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An ellipsoidally shaped body, or more commonly, an ellipsoid of revolution, is generally assumed to serve as a convenient model for evaluating the rotational diffusion properties of macromolecules. If Perrin's equations for the rotational diffusion coefficients of general ellipsoids can be shown to generate all possible rotational diffusion coefficients, then there would exist at least one equivalent ellipsoidal shape for every arbitrarily shaped rigid body. We investigated the problem by first generating a space, r-space, representing all possible ellipsoidal shapes. We then generated another space, D-space, representing all possible combinations of rotational diffusion coefficients. We then mapped r-space into D-space by using Perrin's equations. Ellipsoidal shapes map into diffusion space in a well-defined manner. The mapping is either 1:1, 2:1, or 3:1; several distinctly different regions of r-space map onto the same regions of D-space. Thus, for some combinations of rotational diffusion coefficients, more than one ellipsoid can be used as a model. Not all of D-space is covered by the mapping of r-space. Therefore, there are combinations of rotational diffusion coefficients that cannot be generated from ellipsoidally shaped bodies. Several examples of rigid body shapes with nonellipsoidal diffusion properties are described.

A general ellipsoid cannot always serve as a model for the rotational diffusion properties of arbitrarily shaped rigid molecules