  FeS clusters are a universal biological motif. They carry out electron
transfer, redox chemistry, and even oxygen sensing, in diverse processes
including nitrogen fixation, respiration, and photosynthesis. The low-lying
electronic states are key to their remarkable reactivity, but cannot be
directly observed. Here we present the first ever quantum calculation of the
electronic levels of [2Fe-2S] and [4Fe-4S] clusters free from any model
assumptions. Our results highlight limitations of long-standing models of their
electronic structure. In particular, we demonstrate that the widely used
Heisenberg-Double-Exchange model underestimates the number of states by 1-2
orders of magnitude, which can conclusively be traced to the absence of Fe
d$\rightarrow$d excitations, thought to be important in these clusters.
Further, the electronic energy levels of even the same spin are dense on the
scale of vibrational fluctuations, and this provides a natural explanation for
the ubiquity of these clusters in nature for catalyzing reactions.
