Solvation effects on diffusion processes of a macromolecule: Accuracy required for radial distribution function to calculate diffusion coefficient

We investigate the dependence of the diffusion coefficient of a large solute particle on the solvation structure around a solute. The diffusion coefficient of a hard-sphere system is calculated by using a perturbation theory of large-particle diffusion with radial distribution functions around the solute. To obtain the radial distribution function, some integral equation theories are examined, such as the Percus-Yevick (PY), hypernetted-chain (HNC), and modified HNC theories using a bridge function proposed by Kinoshita (MHNC) closures. In one-component solvent systems, the diffusion coefficient depends on the first-minimum value of the radial distribution function. The results of the MHNC closure are in good agreement with those of calculation using the radial distribution functions of Monte Carlo simulations since the MHNC closure very closely reproduces the radial distribution function of Monte Carlo simulations. In binary-solvent mixtures, the diffusion coefficient is affected by the larger solvent density distribution in the short-range part, particularly the height and sharpness of the first peak and the depth of the first minimum. Since the HNC closure gives the first peak that is higher and sharper than that of the MHNC closure, the calculated diffusion coefficient is smaller than the MHNC closure result. In contrast, the results of the PY closure are qualitatively and quantitatively different from those of the MHNC and HNC closures.