Macromolecular diffusion constants: A calculational strategy

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Abstract
Calculations of diffusion constants for rigid molecules of arbitrary shape are often based on hydrodynamic interactions between freely moving spheres. Molecules can be modeled as collections of spheres, and the interactions are approximated as pairwise additive. Singularities previously associated with nearly linear geometries and with geometries dominated by a large central element can be avoided by including torque-angular velocity and torque-velocity coupling, as well as the usual force-velocity coupling between spheres. I provide explicit formulas for these couplings for both nonoverlapping and overlapping spheres, and also show how to include effects of one sphere on the self-diffusion of another. This formulation is incorporated in an algorithm that involves neither Gauss–Seidel iterations nor direct inversion of a large matrix.
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