To accurately illustrate the performance of different truncated QED Hamiltonians, we test the accuracy of the Hamiltonians discussed in this review on a model molecular system inside a cavity. Fig. shows the potential energy surfaces, diabatic potentials and dipole matrix elements of the model system that we use to benchmark these Hamiltonians, the so-called Shin-Metiu proton-transfer model system. This Shin-Metiu model molecular system 54 contains two fixed ions, one moving electron and a proton (whose position is R), all interacting with each other through modified Coulombic potentials.