  The importance of electrostatic interactions in soft matter and biological
systems can often be traced to non-uniform charge effects, which are commonly
described using a multipole expansion of the corresponding charge distribution.
The standard approach when extracting the charge distribution of a given system
is to treat the constituent charges as points. This can, however, lead to an
overestimation of multipole moments of high order, such as dipole, quadrupole,
and higher moments. Focusing on distributions of charges located on a spherical
surface -- characteristic of numerous biological macromolecules, such as
globular proteins and viral capsids, as well as of inverse patchy colloids --
we develop a novel way of representing spherical surface charge distributions
based on the von Mises-Fisher distribution. This approach takes into account
the finite spatial extension of individual charges, and leads to a simple yet
powerful way of describing surface charge distributions and their multipole
expansions. In this manner, we analyze charge distributions and the derived
multipole moments of a number of different spherical configurations of
identical charges with various degrees of symmetry. We show how the number of
charges, their size, and the geometry of their configuration influence the
behavior and relative importance of multipole magnitudes of different order.
Importantly, we clearly demonstrate how neglecting the effect of charge size
leads to an overestimation of high-order multipoles. The results of our work
can be applied to construct analytical models of electrostatic interactions and
multipole expansion of charged particles in diverse soft matter and biological
systems.
