We propose to consider two different Quantum Mechanics/Molecular Mechanics partitions of peptides. Not only the usual Calpha-Cbeta bond is considered as the frontier but also the less common C-N and N-C peptide bonds are investigated as putative QM/MM boundaries. When the frontier atom is a C atom then the partial double bond character of the peptide bond is naturally taken into account by our scheme. However, when the frontier atom is nitrogen, then special care has to be taken. Instead of the usual mono valence electron description that was previously proposed, the N frontier atom is described with 5 electrons (2 core and 3 valence) to allow him to share part of his valence electrons with the carbon atom, and then to recover the partial double C-N bond of the peptide.