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Inverse design represents a paradigm shift in the development of nanophotonic devices, where optimal geometries and materials are discovered by an algorithm rather than symmetry considerations or intuition. Here we present a very general formulation of inverse design that is applicable to atomic interactions in external environments, and derive from this some explicit formulae for optimisation of spontaneous decay rates, Casimir–Polder forces and resonant energy transfer. Using Purcell enhancement of the latter as a simple example, we employ finite-difference time-domain techniques in a proof-of-principle demonstration of our formula, finding enhancement of the rate many orders of magnitude larger than a selection of traditional designs.