Chemical Bonding Topology of Metal-Centered Polygonal Wheels: Two-Dimensional Analogues of Metallaboranes Related to Benzene and Cyclopentadienide

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 B7H72–, 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-N=CtBu2)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 C=C double bonds in a Kekulé structure of benzene.


INTRODUCTION
An important class of boron compounds consists of the polyhedral boranes and their derivatives including metallaboranes. Such species exhibit three-dimensional structures based on polyhedra having exclusively or mainly triangular faces. 1,2 Such polyhedra having exclusively triangular faces are conveniently known as deltahedra ( Figure 1). Aspects of the chemical bonding topology in these deltahedra classify them as three-dimensional aromatic systems. 3,4 This aromaticity is reflected in their unusual stability relative to other borane derivatives. This is particularly true of icosahedral derivatives such as B 12 H 12 2− and C 2 B 10 H 12 . In a crude sense, the three-dimensional aromaticity in such deltahedral boranes makes them analogues of the iconic twodimensional aromatic compound benzene as well as related species such as cyclopentadienide, C 5 H 5 − , and tropylium, C 7 H 7 + . However, unlike these two-dimensional carbocyclic aromatic species, the three-dimensional aromatic deltahedral boranes have boron triangles as fundamental building blocks. Two-dimensional aromatic systems having triangles as building blocks are much less common and have a much more recent history. The simplest such species are polygonal wheels in which a central atom (the hub) is surrounded by a polygon of atoms (the periphery or rim). In order to maintain a two-dimensional structure, a planar hybridization scheme is required for the central atom. Such n-gonal wheels can be regarded as planar structures with n + 1 vertices and n triangular faces. The group 10 transition metals nickel, palladium, and platinum as well as the coinage metals are ideally suited for the central atom since they can exhibit two-dimensional coordination geometries through trigonal planar or square planar hybridization.
The first example of stable polygonal wheel species was the hexagonal wheel Ni@P 6 Bu t 6 , originally reported by Ahlrichs et al. in 1992 5 and shown by X-ray crystallography to have a hexagonal wheel structure with peripheral phosphorus atoms and a central nickel atom (Figure 2). Much more recently, in 2020, Hayton and co-workers discovered a second hexagonal wheel species, namely, the palladium cluster Pd@Pd 6 (μ-N� CBu t 2 ) 6 separated from the reaction of (CH 3 CN) 2 PdCl 2 with Li[N�CBu t 2 ] (Figure 2). 6 The hexagonal wheel structure of the Pd@Pd 6 (μ-N�CBu t 2 ) 6 molecule is particularly interesting since both the rim and the center of the wheel are the same atom, namely, palladium. Other examples of hexagonal wheel structures include the xenophilic manganese carbonyl anion [Mn@Mn 6 (thf) 6 (CO) 12 ] − containing a central Mn@Mn 6 wheel, 7,8 the cobalt cluster Co@Co 6 (μ 3 -H) 6 {μ-N(SiMe 3 ) 2 } 6 with hydrogen atoms capping each of the triangular faces of the Co@Co 6 hexagonal wheel, 9 and Pd[Re 2 (CO) 8 (μ-SbPh 2 )(μ-H) 2 ] 2 containing a Pd@Re 4 Sb 2 hexagonal wheel with edge bridging hydrogen atoms. In addition, the bimetallic copper iron carbonyl cluster trianion [Cu 5 Fe 4 (CO) 16 ] 3− contains a central Cu@Cu 4 Fe 2 hexagonal wheel with Fe(CO) 4 units bridging two opposite Cu−Cu edges. 10 A key development in the further evolution of the chemistry of metal-centered wheels is the very recent discovery of the goldcentered polygonal ruthenium carbonyl wheel in the anion [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − , structurally characterized as its tetraethylammonium salt. 11 This pentagonal wheel species is particularly significant in representing the third member of an experimentally realized series of polygonal polynuclear carbonyl derivatives of the second and third row group 8 transition metals starting with the triangular M 3 (CO) 12 (M = Ru, 12 Os 13,14 ) followed by the rhombus 15,16 Os 4 (CO) 16 that have been synthesized and structurally characterized by X-ray crystallography ( Figure 3). Assuming the ruthenium atoms in [Au@ Ru 5 (CO) 15 (μ-CO) 4 ] − to be zerovalent as they are in Ru 3 (CO) 12 and Ru 4 (CO) 16 leads to a −1 formal oxidation state for the central gold atom similar to that in the experimentally known cesium auride, CsAu. 17,18 Thus, the anion [Au@Ru(CO) 15 (μ-CO) 4 ] − can alternatively be viewed as a complex of the auride anion with pentagonal planar coordination to five ruthenium carbonyl "ligands".  16 is antiaromatic like the C 4 ring in cyclobutane. This is reflected experimentally in the instability of rhombus Os 4 (CO) 16 , which decomposes in solution under an inert atmosphere at room temperature in a complicated reaction leading to the very stable Os 3 (CO) 12 . 13,14 However, loss of CO groups from Os 4 (CO) 16 to give first Os 4 (CO) 15 with a butterfly structure consisting of two triangles sharing an edge and then Os 4 (CO) 14 with a central Os 4 tetrahedron leads to much more stable structures ( Figure 4).
The successive losses of carbonyl groups from Os 4 (CO) 16 result in the formation of new Os−Os bonds leading to the Os 4 rhombus in Os 4 (CO) 16 , the Os 4 butterfly in Os 4 (CO) 15 , and finally the Os 4 tetrahedron in Os 4 (CO) 14 having four, five, and six Os−Os bonds, respectively. These experimental observations demonstrate the value of σ-aromatic metal triangles in stabilizing metal carbonyl cluster structures.
Adding a central metal atom to a larger outer polygon to generate a wheel structure splits the polygon into a set of triangles thereby stabilizing the system through σ-aromaticity of the metal triangles. The recently synthesized anion [Au@ Ru 5 (CO) 15 (μ-CO) 4 ] − as its stable tetraethylammonium salt is an excellent example. 11 The Ru 5 pentagon in a hypothetical Ru 5 (CO) 20 is dissected into five Ru 2 Au triangles by interaction with the central gold atom. In the [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − structure, all five ruthenium atoms effectively retain the favored     16 → Os 4 (CO) 15 → Os 4 (CO) 14 .
Inorganic Chemistry pubs.acs.org/IC Article 18-electron configuration of the hypothetical Ru 5 (CO) 20 with the two electrons of the "missing" carbonyl group being replaced by one electron from the central gold atom and one electron coming from the negative charge on the anion. The central gold atom can formally be considered to have trigonal planar hybridization with its three gold orbitals converting three of the five Ru−Ru two-center two-electron (2c−2e) bonds in the Ru 5 pentagon into three-center two-electron (3c−2e) Ru 2 Au bonds in a localized bonding model ( Figure 5). Note that the twodimensional pentagonal wheel found in [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − can be generated by flattening the three-dimensional pentagonal bipyramid found in borane species such as the B 7 H 7 2− dianion. This flattening process brings the two axial vertices together as the central vertex of the pentagonal wheel ( Figure 6).

From Tris(Olefin) Metal Complexes to Hexagonal Wheel Structures.
A sequence of triangular, square, and pentagonal precursor structures similar to that for the ruthenium carbonyl clusters (Figure 3) is not known for the two experimentally realized hexagonal wheel structures, namely, Ni@P 6 But 6 and Pd@Pd 6 (μ-N�CBu t 2 ) 6 . Instead, the hexagonal nickel wheel Ni@P 6 But 6 can be related to the experimentally known tris(ethylene) complexes (η 2 -C 2 H 4 ) 3 M (M = Ni, 26 Pt 27−29 as well as the 1,5,9-cyclododecatriene complex (η 2,2,2 -C 12 H 18 )Ni obtained by the trimerization of butadiene 30 in which a trigonal planar sp 2 -hybridized group 10 metal is coordinated to three C�C double bonds (Figure 7). Such nickel(0) trisolefin complexes can also be interpreted as M@C 6 structures in which the group 10 metal is located in the center of a distorted carbon hexagon with alternating short (bonding) and long (nonbonding) edges. Thus the short edges in such hexagons correspond to the coordinated C�C double bonds, whereas the long edges are the nonbonding distances between a given olefinic ligand carbon and the nearest carbon atom in an adjacent olefinic ligand (dashed lines in Figure 7). An undistorted C 6 hexagon, such as that found in benzene, is too small to encapsulate a group 10 metal atom to form a hexagonal wheel structure with outer carbon atoms and the metal atom in the center. Thus, an analogous nickel−carbon hexagonal wheel of the type Ni@C 6 H 12 is not viable since if the Ni−C bonds have a favorable length of 1.85 Å, geometry requires that the C−C bond lengths also be 1.85 Å, which is much too long for effective bonding.
Replacing the carbon vertices of these tris(olefin) structures of the group 10 metals with larger atoms can produce hexagons large enough to encapsulate the central metal atom to form wheel-like structures. This was first realized in the synthesis of the hexagonal wheel structure Ni@P 6 Bu t 6 ( Figure 2). 5 Thus, increasing the size of the peripheral atoms from carbon to phosphorus is enough to provide a peripheral hexagon large enough to enclose a central nickel atom. The chemical bonding in such molecular wheels was examined by molecular orbital methods shortly after the discovery of Ni@P 6 Bu t 6 as well as more recently by topology-based methods providing a valencebond description. 31

Chemical Bonding in Hexagonal Wheel Complexes.
Consider first the hexagonal phosphorus wheel Ni@ P 6 R 6 in which each phosphorus vertex is considered as contributing two internal orbitals, namely, a tangential p orbital and a radial orbital (Figure 8). The radial orbital represents one part of trigonal sp 2 hybridization of the peripheral phosphorus atom, which also includes a P−R bond and a stereochemically active lone pair. The tangential p orbitals on the six phosphorus atoms overlap to form three bonding orbitals, each containing an electron pair, as well as three empty antibonding orbitals. The central nickel atom in Ni@P 6 R 6 exhibits trigonal planar sp 2 hybridization. Each of the three sp 2 hybrid orbitals from the central nickel atom overlaps with the radial orbitals of two adjacent peripheral phosphorus atoms to form a three-center two-electron NiP 2 bond. Thus, the skeletal bonding topology of the Ni@P 6 R 6 phosphorus hexagonal wheels consists of an arrangement of 3c−2e bonds in nonadjacent triangles preserving three-fold symmetry (Figure 9). The two possible ways of filling three nonadjacent NiP 2 triangles represent canonical structures that are the analogues of the two canonical cyclohexatriene Kekuléstructures in benzene. The six electrons involved in the three 3c−2e NiP 2 bonds in a localized chemical bonding

pubs.acs.org/IC
Article topology of Ni@P 6 R 6 can be considered as corresponding to the aromatic sextet in benzene. Now consider the more complicated hexagonal palladium wheel Pd@Pd 6 (μ-N�CBu t 2 ) 6 . The peripheral palladium atoms exhibit linear N−Pd−N coordination to two ketenimine nitrogen atoms requiring two sp hybrid orbitals. The N−Pd− N chains are not perpendicular to the plane of the Pd 6 hexagon so that each coordinating ketenimine carbon atom can bridge two adjacent palladium atoms. The two p orbitals remaining from the sp 3 manifolds of each peripheral palladium atom after forming the linear sp hybrids for the N−Pd−N chain are the internal orbitals for the skeletal bonding within the Pd@Pd 6 hexagonal wheel. Similar to Ni@P 6 R 6 discussed above, one of these p orbitals on each palladium atom is a tangential orbital oriented along the hexagonal periphery to form three bonding and three antibonding orbitals. The other p orbital on each peripheral palladium atom is a radial orbital oriented toward the central palladium atom. Overlap of two radial orbitals from adjacent peripheral palladium atoms with an sp 2 hybrid from the central palladium atom forms a 3c−2e bond in one of the six Pd 3 triangles of the Pd@Pd 6 (μ-N�CBu t 2 ) 6 structure. In this way, the skeletal bonding topology of 3c−2e bonding in three nonadjacent Pd 3 triangles in Pd@Pd 6 (μ-N�CBu t 2 ) 6 preserving three-fold symmetry is completely analogous to the skeletal bonding in the Ni@P 6 R 6 phosphorus wheels discussed above. Theoretical studies 6 on Pd@Pd 6 (μ-N�CBu t 2 ) 6 lead to diatropic (negative) nucleus independent chemical shift (NICS) values confirming the aromaticity in these palladium hexagonal wheels.

Polygonal Wheels as Two-Dimensional Analogues of Deltahedral Borane Structures.
The chemical bonding topology of 3c−2e bonds in half of the triangular faces in a localized bonding model for the Ni@P 6 R 6 and Pd@Pd 6 (μ-N�CBu t 2 ) 6 hexagonal wheels ( Figure 9) corresponding to the aromatic sextet of benzene resembles the chemical bonding topology in some types of metallaboranes. This suggests that the hexagonal wheels are two-dimensional analogues of such systems. The chemical bonding topology of metal-free boranes and carboranes of the types B n H n 2− , C 2 B n−1 H n − , and C 2 B n−2 H n (n = 6−14) consists of the most spherical closo deltahedral canonical structures with an n-center core bond formed by the vertex radial orbitals and a chain of 2c−2e bonds formed by the vertex tangential orbitals. 4,32 However, as boron or carbon vertices are replaced by transition metal vertices with suitable external ligands, the underlying deltahedra become less spherical owing to different vertex degree preferences for transition metals and boron or carbon atoms. Thus, the experimentally known socalled oblatocloso dirhenaboranes (η 5 -Me 5 C 5 ) 2 Re 2 B n−2 H n−2 (n = 8−12) 33−35 have flattened oblate ellipsoidal structures with low surface curvature at degree 6 and/or 7 rhenium vertices and high surface curvature at degree 4 and/or 5 boron vertices ( Figure  10). The chemical bonding topology of such n-vertex dirhenaboranes consists of 3c−2e bonds in n of the 2n − 4 faces of the deltahedron with only a formal Re�Re double bond rather than a multicenter bond in the center of the deltahedron. 36 Note also that flattening completely the threedimensional hexagonal bipyramidal structure, known experimentally 35 in (η 5 -Me 5 C 5 ) 2 Re 2 B 6 H 4 Cl 2 , by bringing the two C 6 axial vertices together at the center of the equatorial hexagon leads to the hexagonal wheel structure ( Figure 6). This flattening process converts a hexagonal bipyramidal dirhenaborane structure into a hexagonal wheel structure and indicates a connection between hexagonal wheels and metallaboranes.
The chemical bonding topology in the gold-centered pentagonal wheel anion [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − resembles that in the hexagonal wheel complexes Ni@P 6 R 6 and Pd@ Pd 6 (μ-N�CBu t 2 ) 6 in having three 3c−2e bonds within the pentagonal wheel ( Figure 5). The six electrons in these three 3c−2e bonds of the pentagonal wheel can be related to the aromatic sextet of the cyclopentadienide anion with a similar pentagonal structure.

CONCLUSIONS
The anion [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − has a pentagonal wheel structure that can be derived from a hypothetical pentagonal ruthenium carbonyl cluster Ru 5 (CO) 20 by insertion of a gold atom in the center. This splits the original Ru 5 pentagon in Ru 5 (CO) 20 into five AuRu 2 triangles leading to considerable stabilization through the σ-aromaticity characteristic of threemembered rings. The six electrons used to form 3c−2e bonds in three of the five AuRu 2 triangles suggest a relationship to the aromatic sextet of the likewise pentagonal cyclopentadienide anion. The pentagonal Ru 5 (CO) 20 origin of the [Au@ Ru 5 (CO) 15 (μ-CO) 4 ] − anion can be considered as the third member of a homologous series starting with the experimentally known very stable Ru 3 (CO) 12 triangle and the relatively unstable Os 4 (CO) 16 rhombus. Furthermore, the pentagonal wheel framework of [Au@Ru 5 (CO) 15 (μ-CO) 4 ] − can be derived from a pentagonal bipyramid, such as that found in the deltahedral borane anion B 7 H 7 2− , by bringing the two C 5 axial vertices together at the center of the equatorial pentagon.
The hexagonal wheel complexes Ni@P 6 R 6 and Pd@Pd 6 (μ-N�CBu t 2 ) 6 with six triangular faces can be derived from a hexagonal bipyramid, such as that found in the dirhenaborane   ■ REFERENCES