  A calculation of the photonic Green's tensor of a structure is at the heart
of many photonic problems, but for non-trivial nanostructures, it is typically
a prohibitively time-consuming task. Recently, a general normal mode expansion
(GENOME) was implemented to construct the Green's tensor from eigenpermittivity
modes. Here, we employ GENOME to the study the response of a cluster of
nanoparticles. To this end, we use the rigorous mode hybridization theory
derived earlier by D. J. Bergman [Phys. Rev. B 19, 2359 (1979)], which
constructs the Green's tensor of a cluster of nanoparticles from the sole
knowledge of the modes of the isolated constituent. The method is applied, for
the first time, to a scatterer with a non-trivial shape (namely, a pair of
elliptical wires) within a fully electrodynamic setting, and for the
computation of the Purcell enhancement and F\"{o}rster Resonant Energy Transfer
(FRET) rate enhancement, showing a good agreement with direct simulations. The
procedure is general, trivial to implement using standard electromagnetic
software, and holds for arbitrary shapes and number of scatterers forming the
cluster. Moreover, it is orders of magnitude faster than conventional direct
simulations for applications requiring the spatial variation of the Green's
tensor, promising a wide use in quantum technologies, free-electron light
sources and heat transfer, among others.
