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Modelling the behaviour of grain boundaries in polycrystalline metals using macroscopic continuum frameworks demands a multi-scale description of the underlying details of the structure and energy of grain boundaries. The objective in this work is the incorporation of a multi-scale atomistic-to-continuum approach of the initial grain boundary structure and energy into a grain boundary extended crystal plasticity framework in order to investigate the role of the grain boundary energetics on the macroscopic response. To this end, the methodology includes: (i) the generalisation of the atomistic-to-continuum results of the initial grain boundary structure and energy, (ii) an analytical analysis of the resulting grain boundary energetics in the continuum framework, (iii) the numerical implementation of the developed framework in the case of a periodic bicrystal subjected to simple shear deformation considering a symmetric tilt boundary system in the full misorientation range. This work provides a step forward towards the physically based continuum modelling of grain boundary interfacial plasticity.