The diffusion of geometrically confined molecules plays a fundamental
role in many areas of physics, biophysics, and chemistry. Under geometric
confinement, translational and rotational mobilities of arbitrarily shaped
molecules become complex functions of their position and orientation relative
to nearby boundaries. This complexity arises from hydrodynamic interactions
with confining surfaces. A variety of numerical approaches exist that
can be used, in principle, to evaluate diffusion coefficients of rigid bodies with
arbitrary shapes under confinement, including boundary integral methods,
finite element and immersed boundary methods, fluctuating hydrodynamics,
and mesoscopic molecular dynamics. Other techniques approximate molecular
geometries using rigid assemblies of spherical subunits, either incorporating
analytical corrections to account for boundary effects or modeling
the boundaries themselves as assemblies of spheres. However, these techniques
can be computationally demanding. While coarse-graining molecular
shapes improves their computational efficiency, it typically introduces errors
into the calculated mobility functions. In this talk, I will present a recent
approach applicable to creeping (Stokes) flows that enables accurate estimation
of translational and rotational diffusion coefficients for arbitrarily shaped
molecules in bounded viscous fluids. The method uses low-resolution, shapebased
coarse-graining combined with a low-level hydrodynamic description
based on the Rotne–Prager–Yamakawa tensor. Accuracy is restored by scaling
the components of the computed mobility matrix using factors derived
from energy-dissipation arguments in Stokes flow. This approach significantly
reduces computational cost while maintaining high accuracy, offering
a practical tool for modeling diffusion in confined geometries.