  Through molecular dynamics simulations, we examined hydrodynamic behavior of
the Brownian motion of fullerene particles based on molecular interactions. The
solvation free energy and the velocity autocorrelation function (VACF) were
calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA)
potentials for the solute-solvent and solvent-solvent interactions and by
changing the size of the fullerene particles. We also measured the diffusion
constant of the fullerene particles and the shear viscosity of the host fluid,
and then the hydrodynamic radius $a_\mathrm{HD}$ was quantified from the
Stokes-Einstein relation. The $a_\mathrm{HD}$ value exceeds that of the
gyration radius of the fullerene when the solvation free energy exhibits
largely negative values using the LJ potential. In contrast, $a_\mathrm{HD}$
becomes comparable to the size of bare fullerene, when the solvation free
energy is positive using the WCA potential. Furthermore, the VACF of the
fullerene particles is directly comparable with the analytical expressions
utilizing the Navier-Stokes equations both in incompressible and compressible
forms. Hydrodynamic long-time tail $t^{-3/2}$ is demonstrated for timescales
longer than the kinematic time of the momentum diffusion over the particles'
size. However, the VACF in shorter timescales deviates from the hydrodynamic
description, particularly for smaller fullerene particles and for the LJ
potential. This occurs even though the compressible effect is considered when
characterizing the decay of VACF around the sound propagation time scale over
the particles' size. These results indicate that the nanoscale Brownian motion
is influenced by the solvation structure around the solute particles
originating from the molecular interaction.
