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In this paper, the Variational Method based on the Hückel Theory is applied to NPs chain and aggregate systems in order to estimate the energy of the plasmon and, in turn, the resonance wavelength shift, which is caused by the interaction of adjacent NPs. This method is based on the analogies of NPs dipole interactions and the π-system in molecules. Differently from the Hartree-Fock method that is a self-consistent model, in this approach, the input data that this method requires is the dimer energy shift with respect to single NPs. This enables us to acquire a simultaneous estimation of the wavefunctions of the NPs system as well as the expectation energy value of every kind of NPs system. The main advantage of this approach is the rapid response and ease of application to every kind of geometries and spacing from the linear chain to clusters, without the necessity of a time-consuming calculation. The results obtained with this model are closely aligned to related literature and open the way to further development of this methodology for investigating other properties of NPs systems.

A Quantum Chemistry Approach Based on the Analogy with π-System in Polymers for a Rapid Estimation of the Resonance Wavelength of Nanoparticle Systems