that in the present case the calculated value of ΔI only changes by a few percent.