Electronic structure theory has recently been used to propose hypothetical compounds in presumed crystal structures, seeking new useful functional materials. In some cases, such hypothetical materials are metastable, albeit with technologically useful long lifetimes. Yet, in other cases, suggested hypothetical compounds may be significantly higher in energy than their lowest-energy crystal structures or competing phases, making their synthesis and eventual device-stability questionable. By way of example, the focus here is on the family of 1:1:1 compounds ABX called “filled tetrahedral structure” (sometimes called Half-Heusler) in the four groups with octet electron count: I-I-VI (e.g., CuAgSe), I-II-V (e.g., AgMgAs), I-III-IV (e.g., LiAlSi), and II-II-IV (e.g., CaZnSn). First-principles thermodynamics is used to sort the lowest-energy structure and the thermodynamic stability of the 488 unreported hypothetical ABX compounds, many of which were previously proposed to be useful technologically. It is found that as many as 235 of the 488 are unstable with respect to decomposition (hence, are unlikely to be viable technologically), whereas other 235 of the unreported compounds are predicted to be thermodynamically stable (hence, potentially interesting new materials). 18 additional materials are too close to determine. The electronic structures of these predicted stable compounds are evaluated, seeking potential new material functionalities.