The Wikipedia page on hypervalent compounds reveals that the concept is almost as old as that of normally valent compounds. The definition there, is “a molecule that contains one or more main group elements formally bearing more than eight electrons in their valence shells” (although it could equally apply to e.g. transition elements that would contain e.g. more than 18 electrons in their valence shell). The most extreme example would perhaps be of iodine (or perhaps xenon). The normal valency of iodine is one (to formally complete the octet in the valence shell) but of course compounds such as IF7 imply the valency might reach 7 (and by implication that the octet of electrons expands to 14). So what of IF7? Well, there is a problem due to the high electronegativity of the fluorine. One could argue that the bonds in this molecule are ionic, and hence that the valence electrons really reside in lone pairs on the F. Thus the apparently hypervalent PF5 could be written PF4+…F–, in which case the P is not really hypervalent after all. We need a compound with un-arguably covalent bonds. Well, what about IH7? One might probably still argue about ionicity (for example H+…IH6–) but that puts electrons on I and not H, and hence does not change any hypervalency on the iodine. Surely, if hypervalency is a real phenomenon, it should manifest in IH7?