Fast and efficient calculations of optical responses using electromagnetic models require computational acceleration and compression techniques. A hierarchical matrix approach is adopted for this purpose. In order to model large-scale molecular structures these methods should be applied over wide frequency spectra. Here we introduce a novel parametric hierarchical matrix method that allows one for a rapid construction of a wideband system representation and enables an efficient wideband solution. We apply the developed method to the modeling of the optical response of bacteriochorophyll tubular aggregates as found in green photosynthetic bacteria. We show that the parametric method can provide one with the frequency and time-domain solutions for structures of the size of 100, 000 molecules, which is comparable to the size of the whole antenna complex in a bacterium. The absorption spectrum is calculated and the significance of electrodynamic retardation effects for relatively large structures, i.e. with respect to the wavelength of light, is briefly studied.
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INTRODUCTIONThe prediction of optical properties is one of the main challenges for the theoretical characterization of molecular aggregates [1][2][3][4]. The complication originates in the disorder and structural variations that span over a broad length scale and include fluctuations of monomer transition frequencies, domain formation and variations in the aggregate shape on the submicron scale [5][6][7]. The periodic lattice approximation is hardly applicable in this case and one may need to model the complete structure. Quantum mechanical methods, for example, open quantum system approaches [8] or quantum mechanics/molecular mechanics methods [9], that became popular recently, can characterize aggregate-light interaction in great details. However, the application of these methods to large systems is constrained by the exponential complexity growth with respect to the number of monomers composing the structure.Aggregates of pigments molecules and fluorescent dyes possess distinct optical properties such as strong absorbance and fluorescence, coherent interaction with photons, and also fast and long-range diffusion of the absorbed energy among the molecules composing the aggregate [1]. There are a number of examples of molecular aggregates. For instance, light-absorbing complexes in plants and photosynthetic bacteria contain aggregates of pigment molecules, chlorophylls and bacteriochlorophylls respectively [2]. Those structures, constructed by nature, collect and process solar energy with high efficiency. Molecular aggregates can also be grown using self-assembly methods in different shapes including pseudo one-dimensional chains [5] two-dimensional films [6] and nanoscale tubes [7,10]. Molecular aggregates can be combined with other photonic structures such as optical cavities [3] or plasmonic nanoparticles [4]. Thus, the interest to molecular aggregates as possible lightprocessing elements grows continuously.In this context, the classical el...