Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions

We calculate the quasistatic electromagnetic density of states for aggregates of touching spheres, in particular, linear chains and computer-generated random fractal aggregates. Multipole moments with orders of up to $L=64$ are taken into account for random aggregates with the number of particles of up to $N=100$ and up to $L=8000$ for linear chains. Extensive comparisons with the dipole approximation and geometrical cluster renormalization method are performed. Extinction spectra are calculated for several metals and black carbon. Long wavelength electromagnetic properties of fractal aggregates are considered in details.