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This paper series aims to establish a complete correspondence betweenfine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropyscaling (introduced in Paper I). While Paper II successfully capturedtranslational motions in CG systems using a hard sphere mapping, the absence ofrotational motions in single-site CG models introduces differences between FGand CG dynamics. In this third paper, our objective is to faithfully recoveratomistic diffusion coefficients from CG dynamics by incorporating rotationaldynamics. By extracting FG rotational diffusion, we unravel, for the first timereported to our knowledge, a universality in excess entropy scaling between therotational and translational diffusion. Once the missing rotational dynamicsare integrated into the CG translational dynamics, an effectivetranslation-rotation coupling becomes essential. We propose two differentapproaches for estimating this coupling parameter: the rough hard sphere theorywith acentric factor (temperature-independent) or the rough Lennard-Jones modelwith CG attractions (temperature-dependent). Altogether, we demonstrate that FGdiffusion coefficients can be recovered from CG diffusion coefficients by (1)incorporating "entropy-free" rotational diffusion with translation-rotationcoupling and (2) recapturing the missing entropy. Our findings shed light onthe fundamental relationship between FG and CG dynamics in molecular fluids.

Understanding Dynamics in Coarse-Grained Models: III. Roles of Rotational Motion and Translation-Rotation Coupling in Coarse-Grained Dynamics