The reverse tricarboxylic acid (rTCA) cycle has been explored from various standpoints as an idealized primordial metabolic cycle. Its simplicity and apparent ubiquity in diverse organisms across the tree of life have been used to argue for its antiquity and its optimality. In 2000 it was proposed that chemoinformatics approaches support some of these views. Specifically, defined queries of the Beilstein database showed that the molecules of the rTCA are heavily represented in such compound databases. We explore here the chemical structure "space," e.g. the set of organic compounds which possesses some minimal set of defining characteristics, of the rTCA cycle's intermediates using an exhaustive structure generation method. The rTCA's chemical space as defined by the original criteria and explored by our method is some six to seven times larger than originally considered. Acknowledging that each assumption in what is a defining criterion making the rTCA cycle special limits possible generative outcomes, there are many unrealized compounds which fulfill these criteria. That these compounds are unrealized could be due to evolutionary frozen accidents or optimization, though this optimization may also be for systems-level reasons, e.g., the way the pathway and its elements interface with other aspects of metabolism.