Endohedral Beryllium Atoms in Germanium Clusters with Eight and Fewer Vertices: How Small Can a Cluster Be and Still Encapsulate a Central Atom?

Structures of the beryllium-centered germanium clusters Be@Ge_<i>n</i>^<i>z</i> (<i>n</i> = 8, 7, 6; <i>z</i> = −4, −2, 0, +2) have been investigated by density functional theory to provide some insight regarding the smallest metal cluster that can encapsulate an interstitial atom. The lowest energy structures of the eight-vertex Be@Ge₈^<i>z</i> clusters (<i>z</i> = −4, −2, 0, +2) all have the Be atom at the center of a closed polyhedron, namely, a <i>D</i>_4<i>d</i> square antiprism for Be@Ge₈^4–, a <i>D</i>_2<i>d</i> bisdisphenoid for Be@Ge₈^2–, an ideal <i>O</i>_<i>h</i> cube for Be@Ge₈, and a <i>C</i>_2<i>v</i> distorted cube for Be@Ge₈²⁺. The Be-centered cubic structures predicted for Be@Ge₈ and Be@Ge₈²⁺ differ from the previously predicted lowest energy structures for the isoelectronic Ge₈^2– and Ge₈. This appears to be related to the larger internal volume of the cube relative to other closed eight-vertex polyhedra. The lowest energy structures for the smaller seven- and six-vertex clusters Be@Ge_<i>n</i>^z (<i>n</i> = 7, 6; <i>z</i> = −4, −2, 0, +2) no longer have the Be atom at the center of a closed Ge_<i>n</i> polyhedron. Instead, either the Ge_<i>n</i> polyhedron has opened up to provide a larger volume for the Be atom or the Be atom has migrated to the surface of the polyhedron. However, higher energy structures are found in which the Be atom is located at the center of a Ge_<i>n</i> (<i>n</i> = 7, 6) polyhedron. Examples of such structures are a centered <i>C</i>_2<i>v</i> capped trigonal prismatic structure for Be@Ge₇^2–, a centered <i>D</i>_5<i>h</i> pentagonal bipyramidal structure for Be@Ge₇, a centered <i>D</i>_3<i>h</i> trigonal prismatic structure for Be@Ge₆^4–, and a centered octahedral structure for Be@Ge₆. Cluster buildup reactions of the type Be@Ge_<i>n</i>^<i>z</i> + Ge₂ → Be@Ge_<i>n</i>+2 ^<i>z</i> (<i>n</i> = 6, 8; <i>z</i> = −4, −2, 0, +2) are all predicted to be highly exothermic. This suggests that interstitial clusters having an endohedral atom inside a bare post transition element polyhedron with eight or fewer vertices are less than the optimum size. This is consistent with the experimental observation of several types of 10-vertex polyhedral bare post transition element clusters with interstitial atoms but the failure to observe such clusters with external polyhedra having eight or fewer vertices

Cobalt-Centered Ten-Vertex Germanium Clusters: The Pentagonal Prism as an Alternative to Polyhedra Predicted by the Wade–Mingos Rules

One of the most exciting recent (2009) discoveries in metal cluster chemistry is the pentagonal prismatic Co@Ge₁₀^3– ion, found in [K­(2,2,2-crypt)]₄[Co@Ge₁₀]­[Co­(1,5-C₈H₁₂)₂]·toluene and characterized structurally by X-ray diffraction. The complete absence of triangular faces in the pentagonal prismatic structure of Co@Ge₁₀^3– contradicts expectations from the well-established Wade–Mingos rules, which predict polyhedral structures having mainly or entirely triangular faces. A theoretical study on Co@Ge₁₀^<i>z</i> systems (<i>z</i> = −5 to +1) predicts a singlet <i>D</i>_5<i>h</i> pentagonal prismatic global minimum for the trianion Co@Ge₁₀^3– in accord with this experimental result. Redox reactions on this pentagonal prismatic Co@Ge₁₀^3– trianion generate low-energy pentagonal prismatic structures for Co@Ge₁₀^<i>z</i> where <i>z</i> = 0, −1, −2, −4, and −5 having quartet, triplet, doublet, doublet, and triplet spin states, respectively. Similar theoretical methods predict a singlet <i>C</i>_3<i>v</i> polyhedral structure for the monoanion Co@Ge₁₀^–, similar to previous theoretical predictions on the isoelectronic neutral Ni@Ge₁₀ and the structure realized experimentally in the isoelectronic Ni@In₁₀^10– found in the K₁₀In₁₀Ni intermetallic. Redox reactions on this <i>C</i>_3<i>v</i> polyhedral Co@Ge₁₀^– monoanion generate low energy <i>C</i>_3<i>v</i> polyhedral structures for Co@Ge₁₀^<i>z</i> where <i>z</i> = 0, −2, −3, and −4 having doublet, doublet, triplet, and quartet spin states, respectively