Numerical solution of the quantum mechanical Schrodinger equation is required to model electronic excitations in the light-harvesting photosynthetic complexes composed of up to millions of atoms. We demonstrate that the modern supercomputers can be used to treat electronic structure calculations in such large molecular aggregates if proper multi-scale massive-parallel approaches are applied. We show that the three-level parallelization scheme based on the novel numerical algorithms assuming fragmentation of a light-harvesting complex allows us to reduce considerably the high scaling of ab initio quantum chemistry methods. More specifically we applied the time-dependent density functional theory based upon the fragment molecular orbital presentation FMO-TDDFT implemented at the modern supercomputers to obtain a realistic estimate of the electronic excitation in the complex. The application shows a good overall scaling.