Silver and copper clusters capped by external chelating dithiolate ligands can be classified according to the cavities in their central coinage metal polyhedra. Silver clusters composed exclusively ...of fused tetrahedra are analogous to simple saturated organic compounds. The only interstitial atom that can be fit into an Ag
4
tetrahedron is hydrogen. Silver polyhedra with larger trigonal prismatic or cubic cavities, including highly distorted cubic cavities, can accommodate halide and chalcogenide anions. The still larger 12-vertex icosahedral and cuboctahedral coinage metal cavities can accommodate oxoanions of the types SO
3
2−
and SO
4
2−
and their heavier congeners or alternatively interstitial coinage or platinum group metals leading to central M′@M
12
units. Copper clusters with central cuboctahedra and silver clusters with central icosahedra possessing interstitial metal atoms approximate sphericality and provide examples of electron-rich metal superatoms with an average metal oxidation state of less than +1. Such copper cluster superatoms have two extra electrons corresponding to a filled 1S
2
superatomic orbital. The silver cluster superatoms are electron richer with eight extra electrons corresponding to filled 1S
2
+ 1P
6
superatomic orbitals. In these silver clusters seven or eight faces of the central Ag
12
icosahedron are capped by additional silver atoms in order to provide these additional electrons.
Silver clusters composed exclusively of fused tetrahedra are analogous to simple saturated organic compounds. Copper clusters with central cuboctahedra and silver clusters with central icosahedra having interstitial metal atoms provide examples of metal superatoms.
The anion Au@Ru5(CO)15(μ-CO)4− has a pentagonal wheel structure that can be derived from a hypothetical pentagonal ruthenium carbonyl cluster Ru5(CO)20 by insertion of a gold atom in the center, ...thereby splitting the original Ru5 pentagon in Ru5(CO)20 into five AuRu2 triangles. The six electrons used to form 3c–2e bonds in three of the five AuRu2 triangles suggest a relationship to the aromatic sextet of the likewise pentagonal cyclopentadienide anion. Furthermore, the pentagonal wheel framework of Au@Ru5(CO)15(μ-CO)4− can be derived from a pentagonal bipyramid, such as that found in the deltahedral borane anion B7H7 2–, by bringing the two C5 axial vertices together at the center of the equatorial pentagon. Similarly, the hexagonal wheel complexes Ni@P6R6 and Pd@Pd6(μ-NCtBu2)6 with six triangular faces can be derived from a hexagonal bipyramid, such as that found in the dirhenaborane (η5-Me5C5)2Re2B6H4Cl2, by bringing the two C6 axial vertices together at the center of the equatorial hexagon. A reasonable chemical bonding model for the hexagonal wheel complexes has three-fold symmetry with 3c–2e bonds in three of these six triangular faces analogous to the CC double bonds in a Kekulé structure of benzene.
The duals of the most spherical
borane deltahedra having from 6 to 16 vertices form a series of homologous spherical trivalent polyhedra with even numbers of vertices from 8 to 28. This series of ...homologous polyhedra is found in endohedral clusters of the group 14 atoms such as the endohedral germanium cluster anions M@Ge
(M = Co, Fe) and Ru@Ge
The next members of this series have been predicted to be the lowest energy structures of the endohedral silicon clusters Cr@Si
and M@Si
(M = Zr, Hf). The largest members of this series correspond to the smallest fullerene polyhedra found in the endohedral fullerenes M@C
(M = Zr, Hf, Th, U). The duals of the oblate (flattened) ellipsoidal deltahedra found in the dirhenaboranes Cp*
Re
B
H
(Cp* = η
-Me
C
; 8 ≤
≤ 12) are prolate (elongated) trivalent polyhedra as exemplified experimentally by the germanium cluster Co
@Ge
containing an endohedral Co
unit.
This survey of metal–metal (MM) bond distances in binuclear complexes of the first row 3d-block elements reviews experimental and computational research on a wide range of such systems. The metals ...surveyed are titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, and zinc, representing the only comprehensive presentation of such results to date. Factors impacting MM bond lengths that are discussed here include (a) the formal MM bond order, (b) size of the metal ion present in the bimetallic core (M2) n+, (c) the metal oxidation state, (d) effects of ligand basicity, coordination mode and number, and (e) steric effects of bulky ligands. Correlations between experimental and computational findings are examined wherever possible, often yielding good agreement for MM bond lengths. The formal bond order provides a key basis for assessing experimental and computationally derived MM bond lengths. The effects of change in the metal upon MM bond length ranges in binuclear complexes suggest trends for single, double, triple, and quadruple MM bonds which are related to the available information on metal atomic radii. It emerges that while specific factors for a limited range of complexes are found to have their expected impact in many cases, the assessment of the net effect of these factors is challenging. The combination of experimental and computational results leads us to propose for the first time the ranges and “best” estimates for MM bond distances of all types (Ti–Ti through Zn–Zn, single through quintuple).
The combination of atomic orbitals to form hybrid orbitals of special symmetries can be related to the individual orbital polynomials. Using this approach, 8-orbital cubic hybridization can be shown ...to be sp
d
f requiring an f orbital, and 12-orbital hexagonal prismatic hybridization can be shown to be sp
d
f
g requiring a g orbital. The twists to convert a cube to a square antiprism and a hexagonal prism to a hexagonal antiprism eliminate the need for the highest nodality orbitals in the resulting hybrids. A trigonal twist of an
octahedron into a
trigonal prism can involve a gradual change of the pair of d orbitals in the corresponding sp
d
hybrids. A similar trigonal twist of an
cuboctahedron into a
anticuboctahedron can likewise involve a gradual change in the three f orbitals in the corresponding sp
d
f
hybrids.
Using a genetic algorithm combined with density functional theory calculations, we perform a global search for the lowest-energy structures of B
clusters with n = 46, 48, 50. Competition among ...different structural motifs including a hollow cage, core-shell, bilayer, and quasi-planar, is investigated. For B
, a core-shell B
@B
structure resembling the larger B
clusters with n ≥ 68 is found to compete with a quasi-planar structure with a central hexagonal hole. A quasi-planar configuration with two connected hexagonal holes is most favorable for B
. More interestingly, an unprecedented bilayer structure is unveiled at B
, which can be extended to a two-dimensional bilayer phase exhibiting appreciable stability. Our results suggest alternatives to the cage motif as lower-energy B
cluster structures with n > 50.
Chemical bonding models based on graph theory or tensor surface harmonic theory demonstrate the analogy between the aromaticity in two-dimensional planar polygonal hydrocarbons such as benzene and ...that in three-dimensional deltahedral borane anions of the type BnHn2- (6 < or = n < or = 12). Such models are supported both by diverse computational studies and experimental determinations of electron density distribution. Related methods can be used to study the chemical bonding in the boron polyhedra found in other structures including neutral binary boron hydrides, metallaboranes, various allotropes of elemental boron, and boron-rich solid-state metal borides.
Doped clusters by Si
cage encapsulating group-IV metal atoms (M@Si
, M = Ti, Zr and Hf) are computationally investigated by both density functional theory (DFT) and high-level CCSD(T) method. Their ...low-energy structures are globally searched using a genetic algorithm based on DFT. The ground state structures of neutral and anionic M@Si
are determined by calculating the vertical and adiabatic detachment energies and comparing them with the experimental data. For neutral Ti@Si
, the Frank-Kasper (FK) deltahedron with T
symmetry and distorted FK isomer with C
symmetry are nearly degenerate as the ground state and may coexist in laboratory, while the distorted FK isomer is the most probable structure for Ti@Si
anion. For neutral and anionic Zr@Si
and Hf@Si
clusters, the ground states at finite temperatures up to 300 K are the fullerene-like D
bitruncated square trapezohedron. These theoretical results establish a more complete picture for the most stable structures of M@Si
clusters, which possess large gaps and may serve as building blocks for electronic and optoelectronic applications.
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