In this communication experimental and theoretical results are reported affording strong evidence that interactions between electron rich atoms and the metal of tetroxide anions of group 7 elements are a new case of attractive and σ‐hole interactions. Single crystal X‐ray analyses, molecular electrostatic potentials, quantum theory of atoms‐in‐molecules, and noncovalent interaction plot analyses show that in crystalline permanganate and perrhenate salts the metal in Mn/ReO4− anion can act as electron acceptors, the oxygen of another Mn/ReO4− anion can act as the donor and supramolecular anionic dimers or polymers are formed. The name matere bond (MaB) is proposed to categorize these noncovalent interactions and to differentiate them from the classical metal‐ligand coordination bond. A new case: Single crystal X‐ray analyses, molecular electrostatic potentials, quantum theory of atoms‐in‐molecules, and noncovalent interaction plot index analyses show that Mn/Tc/ReO4− anions self‐assemble in the solid and in solution and afford dimers and supramolecular polyanionic infinite chains thanks to the matere bond (MaB, Ma=Mn, Tc, Re, (Bh)), a new entry in the palette of σ‐hole interactions.