Hypervalent iodine compounds, in particular λ(3)-iodanes, have become important reagents in organic synthesis for the electrophilic transfer of substituents to arenes and other nucleophiles. The structure and reactivity of these compounds are usually described based on a 3-center-4-electron bond model, involving the iodine central atom and its two trans substituents. The goal of this computational study is to explore Fermi correlation in view of a more advanced description of bonding in these compounds. For that matter, we apply the analysis of Domain Averaged Fermi Holes (DAFH). The DAFH analysis reveals a relationship between the occurrence of multicenter bonding and structural parameters which cannot be easily observed based on simple MO theory. Whereas for λ(3)-iodanes carrying electron-rich ligands pairing of electrons over three centers is indeed observed, compounds with electron-withdrawing substituents fall into a different category: the pairing of electrons is restricted to extend over two centers only, thus challenging the multicenter bonding picture in this case. Accordingly, a drastic reduction of the DAFH three center bond index is observed. The establishment of the multicenter bond in λ(3)-iodanes is driven by a pseudo Jahn-Teller (PJT) effect, whose extent is tightly coupled to the reactivity of the corresponding compound. The PJT stabilization scales with the degree of s-p hybridization of the central atom, which, in return, depends on the electron-withdrawing power of the ligands in the trans position. The response of the multicenter bond to the iodine "ligand field" can be expressed quantitatively in terms of DAFH bond indices. These show, for example, that the activation of the reacting hypervalent species by means of protonation results in a weaker 3-center-4-electron bond, thus making the reagent more reactive. In this work we explain a number of experimentally known facts concerning the reactivity of these compounds. We also show that the DAFH analysis offers a more complete understanding of hypervalency in λ(3)-iodanes, and that it is a tool to assist the search for novel reagents.