Carbene-Metal-Amide light-emitting diodes have recently shown internal quantum efficiencies approaching 100%, and there has been substantial debate concerning the cause of their exceptionally high efficiency. Here we present a theoretical description of CMAs, showing how a simple three-atom model can predict the form of the HOMO and LUMO, determine the polarization of transitions and the feasibility of spin-orbit coupling, as well as the qualitative dependence of excited state energies and oscillator strength on the twist angle. These results clarify many of the claims concerning CMAs and pave the way for the design of more efficient devices.