Bare group 10 metal atoms as vertices in polyhedral metallaboranes: spherical aromaticity in the icosahedral MB₁₁H₁₁ systems

Abstract

The MB_n−1H_n−1 (M = Ni, Pd, Pt; n = 5 to 14) clusters with bare group 10 metal vertices have been examined by density functional theory. The lowest energy structures are found to be the corresponding closo deltahedra. This suggests that the group 10 metal atom can serve as four skeletal electron donors thereby providing the 2n + 2 skeletal electrons for these closo systems in accord with the Wade–Mingos rules. A molecular orbital analysis of the icosahedral NiB₁₁H₁₁ suggests interpretation as a spherical aromatic system with 32 core electrons in a filled 1S²1P⁶1D¹⁰1F¹⁴ shell, analogous to superatomic 3D aromatic species. The molecular orbital analysis indicates that the valence s and d orbitals (mainly d_z²) of the metal participate in delocalized bonding with the boron cage, while the remaining d-electrons reside in non-bonding orbitals localized on the metal. The result is a closed-shell, diamagnetic cluster with substantial aromatic stabilization. Comparisons between Ni, Pd, and Pt reveal similar structural trends, with the Ni-based clusters generally showing the largest stabilization of the closo form. The absence of any protective ligands in these clusters means that the metal centers are coordinatively unsaturated. However, the pronounced stability owing to delocalized skeletal bonding suggests that if isolated, such species would be resilient icosahedral clusters. This theoretical study provides a systematic baseline for bare metal metallaborane clusters, highlighting their viability and unique electronic structure (spherical aromaticity), while also noting the potential (yet untested) reactivity of an exposed transition-metal vertex.

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1. Introduction

Hawthorne and co-workers¹ discovered in the 1960s that the boron vertices in deltahedral boranes and isoelectronic carboranes could be replaced by transition metal vertices. The original 10 to 12 vertex metalladicarbaboranes synthesized by the Hawthorne group using decaborane, B₁₀H₁₄ as the boron source and alkynes as the carbon source were supplemented by smaller metallaboranes synthesized by Grimes and co-workers² using pentaborane, B₅H₉, as the boron source. The external coordination sites of the metal vertices in the metallaboranes initially prepared by Hawthorne, Grimes, and their coworkers and later by a number of other research groups were always protected by suitable external groups. The cyclopentadienyl (Cp) ligand was especially useful for this purpose because of its robust bonds formed with transition metals. Thus polyhedral metallaborane derivatives with CpM vertices can withstand relatively vigorous reaction conditions before rupture of the Cp–M bond leading to destruction of the metallaborane cluster. In this connection a CpCo unit was a vertex in many of the initially discovered metallaboranes since it is isolobal with a BH vertex. Many of the polyhedral metallaboranes synthesized later had other external groups such as arenes, carbonyl, nitrosyl, and/or phosphine ligands bonded to each of the transition metal vertices.

The originally synthesized metallaboranes and metallacarboranes had skeletons based on the most spherical closo deltahedra, which are characterized by vertices as nearly similar as possible and exclusively triangular faces (Fig. 1).^3,4 Thus the closo deltahedra having 6 to 12 vertices have only degree 4 and/or 5 vertices except for the 11-vertex deltahedron, which is topologically required to have a single degree 6 vertex. The number of skeletal electrons in such structures is generally determined by the Wade–Mingos rules,^5–7 which state that n-vertex closo deltahedral boranes are particularly stable if they contain 2n + 2 skeletal electrons. This special stability has been ascribed to three-dimensional aromaticity.^8–10 In accord with the Wade–Mingos rules the so-called closo borane anions B_nH_n²⁻ as well as the isoelectronic closo carboranes CB_n−1H_n⁻ and C₂B_n−2H_n exhibit special stability. Much later work has led to the discovery of metal-free supraicosahedral metallaboranes such as the 13-vertex carboranes^11,12 1,2µ-C₆H₄(CH₂)₂-3-C₆H₅-1,2-C₂B₁₁H₁₀ and 1,2-µ-(CH₂)₃-3-C₆H₅-1,2-C₂B₁₁H₁₀ by Xie and co-workers as well as the 14-vertex carborane (µ-CH₂)₃C₂B₁₂H₁₂.

Fig. 1 The most spherical deltahedra with 5 to 12 vertices with the vertices labeled with their degrees. In addition, degree 3, 4, 5, and 6 vertices are shown in pink, red, black, and green, respectively.

A question of interest is whether polyhedral metallaboranes with bare transition metal vertices are accessible as viable species. If so, these clusters would feature chemically exposed metal sites that could, in principle, interact with other molecules allowing the designing clusters with novel reactivity or catalytic properties. Recent theoretical work by Merino and coworkers¹³ provided a striking example: the B₁₀Rh₂ and B₁₀Ir₂ clusters were predicted as stable 12-vertex icosahedral structures, where two metal atoms occupy vertex positions in a framework otherwise consisting exclusively of boron atoms. These are described as boron-based icosahedral clusters stabilized by electron donation and covalent interactions from the metal atoms. Those findings support the idea that metal atoms can indeed stabilize closo boron clusters even without a full complement of ligands, essentially acting as electron-rich vertices that complete the cluster electron count.

Isolating a ligand-free metallaborane is challenging: without the stabilizing ligand, the metal center might either coordinate adventitiously to any available molecule or cause the cluster to rearrange. However, no such species have been synthesized or even characterized as reactive intermediates. In an attempt to predict the scope of such chemistry of this type we undertook a theoretical study of MB_n−1H_n−1 (M = Ni, Pd, Pt) derivatives using well-established density functional methods. The Group 10 metals were chosen for this initial study for the following reasons:

(1) They have the maximum number of valence electrons for transition metals likely to occur as vertex atoms.

(2) Reagents such as Ni(CO)₄, (η^5,5-C₈H₁₂)₁Ni, (η^2,2,2-cyclo-1,5,9-C₁₂H₁₈)Ni, and (C₂H₄)₃Pt are available that can generate reactive “naked” metal atoms for reactions with boranes such as decaborane B₁₀H₁₄.

The MB₁₁H₁₁ (M = Ni, Pd, and Pt) systems included in this study are related to the icosahedral M₂B₁₀ (M = Rh, Ir) systems studied by Merino and co-workers.¹³ Other bare metal-boron clusters have been proposed for hydrogen storage.¹⁴ The MB₁₁H₁₁ (M = Ni, Pd, and Pt) systems are examples of possible intermediates in such hydrogen storage processes.

The computational studies reported here by standard density functional methods indicate a strong preference for the most spherical closo deltahedral structures for these B_n−1H_n−1M (M = Ni, Pd, Pt) systems. This suggests that each group 10 metal vertex Ni, Pd, and Pt is a donor of four skeletal electrons in order to provide such n-vertex closo deltahedral structures with the preferred 2n + 2 skeletal electrons suggested by the Wade–Mingos rules.^5–7 Details of these studies are presented in this paper.

2. Theoretical methods

The initial chemical structures investigated in this study are based on various B_nH_n²⁻ polyhedral frameworks (including all closo deltahedra from 5 to 14 vertices, and some other structures) where a systematic substitution of one BH vertex led to the generation of 204 different starting structures of the type MB_n−1H_n−1 (M = Ni, Pd, Pt; n = 5 to 14) (see the SI).

Full geometry optimizations were carried out using the PBE0 DFT functional and the triple zeta def2-TZVP basis set for all atoms except for Pd and Pt for which the SDD (Stuttgart–Dresden ECP plus DZ) basis set was used. Single point energy calculations were performed on the lowest energy structures by employing the DLPNO-CCSD(T) method^15–28 coupled with the def2-QZVP//SDD basis set. Zero-point and thermal corrections taken from the PBE0/(def2-TZVP//SDD) computations were added to the final energies.

The nature of the stationary points was characterized by harmonic vibrational frequencies. When significant imaginary frequencies were encountered, the optimization was continued by following the normal modes corresponding to imaginary frequencies to ensure that genuine minima were obtained. All of the low-energy structures have substantial HOMO–LUMO gaps (see the SI). Electronic structures were analyzed by examining Kohn–Sham molecular orbitals, natural population analysis (NPA) charges, and the electron density distribution. We paid special attention to the symmetry and composition of the frontier orbitals to identify patterns consistent with spherical shell models. The adaptive natural density partitioning (AdNDP) method was not explicitly performed in this work, but we refer to literature AdNDP results on related boron clusters²⁹ for interpreting our bonding findings.

All calculations were performed using the Gaussian 09 package³⁰ with the default settings for the SCF cycles and geometry optimizations. Single-point DLPNO-CCSD(T) energy calculations were carried out with the ORCA 3.0.3 software package^31–39 using very tight convergence criteria.

The MB_n−1H_n−1 (M = Ni, Pd, Pt; n = 5 to 14) structures are designated as B(n−1)M-x where n is the total number of polyhedral vertices, and x is the relative order of the structure on the potential energy scale. Only the lowest energy and thus potentially chemically significant structures are considered in detail in this paper. More comprehensive structural information, including higher energy structures and connectivity information not readily seen in the figures, are given in the SI.

The optimized structures for the B_n−1H_n−1M (M = Ni, Pd, Pt) systems are listed in Table 1. The degrees of the metal vertices are starred. Except for the 11-vertex MB₁₀H₁₀ systems the figures depict the structures of the palladium derivatives as examples of similar derivatives of all three metals.

Table 1 Optimized structures for the B_n−1H_n−1M (M = Ni, Pd, Pt) systems with the stars indicating the degree of the metal vertex

Structure (symmetry)	ΔE (kcal mol^−1)			Vertex degrees				Comments
	M = Ni	M = Pd	M = Pt	v 3	v 4	v 5	v 6
5 vertices
B4M-1 (C3v)	0.0	0.0	0.0	2*	3	0	0	Trigonal bipyramid
B4M-2 (Cs)	6.5	3.4	13.4	2	3*	0	0	Trigonal bipyramid (µ-H)
6 vertices
B5M-1 (C4v)	0.0	0.0	0.0	0	6*	0	0	Octahedron
B5M-2 (C1)	32.4	37.8	31.5	2*	2	2	0	Bicapped tetrahedron
7 vertices
B6M-1 (C2v)	0.0	0.0	0.0	0	5*	2	0	Pentagonal bipyramid
B6M-2 (C5v)	21.6	15.7	12.5	0	5	2*	0	Pentagonal bipyramid
8 vertices
B7M-1 (Cs)	0.0	0.0	0.0	0	4*	4	0	Bisdisphenoid
B7M-2 (C1)	17.0	11.7	16.2	2*	0	5	0	Bicapped octahedron
9 vertices
B8M-1 (C2v)	0.0	0.0	1.8	0	3*	6	0	Tricapped trigonal prism
B8M-2 (C1)	11.2	5.8	0.0	0	3	6*	0	Tricapped trigonal prism
10 vertices
B9M-1 (C4v)	0.0	0.0	0.0	0	2*	8	0	Bicap tetragonal antiprism
B9M-2 (Cs)	14.6	10.2	5.3	0	2	8*	0	Bicap tetragonal antiprism
11 vertices
B10M-1 (Cs)	0.0	0.0	0.0	0	2*	8	1	11-vertex closo deltahedron
B10M-2 (C1)	6.6	3.6	4.3	0	2	8	1*	11-v closo deltahed (distorted)
B10M-3 (Cs)	19.9	24.5	16.5	0	2	8	1*	11-vertex closo deltahedron
B10M-4 (Cs)	23.3	17.0	17.8	0	2	8*	1	11-vertex closo deltahedron
12 vertices
B11M-1 (C5v)	0.0	0.0	0.0	0	0	12*	0	Icosahedron
B11M-2 (Cs)	44.6	51.4	42.3	0	2	8	2*	2v6 deltahedron
13 vertices
B12M-1 (C2v)	0.0	1.0	10.8	0	1*	10	2	13-vertex closo deltahedron
B12M-2 (Cs)	6.4	0.0	0.0	0	1	10*	2	13-vertex closo deltahedron
B12M-3 (Cs)	23.9	15.4	16.5	0	1	10*	2	13-vertex closo deltahedron
14 vertices
B13M-1 (Cs)	0.0	2.2	0.0	0	0	12*	2	Bicapped hexagonal antiprism
B13M-2 (C3v)	6.4	0.0	25.1	2*	0	6	6	Bicapped icosahedron
B13M-3 (D6d)	18.7	13.0	4.6	0	0	12	2*	Bicapped hexagonal antiprism

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3. Results

The two lowest energy five-vertex MB₄H₄ (M = Ni, Pd, Pt) structures have a central MB₄ trigonal bipyramid corresponding to the closo 5-vertex deltahedron (Fig. 2 and Table 1). Among the two possible such structures the C_3v structures B4M-1 with the metal atom M located at a degree 3 axial vertex is the lower energy structure. The other trigonal bipyramidal MB₄H₄ structures, namely the C_s structures B4M2 with the metal atom located at a degree 4 equatorial vertex, lie 3.4 kcal mol⁻¹ (M = Pd) to 13.4 kcal mol⁻¹ (M = Pt) in energy above the corresponding B4M-1 structure. In the B4M2 structures one of the hydrogen atoms bridges an edge from an axial degree 3 boron vertex to an equatorial degree 4 vertex.

Fig. 2 The lowest energy five-vertex MB₄H₄ (M = Ni, Pd, Pt) structures.

The lowest energy six-vertex MB₅H₅ (M = Ni, Pd, Pt) structures B5M-1 have a central MB₅ octahedron corresponding to the closo 6-vertex deltahedron (Fig. 3 and Table 1). These C_4v structures appear to be very favorable since the next lower energy MB₅H₅ structures B5M-2 lie 31.5 kcal mol⁻¹ (M = Pt) to 37.8 kcal mol⁻¹ (M = Pd) in energy above B5M-1. The B5M-2 structures have a central MB₅ bicapped tetrahedron with the metal atom located at a degree 3 vertex.

Fig. 3 The lowest energy six-vertex MB₅H₅ (M = Ni, Pd, Pt) structures.

The two lowest energy seven-vertex MB₆H₆ structures have central MB₆ pentagonal bipyramids corresponding to the closo 7-vertex deltahedron (Fig. 4 and Table 1). Among these structures the lower energy structures B6M-1 are C_2v structures with the metal atom located at a degree 4 equatorial vertex. The higher energy C_5v structures B6M-2, lying 12.5 kcal mol⁻¹ (M = Pt) to 21.6 kcal mol⁻¹ (M = Ni) above the corresponding B6M-1 structure (Table 1), have the metal atoms located at a degree 5 axial vertex.

Fig. 4 The lowest energy seven-vertex MB₆H₆ (M = Ni, Pd, Pt) structures.

The lowest energy eight-vertex MB₇H₇ structures B7M-1 have central bisdisphenoids corresponding to the closo 8-vertex deltahedron (Fig. 1) with the metal atoms located at a degree 4 vertex (Fig. 5 and Table 1). The next lowest energy MB₇H₇ structures B7M-2 are C_3v bicapped octahedral structures with the metal atom at one of the degree 3 vertices. Structures B7M-2 lie from 11.7 kcal mol⁻¹ (M = Pd) to 17.0 kcal mol⁻¹ (M = Ni) in energy above the corresponding B7M-1 structures.

Fig. 5 The lowest energy eight-vertex MB₇H₇ (M = Ni, Pd, Pt) structures.

The two lowest energy nine-vertex MB₈H₈ (M = Ni, Pd, Pt) structures have a central MB₈ tricapped trigonal prism corresponding to the closo 9-vertex deltahedron (Fig. 6 and Table 1). The lowest energy structure B8M-1 for the nickel and palladium MB₈H₈ derivatives has the metal atom located at a degree 4 vertex. The isomeric closo structure B8M-2 with the metal located at a degree 5 vertex lies 11.2 kcal mol⁻¹ (M = Ni) or 5.8 kcal mol⁻¹ (M = Pd) above B8M-1. However, the closo structures B8M-2 have an unusually long B–B edge between two of the boron atoms connected to the metal atom. The relative energy order of these two structure types is reversed for the platinum derivative PtB₈H₈ with B8M-2 with the platinum atom at a degree 5 vertex lying 1.8 kcal mol⁻¹ in energy below B8M-1 with the platinum atom at a degree 4 vertex.

Fig. 6 The lowest energy nine-vertex MB₈H₈ (M = Ni, Pd, Pt) structures.

The two lowest energy ten-vertex MB₉H₉ (M = Ni, Pd, Pt) structures have central MB₉ bicapped square antiprisms corresponding to the closo 10-vertex deltahedron (Fig. 7 and Table 1). The lowest energy such structures B9M-1 have C_4v symmetry with the metal atom located at one of the two degree 4 axial vertices. The higher energy such structures B9M-2, lying 5.3 kcal mol⁻¹ (M = Pt) to 14.6 kcal mol⁻¹ (M = Ni) above their lowest energy isomers, have the metal atom located at a degree 5 vertex.

Fig. 7 The lowest energy ten-vertex MB₉H₉ (M = Ni, Pd, Pt) structures.

The situation with the 11-vertex MB₁₀H₁₀ (M = Ni, Pd, Pt) systems is more complicated owing to the lower symmetry of the 11-vertex closo deltahedron which has one degree 6 vertex and eight degree 5 vertices as well as two degree 4 vertices flanking the unique degree 6 vertex (Fig. 1). Four fundamental types of MB₁₀H₁₀ structures are found within a reasonable energy range, all based on the 11-vertex closo deltahedron as illustrated in Fig. 8. The lowest energy B10M-1 structures consistently have the metal atom at one of the two degree 4 vertices. Two types of MB₁₀H₁₀ structures are found with the metal atom at the unique degree 6 vertex. One of these structures, as exemplified by B10Ni-3, lying 19.9 kcal mol⁻¹ in energy above B10Ni-1, has the nickel atom at the degree 6 vertex with all of its six bonds to adjacent boron atoms falling in the narrow range from 2.0 Å to 2.1 Å. However, distortion of the six Ni–B bonds from the degree 6 vertex so that two are elongated to 2.55 Å, two remain at 2.14 Å, and two are shortened to 1.84 Å leads to the much lower energy structure B10Ni-2, lying only 6.6 kcal mol⁻¹ in energy above B10Ni-1. A similar distortion of the MB₁₀H₁₀ structure with the metal atom at the degree 6 vertex was found for both the platinum and the palladium systems. In the lowest energy MB₁₀H₁₀ structures with the metal atom at a degree 5 vertex, as exemplified by B10Ni-4 lying 23.3 kcal mol⁻¹ above B10Ni-1, the metal atom is located at the pseudo-antipodal degree 5 vertex relative to the unique degree 6 vertex.

Fig. 8 The lowest energy 11-vertex NiB₁₀H₁₀ structures.

For the 12-vertex MB₁₁H₁₁ (M = Ni, Pd, Pt) systems the unique icosahedral structures are by far the lowest energy structures (Fig. 9 and Table 1). Thus the lowest energy non-icosahedral MB₁₁H₁₁ isomers B11M-2, lie 42.3 kcal mol⁻¹ (M = Pt) to 51.4 kcal mol⁻¹ (M = Pd) in energy above B11M-1. These C_sB11M-2 structures have two degree 4 and two degree 6 vertices with the metal atom located at one of the degree 6 vertices.

Fig. 9 The lowest energy 12-vertex MB₁₁H₁₁ (M = Ni, Pd, Pt) structures.

The MB₁₁H₁₁ (M = Pd, Pt) systems are related to the M₂B₁₀ (M = Rh, Ir) systems studied by Merino and coworkers¹³ with the bare group 9 rhodium and iridium vertices as donors of three skeletal electrons. They find icosahedral structures for these M₂B₁₀ derivatives with the two metals in antipodal (para) positions of the icosahedron to be the global minima lying 16.7 kcal mol⁻¹ (M = Rh) and 18.0 kcal mol⁻¹ (M = Ir) in energy below the next lowest energy structures.

The lowest-energy structures of the 13-vertex systems MB₁₂H₁₂ (M = Ni, Pd, Pt) are all based on the 13-vertex closo deltahedron, sometimes called the docosahedron because of its 22 faces (Fig. 1). The structure with the metal atom at a degree 5 vertex adjacent to both degree 6 vertices (B12M-1 in Fig. 10) and the structure with the metal atom at the unique degree 4 vertex (B12M-2 in Fig. 10) are the two lowest energy structures for all three metals. However, the relative energies of these two structures are highly dependent on the metal atom (Table 1). Thus these two structures are of similar energy within ∼1 kcal mol⁻¹ for palladium. However, for nickel the structure B12Ni-2 with the nickel atom at the degree 4 vertex lies 6.4 kcal mol⁻¹ in energy below B12Ni-1 with the nickel atom at a degree 5 vertex connected to both degree 6 vertices. The reverse is found for platinum with an energy difference of 10.8 kcal mol⁻¹. Consistently higher in energy by margins ranging from 15.4 kcal mol⁻¹ for palladium to 23.9 kcal mol⁻¹ for nickel are next lowest energy structures with the metal atom at a degree 5 vertex connected to only one of the two degree 6 vertices.

Fig. 10 The lowest energy 13-vertex MB₁₂H₁₂ (M = Ni, Pd, Pt) structures.

The lowest energy structures for the 14-vertex MB₁₃H₁₃ (M = Ni, Pd, Pt) systems (Fig. 11) include structures based on the 14-vertex closo deltahedron, namely the bicapped hexagonal antiprism (Fig. 1) as well as the symmetrically bicapped icosahedron. The bicapped hexagonal antiprism structures B13M-1 with the metal atom at one of the degree 5 vertices are the lowest energy structures for nickel and platinum and lie within 2 kcal mol⁻¹ of the lowest-energy structure for palladium. The bicapped icosahedron structures B13M-2 are the lowest energy structure for palladium, lie 6.4 kcal mol⁻¹ above the lowest energy structure for nickel, but are a high-energy structure for platinum (Table 1). Conversely, the bicapped hexagonal antiprism structures B13M-3 with the metal atom at one of the two degree 6 axial vertices lie only 4.6 kcal mol⁻¹ above the lowest energy for platinum but are high-energy structures for nickel and palladium.

Fig. 11 The lowest energy 14-vertex MB₁₃H₁₃ (M = Ni, Pd, Pt) structures.

4. Discussion

4.1. Electronic structure and bonding analysis

Our theoretical studies show that structures based on closo deltahedra (Fig. 1) are clearly preferred energetically for all of the MB_n−1H_n−1 (M = Ni, Pd, Pt) systems having from 5 to 14 vertices thereby suggesting that these systems have 2n + 2 skeletal electron based on the Wade–Mingos rules.^5–7 Since the BH vertices each provide two skeletal electrons, this means that a group 10 metal vertex (Ni, Pd, Pt) must provide four skeletal electrons. Thus the 10 valence electrons of the neutral group 10 metals are partitioned into four skeletal electrons and six external electrons. The six external electrons correspond to three external lone pairs in these singlet state structures.

The MB_n−1H_n−1 (M = Ni, Pd, Pt) systems also obey the 4m + 2 interstitial electron rule of Jemmis and Schleyer⁴⁰ where m = n + 1. Thus the boron and hydrogen atoms of the B_n−1H_n−1 portion of the deltahedron contribute three and one interstitial electrons, respectively, resulting in 4(n − 1) interstitial electrons from this portion of the molecule. The group 10 transition metal atom (Ni, Pd, Pt) with a d¹⁰ configuration contributes an additional 10 electrons leading to a total of 4(n + 1) + 2 = 4m + 2 interstitial electrons.

In the lowest energy structures of most of the MB_n−1H_n−1 (M = Ni, Pd, Pt) systems, the metal atom is located at a degree 4 vertex rather than a degree 5 vertex. Also, in the trigonal bipyramidal 5-vertex MB₄H₄ systems there is an energetic preference for the location of the metal atom at one of the two degree 3 axial vertices rather than at one of the three degree 4 equatorial vertices. The preferred location of the metal atom at degree 3 vertices is also indicated by structures with metals located at degree 3 vertex caps in bicapped octahedral structures B7M-2 and bicapped icosahedral structures B13M-2 for the 8- and 14-vertex systems, respectively, being energetically competitive with structures based on the corresponding closo deltahedra (Fig. 1), namely the 8-vertex bisdisphenoid and 14-vertex bicapped hexagonal antiprism.

Consider the graph theory derived model for the skeletal bonding in closo boranes and related structures.⁹ Each vertex atom provides three internal orbitals for the skeletal bonding. One of these orbitals from each vertex atom in an n-vertex system, designated as an internal or radial orbital, overlaps with the corresponding orbitals from all of the other vertex atoms in the center of the deltahedron to form an n-center core bond requiring two skeletal electrons. The two other internal orbitals from each vertex atom overlap pairwise on the surface of the deltahedron thereby forming n two-center two-electron (2c–2e) bonds requiring 2n skeletal electrons. In this way the requirement of 2n + 2 skeletal electrons for closo deltahedral structures can be rationalized. Furthermore, a set of n 2c–2e surface bonds can be considered as a canonical form of a resonance structure analogous to a Kekulé structure of benzene. Thus the totality of all possible such sets of n 2c–2e surface bonds provides a delocalized system corresponding to the three-dimensional aromaticity of such systems. This can account for the energetic preference of such closo deltahedral structures for these systems.

By inspecting the Kohn–Sham orbitals of, for instance, NiB₁₁H₁₁, we find that the 4s and 3d orbitals of the nickel atom mix into the delocalized bonding orbitals of the cluster. In the closo icosahedral cluster, the skeletal bonding MOs can be grouped by their symmetry as s-like, p-like, d-like, etc., corresponding to spherical harmonics on the icosahedron. The nickel atom contributes significantly to a few of these. Thus the lowest s-like combination and one set of d-like combinations (analogous to d_z² oriented into the cluster) have noticeable Ni character (>50% localization on Ni in those MO lobes). These orbitals correspond to Ni using one s and approximately two of its five 3d orbitals in bonding (an sd² hybrid, so to speak). The remaining d orbitals (particularly those of E (x²y², xy) and T (xz, yz) symmetry on the icosahedron) do not find good overlap with cluster framework orbitals and end up essentially as Ni-centered lone pairs. This picture aligns with classical ideas of transition metal cluster bonding: not all metal d orbitals will engage in skeletal bonding, only those that that are allowed by symmetry and energy. Nickel uses roughly three valence orbitals (one 4s + two 3d) to form cluster bonds, leaving 3d⁶ worth of electrons essentially on the Ni (as non-bonding or core-like orbitals).

This description is supported by the AdNDP perspective reported for closo boranes:²⁹ in B₁₂H₁₂²⁻, all 26 valence electrons can be classified into multi-center two-electron bonds spanning the cage (with varying degrees of delocalization: some 3-center B–B–B bonds, some 4-center, and an overall 12-center delocalized component). In NiB₁₁H₁₁, we expect a similar situation, except now there are 26 + 4 = 30 skeletal electrons (since the cluster is neutral, we actually have 24 from BH units + 4 from Ni = 28 skeletal bonding electrons by Wade–Mingos counting; plus 2 extra that might occupy a non-bonding or higher antibonding level). The presence of the metal does not localize the bonding into 2-center bonds; rather, it contributes to the delocalized bonds. If one performed an AdNDP, one might find a set of multi-center bonds that include the metal as one of the centers, reflecting Ni–B–B three-center bonds or Ni–B–B–B four-center bonds, etc., alongside the multi-B bonds. The key point is that the bonding remains collective. For instance, the computed Wiberg bond indices (WBI) show that Ni has a non-negligible bond index with each of its neighboring B atoms (∼0.3–0.4 per Ni–B in NiB₁₁H₁₁), summing to ∼1.6, which is close to Ni effectively forming the equivalent of a 2c–2e bond distributed over the cluster. This is very much in line with an isolobal analogy: Ni in NiB₁₁H₁₁ behaves like a 16-electron fragment donating into a boron cage, analogous to CoCp (18e) or Fe(CO)₃ (18e) in other contexts, except here Ni has no external ligands.

The MB_n−1H_n−1 (M = Ni, Pd, Pt) derivatives are clearly coordinatively unsaturated systems since the metal atoms formally use only a six-orbital sd⁵ manifold leaving their three higher-energy p orbitals out of their chemical bonding manifold. The MB_n−1H_n−1 derivatives are thus expected to be highly reactive towards bonding of various ligands to the bare metal atom leading to L₃MB_n−1H_n−1 derivatives such as (η⁶-C₆H₆)MB_n−1H_n−1 or B_n−1H_n−1M(CO)₃. In such structures the metal uses its full nine-orbital sp³d⁵ manifold with the favored 18-electron configuration and also retaining the favorable 2n + 2 skeletal electrons of the central MB_n−1closo deltahedron. However, the viability of the bare metal atom closo deltahedral MB_n−1H_n−1 structures, as suggested by the calculations reported here, suggests that the binding of the ligands L attached to the metal atom in their L₃MB_n−1H_n−1 derivatives is likely to be relatively weak. As a result, the L₃MB_n−1H_n−1 derivatives are predicted to be labile towards substitution reactions involving the ligands L.

The icosahedral MB₁₁H₁₁ (M = Ni, Pd, Pt) structures exhibit the highest symmetry (C_5v) of the MB_n−1H_n−1 (n = 5 to 12) structures investigated. They also appear to be the most stable of the MB_n−1H_n−1 structures as suggested by the thermochemistry of cluster buildup reactions of the type MB_n−1H_n−1 + BH → MB_nH_n which are all exothermic. Thus for n values from 6 to 10 such cluster buildup reactions liberate 95 to 121 kcal mol⁻¹ for each step. However, the cluster buildup reactions from the 11-vertex MB₁₀H₁₀ to the 12-vertex MB₁₁H₁₁ are significantly more exothermic liberating ∼135 kcal mol⁻¹. This suggests greater thermochemical stability of the 12-vertex system.

In order to provide more insight into the chemical bonding in these systems, we investigated the bonding molecular orbitals of the icosahedral nickel structure NiB₁₁H₁₁B11Ni-1 (Fig. 12). The 12-vertex system was chosen because of its greater symmetry as well as its apparent greater thermochemical stability. In NiB₁₁H₁₁ the single nickel atom, 11 boron atoms, and 11 hydrogen atoms have a total of 94 electrons, among which 40 are inner core electrons not involved in the chemical bonding and occupying the core molecular orbitals from 1 to 20. The remaining 54 valence electrons, consisting of 10 electrons from the nickel atom, 33 electrons from the 11 boron atoms, and 11 electrons from the 11 hydrogen atoms, occupy the 27 molecular orbitals from 21 to 47. These 54 valence electrons can be partitioned into 22 external electrons for the 11 external B–H bonds and 32 internal electrons for the bonding within the NiB₁₁ cluster. Note that the 32 internal electrons include the 26 electrons for the skeletal bonding in the NiB₁₁ icosahedron as well as 6 electrons for the three lone pairs in the three external nickel orbitals of its sd⁵ manifold. Furthermore, 32 (= 2(N + 1)² for N = 3) electrons is a “magic number” for a filled 1S²1P⁶1D¹⁰1F¹⁴ set of molecular orbitals in a spherical aromatic system.⁴¹

Fig. 12 Bonding molecular orbitals of the icosahedral NiB₁₁H₁₁ structure B11Ni-1. The orbitals in the 1S²1P⁶1D¹⁰1F¹⁴ cluster bonding manifold are indicated in red and the B–H external orbitals are indicated in green. Orbital energies are given in atomic units.

The nine lowest-energy bonding molecular orbitals from 21 to 29 can clearly be identified by their shapes as the 1S²1P⁶1D¹⁰ part of the internal bonding of the NiB₁₁ core of B11Ni-1 (Fig. 12). The remaining part of the internal core bonding, namely the 1F¹⁴ part, is not quite as clear but appears to corresponding to the molecular orbitals from 31 to 37. Molecular orbital 30, lying between the 1D¹⁰ and 1F¹⁴ parts of the cluster bonding, appears to relate to the B–H external bonding since it is located essentially completely on the B₁₁ part of the central cluster. The remaining 10 bonding molecular orbitals in NiB₁₁H₁₁ from 38 to the HOMO (47) appear to arise mainly from the external B–H bonds with this being clearest for the molecular orbitals from 42 to 44 that, like molecular orbital 30, have little electron density on the nickel atom.

4.2. Stability and potential reactivity of bare-metal clusters

Our calculations firmly establish that, in silico, MB_n−1H_n−1 clusters (M = Ni, Pd, Pt) exhibit closo structures that are particularly stable as compared to other cluster arrangements. The question of whether these clusters could be realized experimentally is connected with their reactivity. A naked metal center on a boron cage is a highly unusual coordination environment in which the metal is short of the favorable 18-electron count. In NiB₁₁H₁₁, Ni is necessarily located at a degree 5 vertex using 4 electrons for cluster bonding leaving 6 non-bonding electrons in external lone pairs thereby totalling 10 valence electrons, which is far below the favorable 18-electron configuration. Such an electronically unsaturated metal atom might be expected to strongly attract ligands or reactants to approach or achieve the favorable 18-electron configuration. On the other hand, the entire cluster is a closed-shell singlet with aromatic stabilization so addition of a ligand might disrupt the delicate electronic balance.

In order to evaluate this, the addition of simple ligands such as CO to the bare metal atom can be considered. For example, if NiB₁₁H₁₁ were exposed to CO, the Ni could in principle bind up to three CO molecules to make an 18-electron Ni(0) complex Ni(CO)₃B₁₁H₁₁. Such a reaction would be

NiB₁₁H₁₁ + 3CO → Ni(CO)₃B₁₁H₁₁

This reaction would require Ni to shift some electron density for bonding to CO ligands. Since CO is a strong field ligand; it would compete for the 3d and 4s electrons that Ni is currently sharing with the B₁₁H₁₁ cluster. Bonding of an external CO ligand to a Ni cluster vertex could require the Ni atom to withdraw some electron donation from the cage to satisfy the CO bonds. This might effectively reduce the skeletal electron count of the cage, possibly destabilizing the closo framework.

In essence, the cluster might need to sacrifice some aromatic stabilization to let Ni achieve a favorable 18-electron configuration. Which effect wins out depends on energetics: Ni–CO bonds are worth on the order of 30–40 kcal mol⁻¹ each in typical complexes, whereas the aromatic stabilization of NiB₁₁H₁₁ (going from an open structure to closo) is ∼50 kcal or more (the gap we saw to alternatives). It is plausible that NiB₁₁H₁₁ doesn’t gain much (or even loses) by binding external CO groups. Our reasoning supports that the cluster is already electronically satisfied, so adding external ligands diminishing returns. Thus if ligands coordinate, their binding might be only be moderate to preserve an intact closo cage.

From another angle, consider chemical reactivity such as oxidative addition or insertion at the metal. A bare Ni(0) site is normally very reactive as shown by Ni(0) organometallics activating C–H bonds. However, in NiB₁₁H₁₁ the Ni(0) is part of an aromatic cage. Thus any reaction that changes electron count will affect the electron count of the entire cage. For instance, oxidative addition to NiB₁₁H₁₁ would formally give something like H–Ni–H bonded to B₁₁H₁₁, thereby disrupting the closo system. (This could lead to a nido or arachno structure with an open face to accommodate Ni(II).) Thus these clusters likely sit in a delicate balance by being kinetically inert because of the aromatic cage, but thermodynamically open to reaction because the metal has unused capacity.

No experimental data are currently available to provide a direct comparison with our theoretical results. However, such clusters might be generated by a transient route such as removal of the CO ligands from a Ni(CO)₃B₁₁H₁₁ complex leading to NiB₁₁H₁₁ in the gas phase for observation by mass spectrometry. The inherent stability of NiB₁₁H₁₁ favors its existence long enough to detect. The high negative charge on the boron atoms and the positive change on the Ni atom might make NiB₁₁H₁i subject to electrophilic attack at boron or nucleophilic attack at Ni.

In summary, these bare-metal closo clusters are likely quite inert to cluster fragmentation owing to strong delocalized bonding so they will not easily undergo dehydrogenation or even fall apart. They are also electron-rich yet coordinatively unsaturated at the metal, so they might form adducts or undergo addition reactions at the metal. However, in doing they compromise their spherical aromaticity. Any practical catalytic application would require a mechanism to harness the reactivity of the metal atom while keeping the cage intact. This could lead to use of the cluster as a bound ligand itself, thereby entering the realm of supraicosahedral chemistry rather than classical catalysis.

5. Summary

The lowest energy structures for the MB_n−1H_n−1 (M = Ni, Pd, Pt; n = 5 to 14) clusters with bare group 10 metal vertices are the corresponding closo deltahedra. This suggests that the group 10 metal vertices use a 6-orbital sd⁵ manifold to become donors of 4 skeletal electrons thereby providing the 2n + 2 skeletal electrons for these closo systems in accord with the Wade–Mingos rules. A molecular orbital analysis of the icosahedral NiB₁₁H₁₁ suggests interpretation as a spherical aromatic system with 32 core electrons in a filled 1S²1P⁶1D¹⁰1F¹⁴ shell. The bare Ni, Pd, Pt metallaboranes studied here reinforce a fundamental principle: the geometry and electron-counting rules of boranes are so robust that even when a vertex is a transition metal with no external ligands, the cluster can remain intact and follow the same Wade–Mingos 2n + 2 skeletal electron rule, gaining extra stability from three-dimensional aromaticity. This expands our understanding of cluster chemical space and hints at the possibility of isolating new types of molecules, namely metallaborane clusters that are ligand-free and aromatic.

Conflicts of interest

The authors have no conflict of interest to declare.

Data availability

Data are available from Prof. Alexandru Lupan upon request.

Supplementary information (SI): initial starting structures; distance matrices and energy rankings for the lowest energy structures; frontier molecular orbitals and their energies for the lowest energy MB₁₁H₁₁ structures; orbital energies and HOMO–LUMO gaps for the lowest energy structures. A concatenated .xyz file containing the Cartesian coordinates of the optimized structures. See DOI: https://doi.org/10.1039/d5cp04106f.

Acknowledgements

This work was supported by a grant of the Ministry of Education and Research of Romania, CCCDI – UEFISCDI, project number PN-IV-PCB-RO-MD-2024-0515, within PNCDI IV. The computational resources were provided by the Babeş-Bolyai University under project POC/398/1/1/124155 – co-financed by the European Regional Development Fund (ERDF) through the Competitiveness Operational Program for Romania 2014–2020.

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