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A thorough understanding of the electronic structure is a necessary firststep for the design of nanoelectronics, chemical/bio-sensors, electrocatalysts,and nanoplasmonics using graphene. As such, theoretical spectroscopictechniques to describe both direct optical excitations and collectiveexcitations of graphene are of fundamental importance. Starting from densityfunctional theory (DFT) we use the time dependent linear response within therandom phase approximation (TDDFT-RPA) to describe the loss function-Im{{\epsilon}\overline{ }^{1}(q,{\omega})} for graphene. To ensure anyspurious interactions between layers are neglected, we employ both a radialcutoff of the Coulomb kernel, and extra vacuum directly at the TDDFT-RPA level.

Theoretical spectroscopy techniques applied to graphene EELS and optics