The aim of this brief is to present in sufficient detail a non-perturbative technique for
calculating optical hyperpolarizabilities. The ability to efficiently compute
hyperpolarizabilities for a variety of different molecular systems makes this brief
invaluable for those engaged in the computational design of new electro-optical materials. The
resulting computation is very predictable and suitable for automation in contrast to
perturbative methods that typically rely on iterative methods. The methodology which is wholly
applicable to atoms molecules clusters (and with some modifications) to condensed matter is
described and illustrated at a level that is accessible to theoreticians and supplemented with
details that should be of interest to practitioners.
