AbstractAs approximations to the wave functions governing quantum chemical systems become more and more complex, it is becoming increasingly important to devise descriptors that help understand the practical results of those approximations by condensing information in insightful ways. Quantum chemical descriptors that are able to capture the statistical signatures of quantum chemical interactions provide such conceptual building blocks. Central to an understanding of these descriptors is the concept of a “domain occupation number operator,” which allows the so‐called “real space” and Hilbert space partitionings to be treated on the same footing. Many of the existing descriptors can be expressed as the (central) densities and density cumulants associated with the domain operators. These densities can be obtained by successive differentiation of generating functions, effectively structuring domain associated densities into hierarchies. Not only do the resulting hierarchies indicate how m