  The efficient use of a multipole expansion of the far field for rapid
numerical modeling and optimization of the optical response from ordered and
disordered arrays of various structural elements is complicated by the
ambiguity in choosing the ultimate expansion centers for individual scatterers.
Since the multipolar decomposition depends on the position of the expansion
center, the sets of multipoles are not unique. They may require constrained
optimization to get the compact and most efficient spatial spectrum for each
scatterer. We address this problem by finding {\em the optimal scattering
centers} for which the spatial multipolar spectra become unique. We separately
derive these optimal positions for the electric and magnetic parts by
minimizing the norm of the poloidal electric and magnetic quadrupoles.
Employing the long-wave approximation (LWA) ansatz, we verify the approach with
the theoretical discrete models and realistic scatterers. We show that the
optimal electric and magnetic scattering centers, in all cases, are not
co-local with the centers of mass. The optimal multipoles, including the
toroidal terms, are calculated for several structurally distinct scattering
cases, and their utility for low-cost numerical schemes, including the
generalized T-matrix approach, is discussed. Expansion of the work beyond the
LWA is possible, with a promise for faster and universal numerical schemes.
