Triple-Decker-Sandwich versus Rice-Ball Structures for Tris(benzene

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Triple-Decker-Sandwich versus Rice-Ball Structures for Tris(benzene)dimetal Derivatives of the First-Row Transition Metals Haibo Liu,† Qian-Shu Li,*,†,‡ Yaoming Xie,§ R. Bruce King,*,†,§ and Henry F. Schaefer, III§ †

Center for Computational Quantum Chemistry, South China Normal University, Guangzhou 510631, P. R. China Institute of Chemical Physics, Beijing Institute of Technology, Beijing 100081, P. R. China § Department of Chemistry and Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602, United States ‡

bS Supporting Information ABSTRACT: Compounds of the type M2Bz3 (Bz = benzene, C6H6) have been of interest since the related triple-decker mesitylenechromium sandwich (1,3,5-Me3C6H3)3Cr2 has been synthesized and characterized structurally by X-ray crystallography. Theoretical studies predict the lowest-energy M2Bz3 structures of the early transition metals Ti, V, and Cr to be the triple-decker sandwiches trans-Bz2M2(η6,η6-μ-C6H6) having quintet, triplet, and singlet spin states, respectively. In these structures, the central benzene ring functions as a hexahapto ligand to each metal atom. The singlet rice-ball cis-Bz2M2(μC6H6) structures with a 2.64-Å MndMn double bond or a 2.81-Å Fe Fe single bond are preferred for the central transition metals Mn and Fe. Singlet triple-decker-sandwich structures transBz2M2(μ-C6H6) return as the lowest-energy structures for the late transition metals Co and Ni but with the central benzene ring only partially bonded to each metal atom. Thus, the lowest-energy cobalt derivative has a trans-Bz2Co2(η3,η3-μ-C6H6) structure in which the central benzene ring acts as a trihapto ligand to each metal atom. Similarly, the lowest-energy nickel derivative has a transBz2Ni2(η2,η2-μ-C6H6) structure in which the central benzene ring acts as a dihapto ligand to each metal atom, leaving an uncomplexed CdC double bond. The metal metal bond orders in the singlet “rice-ball” structures cis-Bz2M2(μ-C6H6) (M = Mn, Fe) and the hapticities of the central benzene rings in the singlet late-transition-metal triple-decker-sandwich structures trans-Bz2M2(μ-C6H6) (M = Co, Ni) are governed by the desirability for the metal atoms to attain the favored 18-electron configuration.

1. INTRODUCTION The chemistry of sandwich compounds originated from the serendipitous discovery of ferrocene, Cp2Fe (Cp = η5-C5H5), in 1951 by two independent research groups (Figure 1).1,2 Shortly thereafter, many other transition metals, particularly those in the first row from vanadium to nickel, were also found to form similar sandwich compounds (η5-C5H5)2M, isostructural with ferrocene. A subsequent milestone was the discovery of the related sandwich compound dibenzenechromium, 3 (η6-C6H6)2Cr, in 1955 (Figure 1). The ability of chromium to form a stable sandwich compound with the stable aromatic hydrocarbon benzene was a complete surprise at the time of the discovery of dibenzenechromium. The structures of such sandwich compounds are characterized by a metal atom sandwiched between two planar carbocyclic rings. The possibility of extending such sandwich structures to larger molecules was first suggested by the observation of Cp3Ni2+ in the mass spectrum of nickelocene as a product of ion molecule reactions.4 This original 1964 proposal of a triple-deckersandwich structure for Cp3Ni2+ was subsequently confirmed in 1972 by Werner and Salzer,5,6 who isolated the stable salt [Cp3Ni2][BF4], The Cp3Ni2 cation was subsequently shown r 2011 American Chemical Society

by X-ray crystallography to have the triple-decker-sandwich structure with one of the Cp rings bridging the two nickel atoms (Figure 2). 7 In 1986, the neutral binuclear mesitylene (1,3,5-Me3C6H3)3Cr2 compound was isolated from the reaction product of chromium vapor with mesitylene at high metal-toligand ratios.8 Subsequent X-ray crystallographic studies confirmed that the sandwich structure of dibenzenechromium is extended to a triple-decker-sandwich structure in (1,3,5Me3C6H3)3Cr2 (Figure 2).9 Species of the type (C6H6)3M2 have also been generated in molecular beams from transition metal atoms and benzene10 14 and have been the subject of theoretical studies.15 21 A limitation in these triple-decker-sandwich structures is that the metal atoms are too far apart for any direct metal metal bonding to supplement the metal ring bonding. Thus, the triple-decker-sandwich structures, such as Cp3Ni2+ and (1,3,5Me3C6H3)3Cr2, have the two metal atoms located on opposite sides of the benzene ring, corresponding to trans stereochemistry. Received: April 28, 2011 Revised: July 8, 2011 Published: July 12, 2011 9022

dx.doi.org/10.1021/jp203956k | J. Phys. Chem. A 2011, 115, 9022–9032

The Journal of Physical Chemistry A

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Figure 1. Original sandwich compounds: ferrocene and dibenzenechromium.

Another possibility is cis stereochemistry, or so-called “rice-ball” structures,22 in which both metal atoms are on the same side of the benzene ring. In cis structures, the two metal atoms are close enough to form a direct metal metal bond. Typically, however, optimizing the metal metal and metal carbon bonding distances in such cis structures leads to bending of the central benzene ring so that it is no longer planar. This article systematically examines the M2Bz3 (Bz = benzene, C6H6) complexes of the first-row transition metals from titanium to nickel, inclusive, using density functional theory methods. Both trans (triple-decker-sandwich) and cis (rice-ball) structures are considered.

2. THEORETICAL METHODS Electron correlation effects were considered using density functional theory (DFT) methods, which have evolved as a practical and effective computational tool, especially for organometallic compounds.23 38 Two DFT methods were used in this study. The first functional is the popular B3LYP method, which is the hybrid Hartree Fock (HF)/DFT method using a combination of the three-parameter Becke functional (B3) with the Lee Yang Parr (LYP) generalized gradient correlation functional.39,40 The other DFT method used in the present article is BP86, which combines Becke’s 1988 exchange functional (B) with Perdew’s 1986 gradient-corrected correlation functional method (P86).41,42 Double-ζ plus polarization (DZP) basis sets were used in this study. For the carbon and hydrogen atoms, the DZP basis sets were Dunning’s standard double-ζ contraction43 of Huzinaga’s primitive sets44 with one set of pure spherical harmonic polarization functions added with orbital exponents Rd(C) = 0.75 and Rd(H) = 0.75. For the first-row transition metals Ti, V, Cr, Mn, Fe, Co, and Ni, Wachters’ primitive sets45 were used in our loosely contracted DZP basis set but augmented by two sets of p functions and one set of d functions, with contraction following Hood et al.,46 and are designated as (14s11p6d/10s8p3d). The geometries of all structures were fully optimized using the DZP B3LYP and DZP BP86 methods and maintaining the symmetry of the starting structure. Vibrational frequencies were determined by evaluating analytically the second derivatives of the energy with respect to the nuclear coordinates at the same levels. All of the computations were carried out with the Gaussian 03 program,47 exercising the fine-grid option (75 radial shells, 302 angular points) for evaluating integrals numerically,48 with the tight designation as the default for the self-consistent field (SCF) convergence. The finer grid (120, 974) was used for more precise resolution of the small imaginary vibrational frequencies. All of the predicted triplet and quintet structures were found to have negligible spin contamination; that is, the determinantal values of S(S + 1) were very close to the ideal outcomes of 2.0 and 6.0, respectively.

Figure 2. Triple-decker sandwiches Cp3Ni2+ and (1,3,5-Me3C6H3)3Cr2.

In the search for minima, low-magnitude imaginary vibrational frequencies are suspect, because of significant limitations in the numerical integration procedures used in standard DFT computations.48 Thus, imaginary vibrational frequencies with magnitudes of less than 50i cm 1 are considered questionable, and in many cases, we do not follow the eigenvectors corresponding to such imaginary frequencies.49 The optimized structures are reported in Tables 1 7 and depicted in Figures 3 9. The structures are designated M-a-bC, where M is the metal atom; a (c or t) is for the cis or trans structure; b orders the structures by their BP86 relative energies; and C indicates the spin state as S (singlet), T (triplet), or Q (quintet). The designations m and n for some of the triple-decker-sandwich structures with D6h point-group symmetry are used to indicate whether the central benzene ring is eclipsed or staggered, respectively, relative to the outer benzene rings, as this distinction does not affect the pointgroup symmetry.

3. RESULTS AND DISCUSSION 3.1. Titanium Derivatives. Six structures (three quintet structures and three singlet structures) were found for the titanium derivative Ti2Bz3 within 15 kcal/mol of the global minimum (Table 1 and Figure 3). All of these structures are tripledecker-sandwich structures with very similar Ti 3 3 3 Ti distances in the range from ∼3.6 to ∼3.7 Å. The global minimum of Ti2Bz3 is the D6h quintet structure Ti-t-1Q. The other two quintet Ti2Bz3 structures, namely, Ti-t-2Q (C6v) and Ti-t-3Q (D6h-n), lie 0.3 and 0.6 kcal/mol, respectively, above Ti-t-1Q. These three structures can be considered to be essentially degenerate in energy. Thus, Ti2Bz3 is a fluxional system with almost free rotation of the benzene rings around the C6 axis. With the BP86 method, the structures Ti-t-2Q and Ti-t-3Q have one small imaginary vibrational frequency. Following the corresponding normal modes leads from Ti-t-2Q (C6v) and Ti-t-3Q (D6h-n) to Ti-t-1Q (D6h-m). All three structures Ti-t-1Q (D6h-m), Ti-t-2Q (C6v), and Ti-t-3Q (D6h-n) have the same η6:η6 bonding of the central benzene ring, giving each Ti atom the 16-electron configuration, similar to that in the simple sandwich compound (η6-CH3C6H5)2Ti.50 The singlet D6h structure Ti-t-4S lies 4.7 kcal/mol (BP86) or 14.8 kcal/mol (B3LYP) in energy above the global minimum Ti-t-1Q (Figure 3 and Table 1). The Ti Ti distance in structure Ti-t-4S of 3.645 Å is somewhat longer than the Ti Ti distance of 3.605 Å in Ti-t-1Q. The singlet structure Ti-t-5S (C6v), lying 5.3 kcal/mol (BP86) in energy above Ti-t-1Q, is predicted to be a transition state because of an imaginary frequency at 41i cm 1 (BP86). Structure Ti-t-6S (D6h-n) lies 5.8 kcal/mol 9023

dx.doi.org/10.1021/jp203956k |J. Phys. Chem. A 2011, 115, 9022–9032


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Table 1. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Ti Ti Distances (Å), HOMO LUMOaEnergy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Ti2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

a

E

ΔE

EZPE

ΔEZPE

Nimg

Ti Ti

structure type

gap

ÆS2æ

Ti-t-1Q (D6h-m)

2396.05135

0.0

2395.76027

0.0

0

3.605

η6:η6

1.143

6.03

Ti-t-2Q (C6v)

2396.05085

0.3

2395.75972

0.4

1 (30i)

3.607

η6:η6

1.116

6.03

Ti-t-3Q (D6h-n)

2396.05035

0.6

2395.75912

0.7

1 (46i)

3.609

η6:η6

1.116

6.03

Ti-t-4S (D6h-m)

2396.04380

4.7

2395.75537

3.1

0

3.645

η6:η6

0.163

0

Ti-t-5S (C6v) Ti-t-6S (D6h-n)

2396.04293 2396.04209

5.3 5.8

2395.75471 2395.75404

3.5 3.9

1 (41i) 2 (45i, 34i)

3.651 3.658

η6:η6 η6:η6

0.163 0.163

0 0

HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital.

Figure 3. The six Bz2Ti2(μ-C6H6) structures within 15 kcal/mol of the BP86 global minimum.

(BP86) or 15.8 kcal/mol (B3LYP) above the global minimum. Following Reiher et al.,51 the high-spin states are favored by B3LYP and the low-spin states are favored by the pure DFT method BP86. Triplet Ti2Bz3 structures lie more than 15 kcal/ mol above the global minimum and thus are not considered here. Among the six Ti2Bz3 triple-decker-sandwich structures, the C C distances in the terminal benzene rings in the quintet structures are ∼1.43 Å (BP86), which are shorter than the corresponding C C distances of ∼1.45 Å (BP86) in the singlet structures. However, the C C distances in the middle benzene rings of the quintet Ti2Bz3 structures are ∼1.46 Å (BP86), which are not much longer than the corresponding C C distances in the singlet structures. These observations suggest that the interaction between the titanium atoms and terminal benzene rings is stronger in the singlet structures than in the quintet structures. This is confirmed by comparing the Ti C distances to the terminal benzene rings in the quintet and singlet structures. 3.2. Vanadium Derivatives. Eight V2Bz3 structures were obtained within 16 kcal/mol of the global minimum based on the BP86 results (Table 2 and Figure 4). The six lowest-energy structures (three triplets and three singlets) are triple-decker-sandwiches

(trans structures), and the other two structures (triplets) are riceball (cis) structures. The global minimum V-t-1T (D6h symmetry) has a V V distance of 3.481 Å. The central benzene ring in V-t-1T is hexahapto to each vanadium atom. This gives each V atom a 17electron configuration corresponding to a binuclear triplet and similar to dibenzenevanadium.52 The V2Bz3 structure V-t-2T (C6v) lies only 0.9 kcal/mol (BP86) in energy higher than V-t-1T, but it has a small imaginary frequency at 48i cm 1 (BP86). Following the corresponding normal mode leads to V-t-1T. The triplet D6h V2Bz3 structure V-t-3T lies 1.8 kcal/mol (BP86) above V-t-1T. The V V distance in V-t-3T is predicted to be 3.493 Å, which is slightly longer than those in structures V-t-1T and V-t-2T (3.481 and 3.487 Å, respectively). Two imaginary vibrational frequencies at 53i and 49i cm 1 (BP86) or 46i and 44i cm 1 (B3LYP) were found in V-t-3T. Following the corresponding normal modes leads to V-t-1T. The middle benzene ring in all three singlet triple-decker V2Bz3 structures is a hexahapto ligand to both V atoms (Table 2 and Figure 4). Structure V-t-4S (D6h-m) is a local minimum, lying 13.6 kcal/mol higher than V-t-1T. However, the B3LYP method predicts a doubly degenerate large imaginary frequency at 570i cm 1. By following the corresponding normal mode, V-t-4S 9024



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Table 2. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), V V Distances (Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the V2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

V V

structure type

gap

ÆS2æ

V-t-1T (D6h-m)

2585.18995

0.0

2584.89734

0.0

0

3.481

η6:η6

2.204

2.04

V-t-2T (C6v)

2585.18851

0.9

2584.89663

0.4

1 (48i)

3.487

η6:η6

2.177

2.04

V-t-3T (D6h-n)

2585.18709

1.8

2584.89593

0.9

2 (53i, 49i)

3.493

η6:η6

2.150

2.04

V-t-4S (D6h-m)

2585.16827

13.6

2584.87600

13.4

0

3.289

η6:η6

0.272

0

V-t-5S (C6v) V-t-6S (D6h-n)

2585.16652 2585.16477

14.7 14.9

2584.87478 2584.87355

14.2 14.9

1 (67i) 2 (83i, 50i)

3.295 3.301

η6:η6 η6:η6

0.272 0.272

0 0

V-c-7T (C2)

2585.16574

15.2

2584.87283

15.4

0

2.487

η4:η4

1.034

2.02

V-c-8T (Cs)

2585.16560

15.3

2584.87298

15.3

0

2.488

η4:η4

1.007

2.02

Figure 4. The eight Bz2V2(μ-C6H6) structures within 16 kcal/mol of the BP86 global minimum.

(D6h-m) collapses to a D2h structure, which is 3.8 kcal/mol lower in energy than the D6h-m structure. The main difference between the D2h and D6h-m structures is the middle benzene carbon carbon distances. Structure V-t-5S (C6v) lies 14.7 kcal/mol above V-t-1T, but with one small imaginary vibrational frequency at 67i cm 1 by BP86. However, the B3LYP method predicts three large imaginary frequencies at 648i, 645i, and 59i cm 1. The singlet D6h V2Bz3 structure V-t-6S lies 14.9 kcal/mol (BP86) in energy above the global minimum V-t-1T, but it has two imaginary vibrational frequencies at 83i and 50i cm 1 predicted by the BP86 method. By following the

corresponding normal mode, V-t-6S collapses first to a C6h structure and then to V-t-4S (D6h-m) (BP86). Four imaginary frequencis with the largest at 753i cm 1 were detected by the B3LYP method. By following the corresponding normal mode, V-t-6S collapses from D6h symmetry to D2 symmetry, which is 6.0 kcal/mol lower than the D6h structure. The main difference between the D6h and D2 structures is the relative positions of the three benzene rings. In addition, the two outer rings are no longer strictly planar in the D2 structure. The two triplet rice-ball V2Bz3 structures V-c-7T and V-c-8T have significantly higher energies than the triple-decker-sandwich 9025



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Table 3. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Cr Cr Distances (Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Cr2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

Cr Cr

structure type

gap

ÆS2æ

Cr-t-1S (D6h-m)

2786.15370

0.0

2785.85849

0.0

0

3.341

η6:η6

1.878

0

Cr-t-2S (C6v)

2786.15196

1.1

2785.85722

0.8

1 (60i)

3.346

η6:η6

1.850

0

Cr-t-3S (D6h-n)

2786.15025

2.2

2785.85596

1.6

2 (73i, 53i)

3.352

η6:η6

1.850

0

Cr-c-4S (C2)

2786.13740

10.2

2785.84209

10.3

0

2.310

η4:η4

0.789

0

Cr-c-5S (Cs) Cr-c-6T (C2)

2786.13631 2786.12948

10.9 15.2

2785.84117 2785.83594

10.9 14.2

1 (18i) 0

2.318 2.636

η4:η4 η4:η4

0.708 1.252

0 2.06

Cr-c-7T (Cs)

2786.12872

15.7

2785.83546

14.5

1 (11i)

2.619

η4:η4

1.197

2.06

Figure 5. The seven Bz2Cr2(μ-C6H6) structures within 16 kcal/mol of the BP86 global minimum.

structures (Table 2 and Figure 4). Thus, the triplet C2 structure V-c-7T lies 15.2 kcal/mol in energy above V-t-1T. The other triplet rice-ball structure V-c-8T (Cs) with all real frequencies lies 15.3 kcal/mol above V-t-1T in energy. The shared benzene rings in V-c-7T and V-c-8T are tetrahapto ligands to each vanadium atom. The VtV distances in V-c-7T and V-c-8T of 2.49 Å (BP86) or 2.52 Å (B3LYP) can correspond to formal triple bonds. This gives each vanadium atom the 17-electron configuration for binuclear triplets. For comparison, the experimental VtV triple bond distance in Cp2V2(CO)5 is 2.459 Å, as determined by X-ray crystallography.53,54

The C C distances in the middle benzene ring in all of the triplet V2Bz3 triple-decker-sandwich structures are ∼1.45 Å, which are shorter than those in the singlet sandwich structures. This suggests a weaker interaction between the V atoms and the middle benzene ring in the triplet structures relative to the singlet structures. 3.3. Chromium Derivatives. Seven Cr2Bz3 structures, including five singlets and two triplets, were obtained within 16 kcal/mol of energy, based on the BP86 results (Table 3 and Figure 5). The global minimum Cr-t-1S is a D6h triple-decker-sandwich structure similar to the experimental structure for (1,3,5-Me3C6H3)3Cr2.8,9 9026



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Table 4. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Mn Mn Distances (Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Mn2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

Mn Mn

structure type

gap

ÆS2æ

Mn-c-1S (C2)

2999.22187

0

2998.92625

0.0

0

2.640

η4:η4

0.735

0

Mn-c-2T (Cs)

2999.21909

1.7

2998.92482

0.9

0

2.645

η4:η4

1.742

2.15

Mn-c-3T (C2)

2999.21407

4.9

2998.92012

3.8

1 (215i)

2.598

η4:η4

1.225

2.08

Mn-t-4S (C1)

2999.20765

8.9

2998.91308

8.3

0

3.611

η5:η3

0.952

0

Mn-t-5T (C2)

2999.20115

13.0

2998.90825

11.3

0

3.664

η4:η4

1.469

2.05

The middle benzene ring in Cr-t-1S functions as a hexahapto ligand to each chromium atom, thereby giving each Cr atom the favored 18-electron configuration. The predicted Cr 3 3 3 Cr distance of 3.341 Å in Cr-t-1S is essentially identical to the experimental Cr 3 3 3 Cr distance of 3.338(1) Å in (1,3,5-Me3C6H3)3Cr2, as determined by X-ray crystallography.9 The Cr2Bz3 structure Cr-t-2S (C6v), lying 1.1 kcal/mol above the global minimum, has an imaginary frequency at 60i cm 1 (BP86) or 48i cm 1 (B3LYP). Following the corresponding normal mode leads ultimately to Cr-t-1S. The Cr Cr distance in structure Cr-t-2S is 3.346 Å (BP86). Structure Cr-t-3S has two imaginary frequencies at 73i and 53i cm 1 (BP86) or 55i and 45i cm 1 (B3LYP) and lies 2.2 kcal/mol (BP86) in energy above the global minimum. Following the corresponding normal modes leads to Cr-t-1S. Four rice-ball (cis) structures (two singlets and two triplets) were optimized for Cr2Bz3 (Table 3 and Figure 5). The first singlet structure Cr-c-4S (C2 symmetry) lies 10.2 kcal/mol (BP86) above Cr-t-1S and has all real frequencies by both BP86 and B3LYP methods. The shared benzene ring in Cr-c-4S functions as a tetrahapto ligand to each chromium atom. The CrtCr bond length of structure Cr-c-4S is predicted to be 2.31 Å by the BP86 method, corresponding to a formal triple bond. This CrtCr triple bond length is similar to the experimental CrtCr triple bond length of 2.280 Å in Cp2Cr2(CO)4, determined by X-ray crystallography.55 A formal CrtCr triple bond in Cr-c-4S gives each chromium atom the favored 18-electron configuration assuming that the six π-electrons of the bridging benzene ring are distributed equally between the two chromium atoms. Another singlet rice-ball Cr2Bz3 structure Cr-c-5S with Cs symmetry lies 10.9 kcal/mol (BP86) above the global minimum. A small imaginary frequency at 18i cm 1 was predicted by the BP86 method, whereas no imaginary frequency was found by the B3LYP method. The only difference between Cr-c-4S and Cr-c-5S is the relative position of the two outer benzene rings. Thus, in Cr-c-4S, the outer benzene rings are staggered with respect to each other, whereas in Cr-c-5S the outer benzene rings are eclipsed relative to each other. The two triplet rice-ball structures Cr-c-6T with C2 symmetry and Cr-c-7T with Cs symmetry are relatively high-energy structures, lying 15 20 kcal/mol above the global minimum Cr-t-1S (Table 3 and Figure 5). The CrdCr bond lengths of ∼2.6 Å in these triplet structures are significantly longer than the CrtCr bond length of ∼2.3 Å in the singlet rice-ball structure Cr-c-4S (2.3 Å). This suggests formal CrdCr double bonds in the triplet structures Cr-c-6T and Cr-c-7T, thereby giving the chromium atoms in these structures 17-electron configurations for binuclear triplets. The distances between the Cr atoms and the benzene carbon atoms in Cr-c-6T are slightly longer than those in Cr-c-4S, suggesting weaker metal ring bonding in the triplet structures relative to the singlet structures.

Figure 6. The five Bz2Mn2(μ-C6H6) structures within 25 kcal/mol of the BP86 global minimum.

3.4. Manganese Derivatives. Five Mn2Bz3 structures were found within 15 kcal/mol of the BP86 global minimum, including two triple-decker-sandwich structures and three rice-ball structures (Table 4 and Figure 6). The lowest-energy Mn2Bz3 structure Mn-c-1S is a singlet rice-ball (cis) structure in which the central benzene ring bonds as a tetrahapto ligand to each metal atom. The MndMn bond length of 2.640 Å (BP86) in Mn-c-1S can be interpreted as the formal double bond required to give each manganese atom the favored 18-electron configuration if the six π-electrons of the central benzene ring are distributed equally between the two manganese atoms. The triplet Cs rice-ball Mn2Bz3 structure Mn-c-2T lies very close to Mn-c-1S in energy, at 1.7 kcal/mol above Mn-c-1S by the BP86 method or 3.7 kcal/mol below Mn-c-1S by the B3LYP method. This is another example of the tendency of the B3LYP 9027



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Table 5. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Fe Fe Distances (Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Fe2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

Fe Fe

structure type

gap

ÆS2æ

Fe-c-1S (C2)

3224.72676

0

3224.43072

0.0

0

2.818

η3:η3

1.878

0

Fe-t-2S (C2)

3224.71481

7.5

3224.42018

6.6

0

3.841

η3:η3

1.551

0

Fe-t-3T (C2h)

3224.70217

15.4

3224.40891

13.7

1 (28i)

4.066

η3:η3

1.442

2.05

Fe-c-4T (C2)

3224.70120

16.0

3224.40727

14.7

0

2.712

η2:η2

0.871

2.05

method to favor higher spin states, as discussed by Reiher and collaborators.51 The MndMn bond length of structure Mn-c-2T of 2.645 Å (BP86) or 2.701 Å (B3LYP) is essentially the same as that in Mn-c-1S and likewise corresponds to a formal double bond. However, in this case, the MndMn double bond is a σ + 2/2π bond with an unpaired electron in each of the orthogonal π orbitals to account for the triplet spin multiplicity. Such a σ + 2/2π double bond is similar to that in triplet dioxygen. A similar FedFe double bond is found in the stable triplet state compound (η5-C5H5)2Fe2(μ-CO)3, which has been structurally characterized by X-ray crystallography.56 58 One of the two benzene rings in Mn-c-2T is rotated by about 30 compared with Mn-c-1S. Another triplet rice-ball Mn2Bz3 structure Mn-c-3T with C2 symmetry lies 4.9 kcal/mol above the global minimum but has a large imaginary vibrational frequency at 215i cm 1 by the BP86 method. Following the corresponding normal mode leads to Mn-c-2T. The lowest-energy triple-decker-sandwich Mn2Bz3 structure Mn-t-4S lies 8.9 kcal/mol (BP86) above the global minimum Mn-c-1S with a Mn Mn distance of 3.611 Å (Table 4 and Figure 6). The middle benzene ring becomes nonplanar with η5:η3 coordination to the upper and lower Mn atoms. The triplet triple-decker-sandwich structure Mn-t-5T is obtained with 13.0 kcal/mol higher than the global minimum. The middle benzene ring is nonplanar with tetrahapto coordination to each manganese atom. 3.5. Iron Derivatives. Four Fe2Bz3 structures, including two cis structures and two trans structures, were found within 16 kcal/mol of the global minimum by the BP86 method (Table 5 and Figure 7). The global minimum is a C2 singlet rice-ball (cis) Fe2Bz3 structure Fe-c-1S with an Fe Fe distance of 2.818 Å (BP86) or 2.804 Å (B3LYP), corresponding to a formal single bond. Each iron atom in Fe-c-1S is within bonding distance of three of the carbon atoms of the central benzene ring, thereby giving each iron atom the favored 18-electron configuration. A C2 triplet-state rice-ball (cis) Fe2Bz3 structure Fe-c-4T, lying 16.0 kcal/mol (BP86) above Fe-c-1S, has an Fe Fe distance of 2.712 Å, predicted by both the BP86 and B3LYP methods. In Fe-c-4T, the central benzene ring functions as a dihapto ligand to each iron atom. This leads to a 17-electron configuration for each iron atom, consistent with a binuclear triplet. Two trans-Bz2Fe2(μ-C6H6) structures were found within 16 kcal/mol of the BP86 global minimum Fe-c-1S, but at significantly higher energies than the lowest-energy cis-Bz2Fe2(μ-C6H6) structures (Table 5 and Figure 7). The lowest-energy trans-Bz2Fe2(μ-C6H6) structure is the C2 structure Fe-t-2S, lying 7.5 kcal/mol (BP86) above Fe-c-1S, with a nonbonding Fe 3 3 3 Fe distance of 3.841 Å (BP86) or 3.850 Å (B3LYP). The highly distorted nonplanar middle benzene ring in Fe-t-2S is a trihapto ligand to each iron atom. A C2h triplet trans-Bz2Fe2(μ-C6H6) structure Fe-t-3T lies 15.4 kcal/mol higher than Fe-c-1S

Figure 7. The four Bz2Fe2(μ-C6H6) structures within 20 kcal/mol of the BP86 global minimum.

by the BP86 method. A small imaginary frequency at 28i cm 1 (BP86) or 8i cm 1 (B3LYP) in Fe-t-3T disappeared when a finer integration grid (120, 974) was used. The center benzene ring in Fe-t-3T functions as a trihapto ligand to each iron atom, thereby giving each iron atom a 17-electron configuration, consistent with a binuclear triplet. 3.6. Cobalt Derivatives. Eight Cp2Co2(μ-C6H6) structures were found within 15 kcal/mol of the BP86 global minimum (Table 6 and Figure 8). The global minimum is the singlet C2h trans-Bz2Co2(η3,η3-μ-C6H6) structure Co-t-1S, which has a Co 3 3 3 Co distance of 4.294 Å (BP86) or 4.263 Å (B3LYP). The middle benzene ring is a trihapto ligand to each cobalt atom, thereby giving each cobalt atom the favored 18-electron configuration. The two small imaginary vibrational frequencies at 32i and 24i cm 1 (BP86) or 19i and 12i cm 1 (B3LYP) becamse real when a finer integration grid (120, 974) was used. A triplet-state C2 trans-Bz2Co2(μ-C6H6) structure Co-t-2T, lying 3.3 kcal/mol above Co-t-1S, is predicted to have a Co 3 3 3 Co distance of 4.582 Å (BP86) or 4.795 Å (B3LYP) (Table 6 and Figure 8). The tilted middle benzene ring in Co-t-2T is bonded as a dihapto ligand to each cobalt atom, leaving an uncomplexed CdC double bond of length 1.399 Å (B3LYP) or 1.372 Å (BP86). Note, of course, that these distances are closer to that in isolated benzene (1.40 Å) than isolated ethylene (1.34 Å). The cobalt atoms in Co-t-2T have 17-electron configurations, consistent with a binuclear triplet. 9028



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Table 6. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Co Co Distances (Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Co2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

Co Co

structure type

gap

ÆS2æ

Co-t-1S (C2h)

3462.88076

0

3462.58737

0.0

2 (32i, 24i)

4.294

η3:η3

1.007

0

Co-t-2T (C2)

3462.87558

3.3

3462.58283

2.9

0

4.582

η2:η2

2.340

2.08

Co-c-3T (C2)

3462.87299

4.9

3462.58047

4.3

0

3.064

η3:η3

1.742

2.11

Co-c-4S (C1)

3462.87120

6.0

3462.57664

6.7

0

2.755

η2:η2

0.871

0

Co-c-5S (C2) Co-t-6S (C2)

3462.86681 3462.86441

8.8 10.3

3462.57328 3462.57154

8.8 9.9

9i 0

3.511 3.822

η3:η3 η3:η3

0.871 0.762

0 0

Co-c-7T (C1)

3462.86431

10.3

3462.57155

9.9

0

2.552

η2:η2

1.714

2.06

Co-c-8S (C2)

3462.85750

14.6

3462.56433

14.5

0

2.925

η2:η2

0.327

0

Figure 8. The eight Bz2Co2(μ-C6H6) structures within 20 kcal/mol of the BP86 global minimum.

Another singlet trans-Bz2Co2(μ-C6H6) structure, Co-t-6S, with C2 symmetry lies 10.3 kcal/mol above Co-t-1S (Table 6 and Figure 8). The Co 3 3 3 Co nonbonding distance in Co-t-6S is

predicted to be 3.822 Å (BP86) or 3.877 Å (B3LYP), which is shorter than those in Co-t-1S and Co-t-2T. The middle benzene ring in Co-t-6S is badly distorted (from D6h symmetry), with an uncomplexed CdC double bond of length 1.378 Å (BP86) or 1.360 Å (B3LYP). Five cis-Bz2Co2(μ-C6H6) structures were obtained within 15 kcal/mol of the BP86 global minimum (Table 6 and Figure 8). The lowest-energy cis-Bz2Co2(μ-C6H6) structure Co-c-3T (C2) lies only 4.9 kcal/mol above Co-t-1S, with a Co Co bond length of 3.064 Å (BP86) or 3.032 Å (B3LYP), assumed to be a formal single bond. The bridging benzene ring is a trihapto ligand to each cobalt atom. This gives each cobalt atom in Co-c-3T a 19-electron configuration for a binuclear triplet. The singlet cis-Bz2Co2(μ-C6H6) structure Co-c-4S lies 6.0 kcal/ mol above the global minimum, with a Co Co bond distance of 2.755 Å (BP86) or 2.713 Å (B3LYP), corresponding to a single bond. The bridging benzene ring is dihapto to each cobalt atom, leaving an uncomplexed CdC bond of predicted length 1.376 Å (BP86) or 1.366 Å (B3LYP). This leads to the favored 18electron configuration for each cobalt atom in Co-c-4S. Another singlet cis-Bz2Co2(μ-C6H6) structure, Co-c-5S, lying 8.8 kcal/mol higher than Co-t-1S, has a nonbonding Co 3 3 3 Co distance of 3.511 Å (BP86) or 3.437 Å (B3LYP). The shared middle benzene ring in Co-c-5S is trihapto to each cobalt atom, thereby giving each cobalt atom the favored 18-electron configuration. Another triplet cis-Bz2Co2(μ-C6H6) structure, Co-c-7T, with a Co Co bond length of 2.552 Å (BP86) lies 10.3 kcal/mol above Co-t-1S. The bridging benzene ring is a dihapto ligand to each Co atom leaving an uncomplexed CdC bond of ∼1.38 Å length. The singlet C2 cis-Bz2Co2(μ-C6H6) structure Co-c-8S lies 14.6 kcal/mol above Co-1S with a Co Co distance of 2.925 Å (BP86) or 2.829 Å (B3LYP), corresponding to a formal single bond. The bridging benzene ring is a dihapto ligand to each metal atom, thereby giving each cobalt atom the favored 18-electron configuration. 3.7. Nickel Derivatives. Six Bz2Ni2(μ-C6H6) structures were found within 15 kcal/mol of the BP86 global minimum (Table 7 and Figure 9). The BP86 global minimum is a C2 triplet transBz2Ni2(μ-C6H6) structure Ni-t-1S, in which the benzene ring bonds as a dihapto ligand to each nickel atom. The very long Ni 3 3 3 Ni distance in Ni-t-1S of 4.742 Å (BP86) or 4.762 Å (B3LYP) indicates the lack of any direct nickel nickel bond. The bridging benzene ring is a dihapto ligand to each nickel atom, thereby leaving an uncomplexed CdC double bond of length 1.385 Å (BP86) or 1.373 Å (B3LYP). Another singlet C2 trans-Bz2Ni2(μ-C6H6) structure, Ni-t-5S, lying 5.5 kcal/mol 9029



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Table 7. BP86 Results for Total Energies (E, in hartrees), Relative Energies (ΔE, in kcal/mol), Numbers of Imaginary Vibrational Frequencies (Nimg), Ni Ni Bond Lengths (in Å), HOMO LUMO Energy Gaps (in eV), and Spin Contamination ÆS2æ Values for the Ni2Bz3 Structures. The Subscript ZPE Indicates Values with the Zero Point Energy Corrections structure

E

ΔE

EZPE

ΔEZPE

Nimg

Ni Ni

structure type

gap

ÆS2æ

Ni-t-1S (C2)

3714.02608

0.0

3713.73384

0.0

0

4.742

η2:η2

2.204

0

Ni-t-2S (Cs)

3714.02164

2.8

3713.72959

2.7

1 (23i)

4.158

η2:η4

1.850

0

Ni-c-3S (C1)

3714.02155

2.8

3713.72912

3.0

0

2.628

η2:η2

1.197

0

Ni-c-4S (Cs)

3714.02054

3.5

3713.72861

3.3

0

2.641

η2:η2

1.279

0

Ni-t-5S (C2) Ni-c-6S (C2)

3714.01731 3714.00824

5.5 11.2

3713.72590 3713.71726

5.0 10.4

0 0

4.927 3.924

η2:η2 η2:η2

1.878 1.905

0 0

Figure 10. Highest-lying bonding molecular orbitals of the singlet Cr2Bz3 structure Cr-t-1S.

Figure 9. The six Bz2Ni2(μ-C6H6) structures within 20 kcal/mol of the BP86 global minimum.

above the global minimum, has a nonbonding Ni 3 3 3 Ni distance of 4.927 Å (BP86) or 4.995 Å (B3LYP). The middle benzene ring is a dihapto ligand to each nickel atom, again giving each nickel atom the favored 18-electron configuration. The difference between Ni-t-5S and Ni-t-1S is the location of the carbon atoms in the central benzene ring bonded to the nickel atoms. Thus, in Ni-t-5S, the pairs of carbon atoms bonded to the nickel atoms are opposite each other, whereas in Ni-t-1S, the pairs of carbon atoms bonded to the nickel atoms are adjacent. The singlet Cs trans-Bz2Ni2(μ-C6H6) structure Ni-t-2S lies 2.8 kcal/mol above Ni-t-1S energetically. In Ni-t-2S, the central benzene ring is a dihapto ligand toward one nickel atom and a tetrahapto ligand toward the other nickel atom. In addition, the outer benzene ring bound to the nickel atom with tetrahapto bonding to the central

benzene ring is only a dihapto ligand, giving that nickel atom only a 16-electron configuration. Three cis-Bz 2 Ni 2 (μ-C 6 H 6 ) structures were found within 15 kcal/mol of the BP86 global minimum (Table 7 and Figure 9). The lowest-energy cis-Bz2Ni2(μ-C6H6) structure Ni-c-3S lies only 2.8 kcal/mol above Ni-t-1S. The outer benzene rings in Ni-c-3S are only dihapto. The central benzene ring in Ni-c-3S is a dihapto ligand to each nickel atom. The NidNi distance of 2.628 Å (BP86) or 2.727 Å (B3LYP) in Ni-c-3S can correspond to a formal double bond to give each nickel atom a 16-electron configuration. This NidNi double bond distance can be compared with the predicted NidNi double bond distance of 2.56 Å in Ni2(CO)6 (= Ni2(CO)4(μ-CO)2),59 in which the presence of the two carbonyl bridges might be expected to lead to significant shortening. The Cs singlet cis-Bz2Ni2(μ-C6H6) structure Ni-c-4S, lying 3.5 kcal/mol above Ni-t-1S, has the central benzene ring functioning as a dihapto ligand toward each nickel atom, leaving an uncomplexed CdC double bond of length 1.395 Å (BP86) or 1.384 Å (B3LYP). The outer benzene rings in Ni-c-4S are only trihapto ligands. The Ni Ni distance of 2.641 Å (BP86) or 2.810 Å (B3LYP) in Ni-c-4S corresponds to a formal single bond. Another singlet cis-Bz2Ni2(μ-C6H6) structure, Ni-c-6S, lying 11.2 kcal/mol above Ni-t-1S, has a nonbonding Ni 3 3 3 Ni distance of 3.924 Å (BP86) or 3.911 Å (B3LYP). In Ni-c-6S, the central benzene ring is a dihapto ligand to each nickel atom, and the outer benzene rings are both hexahapto ligands. This gives each nickel atom the favored 18-electron configuration. 3.8. Molecular Orbital Analysis. The structures of the linear triple-decker-sandwich compounds trans-Bz2M2(μ-C6H6) make their frontier orbitals relatively easy to interpret. Thus, for the singlet trans-Bz2Cr2(μ-C6H6) structure Cr-t-1S analogous to the known8,9 compound (1,3,5-Me3C6H3)3Cr2, the highest occupied molecular orbital (HOMO) and HOMO 1 are the ungerade σu and gerade σg orbitals involving the metal dz2 orbitals (Figure 10). These are followed by a doubly degenerate HOMO 2 and 9030



Figure 11. Frontier molecular orbitals of the singlet V2Bz3 structure V-t-4S.

Figure 12. Occupancy of the frontier MOs in various spin states of the trans-Bz3M2 derivatives.

HOMO 3 pair of gerade δg orbitals involving the metal dx2 y2 and dxy orbitals. Then come the corresponding set of ungerade 4 and HOMO 5. This ordering δu orbitals as HOMO is similar to that found by Chesky and Hall on the related triple-decker sandwich trans-(η5-C5H5)2V2(μ-C6H6), using a Fenske Hall method.60 The HOMO σu orbital of the trans-Bz2Cr2(μ-C6H6) structure Cr-t-1S can be considered a metal metal antibonding orbital. Removal of the electron pair from this orbital gives the singlet trans-Bz2V2(μ-C6H6) structure V-t-4S (Figure 11). In V-t-4S, the appearance of the σg vanadium vanadium bonding orbital has changed, and its energy has dropped below that of the δg degenerate pair (Figure 11). This can be interpreted as a vanadium vanadium bond that pairs the single electrons from the two 17-electron vanadium atoms in the individual (arene)2V subunits to give the diamagnetic structure V-t-4S. Figure 12 summarizes the occupancies of the frontier molecular orbitals of the triple-decker-sandwich structures transBz2M2(μ-C6H6) obtained by removal of electrons from the closed-shell singlet trans-Bz2Cr2(μ-C6H6) structure Cr-t-1S. The position of the degenerate δu pair relative to the nondegenerate σg and σu orbitals varies, depending on the occupancy of these orbitals. However, for all of the trans-Bz2M2(μ-C6H6) derivatives, except for singlet trans-Bz2V2(μ-C6H6), the numbers of electrons (0, 1, or 2) in the bonding σg orbital and the antibonding σu orbitals are the same, consistent with the lack of metal metal bonding.

4. SUMMARY The lowest-energy structures of the early-transition-metal derivatives M2Bz3 (M = Ti, V, Cr) are all trans triple-decker-sandwich structures in which the central benzene ring is a hexahapto ligand to both metal atoms. Such structures are isoelectronic with the previously studied61 trans-Cp2M2(μ-C6H6) derivatives with outer cyclopentadienyl rings where M = V, Cr, Mn, respectively. The singlet closed-shell Cr2Bz3 system has been realized experimentally in the mesitylene triple-decker sandwich (1,3,5-Me3C6H3)3Cr2,

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which was synthesized by Lamanna and characterized structurally by X-ray crystallography.8,9 For V2Bz3, both singlet and triplet triple-decker sandwiches are found, with the singlet structure lying ∼14 kcal/mol above the triplet structure. Analyses of the frontier molecular orbitals (Figures 11 and 12) suggests a long V V single bond of 3.29 Å through the central benzene ring in the singlet trans-Bz2V2(μ-C6H6) structure V-t-4S . The lowest-lying Ti2Bz3 structure is the quintet triple-decker-sandwich structure Ti-t-1Q analogous to trans-Cp2V2(μ-C6H6).61 The lowest-energy M2Bz3 structures for the middle transition metals (M = Mn and Fe) are singlet-state cis rice-ball structures with a MndMn double bond of length 2.64 Å and an Fe Fe single bond of length 2.81 Å. In both cases, the central metal atoms attain the favored 18-electron configuration, assuming that the six π-electrons of the central benzene ring are divided equally between the two metal atoms. The trans triple-decker-sandwich structures return as the lowest-energy M2Bz3 structures for the late transition metals (M = Co, Ni). However, these late-transition-metal triple-decker sandwiches are different from the earlier triple-decker sandwiches in having the transition metal atom bonded to only enough carbon atoms in the central benzene rings to attain the favored electronic configuration of 18 for singlet structures or 17 for triplet structures. Thus, the lowest-energy Co2Bz3 structure is a singlet cis-Bz2Co2(η3,η3-μ-C6H6) structure in which each cobalt atom is bonded to only three carbons of the central benzene ring. Similarly, the lowest-energy Ni2Bz3 structure is a singlet cisBz2Ni2(η3,η3-μ-C6H6) structure in which each nickel atom is bonded to only two carbons of the central benzene ring, leaving an uncomplexed CdC double bond.

’ ASSOCIATED CONTENT

bS

Supporting Information. Tables S1 S50: Atomic coordinates of the optimized (C6H6)2M2(μ-C6H6) structures and frontier molecular orbital energies for the triple-decker sandwiches (C6H6)2M2(η6:η6-μ-C6H6) (M = Ti, V, Cr, Mn). Figures S1 S7: Selected bond lengths in the optimized (C6H6)2M2(μ-C6H6) structures predicted by the BP86 and B3LYP methods. Tables S51 S57: Total energies (E, in hartrees), relative energies (ΔE, in kcal/mol), numbers of imaginary vibrational frequencies (Nimg), M M bond lengths (in Å), HOMO LUMO energy gaps (in eV), and spin contamination ÆS2æ values for the M2Bz3 structures optimized by the B3LYP method. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (R.B.K.).

’ ACKNOWLEDGMENT We are indebted to the 111 Project (B07012) and the National Natural Science Foundation (20873045) of China, as well as the U.S. National Science Foundation (Grants CHE-1054286 and CHE-0716718), for support of this research. ’ REFERENCES (1) Kealy, T. J.; Pauson, P. L. Nature 1961, 168, 1039. (2) Miller, S. A.; Tebboth, J. A.; Tremaine, J. F. J. Chem. Soc. 1952, 632. 9031


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