  A semianalytical approach is developed to calculate the effective pair
potential of rigid arbitrarily shaped macroions with a nonvanishing particle
volume, valid within linear screening theory and the mean-field approximation.
The essential ingredient for this framework is a mapping of the particle to a
singular charge distribution with adjustable effective charge and shape
parameters determined by the particle surface electrostatic potential. For
charged spheres this method reproduces the well-known
Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Further exemplary benchmarks
of the method for more complicated cases, like tori, triaxial ellipsoids, and
additive torus-sphere mixtures, leads to accurate closed-form integral
expressions for all particle separations and orientations. The findings are
relevant for determining the phase behaviour of macroions with experiments and
simulations for various particle shapes.
