Polyhedral Ferraboranes with Iron Carbonyl Vertices: Carbonyl Migration Processes in the Iron Tetracarbonyl Derivatives

The structures and energetics of the neutral Bn–1Hn–1Fe(CO)x (x = 4, 3) and the dianions [Bn–1Hn–1Fe(CO)3]2– (n = 6–14) have been investigated by density functional theory. The low-energy structures of the tricarbonyl dianions [Bn–1Hn–1Fe(CO)3]2– are all found to have closo deltahedral structures in accordance with their 2n+2 skeletal electrons. The low-energy structures of the neutral tricarbonyls Bn–1Hn–1Fe(CO)3 (n = 6–14) with only 2n skeletal electrons are based on capped (n–1)-vertex closo deltahedra (n = 6, 7, 8) or isocloso deltahedra with a degree 6 vertex for the iron atom. The closo 8- and 9-vertex deltahedra are also found in low-energy Bn–1Hn–1Fe(CO)3 structures relating to the nondegeneracy of their frontier molecular orbitals. Carbonyl migration occurs in most of the low-energy structures of the tetracarbonyls Bn–1Hn–1Fe(CO)4. Thus, migration of a carbonyl group from an iron atom to a boron atom gives closo Bn–2Hn–2(BCO)(μ–H)Fe(CO)3 structures with a BCO vertex and a hydrogen atom bridging a B–B deltahedral edge. In other low-energy Bn–1Hn–1Fe(CO)4 structures, a carbonyl group is inserted into the central n-vertex FeBn–1 deltahedron to give a Bn–1Hn–1(CO)Fe(CO)3 structure with a central (n+1)-vertex FeCBn–1 deltahedron that can be an isocloso deltahedron or a μ3–BH face-capped n-vertex FeCBn–2closo deltahedron. Other low-energy Bn–1Hn–1Fe(CO)4 structures include Bn–1Hn–1Fe(CO)2(μ-CO)2 structures with two of the carbonyl groups bridging FeB2 faces (n = 6, 7, 10) or Fe–B edges (n = 12) or structures in which a closo Bn–1Hn–1 ligand (n = 6, 7, 10, 12) is bonded to an Fe(CO)4 unit with exclusively terminal carbonyl groups through B–H–Fe bridges.


INTRODUCTION
The pioneering work on polyhedral metallaboranes and metalladicarbaboranes from the research groups of Hawthorne 1 and Grimes 2 included many derivatives containing a CpCo (Cp = η 5 -C 5 H 5 ) vertex replacing a BH vertex in a borane structure. Both CpCo and BH vertices are donors of two skeletal electrons in the Wade-Mingos electron counting system assuming that each such vertex provides three orbitals for the skeletal bonding 3−5 as discussed more recently in several articles by Teixidor and collaborators. 6−8 Thus, cobaltadicarbaboranes of the types CpCoC 2 B n−3 H n−1 and Cp 2 Co 2 C 2 B n−4 H n−2 have the favored 2n + 2 Wadean skeletal electrons for the most spherical closo deltahedral structures with n vertices (Figure 1). From the synthetic point of view, the two carbon vertices for such structures can originate from alkynes, RC�CR, although that leads to thermodynamically less favored structures having carbon atoms at adjacent deltahedral vertices. Note that the deltahedral structures have only sufficient hydrogen atoms (or other external monovalent groups such as alkyl or aryl) for one external E−H bond from each boron and carbon vertex. No "extra" hydrogen atoms bridging deltahedral edges are found in these structures.
Iron tricarbonyl vertices, Fe(CO) 3 , are valence isoelectronic with CpCo vertices and likewise donate two skeletal electrons for the Wade-Mingos skeletal bonding scheme. 3−5 The iron atom in such an Fe(CO) 3 vertex providing three orbitals for skeletal bonding and three orbitals for σ bonding to the three CO groups can have an allocation of metal valence orbitals similar to that of an octahedral coordination complex FeL 6 with the polyhedral borane fragment functioning as a tridentate ligand. In this connection, the tricarbonylferradicarbaboranes C 2 B n−3 H n−1 Fe(CO) 3 have been synthesized having six, 9 seven, 9,10 and twelve 11 vertices, i.e., n = 6, 7, and 12, respectively. These n-vertex structures all have 2n + 2 Wadean skeletal electrons and exhibit the corresponding most spherical closo deltahedral structures ( Figure 1). However, B n−1 H n−1 Fe(CO) 3 species without the two C−H vertices have only 2n skeletal electrons and thus might be expected to exhibit isocloso structures based on deltahedra having a degree 6 vertex for the iron atom ( Figure 2). 12−14 No examples of B n−1 H n−1 Fe(CO) 3 systems or their substitution products have been synthesized. The only polyhedral borane iron carbonyls without carbon polyhedral vertices that have been synthesized and characterized at least spectroscopically are hydrogen-rich systems derived from the binary nido boranes of the type B n H n+4 by replacement of a BH vertex by an isolobal Fe(CO) 3 vertex ( Figure 3). Examples of such species are tetragonal pyramidal 15 B 4 H 8 Fe(CO) 3 derived from B 5 H 9 and pentagonal pyramidal 16,17 B 5 H 9 Fe(CO) 3 derived from B 6 H 10 . Hexaborane can also serve as a bidentate ligand in an iron tetracarbonyl complex (η 2 -B 6 H 10 )Fe(CO) 4 through formation of a B 2 Fe three-center two-electron bond ( Figure 3). 18,19 The experimentally known examples of closo deltahedral tricarbonylferraboranes increase the number of Wadean skeletal electrons from 2n in a B n−1 H n−1 Fe(CO) 3 derivative to 2n + 2 by replacing two BH vertices with CH vertices to give the corresponding C 2 B n−3 H n−1 Fe(CO) 3 derivatives. The theoretical study reported in this study uses density functional theory methods to explore the structures and thermochemistry of two other types of tricarbonylferraborane structures having the apparent 2n + 2 Wadean skeletal electrons. Thus, a twoelectron reduction of neutral B n−1 H n−1 Fe(CO) 3 to give the corresponding dianion [B n−1 H n−1 Fe(CO) 3 ] 2− converts the neutral 2n skeletal electron system to the 2n + 2 skeletal electron dianion. We show that the energetically preferred structures for the [B n−1 H n−1 Fe(CO) 3 ] 2− dianions are always the most spherical closo deltahedra ( Figure 1). The only real question of interest is the preferred location of the Fe(CO) 3 vertex.
This study reports a comprehensive density functional theory analysis of the following types of polyhedral ferraboranes with iron carbonyl vertices organized in the following ways where n refers to the number of vertices in the central polyhedron: (1) The dianions [B n−1 H n−1 Fe(CO) 3 ] 2− having the 2n + 2 skeletal electrons required for a central FeB n−1 closo deltahedron ( Figure 1). Such ferraborane dianions are unknown experimentally. However, they might be accessible by reductions of the known B n−1 H n+3 Fe(CO) 3 with bridging hydrogen atoms ( Figure 3) with an alkali metal reagent such as potassium on graphite; (2) The neutral species B n−1 H n−1 Fe(CO) 3 with iron tricarbonyl vertices having only 2n skeletal electrons and possibly accessible through mild oxidation of the above dianions; (3) The neutral species B n−1 H n−1 Fe(CO) 4 with iron tetracarbonyl vertices. It might be assumed that adding an "extra" CO group to a B n−1 H n−1 Fe(CO) 3 derivative  Metallaborane isocloso and related deltahedra with 8 to 12 vertices providing at least one degree 6 vertex for a metal atom showing the vertex degrees. Vertices of degrees 3, 4, 5, and 6 are also indicated in pink, red, black, and green, respectively. Note that the 11-vertex isocloso deltahedron is the same as the 11-vertex closo deltahedron, which necessarily already has a degree 6 vertex. having only 2n skeletal electrons would provide the "extra" two skeletal electrons for the 2n + 2 skeletal electrons normally required for closo deltahedral structures ( Figure 1). However, this is found to lead to some interesting complications. Having four CO groups on the iron atom leaves only two valence orbitals for skeletal bonding if the iron remains hexacoordinate as in the B n−1 H n−1 Fe(CO) 3 systems. The topological bonding model 20 rationalizing the Wade-Mingos 2n + 2 skeletal electron rule for closo deltahedra (Figure 1)

THEORETICAL METHODS
The initial model structures are based on various B n H n polyhedral frameworks where systematic substitutions of BH vertices by an Fe(CO) x unit (x = 4, 3) led to 630 initial starting structures of the type B n−1 H n−1 Fe(CO) x (n = 6−14; x = 4, 3) (see the Supporting information). Full geometry optimizations were carried out on the neutral B n − 1 H n − 1 Fe(CO) x (x = 4, 3) and the dianions [B n−1 H n−1 Fe(CO) 3 ] 2− (n = 6−14) using the B3LYP DFT functional 21−24 coupled with the double zeta 6-31G(d) basis set. The lowest energy structures were reoptimized at the PBE0/def2-TZVP level of theory. 25 Single point energy calculations were then performed on the lowest energy structures by using the domain based local pair-natural orbital coupled-cluster method including single and double excitations and perturbative correction for connected triples (DLPNO-CCSD(T)). 26 The quadruple zeta def2-QZVP basis sets were used in these calculations. The final energies were corrected for zero-point energies taken from the PBE0/def2-TZVP computations.
The nature of the stationary points after optimization was checked by calculations of the harmonic vibrational frequencies. If significant imaginary frequencies were found, the optimization was continued by following the normal modes corresponding to imaginary frequencies to insure that genuine minima were obtained. Highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gaps for the lowest energy structures are provided in the Supporting Information.
All calculations were performed using the Gaussian 09 package 27 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 28 using very tight convergence criteria.
The B n−1 H n−1 Fe(CO) x (x = 4, 3) (n = 6−14) structures are designated as B(n−1)FeCm−x where n is the total number of polyhedral vertices, m is the total number of CO ligands, and x is the relative order of the structure on the potential energy scale. However, for the dianions [B n−1 H n−1 Fe(CO) 3 ] 2− (n = 6−14), the shorthand notation B(n−1)FeCmM2-x is used. Only the lowest energy and thus potentially chemically significant structures are considered in detail in this study. More comprehensive structural information, including higher energy structures and connectivity information not readily seen in the figures, is given in the Supporting Information.  Figure 4). The lower energy of these two structures, namely, B6FeC3M2-1, has the Fe(CO) 3 moiety located at a degree 5 axial vertex. The higher energy of these two structures, namely, B6FeC3M2-2 lying 5.6 kcal/mol above B6FeC3M2-1, has the Fe(CO) 3 moiety located at a degree 4 equatorial vertex.
The two low-energy structures for the 8-vertex [B 7 H 7 Fe(CO) 3 ] 2− dianion both have central FeB 7 bisdisphenoids consistent with their 18 skeletal electrons (=2n + 2 for n = 8) for a closo deltahedron ( Figure 5). In the lower energy structure B7FeC3M2-1, the Fe(CO) 3 moiety is located at a degree 4 vertex, which can be considered to resemble locally a cyclobutadiene unit similar to that found in the very stable cyclobutadiene-iron tricarbonyl. 29,30 In the higher    Figure 1). In the lowest energy [B 8 H 8 Fe(CO) 3 ] 2− structure B8FeC3M2-1, the Fe(CO) 3 moiety is located at one of the degree 5 vertices ( Figure 6). However, the isomeric  Figure 7). In the lowest energy [B 9 H 9 Fe(CO) 3 ] 2− structure B9FeC3M2-1, the Fe(CO) 3 moiety is located at one of the degree 4 vertices. The local environment of the iron atom is similar to the very stable cyclobutadiene-iron tricarbonyl, 29 C 4 H 4 Fe(CO) 3 , or the experimentally known B 4 H 8 Fe(CO) 3 (Figure 3). 15 The Fe(CO) 3 moiety is located at a degree 5 vertex in the higher energy [B 9 H 9 Fe(CO) 3 ] 2− structure B9FeC3M2-2, lying 4.5 kcal/mol in energy above B9FeC3M2-1. For the analogous cyclopentadienylcobalt dianion CpCoB 9 H 9 2− , the isomers corresponding to B9FeC3M2-1 and B9FeC3M2-2 with the cobalt atom at a degree 4 and degree 5 vertex, respectively, are found to have the same energies within ∼1 kcal/mol. 31 T h e t w o l o w e s t e n e r g y s t r u c t u r e s f o r t h e [B 10 H 10 Fe(CO) 3 ] 2− dianion are based on the most spherical 11-vertex closo/isocloso deltahedron ( Figure 8). The 24 skeletal electrons in these structures suggest that this deltahedron is functioning as a closo rather than an isocloso deltahedron. The lower energy of these two structures, namely, B10FeC3M2-1, has the Fe(CO) 3 moiety located at one of the degree 4 vertices giving the iron atom a local environment similar to that in cyclobutadiene-iron tricarbonyl 29 or B 5 H 9 Fe(CO) 3 ( Figure  3). 15 The higher energy of these structures, namely, B10FeC3M2-2 lying 7.3 kcal/mol above B10FeC3M2-1, has the Fe(CO) 3 moiety located at a degree 5 vertex not adjacent to the unique degree 6 vertex. For the analogous cyclopentadienylcobalt borane dianion CpCoB 10 H 10 2− , the lowest energy structure is an 11-vertex closo/isocloso deltahedron with the cobalt located at a degree 4 vertex similar to B10FeC3M2-1. A CpCoB 10 H 10 2− dianion with the cobalt atom located at a degree 5 vertex two edges away from the unique degree 6 vertex lies 6.7 kcal/mol in energy above the isomer analogous to B10FeC3M2-1. 31 Thus, for the [B 10 H 10 Fe(CO) 3 ] 2− and CpCoB 10 H 10 2− systems, the two lowest energy structures are completely analogous and have similar relative energies.
Since all 12 vertices of an icosahedron are equivalent like the 6 vertices of an octahedron, there is a unique low-energy [B 11 H 11 Fe(CO) 3 ] 2− structure B11FeC3M2-1 with a central FeB 11 icosahedron ( Figure 8).
The low-energy structures of the 30-skeletal electron 14-vertex dianion [B 13 H 13 Fe(CO) 3 ] 2− are based on the bicapped hexagonal antiprism, which is the most spherical closo 14-vertex deltahedron ( Figure 1). In the lowest energy structure B13FeC3M2-1, the Fe(CO) 3 unit is located at one of the two degree 6 vertices of the bicapped hexagonal     Figure 10). In the higher energy dianion structure B13FeC3M2-2, lying 10.0 kcal/mol above B13FeC3M2-1, the Fe(CO) 3 moiety is located at one of the 12 equiv degree 5 vertices of the bicapped hexagonal antiprism.

Neutral Tricarbonyls B n−1 H n−1 Fe(CO) 3 (n = 6−14)
. The neutral 6-vertex B 5 H 5 Fe(CO) 3 system has 12 skeletal electrons (=2n for n = 6). The expected B 5 Fe polyhedron for this system is the bicapped tetrahedron similar to that found experimentally for the likewise 12-skeletal electron system 32 Os 6 (CO) 18 . In fact, the two lowest energy B 5 H 5 Fe(CO) 3 structures are bicapped tetrahedra ( Figure 11). The lowest energy such structure B5FeC3-1 has the Fe(CO) 3 moiety located at one of the degree 5 vertices, whereas the higher energy structure B5FeC3-2, lying 9.9 kcal/mol in energy above B5FeC3-1, has the Fe(CO) 3 moiety located at one of the degree 4 vertices and a hydrogen bridge between a degree 3 and a degree 4 vertex. The still higher energy B 5 H 5 Fe(CO) 3 structure B5FeC3-3, lying at 18.4 kcal/mol has a central FeB 5 octahedron rather than a bicapped tetrahedron.
The two lowest energy 7-vertex B 6 H 6 Fe(CO) 3 structures have a central capped octahedron consistent with their 14 skeletal electrons (=2n for n = 7). In the lower energy of these structures, namely, B6FeC3-1, the Fe(CO) 3 moiety occupies a degree 5 vertex ( Figure 12). The other capped octahedral B 6 H 6 Fe(CO) 3 structure, namely, B6FeC3-2 lying only 1.7 kcal/mol in energy above B6FeC3-1, differs from B6FeC3-1 only by rotation of the Fe(CO) 3 unit relative to the boron capping vertex.
The next B 6 H 6 Fe(CO) 3 structure in terms of energy, namely, B6FeC3-3, lying still only 3.9 kcal/mol above B6FeC3-1, has a central FeB 6 pentagonal bipyramid with the distance between the axial iron atom and the opposite likewise axial boron atom being reduced to a bonding distance of 2.336 Å, which is only ∼0.2 Å longer than the shortest Fe−B distance to a boron atom in the equatorial B 5 pentagon ( Figure  12). This additional Fe−B(axial) bonding through the center of this squashed FeB 6 pentagonal bipyramid in B6FeC3-3 can compensate for the presence of only 14 rather than 16 skeletal electrons. Also, in B6FeC3-3, the hydrogen atom on one of the equatorial pentagon boron atoms moves to bridge a pentagonal B−B edge with B−H distances of ∼1.36 Å.
Four low-energy structures were found for the 8-vertex 16skeletal electron system B 7 H 7 Fe(CO) 3 ( Figure 13). The lowest energy such structure B7FeC3-1 has a central FeB 7 capped pentagonal bipyramid with the Fe(CO) 3 moiety located at the unique degree 6 vertex. The central pentagonal bipyramid in this structure is consistent with its 16 skeletal electrons. The next two B 7 H 7 Fe(CO) 3 structures, namely, B7FeC3-2 and B7FeC3-3 lying 3.5 and 4.5 kcal/mol, respectively, in energy above B7FeC3-1, are closely related structures with a central FeB 7 bisdisphenoid having the iron atom located at a degree 5 vertex. The 16 skeletal electrons for these two bisdisphenoidal B 7 H 7 Fe(CO) 3 structures rather than 18 skeletal electrons for a closo bisdisphenoid are reasonable in light of the nondegeneracy of the frontier orbitals of the bisdisphenoid. 33 The fourth B 7 H 7 Fe(CO) 3 structure B7FeC3-4, lying 8.5 kcal/mol in energy above B7FeC3-1, also has a central FeB 7 bisdisphenoid but with the iron atom located at a degree 4 vertex. In B7FeC3-4, one of the hydrogen atoms has migrated from a degree 4 vertex adjacent to the iron atom to form an Fe−H−B bridge with an Fe−H distance of 1.652 Å and a B−H distance of 1.310 Å. This bridging hydrogen atom indirectly draws an otherwise nonbonding iron lone pair into the skeletal bonding, effectively giving B7FeC3-4 a skeletal electron count of 18 electrons for a closo bisdisphenoid.
Both closo and isocloso structures were found for the 18skeletal electron systems B 8 H 8 Fe(CO) 3 corresponding to 2n for n = 9 ( Figure 14). The lowest energy structure B8FeC3-1 has the iron atom located at one of the degree 5 vertices of the closo tricapped trigonal prism. Note that a stable tricapped trigonal prism structure can have only 18 skeletal electrons as well as 20 skeletal electrons (=2n + 2 for n = 9) because of the     The Journal of Physical Chemistry A pubs.acs.org/JPCA Article nondegeneracy of its frontier molecular orbitals. 33 The other low-energy B 8 H 8 Fe(CO) 3 structure B8FeC3-2, lying only 2.1 kcal/mol above B8FeC3-1, has the 9-vertex isocloso structure ( Figure 2) expected for an 18-skeletal electron system. In B8FeC3-2, the iron atom is located at the unique degree 6 vertex in accordance with expectation. For the analogous cyclopentadienylcobalt system CpCoB 8 H 8 , the closo tricapped trigonal prism is found to be the lowest energy structure. 31 The isocloso isomer of CpCoB 8 H 8 with a degree 6 cobalt vertex analogous to B8FeC3-2 is predicted to lie 9.2 kcal/mol in energy above the closo structure. The lowest energy B 9 H 9 Fe(CO) 3 structure B9FeC3-1 has a central 10-vertex isocloso deltahedron (Figure 2) with the Fe(CO) 3 moiety located at the unique degree 6 vertex consistent with its 20 skeletal electrons (=2n for n = 10) ( Figure 15). The higher energy B 9 H 9 Fe(CO) 3 structure B9FeC3-2, lying 5.3 kcal/mol in energy above B9FeC3-1, has a central FeB 9 bicapped square antiprism with the Fe(CO) 3 moiety located at a degree 4 vertex. The hydrogen atom on one of the boron vertices adjacent to the iron atom in B9FeC3-2 moves within the bonding distance of the iron atom to form a B−H−Fe bridge with a B−H distance of 1.326 Å and an Fe−H distance of 1.636 Å. This bridging hydrogen atom brings an otherwise external iron lone electron pair into the skeletal bonding so that B9FeC3-2 is effectively a 22-skeletal electron system consistent with its closo bicapped square antiprism geometry. For the analogous cyclopentadienylcobalt system CpCoB 9 H 9 , the isocloso structure analogous to B9FeC3-1 was found to be the lowest energy structure by a more substantial margin with the lowest energy closo structure lying 26.3 kcal/mol in energy above the lowest energy isocloso structure. 31 The lowest energy B 10 H 10 Fe(CO) 3 structure B10FeC3-1 has the central most spherical 11-vertex deltahedron that can function either as a closo or an isocloso deltahedron (Figures 1  and 2). The Fe(CO) 3 moiety is located at the unique degree 6 vertex in accordance with the expectation (Figure 16). The 11vertex deltahedron in this B 10 H 10 Fe(CO) 3 structure B10FeC3-1 has 22 skeletal electrons (=2n for n = 11) and thus functions as an isocloso rather than a closo deltahedron. A CpCoB 10 H 10 structure analogous to B10FeC3-1 based on the 11-vertex closo/isocloso deltahedron with the cobalt atom at the unique degree 6 vertex is found to be the lowest energy structure by more than 19 kcal/mol. 31 The next higher energy B 10 H 10 Fe(CO) 3 structure B10FeC3-2, lying 9.9 kcal/mol in energy above B10FeC3-1, is a very different structure than B10FeC3-1. The central FeB 10 deltahedron is an FeB 9 bicapped square antiprism in which a face including the degree 4 vertex is capped by the tenth boron atom (Figure 16). The Fe(CO) 3 moiety in B10FeC3-2 is located at the degree 4 vertex of the original bicapped square antiprism that is connected to the capping boron vertex to become a degree 5 vertex. The 22 skeletal electrons in B10FeC3-2 are consistent with the requirement for the central bicapped square antiprism as the closo 10-vertex deltahedron (Figure 1).
Icosahedral structures are so favorable in polyhedral borane chemistry that even the lowest energy neutral 12-vertex B 11  ligand is considered to be the very stable dianion, then, the iron atom in B12FeC3-1 must be d 6 Fe(II). Thus, B12FeC3-1 can be considered as a closed-shell octahedral Fe(II) complex with the tridentate B 12 H 12 2− ligand coordinating to the iron atom through three B−H bonds coming from one of the triangular faces of the B 12 icosahedron.
An energetically competitive totally different B 12 H 12 Fe(CO) 3 structure is found, namely, B12FeC3-2, lying 9.8 kcal/mol in energy above B12FeC3-1 (Figure 17). The central FeB 12 deltahedron in B12FeC3-2 is a capped icosahedron with the Fe(CO) 3 moiety located at one of the degree 6 vertices resulting from the capping process. The Fe(CO) 3 moiety and the 12 BH vertices are each donors of two skeletal electrons, thus making B12FeC3-2 a 26-skeletal electron system consistent with the central FeB 11 icosahedron.   The FeB 13 deltahedron found in the two lowest energy structures for the 14-vertex B 13 H 13 Fe(CO) 3 system with only 28 skeletal electrons (=2n for n = 14) can be derived from the bicapped hexagonal antiprism by a diamond-square-diamond rearrangement involving an edge connecting a degree 6 vertex with an adjacent degree 5 vertex (Figure 18). This generates a new deltahedron with three degree 6 vertices and one degree 4 vertex along with 10 degree 5 vertices. Such a 14-vertex deltahedron could be considered as an analogue of an isocloso deltahedron. Structures B13FeC3-1 and B13FeC3-2 are closely related and have essentially the same energy. A higher energy B 13 H 13 Fe(CO) 3 structure B13FeC3-3, lying 10.9 kcal/mol above B13FeC3-1, has an undistorted central bicapped hexagonal antiprism with the Fe(CO) 3 moiety located at one of the degree 6 vertices.

Neutral Tetracarbonyls B n−1 H n−1 Fe(CO) 4 (n = 6− 14)
. Adding the two electrons provided by an "extra" carbonyl group to the tricarbonyls B n−1 H n−1 Fe(CO) 3 (n = 6−14) with only 2n skeletal electrons might be expected to give the corresponding tetracarbonyls B n−1 H n−1 Fe(CO) 4 with 2n + 2 skeletal electrons like the dianions [B n−1 H n−1 Fe(CO) 3 ] 2− and thus exhibiting closo deltahedra (Figure 1). However, in most B n−1 H n−1 Fe(CO) 4 systems, the fourth carbonyl group in the lowest energy structures does not remain on the iron atom as a terminal ligand but instead migrates either to an adjacent boron atom or becomes a vertex in a new (n+1)-vertex FeCB n−1 deltahedron. For example, in the 6-vertex B 5 H 5 Fe(CO) 4 structure B5FeC4-1, two of the carbonyl groups of the Fe(CO) 4 unit are terminal groups and the remaining two carbonyl groups bridge FeB 2 triangular faces ( Figure 19).
The lowest energy structure for the 7-vertex B 6 H 6 Fe(CO) 4 with 16 skeletal electrons (=2n + 2 for n = 7), namely, B6FeC4-1, is not the closo pentagonal bipyramid but instead a capped octahedron (Figure 19). In B6FeC4-1, one of the carbonyl groups has migrated from the iron atom to an adjacent boron atom so that this species can be formulated as B 5 H 5 (HBCO)Fe(CO) 3 . The HBCO vertex in B6FeC4-1 is a donor of two skeletal electrons similar to each of the five BH vertices and the Fe(CO) 3 moiety. This makes B6FeC4-1 a 14-skeletal electron system consistent with its central FeB 5 octahedron. The tendency of the carbonyl group to migrate from iron to the capping boron vertex in B6FeC4-1 with retention of the terminal hydrogen atom appears to be related to the degree 3 of this vertex.
The higher energy B 6 H 6 Fe(CO) 4 structure B6FeC4-2, lying 7.5 kcal/mol in energy above B6FeC4-1, has the expected central FeB 6 pentagonal bipyramid with the iron atom at one of the degree 5 axial vertices ( Figure 19). Two of the carbonyl groups of the Fe(CO) 4 unit remain bonded as terminal groups to the iron atom, whereas the remaining two carbonyl groups migrate to an adjacent FeB 2 face to become face-bridging μ 3 -CO groups. Thus, the 7-vertex structure B6FeC4-2, described more specifically as B 6 H 6 Fe(CO) 2 (μ 3 -CO) 2 , is closely related to the 6-vertex structure B5FeC4-1, which can be described as B 5 H 5 Fe(CO) 2 (μ 3 -CO) 2 .
The 8-vertex closo deltahedron, namely, the bisdisphenoid, has nondegenerate frontier orbitals 33 and thus can be suitable for both 16-and 18-skeletal electron systems as indicated by the stability of the binary boron chloride B 8 Cl 8 , which has only 16 skeletal electrons. 34,35 The lowest energy structure B7FeC4-1 of the 18-skeletal electron system B 7 H 7 Fe(CO) 4 indeed has a central FeB 7 bisdisphenoid ( Figure 20). However, one of the carbonyl groups of the Fe(CO) 4 moiety has migrated to an adjacent boron atom. This carbonyl migration drives the hydrogen atom originally bonded to the boron atom receiving the carbonyl group to a bridging position across an adjacent B−B bond. Coordination of the carbonyl group to the boron atom in B7FeC4-1 allows all three valence electrons of that boron to become skeletal electrons so that the BCO vertex is a donor of three skeletal electrons. There still remains the hydrogen atom bridging the BCO vertex to an adjacent vertex to donate an additional electron. With the Fe(CO) 3 vertex as well as the remaining six BH vertices each functioning as donors of two skeletal electrons, structure B7FeC4-1 has the expected 18-skeletal electrons (=2n + 2 for n = 8) for a closo bisdisphenoid.
The B 7 H 7 Fe(CO) 4 structure B7FeC4-2, lying 3.4 kcal/mol in energy above B7FeC4-1, can be dissected formally into a neutral B 7 H 7 ligand functioning as a two-electron donor to an Fe(CO) 4 unit, thereby giving the iron atom the favored 18-electron configuration ( Figure 20). This can also be regarded formally as a substitution product of the stable Fe(CO) 4 I 2 in which the closo-B 7 H 7 2− dianion has displaced two iodide ions. The B 7 H 7 2− dianion is a trihapto ligand forming an Fe−H bond of length 1.800 Å and two Fe−B bonds of lengths 2.095 and 2.228 Å to the iron atom.
The third low-energy B 7 H 7 Fe(CO) 4 structure, namely, B7FeC4-3 lying 4.2 kcal/mol in energy above B7FeC4-1, is a still different type of structure in which one of the carbonyl groups of the Fe(CO) 4     vertices are all two-electron donors making B7FeC4-3 an 18-skeletal electron system corresponding to 2n for n = 9 (counting, of course, the carbon atom of the carbonyl vertex). A 2n as well a 2n + 2 closo skeletal electron count is reasonable for a tricapped trigonal prism in view of the nondegeneracy of its frontier orbitals. 33 The B 8 H 8 Fe(CO) 4 system has 20 skeletal electrons corresponding to 2n + 2 for n = 9 for the 9-vertex closo deltahedron, namely, the tricapped trigonal prism (Figure 1). However, carbonyl migration occurs in both low-energy B 8 H 8 Fe(CO) 4 structures to give other central deltahedra. In the lowest energy B 8 H 8 Fe(CO) 4 structure B8FeC4-1, one of the carbonyl groups becomes a deltahedral vertex, leading to the 10-vertex isocloso deltahedron (Figure 2) with the iron atom located at the unique degree 6 vertex in accordance with expectation ( Figure 21). The 20 skeletal electrons in B8FeC4-1 corresponding to 2n for n = 10 are consistent with the skeletal electron requirement for a central 10-vertex FeCB 8 isocloso deltahedron.
The carbonyl migration process in the other low-energy 9-vertex B 8 H 8 Fe(CO) 4 structure B8FeC4-2, lying only 2.1 kcal/mol above B8FeC4-1, is of a different type involving migration from iron to an adjacent boron atom ( Figure 21). The situation in B8FeC4-2 is similar to that in the lowest energy 8-vertex B 7 H 7 Fe(CO) 4 structure B7FeC4-1 ( Figure  20). Thus the carbonyl migration in B8FeC4-2 drives the hydrogen bonded to the boron receiving the carbonyl group into a bridging position to an adjacent boron atom. As for B7FeC4-1 this carbonyl migration in B8FeC4-2 preserves the 20 skeletal electrons (=2n + 2 for n = 9) of the B 7 H 7 Fe(CO) 4 system consistent with its central closo 9-vertex tricapped trigonal prism. In B8FeC4-2, the iron atom is located at a degree 5 vertex, and the BCO unit is located at one of the three degree 4 vertices.
The two lowest energy 10-vertex B 9 H 9 Fe(CO) 4 structures have an FeB 9 bicapped square antiprism consistent with their 22 skeletal electrons (=2n + 2 for n = 10) for this 10-vertex closo deltahedron (Figure 22). In the lowest energy such structure B9FeC4-1, the iron atom is located at one of the degree 5 vertices, but one of the carbonyl groups originally bonded to iron has migrated to an adjacent degree 5 boron vertex. The hydrogen originally bonded to the boron vertex receiving the carbonyl group in B9FeC4-1 becomes a bridging hydrogen from a degree 4 boron vertex to a degree 5 boron vertex. This carbonyl migration process preserves the 22 skeletal electron configuration. In the higher energy bicapped square antiprism B 9 H 9 Fe(CO) 4 structure B9FeC4-2, lying 5.9 kcal/mol in energy above B9FeC4-1, the Fe(CO) 4 moiety is located at one of the degree 4 vertices and there is no carbonyl migration.
The next higher energy B 9 H 9 Fe(CO) 4 structure B9FeC4-3, lying 14.3 kcal/mol in energy above B9FeC4-1, is based on a central closo/isocloso 11-vertex FeCB 9 deltahedron (Figures 1  and 2) in which one of the carbonyl groups bonded to the iron atom is inserted in the central deltahedral structure ( Figure  22). The remaining Fe(CO) 3 moiety occupies the unique degree 6 vertex and the carbonyl carbon occupies one of the two degree 4 vertices. Since the Fe(CO) 3 , carbonyl, and BH vertices are each two skeletal electron donors, B9FeC4-3 is a 22 skeletal electron system, suggesting that the central 11vertex FeCB 9 deltahedron is functioning as an isocloso deltahedron, as shown in Figure 2.
The lowest energy structure of the 11-vertex B 10 H 10 Fe(CO) 4 system B10FeC4-1 is unusual since it is not a deltahedron but a polyhedron with a single tetragonal B 4 face ( Figure 23). One of the carbonyl groups of the original Fe(CO) 4 unit has migrated to an adjacent boron vertex that is part of the tetragonal face leaving an Fe(CO) 3 moiety to occupy a degree 5 vertex. The hydrogen attached to the boron vertex receiving the carbonyl group moves to bridge one of the B−B edges of the tetragonal B 4 face. Since the single Fe(CO) 3 vertex and the nine BH vertices are each two skeletal electron donors, the BCO vertex is a three skeletal electron donor, and the bridging hydrogen atom a source of an additional skeletal electron, the B 10 H 10 Fe(CO) 4 structure B10FeC4-1 becomes a 24-skeletal electron system (=2n + 2 for n = 11). This skeletal electron count is that expected for a 11-vertex closo deltahedron. The actual 11-vertex FeB 10 polyhedron found in B10FeC4-1 can be derived from the 11-vertex closo deltahedron (Figure 1) by breaking an edge connecting its unique degree 6 vertex with one of the adjacent degree 5 vertices to form the tetragonal face.
The next B 10 H 10 Fe(CO) 4 structure B10FeC4-2, lying 10.7 kcal/mol in energy above B10FeC4-1, has a central 12vertex FeCB 10 deltahedron in which one of the carbonyl groups of the Fe(CO) 4 unit is inserted into an 11-vertex deltahedron ( Figure 23). In order to provide a degree 4 vertex for this carbonyl carbon atom, the central FeCB 10 deltahedron cannot be the regular icosahedron which has only degree 5 vertices. Instead, the 12-vertex deltahedron has two degree 4 vertices including one for the carbon atom, and two degree 6 vertices including one for the iron atom. This 12-vertex deltahedron is found experimentally in the dirhodium   The Journal of Physical Chemistry A pubs.acs.org/JPCA Article complexes Cp* 2 Rh 2 B 10 H 9 (OH) and Cp* 2 Rh 2 B 10 H 8 (OH) 2 shown by X-ray crystallography to have the rhodium atoms located at the two degree 6 vertices in these 24 skeletal electron systems. 36 Structure B10FeC4-2 is also a 24 skeletal electron system since the Fe(CO) 3 vertex, the carbonyl vertex, and the ten BH vertices each contribute two skeletal electrons to this system. The iron vertex in the icosahedral structure of the neutral 12-vertex species B 11 H 11 Fe(CO) 4 , namely, B11FeC4-1, bears only two terminal carbonyl groups (Figure 24). The remaining two carbonyl groups in B11FeC4-1 bridge the iron atom to adjacent boron atoms. Furthermore, the icosahedral B 12 H 12 unit is such a favorable one that it functions as a ligand to an The lowest energy structure of the 30-skeletal electron neutral 14-vertex system B 13 H 13 Fe(CO) 4 , namely, B13FeC4-1, has a central FeB 13 bicapped hexagonal antiprism ( Figure 24). However, in B13FeC4-1, one of the carbonyl groups of the Fe(CO) 4 unit has migrated to an adjacent boron atom with the concurrent migration of the terminal hydrogen originally on this boron atom to a bridging position. This process is analogous to that discussed above for the structures B10FeC4-1, B9FeC4-1, B8FeC4-2, and B7FeC4-1 with 11, 10, 9, and 8 vertices, respectively, in which the carbonyl migration from iron to boron does not affect the skeletal electron count.

DISCUSSION
The tricarbonyl dianions [B n−1 H n−1 Fe(CO) 3 ] 2− have the 2n + 2 skeletal electrons expected for closo deltahedral structures. Therefore, it is not surprising that the central FeB n−1 polyhedra in all of the low-energy [B n−1 H n−1 Fe-(CO) 3 ] 2− structures are the corresponding most spherical closo deltahedra (Figure 1). For 8-to 14-vertex [B n−1 H n−1 Fe-(CO) 3 ] 2− structures with a degree 4 vertex in the central FeB n−1 deltahedron, the preferred location of the Fe(CO) 3 group is the degree 4 vertex. This gives the iron atom in such structures a local environment similar to that in cyclobutadiene-iron tricarbonyl, 29 C 4 H 4 Fe(CO) 3 , or the known borane iron carbonyl 15 B 4 H 8 Fe(CO) 3 . In the smaller [B 6 H 6 Fe-(CO) 3 ] 2− system, the local environment of the iron atom at a degree 4 vertex deviates significantly from that in C 4 H 4 Fe-(CO) 3 and B 4 H 8 Fe(CO) 3 so that the isomeric structure with the iron atom located at a degree 5 vertex is energetically favored. In the supraicosahedral [B n−1 H n−1 Fe(CO) 3 ] 2− sys-tems (n = 13, 14), the lowest energy structures have the Fe(CO) 3 group located at a degree 6 vertex.
The neutral tricarbonyls B n−1 H n−1 Fe(CO) 3 have only 2n skeletal electrons and thus might be expected to have either central isocloso FeB n−1 deltahedra ( Figure 2) or (n−1)-vertex closo FeB n−2 deltahedra with one face capped by the remaining BH group as a degree 3 vertex. For the smallest B n−1 H n−1 Fe(CO) 3 systems, capped closo (n−1)-vertex deltahedral structures are energetically preferred as exemplified by the bicapped tetrahedral (�capped trigonal bipyramidal) structures B5FeC3-1 and B5FeC3-2 for B 5 H 5 Fe(CO) 3 , the capped octahedral structures B6FeC3-1 and B6FeC3-2 for B 6 H 6 Fe-(CO) 3 , the capped pentagonal bipyramidal structure B7FeC3-1 for B 7 H 7 Fe(CO) 3 , the capped bicapped square antiprismatic structure B10FeC3-2 for B 10 H 10 Fe(CO) 3 , and the capped icosahedral B 12 H 12 Fe(CO) 3 structure B12FeC3-2 for B 12 H 12 Fe(CO) 3 . The closo 8-and 9-vertex deltahedra, namely, the bisdisphenoid and tricapped trigonal prism, have nondegenerate frontier molecular orbitals 33 and thus can be preferred structures for not only 2n + 2 but also 2n skeletal electron systems. In the borane iron tricarbonyls, this is exemplified by the bisdisphenoidal B 7 H 7 Fe(CO) 3 structures B7FeC3-2, B7FeC3-3, and B7FeC3-4 and the tricapped trigonal prismatic B 8 H 8 Fe(CO) 3 structure B8FeC3-1. Isocloso deltahedra ( Figure 2) begin to appear in the 9-vertex systems as exemplified by the 9-vertex B8FeC3−2 and the 10-vertex B9FeC3-1. The 11-vertex structure B10FeC3-1 is also of this type having the iron atom at the unique degree 6 vertex of the most spherical 11-vertex deltahedron (Figures 1 and 2) that can be either a closo or isocloso deltahedron. The 14-vertex deltahedron found in the B 13 H 13 Fe(CO) 3 structures B13FeC3-1 and B13FeC3-2 has three degree 6 vertices and one degree 4 vertex as well as 10 degree 5 vertices and is derived from the bicapped hexagonal antiprism by a diamondsquare-diamond rearrangement. This deltahedron may be regarded as the equivalent of an isocloso deltahedron for 14-vertex structures.
The 12-vertex B 11 H 11 Fe(CO) 3 structure B11FeC3-1 has a central FeB 11 icosahedron despite having only 24 (=2n for n = 12) rather than the 26 (=2n + 2 for n = 12) skeletal electrons expected for the most spherical closo icosahedron. However, a terminal hydrogen on a boron atom adjacent to the iron atom in B11FeC3-1 moves over to form a B−H−Fe bridge with the iron atom, thereby drawing an otherwise external iron lone pair into the skeletal bonding and effectively adding two skeletal electrons. Thus, this bridging hydrogen atom in B11FeC3-1 makes this a 26 skeletal electron structure consistent with its central FeB 11 icosahedron. A hydrogen atom forms a similar B−H−Fe bridge in the 10-vertex B 9 H 9 Fe(CO) 3 structure B9FeC3-2 with a central closo deltahedron, namely, the bicapped square antiprism.
The special stability of boron icosahedra leads to a special structure B12FeC3-1 as the lowest energy structure for the 13-vertex B 12 H 12 Fe(CO) 3 system. Thus, B12FeC3-1 has an icosahedral B 12 H 12 tridentate ligand bonding to an external Fe(CO) 3   Another type of CO migration away from the iron atom in B n−1 H n−1 Fe(CO) 4 structures involves insertion of a CO group into the central FeB n−1 deltahedron to give a central (n + 1)vertex FeCB n−1 deltahedron. Since the CO vertex as well as the BH and Fe(CO) 3 vertices are each donors of two skeletal electrons, these B n−1 H n−1 (CO)Fe(CO) 3 systems are 2(n + 1) skeletal electron systems and thus might be expected to exhibit either (n + 1)-vertex isocloso structures with the iron atom at a degree 6 vertex ( Figure 2) or a capped n-vertex deltahedral structure. Low-energy B n−1 H n−1 (CO)Fe(CO) 3 structures having a CO vertex in a central (n + 1)-vertex FeCB n−1 deltahedron include B7FeC4-3, B8FeC4-1, B9FeC4-3, and B10FeC4-2 ( Figure 26). The central FeCB n−1 deltahedra in B8FeC4-1, B9FeC4-3, and B10FeC4-2 are the corresponding (n + 1)-vertex isocloso deltahedra (Figure 2) with the iron atom at a degree 6 vertex. Note that the 11-vertex isocloso deltahedron is the same as the 11-vertex closo deltahedron, and the 12-vertex isocloso deltahedron necessarily has two degree 6 vertices, one of which is occupied by the iron atom in B10FeC4-2. Also, note that in the only lowest-energy B n−1 H n−1 (CO)Fe(CO) 3 structure B8FeC4-1, the central 10-vertex isocloso deltahedron has been shown to be a particularly favorable isocloso deltahedron in systematic theoretical studies on other 2n skeletal electron systems such as Cp 2 Fe 2 C 2 B n−4 H n−4 37 and CpMC 2 B n−3 H n−3 (M = Mn, Re). 38 T h e B n − 2 H n − 2 ( B C O ) ( μ − H ) F e ( C O ) 3 a n d B n−1 H n−1 (CO)Fe(CO) 3 structures are the only examples of low-energy structures where a CO group has migrated completely away from the iron atom fully severing the Fe− CO bond. In another type of low-energy B n−1 H n−1 Fe(CO) 4 structure, two of the carbonyl groups of the Fe(CO) 4 moiety become bridging carbonyl groups either across Fe−B edges or FeB 2 faces. Such B n−1 H n−1 Fe(CO) 2 (μ−CO) 2 structures include B5FeC4-1, B6FeC4-1, and B11FeC4-1 in which the central FeB n−1 deltahedra are the corresponding most spherical closo deltahedra (Figure 1), namely, the 6-vertex octahedron, the 7-vertex pentagonal bipyramid, and the 12-vertex icosahedron, respectively. In the two smaller such structures, namely, B5FeC4-1 and B6FeC4-1, the bridging carbonyl groups are μ 3 -CO groups bridging FeB 2 faces. However, in B11FeC4-1, the bridging carbonyl groups are μ-CO groups bridging FeB edges. The 10-vertex B 9 H 9 Fe(CO) 4 structure B9FeC4-2 with a central bicapped square antiprism may also be considered in this category with two weakly face semibridging μ 3 -CO groups with B−C distances of 2.26, 2.27, and 2.27 Å.
A few low-energy B n−1 H n−1 Fe(CO) 4 structures are found containing an intact Fe(CO) 4 unit with all terminal carbonyl groups. Such structures may be formally regarded as an Fe(CO) 4 complex of a B n−1 H n−1 ligand. In all such structures, the B n−1 H n−1 unit has a closo deltahedral structure (Figure 1) and thus formally can be considered as the dianion B n−1 H n−1 2− . This makes the Fe(CO) 4 unit formally an Fe(II) dication Fe(CO) 4 2+ . Thus B n−1 H n−1 Fe(CO) 4 complexes can be generated formally be replacing the two halides in Fe(CO) 4 X 2 (X = Cl, Br, I) derivatives with the B n−1 H n−1 2− dianion. Alternatively, such complexes can be obtained formally by replacing one carbonyl group in Fe(CO) 5 by a neutral B n−1 H n−1 ligand, which is formally a two-electron donor ligand, to preserve the favored 18-electron configuration of the iron atom. The two low-energy structures of this type are  B7FeC4-2, in which a B 7 H 7 pentagonal bipyramid is bonded to the Fe(CO) 4 unit through an Fe−H−B bridge and a direct Fe−B bond ( Figure 20) and B12FeC4-1, in which a B 12 H 12 icosahedron is bonded to the Fe(CO) 4 unit through two Fe− H−B bridges ( Figure 24).

SUMMARY
The dianions [B n−1 H n−1 Fe(CO) 3 ] 2− (n = 6−14) have 2n + 2 skeletal electrons. This is consistent with the observation that all of their low-energy structures exhibit the most spherical closo deltahedral structures expected for this skeletal electron count without any examples of carbonyl migration.
The situation with the neutral B n−1 H n−1 Fe(CO) n (n = 3, 4) derivatives is more complicated. The B n−1 H n−1 Fe(CO) 3 (n = 6−14) tricarbonyl systems have only 2n skeletal electrons and thus might be expected to exhibit low-energy capped (n−1)vertex closo deltahedral structures or isocloso structures with a degree 6 vertex for the iron atom. Low-energy capped deltahedral structures are found for the smaller systems having 6 to 8 vertices, whereas isocloso structures are found for the systems with 9 to 11 vertices. In addition, the closo 8-and 9vertex deltahedra appear in low-energy B n−1 H n−1 Fe(CO) 3 structures consistent with the nondegeneracy of their frontier orbitals. 33 The lowest energy B 13 H 13 Fe(CO) 3 structure is a novel 14-vertex isocloso deltahedron.
The stability of boron icosahedra leads to special types of low-energy B n−1 H n−1 Fe(CO) 3 (n = 12, 13) structures for the 12-and 13-vertex tricarbonyl systems. Thus, the lowest energy B 11 H 11 Fe(CO) 3 structure has a central FeB 11 icosahedron with a bridging hydrogen along one of the Fe−B edges. The lowest energy B 12 H 12 Fe(CO) 3 structure has an icosahedral B 12 H 12 ligand coordinated to the Fe(CO) 3 moiety through three B−H−Fe bridges.
The B n−1 H n−1 Fe(CO) 4 (n = 6−14) tetracarbonyl systems have 2n + 2 skeletal electrons, suggesting the most spherical closo deltahedral structures. However, in most of the lowenergy B n−1 H n−1 Fe(CO) 4 structures, one of the carbonyl groups migrates from the iron atom to give structures of one of the following two types: (1) Migration from an iron atom to a boron atom gives a B n−2 H n−2 (BCO)(μ-H)Fe(CO) 3 structure with a BCO vertex and a hydrogen atom bridging a B−B deltahedral edge. Such a carbonyl migration retains the 2n + 2 skeletal electron count and leads to structures with central FeB n−1 closo deltahedra. (2) Insertion of the carbonyl group into the central n-vertex FeB n−1 deltahedron to give a B n−1 H n−1 (CO)Fe(CO) 3 structure with a central (n + 1)-vertex FeCB n−1 deltahedron having 2(n + 1) skeletal electrons. This corresponds either to an n-vertex closo FeCB n−2 deltahedron with a face capped by a degree 3 boron vertex or to an (n + 1)-vertex isocloso deltahedron. Other low-energy B n−1 H n−1 Fe(CO) 4 structures are of the following types: (1) B n−1 H n−1 Fe(CO) 2 (μ−CO) 2