Composite many-electron systems are considered in terms of the wavefunctions for the different component subsystems (e.g., atoms). In this weak-interaction limit, there may be degrees of freedom, which arise from that of the degeneracies of the wave-functions for each of the isolated subsystems, and which then are describable in terms of an effective Hamiltonian for the couplings and liftings of these degeneracies in the composite system. The representation of an ordinary Schrdinger Hamiltonian in such a 0-order model space is developed in the context of an example of a (possibly macroscopically large) set of H atoms interacting with one another, to obtain a Heisenberg spin-Hamiltonian, which is formally "complete" in not neglecting any higher-order permutations. At the same time, the interactions are hierarchically ordered to manifest the more important ones first, all in a "linked" size-consistent manner, avoiding various earlier-encountered "catastrophes." A classical electrostatic interpretation of the higher order exchange matrix elements is made, and some novel spin-coupling dependences are found with a decay like an inverse power-law range (rather than exponential). 2010 Wiley Periodicals, Inc.