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Article Cite This: Inorg. Chem. 2017, 56, 15015−15025

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Deviations from the Most Spherical Deltahedra in Rhenatricarbaboranes Having 2n + 2 Wadean Skeletal Electrons Amr A. A. Attia,† Alexandru Lupan,*,† and R. Bruce King*,2 † 2

Faculty of Chemistry and Chemical Engineering, Babeş-Bolyai University, Cluj-Napoca 400084, Romania Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States

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S Supporting Information *

ABSTRACT: Density functional theory studies on the rhenatricarbaboranes C3Bn−4Hn−1Re(CO)3 (n = 7−12) show that the lowest energy polyhedra for n−vertex metallaboranes having 2n + 2 skeletal electrons and sufficiently dissimilar vertex atoms can deviate from the most spherical closo deltahedra predicted by application of the Wade−Mingos rules. Furthermore, the lowest energy structures of these rhenatricarbaboranes are found to avoid C−C edges and have carbon atoms located at degree 4 rather than degree 5 vertices. The lowest energy structures for the 7-vertex C3B3H6Re(CO)3 system all have a central C3B3Re closo deltahedron, namely the pentagonal bipyramid with the rhenium atom at a degree 5 axial vertex and all three carbon atoms at degree 4 equatorial vertices. However, the lowest energy structure for the 8-vertex C3B4H7Re(CO)3 is not the most spherical closo 8-vertex deltahedron, namely the bisdisphenoid, but instead a central C3B4Re hexagonal bipyramid with mutually nonadjacent degree 4 vertices for the carbon atoms. Similarly, the lowest energy 10-vertex C3B6H9Re(CO)3 structures are derived from isocloso deltahedra having three degree 4 vertices for all three carbon atoms rather than from the most spherical 10-vertex closo deltahedron, namely the bicapped square antiprism with only two degree 4 vertices. However, for the 9-vertex C3B5H8Re(CO)3 system, the most spherical closo deltahedron, namely the tricapped trigonal prism, has three mutually nonadjacent degree 4 vertices, which is ideal for the three carbon atoms and thus is the preferred deltahedron. The preferred deltahedron for the 11-vertex C3B7H10Re(CO)3 remains the most spherical closo deltahedron despite having only two degree 4 vertices for the carbon atoms. Furthermore, the six lowest energy 12-vertex C3B8H11Re(CO)3 structures are all based on the regular icosahedron generally favored in polyhedral borane chemistry despite its complete lack of degree 4 vertices for the carbon atoms.

1. INTRODUCTION The high thermodynamic and kinetic stability of selected metallacarborane complexes of second- and third-row d-block transition metals make them of interest in medicine as drug delivery vehicles for therapeutic and diagnostic applications. The robustness of such metallacarboranes allows them to survive reaction conditions required to introduce functionalities required to optimize their introduction into biological systems. In addition, such kinetically inert species can survive metabolic degradation. Motivated by such considerations as well as by the use of technetium as the most common radioimaging isotope, Valliant and coworkers used rhenacarborane model systems to develop synthetic methods for technetacarborane imaging agents.1−3 The original rhenacarborane was the icosahedral dicarbaborane rhenium carbonyl monoanion [3,1,2-C2B9H11Re(CO)3]− initially synthesized by Hawthorne and coworkers4,5 more than a half-century ago as its cesium salt. The hydrogen atoms on the cage boron and carbon atoms in this parent system can be replaced by other monovalent groups such as alkyl and aryl. Similarly, the carbonyl groups in the Re(CO)3 moiety can be replaced with other ligands. In the latter connection, replacement of one CO group by the isoelectronic NO+ group gives the neutral rhenium carbonyl nitrosyl derivative © 2017 American Chemical Society

3,1,2-C2B9H11Re(CO)2(NO). This nitrosyl system has been used as the parent system for the synthesis of carborane derivatives as drug delivery vehicles by Jelliss and coworkers.6 The early work on rhenacarborane chemistry involved exclusively dicarbaborane derivatives reflecting the use of alkynes as the ultimate source of the two carbon atoms in the carborane cage. More recently, tricarbaborane ligands have become available as reagents for the synthesis of metallatricarbaboranes. The tricarbaborane [C3Bn−3Hn−3]− anions and their substitution products are direct analogues of the ubiquitous cyclopentadienyl anion and bind similarly to transition-metal fragments. Thus, species of the type CpFeC3Bn−3Hn−3 (Cp = η5-C5H5) and Fe(C3Bn−3Hn−3)2 are direct analogues of ferrocene, Cp2Fe. Similarly, species of the type (C3Bn−3Hn−3)Re(CO)3 are direct analogues of the very stable CpRe(CO)3. The first metallatricarbaborane to be prepared was the pentagonal bipyramidal MeC3B3H5Mn(CO)3 first synthesized by Howard and Grimes in 19697,8 by a thermal reaction of Mn2(CO)10 with the tricarbaborane MeC3B3H7 at 175−200 °C. Early attempts to develop further the chemistry of such Received: September 12, 2017 Published: November 29, 2017 15015

DOI: 10.1021/acs.inorgchem.7b02348 Inorg. Chem. 2017, 56, 15015−15025

Article

Inorganic Chemistry

Figure 1. Generation of the 11-vertex and 10-vertex [M]C3Bn−3Hn−4R (n = 10, 11) metallatricarbaboranes from icosahedral dicarbaboranes using a nitrile as the source of the third carbon vertex. Unlabeled vertices are boron atoms, and external hydrogen atoms are omitted for clarity.

7-vertex metallacarboranes by reactions of MeC3B3H6− with various transition-metal derivatives were unpromising. However, approximately 20 years later, Sneddon and coworkers developed the chemistry of 11-vertex metallatricarboranes of the type [M](C3Bn−3Hn−4R) ([M] = transition metal with surrounding ligands such as CpM or M(CO)3; R = alkyl or aryl) (Figure 1). The most extensive studies of these systems were done with CpFeC3B7H9R and Fe(C3B7H9R)2 derivatives that are direct analogues of ferrocenes.9−16 However, similar 11-vertex metallatricarbaboranes with vanadium,17 niobium,17 manganese,9,18,19 rhenium,19 ruthenium,12 osmium,12 cobalt,10,20 rhodium,20 iridium,20 and nickel9 have also been synthesized and structurally characterized. The 11-vertex metallatricarbaboranes CpM(C3B7H9Ph) (M = Fe, Ru) can be deboronated to give the corresponding 10-vertex metallatricarbaboranes CpM(C3B6H8Ph) using [nBu4N]F in tetrahydrofuran.21 These 10-vertex metallatricarbaboranes have a central MC3B6 bicapped square antiprism framework with two of the three carbon atoms at the degree 4 vertices and the third carbon atom adjacent to one of these carbon atoms and to the metal atom. A similar 10-vertex MC3B6 bicapped square antiprism is found in the iridium complex (η2,2-1,5-C8H12)Ir(C3B6H8Ph).20 The starting material for the syntheses of these 11-vertex metallatricarbaboranes was obtained by degradation of the icosahedral closo-dicarbaborane meta-C2B10H12 to give arachnoC2B7H13 followed by insertion of the third cage carbon atom from a nitrile, RCN, after deprotonation with NaH (Figure 1). The resulting 10-vertex tricarbaborane anion [C3B7H9R]− has a nido structure with a hexagonal open face containing all three carbon vertices and one C−C bond. This structure is retained upon initial reaction with metal complexes to provide a closo 11-vertex structure with the metal atom at the degree 6 vertex, the two degree 4 vertices occupied by two of the three carbon atoms, a C−C edge, and three M−C edges. Pyrolysis at sufficiently high temperatures can lead to cage rearrangements to an isomer with no C−C edges but only two M−C edges.11 Icosahedral metallatricarbaboranes of the type [M]C3B8H10R (R = H or alkyl) have also been synthesized. The required 11-vertex nido tricarbaborane anions can be obtained from the 10-vertex nido-dicarbaborane anion [C2B8H11]− using cyanide

or an alkyl isocyanide as the source of the third carbon vertex.22 Most of the known icosahedral metallatricarbaboranes are the cyclopentadienyliron derivatives CpFeC3B8H10R (R = alkyl, aryl, etc.) which are direct analogues of ferrocene.23,24 In general, the central MC3Bn−4 polyhedra in these experimentally known metallatricarbaboranes are the most spherical closo deltahedra also found in the parent borane dianions BnH2− n (n = 6−12) having vertices as nearly similar as possible (Figure 2). The Wade−Mingos rules25−27 recognize

Figure 2. Most spherical (closo) deltahedra have 7−12 vertices, indicating their vertex degrees. Vertices of degree 4, 5, and 6 are indicated in red, black, and green, respectively.

such n−vertex systems as having 2n + 2 skeletal electrons where a BH vertex contributes two skeletal electrons. Replacing two of the boron vertices in the BnH2− n dianions with carbon vertices to give the isoelectronic neutral dicarbaboranes C2Bn−2Hn does not affect the clear preference for closo deltahedra. Even if one or two BH vertices are replaced by CpCo vertices, which are also donors of two skeletal electrons, closo deltahedral structures of CpCoC 2 B n−3 H n−1 and Cp 2 Co 2 C 2 B n−4 H n−2 derivatives are still preferred.28−32 15016


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Inorganic Chemistry The preference for the most spherical closo deltahedra arises from the similarity of all of the vertex atoms. However, even a comparison of the neighboring atoms boron and carbon reveals a preference of carbon for lower degree vertices in closo carborane structures with dissimilar vertices. Transition-metal atoms, particularly those of the second and third rows, prefer higher degree vertices. This can lead to structures with considerable nonsphericity. Notable examples are the so-called oblatocloso33 dirhenaboranes of the type Cp*2Re2Bn−2Hn−2 (n = 8−12) in which the rhenium atoms are located at vertices of degrees 6 and/or 7, and the boron atoms are located at vertices of degrees 4 and/or 5.34−37 This disparity in vertex degrees for the rhenium and boron atoms leads to flattened structures in which the rhenium vertices are located at sites of low local curvature and the boron atoms are located at sites of high local curvature. Using the Wade−Mingos rules25−27 leads to a skeletal electron count of 2n − 4 for the Cp*2Re2Bn−2Hn−2 (n = 8 to 12) systems because the Cp*Re vertices contribute zero skeletal electrons. Thus, these dirhenaboranes are highly hypoelectronic and might be expected on that basis to exhibit structures different from the most spherical closo deltahedra (Figure 1). However, the tricarbaborane rhenium carbonyl derivatives C3Bn−4Hn−1Re(CO)3 have 2n + 2 skeletal electrons because an Re(CO)3 vertex is a donor of one skeletal electron. Thus, the Wade−Mingos rules suggest that these rhenatricarbaboranes would exhibit closo deltahedral structures. However, the central C3Bn−4Re units in these rhenatricarbaboranes contain three dissimilar types of atoms with distinctly different vertex degree preferences. Thus, the carbon atoms prefer degree 4 vertices, and the boron atoms prefer degree 4 or 5 vertices whereas the rhenium atom prefers a vertex of degree at least 5 with vertices of degrees 6 or even 7 also being reasonable for rhenium atoms. A question of interest is whether the three types of vertex atoms in the C3Bn−4Hn−1Re(CO)3 systems are so dissimilar that deltahedra other than the most spherical closo deltahedra will be energetically preferred in these 2n + 2 Wadean skeletal electron systems. Less spherical alternatives to the most spherical closo deltahedra for the 9- and 10-vertex systems are the isocloso deltahedra which, unlike the closo deltahedra, provide a single degree 6 vertex for a metal atom (Figure 3).38−40 A similar

topology than the closo metallaboranes.41 However, a question of interest is whether 9- and 10-vertex metallaboranes can be found with 2n + 2 skeletal electrons where the preference of a metal atom for a degree 6 rather than a degree 5 vertex leads to an isocloso structure rather than the expected closo structure. This might occur in a system containing other vertex atoms such as carbon preferring degree 4 rather than degree 5 vertices. This could lead to a less spherical isocloso structure of energy lower than that of the isomeric closo structure normally expected for a 2n + 2 skeletal electron system. The rhenatricarbaboranes C3Bn−4Hn−1Re(CO)3 present an opportunity to observe this phenomenon by combining a rhenium atom preferring a high degree vertex with three carbon atoms preferring low degree vertices. To investigate this possibility, we performed a comprehensive density functional theory study of the 7- to 12-vertex C3Bn−4Hn−1Re(CO)3 systems. We report the results in this paper. The theoretical methods used in this paper are similar to those used in our previously reported studies on the metallatricarbaborane systems CpMC3Bn−4Hn−1 (M = Fe,42 Mo43).

Figure 3. Alternative metallaborane deltahedra with 8, 9, and 10 vertices providing a 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.

3. RESULTS AND DISCUSSION 3.1. Seven-Vertex C3B3H6Re(CO)3 Structures. Four 7vertex C3B3H6Re(CO)3 structures were found within 35 kcal/ mol of the lowest energy structure B3C3Re-1 (Figure 4). All four structures have a central C3B3Re pentagonal bipyramid corresponding to the seven-vertex closo deltahedron (Figure 2). In all four structures, the carbon atoms are located at degree 4 equatorial vertices, and the rhenium atom is located at a degree 5 axial vertex. The two lowest energy structures B3C3Re-1 and B3C3Re-2, lying 7.6 kcal/mol in energy above B3C3Re-1, have the three carbon atoms located in 1,2,4-positions in the equatorial pentagon so that there is only one C−C edge.

2. THEORETICAL METHODS The rhenatricarbaborane structures investigated in this study are derived from the borane dianions BnH2− n by substituting a BH vertex with an Re(CO)3 unit followed by the replacement 48 polyhedral frameworks ranging from 7−12 vertices and were generated in this way, leading to 4339 initial structures of the type C3Bn−4Hn−1Re(CO)3 (n = 7−12) (see Supporting Information). Geometry optimizations of these initial structures were carried out using the B3LYP DFT functional coupled with the SDD (Stuttgart Dresden ECP plus DZ) basis set for rhenium and the double-ζ 631G(d) basis set for the lighter atoms as implemented in the Gaussian09 suite of programs.44 All optimized structures were characterized by harmonic vibrational frequencies. Saddle point structures with imaginary vibrational frequencies were reoptimized by following the normal modes to obtain genuine minima. The energetically most stable isomers were further optimized by employing the PBE0 DFT functional and the def2-TZVP//SDD basis sets. To further refine the energies, coupled cluster single point energy calculations were performed on the lowest energy isomers using the DLPNO−CCSD(T) coupled cluster method45−58 and the def2QZVP//SDD basis sets as implemented in the ORCA 3.03 software package.59−67 The final energies were then corrected for zero-point energies obtained from the PBE0/(def2-TZVP//SDD) calculations. All of the resulting structures were found to have substantial HOMO− LUMO gaps ranging from 8.5 to 11.6 eV (see the Supporting Information). The shorthand notation B(n−4)C3Re-x was assigned to all structures discussed in this work, where n is the total number of polyhedral vertices and x is the energy ranking of the structure on the potential energy surface. Additional information on higher energy structures and connectivities can be viewed in the Supporting Information.

possibility for the 8-vertex system is the capped pentagonal bipyramid, which provides a degree 6 vertex for the metal atom. However, the capped pentagonal bipyramid has a degree 3 capping vertex. A hexagonal bipyramid has two degree 6 vertices and avoids the apparently unfavorable degree 3 vertex. The isocloso metallaboranes with 2n rather than 2n + 2 skeletal electrons appear to have a different skeletal bonding 15017


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Inorganic Chemistry

Figure 4. Four optimized 7-vertex C3B3H6Re(CO)3 structures within 35 kcal/mol of the lowest energy structure.

Figure 5. Four optimized 8-vertex C3B4H7Re(CO)3 structures within 23 kcal/mol of the lowest energy structure.

Structures B3C3Re-1 and B3C3Re-2 differ in the orientation of the Re(CO)3 unit relative to the equatorial pentagon. The next two structures B3C3Re-3 and B3C3Re-4 are considerably higher energy structures, lying 19.7 and 21.3 kcal/mol in energy above B3C3Re-1. Structures B3C3Re-3 and B3C3Re-4 have the carbon atoms located in 1,2,3-positions at degree 4 equatorial pentagon vertices so that there are two C−C edges. The significantly higher energies of B3C3Re-3 and B3C3Re-4 with two C−C edges relative to B3C3Re-1 and B3C3Re-2 with only one C−C edge indicate how C−C edges are energetically disfavored in metallacarborane structures. Again, structures B3C3Re-1 and B3C3Re-2 differ in the orientation of the Re(CO)3 unit relative to the equatorial pentagon. The experimental structure of the manganese carbonyl derivative MeC3B3H5Mn(CO)3 is suggested by NMR to have a C−C−C chain in the equatorial pentagon similar to the higher energy structures B3C3Re-3 and B3C3Re-4.7,8 The formation of these high energy structures reflects the structure of the tricarbaborane anion [MeC3B3H6]− starting material used for their synthesis. 3.2. Eight-Vertex C3B4H7Re(CO)3 Structures. The eightvertex closo deltahedron, namely the bisdisphenoid (Figure 2), has four degree 4 vertices available for the three carbon atoms in a metallatricarbaborane structure. However, these degree 4 vertices in the bisdisphenoid form two C2 edges so that it is not possible to avoid a C−C edge in placing three carbon atoms at degree 4 vertices in a bisdisphenoidal framework. As a result, the lowest energy C3B4H7Re(CO)3 structure B4C3Re-1 has a central C3B4Re hexagonal bipyramid rather than a bisdisphenoid with the rhenium atom at one of the degree 6 axial vertices and the carbon atoms at alternating positions in the hexagonal belt, thereby avoiding any C−C edges (Figure 5 and Table 1). The predicted interaxial Re···B distance of 2.901 Å is too long to be considered a direct bonding interaction. In this way, B4C3Re-1 differs from the flattened oblatocloso Cp2Re2B6H6 derivatives in which the interaxial ReRe

Table 1. Four Optimized 8-Vertex C3B4H7Re(CO)3 Structures within 23 kcal/mol of the Lowest Energy Structure vertex degrees structure (symmetry) B4C3Re-1 B4C3Re-2 B4C3Re-3 B4C3Re-4

(C2v) (C1) (Cs) (C1)

ΔE

Re

C

0.0 17.2 17.5 19.1

6 5 5 5

4,4,4 4,4,4 4,4,4 4,4,4

edges Re−C C−C 3 2 3 2

0 1 1 1

comments hex bipyramid bisdisphenoid bisdisphenoid bisdisphenoid

distances of ∼2.7 Å are short enough for a formal double bond through the center of the hexagonal bipyramid. However, the Wadean skeletal electron count of 12 (= 2n − 4 for n = 8) for Cp2Re2B6H6 is significantly different from that of 18 (= 2n + 2 for n = 8) in C3B4H7Re(CO)3, so it is not surprising that the internal bonding within the hexagonal bipyramid is different in these two structures. The hexagonal bipyramidal C3B4H7Re(CO)3 structure B4C3Re-1 is obviously favorable structure because it lies more than ∼17 kcal/mol in energy below the next lowest energy structures (Figure 5 and Table 1). The next three C3B4H7Re(CO)3 structures in terms of relative energy are three closely energetically spaced bisdisphenoidal structures B4C3Re-2, B4C3Re-3, and B4C3Re-4 at ∼18 kcal/mol above B4C3Re-1 (Figure 4 and Table 1). Each of these structures has a central C3B4Re bisdisphenoid with all three carbon atoms at degree 4 vertices necessarily leading to one C−C edge. Structures B4C3Re-2 and B4C3Re-4 have two Re−C edges, whereas B4C3Re-3 has three Re−C edges. This structural difference does not appear to have a significant effect on the relative energies. 3.3. Nine-Vertex C3B 5H 8Re(CO) 3 Structures. The 9-vertex closo deltahedron, namely the tricapped trigonal prism (Figure 2), has three isolated degree 4 vertices as caps 15018


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Inorganic Chemistry

Figure 6. Three optimized 9-vertex C3B5H8Re(CO)3 structures within 25 kcal/mol of the lowest energy structure.

However, the underlying ReB5 trigonal prism in B5C3Re-1 is distorted significantly with five B−B edges having lengths ranging from 1.78 to 1.86 Å but a sixth elongated B−B edge of length 2.379 Å. This elongated B−B edge is located in the ReB2 triangular face of the underlying ReB5 trigonal prism. The next higher energy C3B5H8Re(CO)3 structure B5C3Re2, lying 14.2 kcal/mol in energy above B5C3Re-1, has a central C3B5Re isocloso deltahedron (Figure 3) with the rhenium atom located at the unique degree 6 vertex (Figure 6 and Table 2). This necessarily introduces one C−C edge. Structure B5C3Re3, lying 18.3 kcal/mol in energy above B5C3Re-1, is also derived from a central C3B5Re isocloso deltahedron with one of the three carbon atoms at a degree 5 vertex and the other two carbon atoms at degree 4 vertices. However, the Re···C distance to the original degree 5 carbon vertex of this isocloso deltahedron is lengthened to a nonbonding 2.940 Å thereby creating a quadrilateral face and reducing the degree of the originally degree 5 carbon vertex to 4 and that of the rhenium atom from 6 to 5. If structure B5C3Re-3 is considered as an isonido structure, then it has the expected 2n + 2 skeletal electrons (= 20 for n = 9). 3.4. Ten-Vertex C3B6H9Re(CO)3 Structures. The potential energy surface for the 10-vertex C3B6H9Re(CO)3 system is

for the rectangular edges of the underlying trigonal prism. Thus, a central C3B5Re tricapped trigonal prism is well-situated to accommodate the three carbon atoms at degree 4 vertices without any C−C edges. It is therefore not surprising that the lowest energy C3B5H8Re(CO)3 structure B5C3Re-1 by more than ∼14 kcal/mol is the unique tricapped trigonal prismatic structure with degree 4 carbon vertices (Figure 6 and Table 2). Table 2. Three Optimized 9-Vertex C3B5H8Re(CO)3 Structures within 25 kcal/mol of the Lowest Energy Structure vertex degrees

edges

structure (symmetry)

ΔE

Re

C

B5C3Re-1 (Cs)

0.0

5

4,4,4

2

0

B5C3Re-2 (C1) B5C3Re-3 (C1)

14.2 18.3

6 6

4,4,4 4,4,5b

3 3

1 1

Re−C C−C

comments tricap trig prisma 9-vertex isocloso 9-vertex isonido

a B5C3Re-1 has a relatively long 2.379 Å B−B edge opposite the rhenium vertex. bThe Re−C edge to the originally degree 5 carbon vertex in the isocloso deltahedron of B5C3Re-3 is lengthened to a nonbonding 2.940 Å.

Figure 7. Seven optimized 10-vertex C3B6H9Re(CO)3 structures within 12 kcal/mol of the lowest energy structure. 15019


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lying 5.4 kcal/mol in energy above B6C3Re-1, is the only possible isocloso deltahedral C3B6H9Re(CO)3 structure with the rhenium atom located at the unique degree 6 vertex and the three carbon atoms located at the three degree 4 vertices. The lowest energy C3B6H9Re(CO)3 structure based on the closo 10-vertex deltahedron, namely the bicapped tetragonal antiprism (Figure 2), is B6C3Re-3, lying 5.1 kcal/mol in energy above B6C3Re-1 (Figure 7 and Table 3). Only one of the three carbon atoms in B6C3Re-3 is located at a degree 4 vertex. The arrangement of two of the three carbon atoms at degree 5 vertices on the central C3B6Re bicapped tetragonal antiprism avoids an unfavorable C−C edge. The slightly higher energy bicapped tetragonal antiprism C3B6H9Re(CO)3 structure B6C3Re-5, at 6.7 kcal/mol in energy above B6C3Re-1, has two of the three carbon atoms located antipodally at the two degree 4 vertices. However, in B6C3Re-5, the third carbon atom at one of the degree 5 vertices necessarily forms a C−C edge with one of the degree 4 vertex carbon atoms. Structure B6C3Re-5 has two Re−C edges. The bicapped tetragonal antiprism C3B6H9Re(CO)3 structure B6C3Re-6, lying 7.9 kcal/ mol in energy above B6C3Re-1, is similar to B6C3Re-5 except the degree 5 carbon vertex in B6C3Re-6 is located to form only one Re−C edge. Structure B6C3Re-7, lying 9.0 kcal/mol in energy above B6C3Re-1, is closely related to B6C3Re-5 likewise with one C−C edge and one Re−C edge and two of the three carbon atoms at degree 4 vertices. However, in B6C3Re-6 the degree 5 carbon vertex lies on the symmetry plane of a Cs, structure whereas B6C3Re-7 has no symmetry. The 10-vertex C3B6H9Re(CO)3 system differs significantly from the previously studied related CpFeC3B6H9 system.42 Thus, for the C3B6H9Re(CO)3 system, the two lowest energy structures have degree 6 vertices for the rhenium atom, whereas the lowest energy CpFeC3B6H9 structure, which is found experimentally in CpFe(C3B6H8Ph) and (η2,2-1,5-C8H12)Ir(C3B6H8Ph),20,21 is a bicapped tetragonal antiprism corresponding to B6C3Re-5 (Figure 6). The lowest energy bicapped tetragonal antiprism C3B6H9Re(CO)3 structure B6C3Re-3 lies 5.1 kcal/mol in energy above the lowest energy structure

more complicated than those of the 8- and 9-vertex systems because seven structures lie within 12 kcal/mol of the lowest energy structure B6C3Re-1 (Figure 7 and Table 3). Three of Table 3. Seven Optimized 10-Vertex C3B6H9Re(CO)3 Structures within 12 kcal/mol of the Lowest Energy Structure vertex degrees

edges


ΔE

Re

C

B6C3Re-1 (C1)

0.0

6

4,4,4

2

0

B6C3Re-2 B6C3Re-3 B6C3Re-4 B6C3Re-5 B6C3Re-6 B6C3Re-7

3.9 5.1 5.4 6.7 7.9 9.0

6 5 6 5 5 5

4,4,4 4,5,5 4,4,4 4,4,5 4,4,5 4,4,5

2 2 3 2 1 1

0 0 0 1 1 1

(C1) (Cs) (Cs) (C1) (Cs) (C1)

Re−C C−C

comments two degree 6 vertices isonido (1 f4) bicap tetrag antipr 10-vertex isocloso bicap tetrag antipr bicap tetrag antipr bicap tetrag antipr

the four lowest energy C3B6H9Re(CO)3 structures have the rhenium atom at a degree 6 vertex, and all three carbon atoms at degree 4 vertices with no C−C edges. This is not possible for the closo 10-vertex deltahedron, namely the bicapped tetragonal antiprism (Figure 1), which has only two degree 4 vertices and no degree 6 vertices. The lowest energy C3B6H9Re(CO)3 structure B6C3Re-1 is derived from a 10-vertex deltahedron having two degree 6 vertices with the rhenium atom at one of the degree 6 vertices and a boron atom at a degree 6 vertex not connected to the rhenium atom (Figure 7 and Table 3). However, an edge from the original degree 6 boron vertex to a degree 5 boron vertex adjacent to the rhenium atom is lengthened to a nonbonding 2.563 Å, thereby generating a tetragonal face. Structure B6C3Re-2, lying 3.9 kcal/mol in energy above B6C3Re-1 is closely related to B6C3Re-1 but with a different placement of the carbon atoms at the degree 4 vertices. Structure B6C3Re-4,

Figure 8. Five optimized 11-vertex C3B7H10Re(CO)3 structures within 20 kcal/mol of the lowest energy structure. 15020


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Inorganic Chemistry

1 (Figure 8 and Table 4). This reflects the structure of the [C3B7H9R]− anion obtained from C2B7H13 and RCN used for its synthesis (Figure 1). Thus, these 11-vertex metallatricarbaboranes correspond to kinetically stable isomers, reflecting their method of synthesis and thus having a high energy barrier for conversion to the lower energy thermodynamic favored isomers. An indication of this is the experimentally observed pyrolysis at 250 °C of the brown-red Fe(C3B7H9Me)2 isomer, in which both FeC3B7 units have structures similar to B7C3Re-4 to give a green Fe(C3B7H9Me)2 isomer in which both FeC3B7 units have structures similar to B7C3Re-1.10,11 An earlier theoretical study on the cobaltdicarbaboranes 68 CpCoC2Bn−3Hn−1, for which much more extensive experimental data are available from Hawthorne and coworkers,69 shows that many of the kinetically stable products are actually high energy species relative to the thermodynamically favored isomers. The [M](C3B7H9R) compounds synthesized by Sneddon and coworkers19 include PhC3B7H9Re(CO)3, which is shown by X-ray crystallography to be a phenyl derivative of B7C3Re-4 with the phenyl group attached to the degree 4 carbon vertex sharing an edge with the unique degree 5 carbon vertex.19 The predicted Re−C distances in B7C3Re-4 of 2.152 and 2.221 Å to the degree 4 carbon vertices and of 2.572 Å to the degree 5 carbon vertex agree well with the corresponding experimental values of 2.169, 2.202, and 2.546 Å in PhC3B7H9Re(CO)3. Similarly, the predicted Re−B distances in B7C3Re-4 of 2.415, 2.461, and 2.582 Å agree well with the corresponding experimental values of 2.432, 2.450, and 2.543 Å PhC3B7H9Re(CO)3 with the longest Re−B distance being to the boron atom connected directly to two carbon atoms. The predicted C−C edge length of 1.499 Å in B7C3Re-4 is close to the experimental value of 1.517 Å in PhC3B7H9Re(CO)3. 3.6. Twelve-Vertex C3B8H11Re(CO)3 Structures. The six lowest energy 12-vertex C3B8H11Re(CO)3 structures are all based on the regular icosahedron with exclusively degree 5 vertices (Figure 9 and Table 5). The lowest energy of these structures B8C3Re-1 as well as the two next higher energy structures B8C3Re-2 and B8C3Re-3, lying ∼5 kcal/mol in energy above B8C3Re-1, have arrangements of carbon atoms that avoid any C−C edges. The next C3B8H11Re(CO)3 structure in terms of energy, namely B8C3Re-4 lying 10.5 kcal/mol in energy above B8C3Re-1, has all three carbon vertices adjacent to the rhenium vertex but necessarily has the undesirable feature of a C−C edge. The three C3B8H11Re(CO)3 structures B8C3Re-5, B8C3Re-6, and B8C3Re-8, lying 14.9, 15.9, and 16.8 kcal/mol in energy, respectively, above B8C3Re-1 have one C−C edge and only two Re−C edges. Most of the experimentally known 12-vertex [M]C3B8H11 structures are obtained by reaction of a suitable metal derivative with an 11-vertex tricarbaundecaboranide ion C3B8H−11 with a nido-⟨5⟩ structure having all three carbon atoms on the pentagonal open face.22,23 Because of this synthetic method, the resulting metallatricarbadodecaboranes [M]C3B8H11 do not have structures corresponding to any of the eight lowest energy isomers. Instead their structures correspond to the higher energy C3B8H11Re(CO)3 isomer B8C3Re-13, lying 28.5 kcal/ mol above the lowest energy isomer B8C3Re-1 (Figure 9 and Table 5). The high energy of B8C3Re-13 relates to the presence of two C−C edges in the underlying ReC3B8 icosahedron. These 12-vertex metallatricarbaboranes of the type [M]C3B8H11 having an MC3B8 framework similar to B8C3Re-13 appear to be examples of kinetically favored

B6C3Re-3. These differences appear to relate to the greater preference of the third row transition-metal rhenium for degree 6 rather than degree 5 vertices relative to the first row transition-metal iron. 3.5. Eleven-Vertex C3B7H10Re(CO)3 Structures. The 11vertex closo deltahedron (Figure 2) necessarily has a degree 6 vertex and thus can function also as an 11-vertex isocloso deltahedron. The central C3B7Re units in all five C3B7H10Re(CO)3 structures lying within 20 kcal/mol of the lowest energy structure B7C3Re-1 all have this deltahedron with the rhenium atom at the unique degree 6 vertex (Figure 8 and Table 4). The Table 4. Five Optimized 11-Vertex C3B7H10Re(CO)3 Structures within 20 kcal/mol of the Lowest Energy Structure vertex degrees

edges


ΔE

Re

C

Re−C

C−C

B7C3Re-1 (C1)

0.0

6

4,4,5

2

0

B7C3Re-2 (Cs)

8.5

6

4,5,5

3

0

B7C3Re-3 (C1)

10.2

6

4,5,5

2

0

B7C3Re-4 (C1)

10.9

6

4,4,5

3

1

B7C3Re-5 (Cs)

12.7

6

4,4,5

2

1

comments 11v closo/ isocloso 11v closo/ isocloso 11v closo/ isocloso 11v closo/ isocloso 11v closo/ isocloso

lowest energy C3B7H10Re(CO)3 structure B7C3Re-1 is the unique structure with carbon atoms located at the two degree 4 vertices and the third carbon atom located at a degree 5 vertex not adjacent to either degree 4 vertex. The structure B7C3Re-1 appears to be a reasonably favorable structure because the next lowest energy C3B7H10Re(CO)3 structure B7C3Re-2 lies 8.5 kcal/mol in energy above B7C3Re1 (Figure 8 and Table 4). Structure B7C3Re-2 as well as the slightly higher energy isomer B7C3Re-3, lying 10.2 kcal/mol above B7C3Re-1, have one of the three carbon atoms located at a degree 4 vertex and the other two carbon atoms located at degree 5 vertices not adjacent to each other nor to the degree 4 vertex carbon atom. The three carbon atoms in B7C3Re-2 are located in alternating positions in the hexagonal boat surrounding the rhenium atom so that there are three Re−C edges but no C−C edges. In B7C3Re-3, only two of the three carbon atoms are located on the hexagonal boat so that there are only two Re−C edges. The next two C3B7H10Re(CO)3 structures in terms of energy, namely B7C3Re-4 and B7C3Re-5, lying 10.9 and 12.7 kcal/mol in energy above B7C3Re-1, have two of the three carbon atoms located at the degree 4 vertices (Figure 8 and Table 4). However, the third carbon vertex has the undesirable feature of being adjacent to one of the degree 4 carbon vertices. In the lower energy of these two structures, namely B7C3Re-4, all three carbon atoms are located on the hexagonal boat surrounding the rhenium atom so that there are three Re−C edges, similar in this respect to B7C3Re-2. However, in B7C3Re-5, the degree 5 carbon atom is not adjacent to the rhenium atom so there are only two Re−C edges. Most of the [M](C3B7H9R) compounds synthesized by Sneddon and coworkers have a central MC3B7 polyhedron corresponding to the C3B7H10Re(CO)3 structure B7C3Re-4, lying ∼11 kcal/mol above the lowest energy structure B7C3Re15021


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Figure 9. Eight optimized 12-vertex C3B8H11Re(CO)3 structures within 18 kcal/mol of the lowest energy structure as well as a higher energy C3B8H11Re(CO)3 related to experimentally known [M]C3B8H11structures of other metals.

a still higher temperature of 165 °C (boiling mesitylene), further rearrangement of CpFeC3B8H11 occurs to give a third isomer having a central FeC3B8 icosahedron corresponding to the lowest energy C3B8H11Re(CO)3 isomer B8C3Re-1. The lowest energy nonicosahedral C3B8H11Re(CO)3 structure B8C3Re-7 lies 16.5 kcal/mol in energy above the lowest energy isomer B8C3Re-1 (Figure 9 and Table 5). This indicates that C3B8H11Re(CO)3 structures based on the regular icosahedron with exclusively degree 5 vertices are highly preferred despite the lack of any degree 4 vertices for the carbon atoms. This is in accord with the general preference of boron clusters for regular icosahedral structures.70−73 The deltahedron found in the nonicosahedral structure B8C3Re-7 has Cs symmetry with three mutually nonadjacent degree 4 vertices occupied by the three carbon atoms without any C−C edges. These three degree 4 vertices are balanced by three degree 6 vertices, one of which is occupied by the rhenium atom.

Table 5. Eight Optimized 12-Vertex C3B8H11Re(CO)3 Structures within 18 kcal/mol of the Lowest Energy Structure and the Higher Energy B8C3Re-13 Structure (Figure 8) vertex degrees structure (symmetry)

ΔE

Re

C

B8C3Re-1 (Cs) B8C3Re-2 (Cs) B8C3Re-3 (Cs) B8C3Re-4 (Cs) B8C3Re-5 (C1) B8C3Re-6 (C1) B8C3Re-7 (Cs) B8C3Re-8 (C1) B8C3Re-13 (Cs)

0.0 4.7 5.0 10.5 14.9 15.9 16.5 16.8 28.5

5 5 5 5 5 5 6 5 5

5,5,5 5,5,5 5,5,5 5,5,5 5,5,5 5,5,5 4,4,4 5,5,5 5,5,5

edges Re−C C−C 2 1 2 3 2 2 2 2 3

0 0 0 1 1 1 0 1 2

comments icosahedron icosahedron icosahedron icosahedron icosahedron icosahedron 3v6 deltahedron icosahedron icosahedron

metallaboranes with a high energy barrier for conversion to lower energy isomers. Pyrolysis of CpFeC3B8H11 with a structure similar to B8C3Re-13 at 110 °C (boiling toluene) gives an CpFeC3B8H11 with a structure similar to B8C3Re-4. At

4. CONCLUSION These studies on the rhenatricarbaboranes C3Bn−4Hn−1Re(CO)3 (n = 7−12) show that the preferred polyhedra for n− 15022


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vertex metallaboranes having 2n + 2 skeletal electrons and sufficiently dissimilar vertex atoms can deviate from the most spherical closo deltahedra (Figure 1) predicted by application of the Wade−Mingos rules.25−27 These rhenatricarbaboranes thus avoid structures with C−C edges and prefer structures with carbon atoms located at degree 4 rather than degree 5 vertices. These considerations can lead to lowest energy rhenatricarborane structures different from the closo deltahedra despite their 2n + 2 Wadean skeletal electrons. Thus, for the 8-vertex C 3 B4 H 7 Re(CO)3 , the lowest energy structure B4C3Re-1 has a central hexagonal bipyramid rather than the 8-vertex closo deltahedron, namely the bisdisphenoid. All three carbon atoms can be placed at nonadjacent degree 4 vertices in the hexagonal bipyramid but not in the bisdisphenoid. Similarly, the lowest energy 10-vertex C3B6H9Re(CO)3 structures are derived from isocloso deltahedra having three degree 4 vertices for the three carbon atoms rather than from the most spherical 10-vertex closo deltahedron, namely the bicapped square antiprism, with only two degree 4 vertices for the three carbon atoms. For the 9-vertex C3B5H8Re(CO)3 system, the most spherical closo deltahedron, namely the tricapped trigonal prism, has three mutually nonadjacent degree 4 vertices for the three carbon atoms and thus is the preferred deltahedron as found in B5C3Re-1. The preferred deltahedron for the 11-vertex C3B7H10Re(CO)3 remains the most spherical closo deltahedron despite having only two degree 4 vertices for the carbon atoms. Furthermore, the six lowest energy 12-vertex C3B8H11Re(CO)3 structures are all based on the regular icosahedron generally favored in polyhedral borane chemistry despite its complete lack of degree 4 vertices for the carbon atoms. This differs from the 12-vertex dicarbalanes C2Al10Me12, also with 2n + 2 Wadean skeletal electrons, which were recently shown by density functional theory to insist on degree 4 vertices for both carbon atoms, thereby avoiding low-energy structures based on the icosahedron.74 In general, the preferred deltahedra for the rhenatricarbaboranes, when not the most spherical closo deltahedra, can be derived from the most spherical deltahedra by series of diamond−square−diamond transformations.75 In addition, the chemical bonding models for closo deltahedral borane structures with 2n + 2 skeletal electrons based on graph theory76 or tensor surface harmonics77 do not consider the detailed topology of the deltahedron but only its approximation by a sphere. Therefore, some distortion of the most spherical closo deltahedra in metallaboranes with diverse types of vertex atoms through successive diamond−square−diamond transformations can be tolerated before these chemical bonding models become no longer valid.

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Article

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

R. Bruce King: 0000-0001-9177-5220 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Funding from the Romanian Ministry of Education and Research (Grant PN-II-RU-TE-2014-4-1197) is gratefully acknowledged. Computational resources were provided by the high-performance computational facility of the Babeş-Bolyai University (MADECIP, POSCCE, COD SMIS 48801/1862) cofinanced by the European Regional Development Fund.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02348. Initial C3B3H6Re(CO)3 structures, distance tables, energy rankings, CO vibrational frequencies for the lowest energy structures, and orbital energies and HOMO−LUMO gaps (PDF) Cartesian coordinates of the optimized structures (XYZ) 15023


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Inorganic Chemistry

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