On the origins of the Finnis–Sinclair potentials

I trace back the origins of the famous Finnis–Sinclair potentials. These potentials mimic the results of tight binding theory through their use of the square root embedding function. From the tentative beginnings of tight binding in the 1930s to 1984 or so, Bloch, Seitz, Montroll, Friedel, Cyrot-Lackmann and Ducastelle are some of the famous names involved, to name just a few. The application of the method of moments to the description of densities of states and its connection to the physics of closed paths linking nearest neighbours interacting atoms helped to formalise Friedel's rectangular band model for the d electrons in transition metals. Extension from perfectly periodic to defective structures could not be but a slow process due to the change of paradigm for solid state scientists and to the necessary caution to be paid to self-consistency. British scientists also contributed significantly in the 1980s. Computer progress and pragmatism helped to go from mainly analytical developments to numerical experiments (another change of paradigm). I also digress on various not so well-known historical points of interest to this story.