Atoms in highly symmetric environments: H in rhodium and cobalt cages, H in an octahedral hole in MgO, and metal atoms Ca-Zn in C20 fullerenes

An atom trapped in a crystal vacancy, a metal cage, or a fullerene might have many immediate neighbors. Then, the familiar concept of valency or even coordination number seems inadequate to describe the environment of that atom. This difficulty in terminology is illustrated here by four systems: H atoms in tetragonal-pyramidal rhodium cages, H atom in an octahedral cobalt cage, H atom in a MgO octahedral hole, and metal atoms in C20 fullerenes. Density functional theory defines structure and energetics for the systems. Interactions of the atom with its container are characterized by the quantum theory of atoms in molecules (QTAIM) and the theory of non-covalent interactions (NCI). We establish that H atoms in H2Rh13(CO)24 trianion cannot be considered pentavalent, H atom in HCo6(CO)15 anion cannot be considered hexavalent, and H atom in MgO cannot be considered hexavalent. Instead, one should consider the H atom to be set in an environmental field defined by its 5, 6, and 6 neighbors; with interactions described by QTAIM. This point is further illustrated by the electronic structures and QTAIM parameters of M@C20, M=Ca to Zn. The analysis describes the systematic deformation and restoration of the symmetric fullerene in that series.