Paramagnetism in Metallacarboranes: The Polyhedral

Article pubs.acs.org/IC

Paramagnetism in Metallacarboranes: The Polyhedral Chromadicarbaborane Systems Szabolcs Jákó,† Alexandru Lupan,*,‡ Attila-Zsolt Kun,*,† and R. Bruce King*,§ †

Department of Chemistry and Chemical Engineering, Hungarian Line of Study, Faculty of Chemistry and Chemical Engineering, Babeş-Bolyai University, Cluj-Napoca, Romania ‡ Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babeş-Bolyai University, Cluj-Napoca, Romania § Department of Chemistry and Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia, United States S Supporting Information *

ABSTRACT: The chromadicarbaboranes CpCrC2Bn−3Hn−1 (8 ≤ n ≤ 12) are of interest in providing stable paramagnetic deltahedral metallaboranes among which the 12-vertex CpCrC2B9H11 has been synthesized by Hawthorne and co-workers. Density functional theory shows that the lowest-energy such structures are quartet spin-state Cr(III) structures in which the central CrC2Bn−3 units exhibit most spherical closo deltahedral geometries similar to those found in the borane dianions BnHn2−. Higher-energy doublet CpCrC2Bn‑3Hn−1 (8 ≤ n ≤ 11) structures are found exhibiting central CrC2Bn−3 isocloso deltahedral geometries, thereby providing a degree 6 vertex for the chromium atom. The lowest-energy CpCrC2Bn‑3Hn−1 (8 ≤ n ≤ 11) structures all have both carbon atoms at degree 4 vertices. However, the lowest-energy CpCrC2B9H11 structures all have central CrC2B9 icosahedra and thus lack degree 4 vertices for the carbon atoms. For all of the CpCrC2Bn−3Hn−1 (8 ≤ n ≤ 12) systems the lowest-energy isomers are those with the maximum number of Cr−C edges in contrast to the related CpCoC2Bn−3Hn−1 systems.

1. INTRODUCTION The initial metalladicarbaboranes synthesized by Hawthorne and co-workers1 were formally cobalt(III) derivatives of the types CpCoC2Bn−3Hn−1 (Cp = η5-C5H5), [Co(C2BnHn+2)2]−, and their substitution products with Cp− and C2Bn−3Hn−12− as ligands. Thus, according to the Wade−Mingos skeletal electron counting rules2−4 a CpCo vertex with the favored 18-electron configuration for the cobalt atom is a donor of two skeletal electrons similar to a BH vertex, so that the CpCoC2Bn−3Hn−1 and [Co(C2Bn−3Hn−1)2]− systems have the favored 2n + 2 skeletal electrons. The favored CoC2Bn−3 polyhedra for such systems are the most spherical closo deltahedra in accord with the Wade−Mingos rules (Figure 1). An approach to paramagnetic metalladicarbaboranes is to replace the cobalt atom in the CpCo vertex with a metal to the left of cobalt in the periodic table having fewer valence electrons. Chromium is of particular interest in this connection because of the stability of the favored +3 chromium oxidation state. In this connection a CpCr vertex having the favored 18electron configuration would be a donor of −1 skeletal electron (i.e., an acceptor of one skeletal electron) making it difficult to approach the 2n + 2 skeletal electrons for closo deltahedral structures. However, chromium(III) complexes are normally quartet ground states with three unpaired electrons. In such a case a CpCr vertex has a 15-electron configuration, thereby making a CpCr vertex in a quartet spin-state chromaborane structure a donor of two skeletal electrons similar to a CpCo vertex in a singlet cobaltaborane structure. Thus, quartet © 2017 American Chemical Society

Figure 1. Most spherical deltahedra having from 8 to 12 vertices.

CpCrC2Bn−3Hn−1 structures become 2n + 2 skeletal electron systems. They would be expected to exhibit the same central closo MC 2 B n−3 deltahedra as singlet CpCoC 2 B n−3 H n−1 structures, which have been the subject of a comprehensive Received: June 4, 2017 Published: September 6, 2017 11059

DOI: 10.1021/acs.inorgchem.7b01422 Inorg. Chem. 2017, 56, 11059−11065

Article

Inorganic Chemistry theoretical study5 in addition to many known experimental examples.1 This behavior of a CpCr vertex in a quartet spinstate structure was first recognized by Grimes and co-workers in a study of CpCrC4B8H8Et4 and related complexes.6 Comparison between the skeletal electron bookkeeping in metallaboranes containing CpCo and CpCr vertices is summarized in Table 1. The cobalt atom in a CpCo vertex in Table 1. Comparison of the Skeletal Electron Bookkeeping in Metallaboranes Containing CpCo and CpCr Vertices metal orbitals spin state metal valence electrons Cp→Cp− uses one metal electron for σ + 2π metal-ring bonding nonbonding orbitals can hold three lone pairs CpM skeletal electrons electron pairing in the three nonbonding orbitals holes in the three nonbonding orbitals metal electron configuration = 18 − number of holes

CpCr vertex

CpCo vertex

Figure 2. Isocloso deltahedra with a degree 6 vertex for a metal atom differing from the closo deltahedra with the same number of vertices.

CpCr vertex

3

singlet 9 −1

quartet 6 −1

doublet 6 −1

3

−6 (filled)

3

2 ↑↓ ↑↓ ↑↓

−3 (halffilled) 2 ↑↑↑

−5 (one hole) 0 ↑↓ ↑↓ ↑

0

3

1

18

15

17

deltahedra in doublet CpCrC2Bn‑3Hn‑1 structures are expected to be similar to those in singlet CpMnC2Bn−3Hn−1 structures, which have been the subjects of a comprehensive theoretical study.15 Thus, the CpCrC2Bn−3Hn−1 systems have the novel feature of the spin state (quartet or doublet) determining the skeletal electron count and thus the preferred central CrC2Bn−3 polyhedron. Experimental work on chromadicarbaboranes and related species is somewhat limited. Ruhle and Hawthorne16 report the reaction of CrCl3 with NaCp + Na2C2B9H11 to give dark red CpCrC2B9H11, but the structure of this species apparently has not been determined. Bis(dicarbaborane)chromium anions with the chromium atom common to two identical dicarbaborane deltahedra have been more extensively studied with structural information available for the 7-vertex [Cr{(Me3Si)2C 2B4H4} 2]− and 12-vertex [Cr(Me2C 2B9H9) 2]− systems from X-ray crystallography (Figure 3).17,18

singlet cobaltaborane structures has nine valence electrons and nine orbitals in its sp3d5 valence manifold. Reduction of the neutral Cp ligand to the Cp− anion uses one of the nine cobalt valence electrons as well as three of the nine cobalt orbitals for the σ + 2π Cp-Co bonding. The cobalt vertex then provides three of its remaining six orbitals for the skeletal bonding. This leaves three formally nonbonding cobalt orbitals. Filling these three orbitals with lone pairs uses six of the remaining eight cobalt valence electrons after reducing Cp to Cp−. The resulting filled nine-orbital sp3d5 manifold corresponds to an 18-electron cobalt configuration. The remaining two cobalt valence electrons then become available as skeletal electrons. Now consider chromaboranes exhibiting a quartet spin state. Such a quartet spin state corresponds to single electrons rather than electron pairs in each of the three chromium nonbonding orbitals, so that these three orbitals are half-filled with parallel spins (Table 1). This leaves three holes in the 18-electron chromium sp3d5 manifold corresponding to a 15-electron chromium configuration. Otherwise the electron bookkeeping in singlet cobaltaboranes and quartet chromaboranes is completely analogous. There is also the possibility of doublet spin-state CpCrC2Bn−3Hn−1 structures. Such structures have five electrons and thus one hole in the set of three formally nonbonding chromium orbitals corresponding to the doublet spin state (Table 1). The presence of this hole in the otherwise closed shell corresponds to a 17-electron configuration for the chromium atom in the CpCr vertex and makes the CpCr vertex a formal donor of zero skeletal electrons. Thus, doublet CpCrC2Bn−3Hn−1 structures are 2n skeletal electron systems and would be expected to exhibit deltahedral geometries with a degree 6 vertex for the metal atom (Figure 2).7−10 Such deltahedra are called isocloso11 or hypercloso12−14 deltahedra; we will use the term isocloso here to be consistent with our previous papers. The isocloso geometries of the central MC2Bn−3Hn−1

Figure 3. Structures of the experimentally known and structurally characterized bis(dicarbaborane) chromium(III) monoanions. External hydrogen atoms and alkyl groups are omitted for clarity.

We now report comprehensive density functional theory (DFT) studies on the cyclopentadienylchromium dicarbaborane systems CpCrC2Bn−3Hn−1. The generally favored quartet spin-state structures are compared with those previously found for the analogous cobalt CpCoC2Bn−3Hn−1 systems.5 In addition, the relatively few low-energy doublet structures are compared with those previously found for the analogous manganese CpMnC2Bn−3Hn−1 systems.15

2. THEORETICAL METHODS The initial CpCrC2Bn−3Hn−1 structures were constructed by systematic substitution of one boron vertex in BnHn2− with a chromium atom followed by two carbon atoms in various n-vertex polyhedra. Thus, 244 structures of the 8-vertex clusters CpCrC2B5H7, 234 structures of the 9-vertex clusters CpCrC2B6H8, 556 structures of the 10-vertex clusters CpCrC2B7H9, 1352 structures of the 11-vertex clusters CpCrC2B8H10, 11060


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Inorganic Chemistry and 578 structures of the 12-vertex Cp2M2B9H11 clusters were chosen as starting points for the optimizations (see the Supporting Information). Full geometry optimizations were performed on these CpCrC2Bn−3Hn−1 starting structures at the B3LYP/6-31G(d)19−22 level for all atoms. The lowest-energy structures were then reoptimized at a higher level, that is, PBE0/6-311G(d,p), and these are the structures presented in the manuscript.23 The nature of the stationary points after optimization were 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 ensure that genuine minima were obtained. Normally this resulted in reduction of the molecular symmetry. The low-energy CpCrC2Bn−3Hn−1 structures were found to have substantial highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gaps, typically ranging from 3.7 to 5.7 eV. All calculations were performed using the Gaussian 09 package24 with the default settings for the self-consistent field (SCF) cycles and geometry optimization, namely, the fine grid (75 302) for numerically evaluating the integrals, 1 × 10−8 hartree for the SCF convergence, maximum force of 0.000 450 hartree/bohr, root-mean-square (RMS) force of 0.000 300 hartree/bohr, maximum displacement of 0.001 800 bohr, and RMS displacement of 0.001 200 bohr. The structures, total and relative energies (PBE0/6-311G(d,p) including zero-point corrections), and relevant interatomic distances for all optimized structures are given in the Supporting Information. These structures are designated as B(n−3)C2Cr-xX, where n is the number of vertices, x is the relative order of the structure on the energy scale, and X is the spin state (Q = quartet and D = doublet). This designation scheme is similar to that used for the previous theoretical papers on the CpMC2Bn−3Hn−1 (M = Co5 and Mn15) systems. However, in the previous papers the spin states were not included in the structure designations, since only singlet structures were considered. Only the lowest energy and thus potentially chemically significant structures (Figures 4 to 8 and Tables 1 to 5) are considered in detail in this paper. However, more comprehensive lists of structures, including higher-energy structures, are provided in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. 8-Vertex CpCrC2B5H7 Structures. The three lowestenergy 8-vertex CpCrC2B5H7 structures are all quartet structures with central CrC2B5 bis-disphenoids (Figure 4 and Table 2). The lowest energy of these structures, namely, Table 2. Four 8-Vertex CpCrC2B5H7 Structures within 16 kcal/mol of the Lowest-Energy Structure vertex degrees isomer B5C2Cr-1Q B5C2Cr-2Q B5C2Cr-3Q B5C2Cr-4D

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

ΔE

Cr

C

comments

0.0 1.0 7.9 9.2

5 5 4 6

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

bis-disphenoid 2Cr−C bis-disphenoid 1Cr−C bis-disphenoid 1Cr−C cap pent bipy 2Cr−C

B5C2Cr-1Q, has the chromium atom at a degree 5 vertex and the carbon atoms at the two degree 4 vertices adjacent to the chromium vertex. The slightly higher-energy structure C2B5Cr-2Q, at only 1.0 kcal/mol above B5C2Cr-1Q, and the significantly higher-energy structure B5C2Cr-3Q, at 7.9 kcal/mol above B5C2Cr-1Q, also have the chromium atom at a degree 5 vertex and the carbon atoms at degree 4 vertices. However, in both B5C2Cr-2Q and B5C2Cr-3Q unlike B5C2Cr-1Q only one of the two carbon vertices is adjacent to the chromium vertex. The lowest-energy doublet CpCrC2B5H7 structure B5C2Cr4D, lying 9.2 kcal/mol in energy above B5C2Cr-1Q, has a central CrC2B5 capped pentagonal bipyramid with the chromium atom at the unique degree 6 vertex and both carbon atoms at degree 4 vertices, which necessarily are adjacent to the chromium vertex (Figure 4 and Table 2). 3.2. 9-Vertex CpCrC2B6H8 Structures. The lowest-energy 9-vertex CpCrC2B6H8 structure B6C2Cr-1Q is the unique tricapped trigonal prismatic structure with the chromium atom located at a degree 5 vertex and both carbon atoms located at adjacent degree 4 vertices (Figure 5 and Table 3). However, only 2.0 kcal/mol in energy above B6C2Cr-1Q lies B6C2Cr2Q, which is the other possible tricapped trigonal prismatic CpCrC2B6H8 structure with the chromium atom located at a degree 5 vertex and each carbon atom located at a degree 4 vertex. However, in B6C2Cr-2Q, unlike B6C2Cr-1Q, only one of the two carbon vertices is adjacent to the chromium vertex. A higher-energy tricapped trigonal prismatic CpCrC2 B 6 H 8 structure B6C2Cr-5Q, lying 12.3 kcal/mol in energy above B6C2Cr-1Q, is the unique structure with the chromium atom as well as each carbon atom located at degree 4 vertices. Two energetically closely spaced doublet CpCrC2B6H8 structures are found, namely, the C2 structure B6C2Cr-4D and the Cs structure B6C2Cr-6D lying 10.9 and 12.4 kcal/mol, respectively, in energy above B6C2Cr-1Q (Figure 5 and Table 3). Both have the expected isocloso 9-vertex geometry (Figure 2) with the chromium atom located at the unique degree 6 vertex and the carbon atoms located at necessarily adjacent degree 4 vertices. A quartet isocloso structure B6C2Cr-3Q is also found lying 8.9 kcal/mol in energy above B6C2Cr-1Q that is geometrically similar to B6C2Cr-4D. Comparison of the quartet CpCrC2B6H8 structures with the corresponding singlet CpCoC2B6H8 structures show that the chromium systems energetically favor direct Cr−C edges relative to the cobalt systems. Thus, the CpCoC2B6H8 structure B6C2Co-2 with two Co−C edges analogous to the

Figure 4. Four 8-vertex CpCrC2B5H7 structures within 16 kcal/mol of the lowest-energy structure. 11061


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Figure 6. Six 10-vertex CpCrC2B7H9 structures within 21 kcal/mol of the lowest-energy structure. Figure 5. Six 9-vertex CpCrC2B6H8 structures within 16 kcal/mol of the lowest-energy structure.

whereas the other carbon atom is separated by one boron vertex from the chromium atom. The next three 10-vertex CpCrC2B7H9 structures, namely, B7C2Cr-2Q, B7C2Cr-3Q, and B7C2Cr-4Q at 14.9, 18.2, and 18.6 kcal/mol, respectively, in energy above B7C2Cr-1Q, as well as B7C2Cr-6Q lying 19.5 kcal/mol above B7C2Cr-1Q, also have a central CrC2B7 bicapped square antiprism but necessarily with one of the two carbon atoms located at a degree 5 rather than a degree 4 vertex (Figure 6 and Table 4). The high energies of these four structures relative to B7C2Cr1Q having both carbon atoms located at degree 4 vertices underscores the high-energy penalty of having a carbon atom located at a degree 5 vertex rather than a degree 4 vertex. The lowest energy of the four CpCrC2B7H9 structures with one carbon atom located at a degree 5 vertex, namely, B7C2Cr-2Q, is the unique bicapped square antiprismatic 10-vertex structure with both carbon atoms adjacent to the chromium atom. A previous theoretical study of the diferradicarbaboranes Cp2Fe2C2Bn−4Hn−2, which are slightly hypoelectronic 2n skeletal electron systems, shows that isocloso structures (Figure 2) are more favored in the 10-vertex system relative to the 9vertex system.25 However, for the 10-vertex CpCrC2B7H9 system with a doublet spin state corresponding to the 2n = 20 for n = 10 isocloso skeletal electron count, the lowest-energy

CpCrC2B6H8 lowest-energy structure B6C2Cr-1 lies ∼6 kcal/ mol in energy above the lowest-energy CpCoC2B6H8 structure B6C2Co-1.5 The quartet CpCrC2B6H8 isocloso structure B6C2Cr-3Q, which, like the closo structure B6C2Cr-1Q, has two Cr−C edges, lies only ∼9 kcal/mol in energy above B6C2Cr-1Q. However, in the cobalt system the analogous singlet CpCoC2B6H8 isocloso structure B6C2Co-5 is a significantly higher-energy structure, lying ∼15 kcal/mol above B6C2Co-1.5 For the doublet CpCrC2B6H8 structures B6C2Cr-4D and B6C2Cr-6D, each with two Cr−C edges, the energy order is the same as the corresponding singlet CpMnC2B6H8 structures B6C2Mn-1 and B6C2Mn-2.15 3.3. 10-Vertex CpCrC2B7H9 Structures. The four lowestenergy 10-vertex CpCrC2B7H9 structures are all quartet spinstate structures with a central CrC2B7 bicapped square antiprism, which is the 10-vertex closo deltahedron (Figure 6 and Table 4). The lowest energy of these four structures by nearly 15 kcal/mol, namely, B7C2Cr-1, is the unique bicapped square antiprism structure with carbon atoms located at each of the two degree 4 vertices in antipodal positions relative to each other. The chromium atom is located at a degree 5 vertex, so one of the carbon atoms is adjacent to the chromium atom,

Table 3. Comparison of the Six 9-Vertex CpCrC2B6H8 Structures within 16 kcal/mol of the Lowest-Energy Structure (Figure 5) with the Corresponding Singlet CpMC2B6H8 Structuresa vertex degrees isomer B6C2Cr-1Q B6C2Cr-2Q B6C2Cr-3Q B6C2Cr-4D B6C2Cr-5Q B6C2Cr-6D

(Cs) (C1) (C1) (C2) (C2v) (Cs)

CpMC2B6H8

ΔE

Cr

C

comments

analogue

0.0 2.1 8.9 10.9 12.3 12.4

5 5 6 6 4 6

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

tricap trig prism 2Cr−C tricap trig prism 1Cr−C 9-vertex isocloso 2Cr−C 9-vertex isocloso 2Cr−C tricap trig prism no Cr−C 9-vertex isocloso 2Cr−C

B6C2Co-2 B6C2Co-1 B6C2Co-5 B6C2Mn-1 B6C2Co-3 B6C2Mn-2

a

Where M = Co and Mn for the quartet and doublet CpCrC2B6H8 structures, respectively. Structure designations are those used in the previous theoretical papers.5,15 11062


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Table 4. Comparison of the Six 10-Vertex CpCrC2B7H9 Structures within 21 kcal/mol of the Lowest-Energy Structure (Figure 6) with the Corresponding Singlet CpMC2B7H9 Structuresa vertex degrees isomer B7C2Cr-1Q B7C2Cr-2Q B7C2Cr-3Q B7C2Cr-4Q B7C2Cr-5D B7C2Cr-6Q

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

CpMC2B7H9

ΔE

Cr

C

comments

analogue

0.0 14.9 18.2 18.6 19.4 19.5

5 5 5 5 6 4

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

bicap sq antiprism 1Cr−C bicap sq antiprism 2Cr−C bicap sq antiprism 1Cr−C bicap sq antiprism 1Cr−C 10-vertex isocloso 2Cr−C bicap sq antiprism 1Cr−C

B7C2Co-1 B7C2Co-5 B7C2Co-2 B7C2Co-4 B7C2Mn-1 B7C2Co-6

a

Where M = Co and Mn for the quartet and doublet CpCrC2B7H9 structures, respectively. Structure designations are those used in the previous theoretical papers.5,15

such structure B7C2Cr-5D is a relatively high-energy structure, lying 19.4 kcal/mol above B7C2Cr-1Q (Figure 6 and Table 4). However, the 10-vertex isocloso CrC2B7 deltahedron (Figure 2) in B7C2Cr-5D has the favorable arrangement of the chromium atom at the unique degree 6 vertex and each carbon atom at a degree 4 vertex adjacent to the degree 6 chromium vertex. The relative energies of the 10-vertex quartet CpCrC2B7H9 structures are similar to those of their singlet CpCoC2B7H9 analogues,5 except the structure B7C2Cr-2Q having two Cr−C edges is the lowest energy of the four structures with one carbon located at a degree 5 vertex (Table 3). By contrast the corresponding singlet CpCoC2B7H9 structure is the fifth lowest-energy isomer.5 The previous theoretical study on CpCoC2B7H9 found a bicapped square antiprismatic structure B7C2Co-3 with no Co−C edges to be the third lowest-energy structure. The corresponding CpCrC2B7H9 structure with no Cr−C edges is the seventh lowest-energy isomer but at the relatively high energy of 21.4 kcal/mol above B7C2Cr-1Q (see Supporting Information). These observations support the greater tendency for CpCrC2Bn−3Hn−1 systems to have Cr−C edges in their low-energy structures relative to CpCoC2Bn−3Hn−1 systems. 3.4. 11-Vertex CpCrC2B8H10 Structures. The 11-vertex closo deltahedron necessarily has a degree 6 vertex and thus also serves as the 11-vertex isocloso deltahedron (Figure 1). All five CpCrC2B8H10 structures within 16 kcal/mol of the lowestenergy isomer B8C2Cr-1Q have this deltahedron for the central CrC2B8 unit (Figure 7 and Table 5). The lowest-energy CpCrC2B8H10 structure B8C2Cr-1Q is a quartet structure with the chromium atom located at the unique degree 6 vertices and carbon atoms at the two degree 4 vertices, which are both adjacent to the chromium atom. The lowest-energy doublet CpCrC2B8H10 structure B8C2Cr-2D, lying 7.4 kcal/mol in energy above B8C2Cr-1Q, has the same arrangement. This relates to the uniqueness of the arrangements of B8C2Cr-1Q and B8C2Cr-2D in providing a degree 6 vertex for the cobalt atom and adjacent degree 4 vertices for both carbon atoms. The next two CpCrC2B8H10 structures in terms of energy, namely, B8C2Cr-3Q and B8C2Cr-4Q at 10.6 and 11.3 kcal/mol, respectively, above B8C2Cr-1Q, also have both carbon atoms located at degree 4 vertices, but the chromium atom is located at a degree 5 vertex adjacent to one of the carbon vertices. Structure B8C2Cr-5Q, lying 12.4 kcal/mol in energy above B8C2Cr-1Q, is the lowest-energy CpCrC2B8H10 structure with one of the carbon atoms located at a degree 5 vertex. The energy penalty of this undesirable structural feature is partially balanced by the energetic desirability of two Cr−C edges in B8C2Cr-5Q.

Figure 7. Five 11-vertex CpCrC2B8H10 structures within 16 kcal/mol of the lowest-energy structure.

Table 5. Comparison of the Five 11-Vertex CpCrC2B8H10 Structures within 21 kcal/mol of the Lowest-Energy Structure (Figure 7) with the Corresponding Singlet CpMC2B8H10 Structuresa vertex degrees isomer B8C2Cr-1Q B8C2Cr-2D B8C2Cr-3Q B8C2Cr-4Q B8C2Cr-5Q

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

CpMC2B8H10

ΔE

Cr

C

Cr−C

analogue

0.0 7.4 10.6 11.3 12.4

6 6 5 5 6

4,4 4.4 4,4 4,4 5,4

2 2 1 1 2

B8C2Co-1 B8C2Mn-1 B8C2Co-3 B8C2Co-4 B8C2Co-10

a

Where M = Co and Mn for the quartet and doublet CpCrC2B8H10 structures, respectively. Structure designations are those used in the previous theoretical papers.5,15 Note that all five CpCrC2B8H10 structures have a central CrC2B8 11-vertex closo/isocloso deltahedron (Figure 1).

The relative energies of the 11-vertex CpCrC2B8H10 and CpCoC2C8H10 structures provide two examples of the energetic desirability of Cr−C bonds in the chromium system relative to Co−C bonds in the cobalt system (Figure 7 and Table 5). First, the cobalt analogue B8C2Co-1Q of the CpCrC2B8H10 structure B8C2Cr-5Q with two Co−C edges is 11063


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Inorganic Chemistry the 10th highest-energy CpCoC2B8H10 structure, lying ∼21 kcal/mol above the lowest-energy CpCoC2B8H10 structure B8C2Co-1.5 More strikingly, the CpCrC2B8H10 structure analogous to the second lowest-energy CpCoC2B8H10 structure B8C2Co-2 with no Co−C edges lying only ∼2 kcal/mol above B8C2Co-1, is a high-energy structure lying 18.3 kcal/mol above B8C2Cr-1Q (see Supporting Information). 3.5. 12-Vertex CpCrC2B9H11 Structures. The nine lowestenergy structures for the 12-vertex CpCrC2B9H11 system are the nine possible regular icosahedral isomers in the quartet spin state (Figure 8 and Table 6). The CpCrC2B9H11 isomers are

position of the two carbon atoms. In both cases the relative positions are designated as adjacent or ortho (o), nonadjacent nonantipodal or meta (m), and antipodal or para (p). The relative position of the two carbon atoms in the CpCrC2B9H11 isomers is the most important factor in determining their relative energies as was previously found for the cobalt analogues CpCoC2B9H11.5 Thus, for both the chromium and cobalt systems the four highest energy of the nine icosahedral isomers are those with adjacent carbon atoms (Figure 8 and Table 6). However, the CpCrC2B9H11 system differs from the CpCoC2B9H11 system in preferring energetically structures with carbon atoms adjacent to the metal atom. Thus, the lowest-energy CpCrC2B9H11 structure is the unique structure with two Cr−C edges and nonadjacent carbon atoms, namely, the oo-m structure B9C2Cr-1Q. The corresponding oom CpCoC2B9H11 structure B9C2Co-4 lies ∼3 kcal/mol in energy above the lowest-energy structure.5 Similarly the lowestenergy CpCrC2B9H11 structure with adjacent carbon atoms and two Cr−C edges, namely, the oo-o structure B9C2Cr-6Q, is the lowest energy of the four quartet icosahedral CpCrC2B9H11 structures having adjacent carbon atoms. This differs from the CpCoC2B9H11 system, where the corresponding oo-o structure with adjacent carbon atoms and two Co−C edges, namely, B9C2Co-9 is the highest energy of the nine isomeric icosahedral structures.

4. SUMMARY The lowest-energy CpCrC2Bn−3Hn−1 (8 ≤ n ≤ 11) structures are quartet spin-state structures in which the central CrC2Bn−3 polyhedron is the most spherical closo deltahedron similar to the deltahedra found in the borane dianions BnHn2−. This corresponds to the CpCrIII vertex having a 15-electron configuration and thus three unpaired electrons thereby providing two skeletal electrons. In this way the quartet CpCrC2Bn−3Hn−1 structures become 2n + 2 skeletal electron systems consistent with their closo deltahedral geometries (Figure 1). Among such structures the isomers with nonadjacent carbon atoms located at degree 4 vertices are energetically preferred. The lowest-energy isomers with degree 4 carbon vertices maximize the number of Cr−C edges in contrast to the corresponding structures of the cobalt derivatives CpCoC2Bn−3Hn−1. Higher-energy doublet CpCrC2Bn−3Hn−1 (8 ≤ n ≤ 11) structures are also found in which the CpCr vertex has a 17electron configuration and thus is a donor of zero skeletal electrons. Such structures with n vertices are 2n skeletal electron systems and thus exhibit isocloso deltahedral geometries with a degree 6 vertex for the chromium atom. All lowenergy such doublet CpCrC2Bn−3Hn−1 isocloso structures have the carbon atoms at degree 4 vertices adjacent to the chromium atom. All of the low-energy 12-vertex CpCrC2B9H11 structures are quartet spin-state structures with a central CrC2B9 icosahedron. Of the nine possible isomers of this type the four structures with adjacent carbon atoms are the highest-energy structures. The overall lowest-energy CpCrC2B9H11 structure as well as the lowest-energy structure with adjacent carbon atoms both have two Cr−C edges.

Figure 8. Nine icosahedral quartet spin-state CpCrC2B9H11 isomers. No nonicosahedral isomers or doublet spin-state 12-vertex structures were found in this energy range.

Table 6. Comparison of the Nine Icosahedral Quartet SpinState CpCrC2B9H11 Isomers with Their CpCoC2B9H11 Analogues isomer B9C2Cr-1 B9C2Cr-2 B9C2Cr-3 B9C2Cr-4 B9C2Cr-5 B9C2Cr-6 B9C2Cr-7 B9C2Cr-8 B9C2Cr-9

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

ΔE

C and Cr arrangement

cobalt analogue

ΔE

0.0 3.2 5.5 5.6 10.7 15.4 20.8 25.6 25.7

oo-m om-p om-m op-m mm-m oo-o om-o mp-o mm-o

B9C2Co-4 B9C2Co-1 B9C2Co-3 B9C2Co-5 B9C2Co-2 B9C2Co-9 B9C2Co-7 B9C2Co-8 B9C2Co-6

3.3 0.0 2.4 4.4 1.7 19.4 18.5 19.2 17.7

designated as xy-z as in the previous study on CpCoC2B9H11 derivatives,5 where x and y refer to the positions of each carbon atom relative to the chromium atom, and z refers to the relative 11064


Article

Inorganic Chemistry

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(11) Kennedy, J. D. Structure and bonding in some recently isolated metallaboranes. Inorg. Chem. 1986, 25, 111−112. (12) Baker, R. T. Hyper-closo metallaboranes. Inorg. Chem. 1986, 25, 109−111. (13) Johnston, R. L.; Mingos, D. M. P. Molecular orbital calculations relevant to the hypercloso vs. iso-closo controversy in metallaboranes. Inorg. Chem. 1986, 25, 3321−3323. (14) Johnston, R. L.; Mingos, D. M. P.; Sherwood, P. Bonding and electron counting in hyper-closo metallaboranes and metallacarbaboranes. New J. Chem. 1991, 15, 831−841. (15) Lupan, A.; King, R. B. The prevalence of isocloso deltahedra in low-energy hypoelectronic metalladicarbaboranes with a single metal vertex: manganese and rhenium derivatives. Dalton Trans 2012, 41, 7073−7081. (16) Ruhle, H. W.; Hawthorne, M. F. π-Carbollyl derivatives of chromium. metallocene analogues. Inorg. Chem. 1968, 7, 2279−2282. (17) Oki, A. R.; Zhang, H.; Maguire, J. A.; Hosmane, N. S.; Ro, H.; Hatfield, W. E.; Moscherosch, M.; Kaim, W. Chemistry of Ctrimethylsilyl-substituted heterocarboranes. 10. Syntheses, structures, and properties of anionic chromium(III) and neutral chromium(IV) sandwiched metallacarborane complexes. Organometallics 1992, 11, 4202−4213. (18) St. Clair, D.; Zalkin, Z.; Templeton, D. H. The crystal structure of cesium 3,3′-commo-bis[nonahydro-1,2-dimethyl-1,2-dicarba-3-chroma-closo-dodecaborate] hydrate, a hydrate of a chromium metallocarborane salt. Inorg. Chem. 1971, 10, 2387−2395. (19) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 1980, 58, 1200−1211. (20) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5653. (21) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 1994, 98, 11623−11627. (22) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (23) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158−6170. (24) Gaussian 09, Revision E.01; Gaussian, Inc.: Wallingford, CT, 2009. The complete reference is given in the Supporting Information. (25) Lupan, A.; King, R. B. Limited occurrence of isocloso deltahedra with 9 to 12 vertices in low-energy hypoelectronic diferradicarbaborane structures. Inorg. Chem. 2011, 50, 9571−9577.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01422. Distance and energy ranking tables, initial structures, orbital energies and HOMO/LUMO gaps, complete Gaussian09 reference (PDF) Concatenated .xyz file containing the optimized structures, which can be visualized with free software such as the Mercury program (XYZ)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (A.L.) *E-mail: [email protected]. (R.B.K.) *E-mail: [email protected]. (A.-Z.K.) ORCID

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding from the Romanian Ministry of Education and Research, (Grant No. 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 of the European Union.

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REFERENCES

(1) Callahan, K. P.; Hawthorne, M. F. Ten years of metallocarboranes. Adv. Organomet. Chem. 1976, 14, 145−186. (2) Wade, K. The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. J. Chem. Soc. D 1971, 792−793. (3) Mingos, D. M. P. A General theory for cluster and ring compounds of the main group and transition elements. Nature, Phys. Sci. 1972, 236, 99−102. (4) Mingos, D. M. P. Polyhedral skeletal electron pair approach. Acc. Chem. Res. 1984, 17, 311−319. (5) King, R. B.; Silaghi-Dumitrescu, I.; Şovago, I. Kinetic versus thermodynamic isomers of the deltahedral cobaltadicarboranes. Inorg. Chem. 2009, 48, 5088−5095. (6) Maynard, R. B.; Wang, Z.-T.; Sinn, E.; Grimes, R. N. Carbon-rich metallacarboranes. 12. Synthesis and structures of chromium(III) complexes with “nonconforming” cage geometries. Inorg. Chem. 1983, 22, 873−878. (7) Bould, J.; Kennedy, J. D.; Thornton-Pett, M. Ten-vertex metallaborane chemistry. Aspects of the iridadecaborane closo→ isonido→isocloso structural continuum. J. Chem. Soc., Dalton Trans. 1992, 563−576. (8) Kennedy, J. D.; Štibr, B. In Current Topics in the Chemistry of Boron; Kabalka, G. W., Ed.; Royal Society of Chemistry: Cambridge, England, 1994; pp 285−292. (9) Kennedy, J. D. In The Borane-Carborane-Carbocation Continuum; Casanova, J., Ed.; Wiley: New York, 1998; pp 85−116. (10) Štibr, B.; Kennedy, J. D.; Drdáková, E.; Thornton-Pett, M. Ninevertex polyhedral iridamonocarbaborane chemistry. Products of thermolysis of [(CO)(PPh3)2IrCB7H8] and emerging alternative cluster-geometry patterns. J. Chem. Soc., Dalton Trans. 1994, 229−236. 11065


Paramagnetism in Metallacarboranes: The Polyhedral

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