Binuclear butadiene chromium carbonyls: Comparison with their trimethylenemethane isomers

Inorganica Chimica Acta 407 (2013) 181–188

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Binuclear butadiene chromium carbonyls: Comparison with their trimethylenemethane isomers Qunchao Fan a, Hao Feng a,b,⇑, Weiguo Sun a,b, Huidong Li b, Yaoming Xie c, R. Bruce King c,⇑ a

School of Physics and Chemistry, Research Center for Advanced Computation, Xihua University, Chengdu 610039, China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, China c Department of Chemistry and Center for Computational Chemistry, University of Georgia, Athens, GA 30602, USA b

a r t i c l e

i n f o

Article history: Received 29 May 2013 Received in revised form 16 July 2013 Accepted 18 July 2013 Available online 31 July 2013 Keywords: Chromium Butadiene complexes Metal–metal bonding Metal carbonyls Density functional theory

a b s t r a c t Butadiene is known to form a chromium carbonyl complex (g4-C4H6)Cr(CO)4, which has been structurally characterized by X-ray crystallography. The structures and energetics of the butadiene chromium carbonyl complexes (C4H6)Cr(CO)m (m = 5, 4, 3, 2) and (C4H6)2Cr2(CO)n (n = 7, 6, 5) have now been investigated by density functional theory. The lowest energy (C4H6)2Cr2(CO)7 structure is a singlet singly bridged structure with a Cr–Cr single bond distance of 3.1 Å. This structure is predicted to be disfavored with respect to dissociation into mononuclear fragments. The lowest energy singlet (C4H6)2Cr2(CO)6 structure is an unbridged structure with a Cr@Cr double bond distance of 2.7 Å. However, a doubly bridged isomeric singlet (C4H6)2Cr2(CO)4(l-CO)2 structure with two bridging CO groups and a similar Cr@Cr double bond lies only slightly higher in energy. Related triplet (C4H6)2Cr2(CO)6 structures with longer Cr–Cr distances of 3.0 Å corresponding to formal single bonds are comparable in energy to the singlet structures. The hexacarbonyl (C4H6)2Cr2(CO)6 is predicted to be energetically disfavored with respect to disproportionation into (C4H6)2Cr2(CO)7 + (C4H6)2Cr2(CO)5. The lowest energy (C4H6)2Cr2(CO)5 structure has all terminal CO groups and a short Cr„Cr triple bond distance of 2.4 Å. A higher energy (C4H6)2Cr2(CO)5 structure by 4 kcal/mol has a four-electron donor g2-l-CO group and a Cr@Cr double bond distance of 2.7 Å. These (C4H6)2Cr2(CO)n (n = 7, 6, 5) structures are similar to the isomeric [(CH2)3C]2Cr2(CO)n structures that are previously reported except for some differences in the arrangements of the bridging carbonyl groups. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The chemistry of butadiene metal carbonyl derivatives dates back to the 1930 synthesis of butadiene iron tricarbonyl by Reihlen et al. [1] by reaction of butadiene with Fe(CO)5 at elevated temperatures in an autoclave. However, the structure of butadiene iron tricarbonyl remained obscure for many years until its reinvestigation by Hallam and Pauson [2] in 1958 a few years after the discovery of ferrocene [3,4]. The tetrahapto (g4-C4H6)Fe(CO)3 structure of butadiene–iron tricarbonyl anticipated from consideration of the 18-electron rule [5,6] (Fig. 1) was confirmed by Mills and Robinson [7] in 1963 using X-ray crystallography at 40 °C. Syntheses of butadiene derivatives of metal carbonyls other than iron began shortly after the elucidation of the structure of butadiene iron tricarbonyl. In general, such syntheses are more delicate than the synthesis of butadiene iron tricarbonyl and typically involve photolysis under mild conditions rather than simply heating butadiene with a metal carbonyl in an autoclave. Thus ⇑ Corresponding authors. Tel.: +1 7065421901; fax: +1 7065429454 (R.B. King). E-mail addresses: [email protected] (H. Feng), [email protected], [email protected] (R.B. King). 0020-1693/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ica.2013.07.042

the photolysis of butadiene with Co2(CO)8 was reported in 1961 by Fischer et al. [8] to give bis(butadiene)dicobalt tetra-carbonyl (g4-C4H6)2Co2(CO)4, which is of interest in being the first binuclear butadiene metal carbonyl derivative. Similarly, photolysis of butadiene with Cr(CO)6 at 40 °C gives the mononuclear (g4-C4 H6)Cr(CO)4 (Fig. 1), which surprisingly is significantly less stable than butadiene iron tricarbonyl [9]. The expected (g4-C4H6)Cr(CO)4 structure analogous to (g4-C4H6)Fe(CO)3 (Fig. 1) was recently confirmed by X-ray crystallography [10]. Such (diene)chromium tetracarbonyl complexes are of interest as intermediates in the photocatalytic hydrogenation of conjugated diolefins with Cr(CO)6 as the catalyst precursor [11,12]. In general the chemistry of binuclear chromium carbonyl derivatives, particularly those with formal metal–metal bonds, is very limited. Thus the saturated binary chromium carbonyl Cr2(CO)11 is predicted theoretically to be disfavored relative to its mononuclear dissociation products Cr(CO)6 + Cr(CO)5 consistent with the fact that Cr2(CO)11 has not been synthesized [13]. The unsaturated Cr2(CO)10 [14] and Cr2(CO)9 [15] are predicted to be more stable towards dissociation into mononuclear fragments than Cr2(CO)11. However, if Cr2(CO)11 is not a viable species, it is clearly not available as a precursor for the synthesis of Cr2(CO)10 or Cr2(CO)9.

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Co

Fe C O C O

C O

(η4-C4H6)Fe(CO)3

C O

O C

Co C O C O

(η4-C4H6)2Co2(CO)4

OC OC

Cr C O

CO

(η4-C4H6)Cr(CO)4

Fig. 1. Some simple butadiene metal carbonyl derivatives.

We have also used density functional theory to study binuclear trimethylene-methane chromium carbonyls of the type [(CH2)3C]2Cr2(CO)n in which two CO groups on each Cr atom are replaced by the umbrella-shaped trimethylenemethane ligand [16]. This substitution does not appear to have a major effect on the relative stabilities of mononuclear and binuclear derivatives. Thus [(CH2)3C]2Cr2(CO)7, which is predicted to have a structure closely related to that of Cr2(CO)11, is disfavored by 14 kcal/mol with respect to dissociation into (CH2)3CCr(CO)4 + (CH2)3CCr(CO)3. However, the unsaturated derivatives [(CH2)3C]2Cr2(CO)6 and particularly [(CH2)3C]2Cr2(CO)5 are predicted to be viable with respect to dissociation into the corresponding mononuclear fragments. This paper describes similar density functional theory studies of the binuclear butadiene chromium carbonyl derivatives (C4H6)2Cr2(CO)n (n = 7, 6, 5), which are isomers of the previously studied [16] trimethylenemethane derivatives [(CH2)3C]2Cr2(CO)n. However, there are important differences between the trimethylene-methane and butadiene ligands. Thus the branched trimethylenemethane ligand is more symmetrical and more compact than the straight chain butadiene ligand. Furthermore, since trimethylenemethane is not a stable molecule, it is not a good leaving group. In contrast, butadiene is a stable molecule and thus a good leaving group. In fact, a recent study [17] comparing the energetics of butadiene and CO losses from binuclear butadiene cobalt carbonyl derivatives find butadiene and CO loss processes to require similar energies. 2. Theoretical methods Double-f plus polarization (DZP) basis sets were used in this work. For carbon and oxygen, one set of pure spherical harmonic d functions is added with orbital exponents ad(C) = 0.75 and ad(O) = 0.85 to the Huzinaga–Dunning standard contracted DZ sets, and they are designated (9s5p1d/4s2p1d) [18,19]. For hydrogen, a set of p polarization functions ap(H) = 0.75 is added to the Huzinaga–Dunning DZ sets. For chromium, in our loosely contracted DZP basis set, the Wachters’ primitive set is used but is augmented by two sets of p functions and one set of d functions, contracted following Hood et al., and designated (14s11p6d/ 10s8p3d) [20,21]. Electron correlation effects have been included by employing density functional theory (DFT) methods, which have been suggested as a practical and effective computation tool, especially for organometallic compounds [22–29]. In our previous studies, two DFT methods (B3LYP [30,31] and BP86 [32,33]) were found to perform quite well. In order to be consistent and comparable with these previous studies, the same two DFT methods were used in the present study. The B3LYP and the BP86 methods are constructed in very different ways. The B3LYP method is a hybrid HF/DFT method using a combination of the three-parameter Becke functional (B3) with the Lee–Yang–Parr (LYP) correlation functional. This method includes exact exchanges and is calibrated by fitting three parameters to a set of experimental results. The BP86 method combines Becke’s 1988 exchange functional (B) with Perdew’s 1986 correlation functional method (P86). This method is mainly deduced by forcing the functional to satisfy certain exact

constraints based on first principles. When these two very different DFT methods agree, confident predictions can be made. The geometries of all structures were fully optimized using both the DZP B3LYP and DZP BP86 methods. The harmonic vibrational frequencies were determined at the same levels by evaluating analytically the second derivatives of the energy with respect to the nuclear coordinates. The corresponding infrared intensities were also evaluated analytically. All of the computations were carried out using the GAUSSIAN 09 program [34], in which the fine grid (75, 302) is the default for evaluating integrals numerically, and the tight designation is the default for the energy convergence. In the present paper each (C4H6)Cr(CO)n and (C4H6)2Cr2(CO)n structure is designated as ma-Xb where m is the number of Cr atoms, a is the number of CO groups (also the number of C4H6 ligands), X designates the spin state (S = singlet and T = triplet), and b orders the structures of a given spin state according to their BP86 relative energies. Thus the energetically lowest singlet (C4 H6)2Cr2(CO)7 structure predicted by BP86 is designated 27-S1. The relative energies of the structures discussed in this paper do not include the zero point energy corrections. The energies with zero point corrections are listed in the Supporting information (Table S49). The maximum zero point energy correction for the structures discussed in this paper is 2.0 kcal/mol. Most of the zero point energy corrections were less than 1 kcal/mol. 3. Results and discussion 3.1. Binuclear (C4H6)2Cr2(CO)n structures 3.1.1. (C4H6)2Cr2(CO)7 Only one low energy (C4H6)2Cr2(CO)7 structure is found using the B3LYP and the BP86 methods (Fig. 2 and Table 1). This structure 27-S1 is a singly bridged C1 singlet structure. The bridging CO group, which exhibits a relatively low m(CO) frequency of 1773 cm1 (BP86), is slightly unsymmetrical with a short Cr–C distance of 2.005 Å (B3LYP) or 2.036 Å (BP86) and a long Cr–C distance of 2.262 Å (B3LYP) or 2.152 Å (BP86). The Cr–Cr distance of 3.180 Å (B3LYP) or 3.089 Å (BP86) in 27-S1 can be interpreted as the formal single bond needed to give each chromium atom the favored 18-electron configuration. 2

1

3 4

O

1.160 1.174

1.866 1.858 1.916 Cr1 1.903

C

O

C 1.161 1.176

1.882 1.866

1.162 1.176

O

O C 1.181

3.180 3.089

O 1.173 1.909 C 1.896

C

2.262 2.152

C

1.164 O 1.177 1.159

1.900 1.884

1.201 2.005 2.036 1.914

Cr2 1.900

C

1.159 1.174

O

8 7

5

6

27-S1 (C1) Fig. 2. The optimized (C4H6)2Cr2(CO)7 structure. The upper distances were obtained by the B3LYP method and the lower distances were obtained by the BP86 method.

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The bridging CO groups in 26-S2 exhibit relatively low m (CO) frequencies of 1764 and 1785 cm1. The Cr@Cr distance of 2.741 Å (B3LYP) or 2.732 Å (BP86) in 26-S2 is similar to that in 26-S1 and likewise may be interpreted as a formal double bond. This gives each Cr atom the favored 18-electron configuration. The BP86 method predicts 26-S2 to have only real vibrational frequencies. However, the B3LYP method predicts 26-S2 to have a large imaginary vibrational frequency of 170i cm1. Following the corresponding normal mode leads to a C1 structure 26-S3 and lowers the energy to 0.2 kcal/mol below 26-S1. Reoptimizing the B3LYP structure 26-S3 using the BP86 method reverts to 26S2. Structure 26-S3 has a four-electron donor bridging g2-l-CO group with a Cr–Cr distance of 2.929 Å (B3LYP) corresponding to a formal single bond. Thus each Cr atom has the favored 18-electron configuration in 26-S3 as in 26-S2. Conversion of a two-electron donor bridging CO group in 26-S2 to a four-electron donor CO group in 26-S3 balances out the reduction of the formal Cr–Cr bond order from 2 in 26-S2 to 1 in 26-S3. The lowest lying triplet (C4H6)2Cr2(CO)6 structure 26-T1 is a C1 doubly semibridged structure lying 4.7 kcal/mol (B3LYP) below or 3.0 kcal/mol (BP86) above 26-S1 (Fig. 3 and Table 2). The

Table 1 Total energies (E in hartree) and Cr–Cr bond distances (in Å) for the (C4H6)2Cr2(CO)7 structure 27-S1. 27-S1 (C1)

Cr–Cr E

B3LYP

BP86

3.180 3194.58714

3.089 3194.99860

3.1.2. (C4H6)2Cr2(CO)6 Four low-lying (C4H6)2Cr2(CO)6 structures were found using the B3LYP and BP86 methods, namely the singlet structures 26-S1 and 26-S2 and the triplet structures 26-T1 and 26-T2 (Fig. 3 and Table 2). The global minimum is the unbridged C2 singlet (C4H6)2Cr2(CO)6 structure 26-S1. The Cr@Cr distance of 2.767 Å (B3LYP) or 2.689 Å (BP86) in 26-S1 is 0.4 Å shorter than the formal Cr–Cr single bond in 27-S1 and thus can be interpreted as a formal double bond. This gives each chromium atom the favored 18-electron configuration. The second singlet (C4H6)2Cr2(CO)6 structure is a Cs doubly bridged structure 26-S2 lying 4.0 kcal/mol (B3LYP) or 0.6 kcal/ mol (BP86) above the global minimum 26-S1 (Fig. 3 and Table 2).

1

1 2

2 3

4 1.157 O 1.173

4

1.924 1.903

C

C r1 1.891 1.883 C 1.861 O 1.861 C 1.166 1.178 2.767 2.689 O

O

C

C

1

3

O C

O

3.004 2.354 O

O

Cr 2

5

1.166 1.192

C

C 1.894 1.912

1.161 1.176

O

O

C C

1.157 1.175

1.901 1.886

C r1

1.908 1.886

1.916 1.874

1.165

C 1.182 O

3.086 2.963

O C 1.164 Cr 2 1 .89 8 1.176 1 .88 2

O O

O C

C

C

Cr 2

6 5

5

1.164 O 1.177

26-S1 (C2)

6 7

8

26-T1 (C1)

26-T2 (C2)

O

O

1.158

O

O

C

1.160 1.174

O 1.161 1.175

C 1.873 1.856

1

C

1.202

1.878 2.038 1.869 2.044 2.741 Cr1 2.732 2.099 2.062

4 2

O 1.185

C

1.178 1.199

3

C O

O

C

1.919

C Cr2

7

1.164

C

O 1.182

1.859 2.146

4 2

2.929

26-S2 (Cs)

C

C

1.164

Cr2 5

C

3.003

O

26-S3 (C1, B3LYP) Fig. 3. The optimized (C4H6)2Cr2(CO)6 structures.

O

2.524 1.174

3

1.160

C 2.0191.889 1.841

1.879

5

6

O

Cr1

1

8

3

4

C r1 1.902 1.942 1 .16 9 1 .19 4 C O

7 1.856 C 1.849

2

O

3 .06 8 2 .80 0 2 .99 7 2 .31 2

8

6 7

8

1.919 1.875

1 .15 9 1 .91 5 1 .17 2 1 .89 9

1.166 1.183

C

1 .15 6 1 .17 4

8 7

6

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Table 2 Total energies (E in hartree), relative energies (DE in kcal/mol), Cr–Cr bond distances (in Å), numbers of imaginary vibrational frequencies (Nimg), and spin expectation values (hS2i) for the (C4H6)2Cr2(CO)6 structures. 26-S1 (C2)

Cr–Cr E DE Nimg

26-S2 (Cs) BP86

B3LYP

BP86

B3LYP

2.767 3081.21677 0.0 none

2.689 3081.62879 0.0 none

2.741 3081.21034 4.0 1(170i)

2.732 3081.62785 0.6 none

2.929 3081.21653 0.2 none

26-T1 (C1)

Cr–Cr E DE Nimg hS2i

26-S3 (C1)

B3LYP

26-T2 (C2)

B3LYP

BP86

B3LYP

BP86

3.068 3081.22423 –4.7 none 2.11

2.800 3081.62393 3.0 none 2.03

3.086 3081.22703 –6.4 none 2.07

2.963 3081.61914 6.1 none 2.03

discrepancy between the single–triplet splittings using the B3LYP and the BP86 methods is not surprising, since Reiher and co-workers [35,36] found that the B3LYP method always favors the high spin electronic state and the BP86 method favors the low spin state. The true singlet–triplet splitting should lie between the B3LYP and BP86 predictions. The B3LYP method predicts very weakly semibridging CO groups in 26-T1 with short Cr–C distances of 1.90 Å and long Cr–C distances of 3.0 Å combined with a Cr– Cr distance of 3.068 Å. However, the BP86 method predicts much stronger semibridging CO groups in 26-T1 with short Cr–C distances of 1.93 Å and long Cr–C distances of 2.33 Å combined with a shorter Cr–Cr distance of 2.800 Å. These semibridging CO groups in 26-T1 exhibit m(CO) frequencies of 1812 and 1827 cm1, which are 100 cm1 below the lowest terminal m(CO) frequency. The shortening of a Cr–Cr distance of a given formal bond order with increasing strength of the bridging CO group is consistent with past observations. A formal Cr–Cr single bond in 26-T1 gives each chromium atom a 17-electron configuration for a binuclear triplet. The other triplet (C4H6)2Cr2(CO)6 structure 26-T2 is an unbridged C2 structure lying 6.4 kcal/mol (B3LYP) below or 6.1 kcal/ mol (BP86) above 26-S1 (Fig. 3 and Table 2). The Cr–Cr distance of 3.086 Å (B3LYP) or 2.963 Å (BP86) in 26-T2 is similar to that in 27-S1 and can likewise be interpreted as a formal single bond. This gives each chromium atom the 17-electron configuration for a binuclear triplet. 3.1.3. (C4H6)2Cr2(CO)5 The six low-lying (C4H6)2Cr2(CO)5 structures include the three singlet structures 25-S1, 25-S2, and 25-S3 and the three triplet structures 25-T1, 25-T2, and 25-T3 (Fig. 4 and Table 3). Two higher energy quintet structures 25-Q1 and 25-Q2 were found having energies by the BP86 method more than 18 kcal/mol above 25S1. Because of their high energies, these quintet structures are not discussed in this paper. The doubly semibridged C1 singlet structure 25-S1 is the (C4H6)2Cr2(CO)5 global minimum (Fig. 4 and Table 3). The semibridging CO groups have short Cr–C distances of 1.85 Å and long Cr–C distances of 2.5 Å and exhibit m(CO) frequencies at 1877 and 1885 cm1 (BP86), which are 30 cm1 below the lowest terminal m(CO) frequency. The Cr„Cr distance in 25-S1 of 2.385 Å (B3LYP) or 2.361 Å (BP86) is 0.3 to 0.4 Å shorter than the formal Cr@Cr double bond distance in 26-S1 thus suggesting a formal triple bond in 25-S1. This gives each chromium atom the favored 18-electron configuration. The formal Cr„Cr triple bond in the cyclopentadienylchromium carbonyl derivative (g5-Me5C5)2Cr2(CO)4 is found experimentally by X-ray crystallography [37] to be somewhat shorter at 2.24 Å.

The (C4H6)2Cr2(CO)5 structure 25-S2, lying 4.9 kcal/mol (B3LYP) or 3.1 kcal/mol (BP86) above 25-S1, is also a C1 doubly bridged structure (Fig. 4 and Table 3). One of the bridging CO groups in 25-S2 is a four-electron donor g2-l-CO group as indicated by a short Cr–O distance of 2.195 Å (B3LYP) or 2.262 Å (BP86) and a very low m(CO) frequency of 1700 cm1. The other bridging CO group in 25-S2 is a two-electron donor semibridging CO group with a short Cr–C distance of 1.935 Å (B3LYP) or 1.915 Å (BP86) and a long Cr–C distance of 2.393 Å (B3LYP) or 2.356 Å (BP86). This l-CO group exhibits a m(CO) frequency of 1832 cm1, which lies between the m(CO) frequency of the four-electron donor g2-l-CO group and those of the terminal CO groups. The Cr@Cr distance of 2.853 Å (B3LYP) or 2.750 Å (BP86) in 25-S2 is 0.4 Å longer than that of the Cr„Cr triple bond in 25-S1 and thus suggests a formal double bond in 25-S2. This gives each chromium atom in 25-S2 the favored 18-electron configuration after allowing for the four electrons donated by the g2-l-CO group to the central Cr2 unit. The third singlet (C4H6)2Cr2(CO)5 structure 25-S3 is a singly semibridged structure lying 1.2 kcal/mol (B3LYP) below or 7.8 kcal/mol (BP86) above 25-S1 (Fig. 4 and Table 3). The B3LYP method predicts an unsymmetrical semibridging CO group in 25-S3 with a short Cr–C distance of 1.865 Å and a long Cr–C distance of 2.342 Å combined with a Cr@Cr distance of 2.423 Å. However, the BP86 method predicts a more nearly symmetrical semibridging CO group in 25-S3 with a short Cr–C distance of 1.847 Å and a long Cr–C distance of 2.055 Å combined with a longer Cr@Cr distance of 2.652 Å. The semibridging CO group in 25-S3 exhibit a m(CO) frequency of 1723 cm1, which is 170 cm1 below the lowest terminal m(CO) frequency. In 25-S3 the Cr„Cr distance of 2.423 Å obtained by the B3LYP method can correspond to a formal triple bond, thereby giving each chromium atom the favored 18-electron configuration. The significantly longer Cr@Cr distance of 2.652 Å in 25-S3 by the BP86 method is more likely to be a formal double bond. This gives one of the chromium atoms the favord 18-electron configuration but the other chromium atom only a 16-electron configuration. The triplet (C4H6)2Cr2(CO)5 structure 25-T1, lying 1.5 kcal/mol (B3LYP) or 8.4 kcal/mol (BP86) above 25-S1, is a C1 singly bridged isomer (Fig. 4 and Table 3). The bridging CO group in 25-T1 is a four-electron donor g2-l-CO group as indicated by a short Cr–O distance of 2.206 Å (B3LYP) or 2.238 Å (BP86) and a very low m(CO) frequency of 1671 cm1. The Cr–Cr distance of 3.088 Å (B3LYP) or 2.948 Å (BP86) in 25-T1 suggests a formal single bond. This gives each chromium atom a 17-electron configuration for a binuclear triplet after allowing for the four electrons donated by the g2-l-CO group to the central Cr2 unit. The (C4H6)2Cr2(CO)5 structure 25-T2, lying 5.8 kcal/mol (B3LYP) or 14.1 kcal/mol (BP86) in energy above 25-S1, is a C1 triply semibridged structure (Fig. 4 and Table 3). The Cr@Cr distance of

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1

4

O

3

1.165 C 1.180 1.849 1.828 1.174 1.188 C

O

O

Cr 1

1.849 1.846

1.158 1.172

2.515 2.569

2.385 2.361 C 1.852 1.850

2.529 2.542

C

4

O

O C

3

1.163 1.181 C 1.845 1.824 C r1 2.195 1.935 2.262 1.915

1.207 1.222

1.172 1.184

1.899 1.891

C r2

1.918 1.903

O

2

C

2.116 2.025 2.853 2.750

C

1.806 1.823 1.884 1.160 1.174 1.876

O

1.168 1.185

O C

1 2

O

O

1.841 1.859

O

C

1.161 1.183 1.880 Cr1 1.827

2.393 2.356

7

1.861 1.846

5

7

6

O

25-S1 (C1)

O C C

1.927 1.877

1.160 1.178

1.896 1.851

Cr1

1

O 1.165 1.184 3.088 2.948

1.832 1.810

2

4

C

C

O

1.925 1.891

1.861 1.839

8

Cr2

2.155 2.119 2.205 C 2.238 1.210 O 1.225

3

1.157 1.174

C 1.174 1.193

2.468 2.269

C

8

1.164 1.176

O 1.166 Cr 1 1.884 1.877

C

2.851 2.751

1.153 1.173

1.180

O

2.623 2.506

C

C

O

C Cr1

1

O

1.194

C

3

8

25-T2 (C1)

5

1.853 1.833

Cr2

2.766 2.623

C O

O

C

1.884 1.888

1.958 2.417 1.892 2.281

4 2

1.165 1.179

O 1.178

1.173

2.552 2.421

7

6

O 1.155

1.979 1.895

1.171 1.937 1.188 1.901 Cr 2 1.989 1.920 C 1.152 1.172

5 6

25-T1 (C1)

7

3

2

2.747 2.607

7 5

Cr2

4 C

1.157 1.175

5

25-S3 (C1)

1

1.164 1.177 1.854 1.840 1.876 1.893

O

6

1.909 1.870

1.908 1.882

O

25-S2 (C1)

O

O

1.160 1.175

C

4

1

5

1.163 1.176

C

2.423 2.652

2

6

8

O

2.342 1.865 2.055 1.847

3

C

8

1.176 1.216

C

1.177 1.193

C r2

O

1.166 1.181

1.878 1.870

1.175 1.191

6 8 7

25-T3 (C1)

Fig. 4. The optimized singlet and triplet (C4H6)2Cr2(CO)5 structures.

Table 3 Total energies (E in hartree), relative energies (DE in kcal/mol), Cr–Cr bond distances (in Å), numbers of imaginary vibrational frequencies (Nimg), and spin expectation values (hS2i) for the (C4H6)2Cr2(CO)5 structures. None of these structures has any imaginary vibrational frequencies. 25-S1 (C1)

Cr–Cr E DE

25-S2 (C1) BP86

B3LYP

BP86

B3LYP

BP86

2.385 2967.87065 0.0

2.361 2968.27095 0.0

2.853 2967.86279 4.9

2.750 2968.26602 3.1

2.423 2967.87249 1.2

2.652 2968.25858 7.8

25-T1 (C1)

Cr–Cr E DE hS2i

25-S3 (C1)

B3LYP

25-T2 (C1)

25-T3 (C1)

B3LYP

BP86

B3LYP

BP86

B3LYP

BP86

3.088 2967.86823 1.5 2.09

2.948 2968.25762 8.4 2.03

2.747 2967.86138 5.8 2.55

2.607 2968.24848 14.1 2.10

2.766 2967.85807 7.9 2.66

2.623 2968.24690 15.1 2.09

2.747 Å (B3LYP) or 2.607 Å (BP86) suggests a formal double bond thereby giving each chromium atom a 17-electron configuration corresponding to a binuclear triplet. The (C4H6)2Cr2(CO)5 structure 25-T3, lying 7.9 kcal/mol (B3LYP) or 15.1 kcal/mol (BP86) above 25-S1, is a C1 doubly semibridged structure similar to 25-S2 (Fig. 4 and Table 3). The semibridging CO groups in the B3LYP 25-T3 structure have short Cr–C distances of 1.878 and 1.884 Å and long Cr–C distances of 2.552 and 2.417 Å

across a 2.766 Å Cr@Cr bond. The semibridging CO groups in the BP86 25-T3 structure are somewhat stronger with short Cr–C distances of 1.870 and 1.888 Å and long Cr–C distances of 2.421 and 2.281 Å across a somewhat shorter 2.623 Å Cr@Cr double bond. The semibridging CO groups are predicted to exhibit m(CO) frequencies at 1814 and 1844 cm1 (BP86), which is 100 cm1 below the lowest terminal m(CO) frequency. The Cr@Cr distance of 2.766 Å (B3LYP) or 2.623 Å (BP86) in 25-T3 suggests a formal

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double bond. This gives each chromium atom in 25-T3 the 17-electron configuration for a binuclear triplet.

3 2

3.2. Mononuclear (C4H6)Cr(CO)n structures

3.2.2. (C4H6)Cr(CO)4 The triplet (C4H6)Cr(CO)4 structures are not reported in the present paper because of their very high energies relative to the singlet structure similar to the (C4H6)Cr(CO)5 system discussed above. Thus only one singlet (C4H6)Cr(CO)4 structure 14-S1 is reported in this paper (Fig. 5). In this Cs structure the chromium atom has four carbonyl groups and a tetrahapto butadiene ligand thereby giving the chromium atom in 14-S1 the favored 18-electron configuration. This predicted structure for (C4H6)Cr(CO)4 is similar to the experimental structure, determined by X-ray crystallography [10]. 3.2.3. (C4H6)Cr(CO)3 Two optimized (C4H6)Cr(CO)3 structures were obtained with each of the B3LYP and the BP86 methods (Fig. 6 and Table 4). The singlet Cs structure 13-S1 is the lowest energy of these structures. The C1 triplet structure 13-T1 lies 9.4 kcal/mol (B3LYP) or 14.9 kcal/mol (BP86) in energy above 13-S1. The central chromium atoms in 13-S1 and 13-T1 each have a 16-electron configuration. 3.2.4. (C4H6)Cr(CO)2 Singlet, triplet, and quintet (C4H6)Cr(CO)2 structures were obtained using each of the B3LYP and the BP86 methods (Fig. 7 and Table 5). The C1 triplet structure 12-T1 is the global minimum. The singlet (C4H6)Cr(CO)2 structure 12-S1 lies 12.6 kcal/mol (B3LYP) or 7.7 kcal/mol (BP86) above 12-T1. The quintet (C4H6)Cr(CO)2 structure 12-Q1 has Cs symmetry (B3LYP) or C1 symmetry (BP86), and lies in energy 0.9 kcal/mol (B3LYP) or 8.9 kcal/mol (BP86) above the 12-T1 global minimum. The chromium atoms in all three (C4H6)Cr(CO)2 structures have a 14 electron configuration.

4

2

O

1.156 1.171 1.921 C 1.906

1

Cr 1.911 1.915 C C 1.898 1.900 1.158 O O 1.159 1.875 1.173 1.173 1.862 C 1.165 1.174 O

15S-1 (C1)

1.833 1.880 1.168 1.808 Cr 1.861 1.162 1.185 C C 1.178 1.880 O 1.861 O C 1.162 1.178 O

4

1 Cr

O

1.906 1.872

1.161 C 1.949 C 1.178 1.936 1.158 1.912 1.890 O 1.175 C 1.158 1.175 O

13-S1 (Cs)

13-T1 (C1)

Fig. 6. The two optimized (C4H6)Cr(CO)3 structures.

Table 4 Total energies (E in hartree) and relative energies (DE in kcal/mol) for the (C4H6)Cr(CO)3 structures. Neither structure has any imaginary vibrational frequencies. 13-S1 (Cs)

E DE

13-T1 (C1)

B3LYP

BP86

B3LYP

BP86

1540.62146 0.0

1540.81660 0.0

1540.60647 9.4

1540.79287 14.9

3.3. Atomic population, natural bonding orbital (NBO) analyses, and chromium–chromium bonding Table 6 lists the Wiberg bond indices (WBIs) and bond distances for the Cr–Cr bonds in the singlet (C4H6)2Cr2(CO)n structures (n = 7, 6, 5) using the BP86 method. The WBIs are seen to follow a consistent pattern. Thus the Cr–Cr single bond in 27-S1 of length 3.089 Å has a WBI of 0.26. Formal Cr@Cr double bonds in the singlet (C4H6)2Cr2(CO)n structures ranging in length from 2.652 to 2.750 Å have WBIs ranging from 0.55 to 0.76. The one example of a formal Cr„Cr triple bond occurs in the (C4H6)2Cr2(CO)5 structure 25-S1 with a Cr„Cr distance of 2.361 Å and a WBI of 0.88. These WBI values for the chromium–chromium bonds in the (C4H6)2Cr2(CO)n derivatives are consistent with previous studies [38] on metal–metal bonded derivatives, which suggest typical WBI values of 0.2 to 0.3 for unbridged formal metal–metal single bonds. Thus, for at least the singlet (C4H6)2Cr2(CO)n derivatives (n = 7, 6, 5), the WBI values support the metal–metal bond order assignments based on metal– metal distances and electron counting discussed above. The natural charge on a given Cr atom appears to be related mainly to the number of the carbonyl groups to which it is bonded (Table 6) with an increasing number of Cr–CO bonds leading to an increased natural negative charge. This suggests that the negative charge on the Cr atom from OC ? Cr forward bonding is not completely counterbalanced by the concurrent Cr ? CO p ? p⁄ back-bonding. 3.4. Dissociation energies

2 1.158 1.914 1.172 O 1.898 C

3 2

1

3.2.1. (C4H6)Cr(CO)5 Both singlet and triplet state (C4H6)Cr(CO)5 structures were optimized. However, the triplet structures were found to lie at least 48 kcal/mol above the singlet structures and thus are not discussed in this paper (Fig. 5). Thus only the singlet (C4H6)Cr(CO)5 structure 15-S1 is reported here. Structure 15-S1 has a dihapto butadiene ligand thereby giving the chromium atom the favored 18-electron configuration. The midpoint of the central C–C bond of the butadiene ligand and the five CO groups form an octahedron around the central chromium atom in 15-S1.

3

4

3 1

4

1.899 1.910 1.161 1.882 Cr 1.894 1.159 1.176 C C 1.173 O 1.872 O 1.858 1.872 1.858 C 1.162 C 1.162 1.176 1.176 O O

14S-1 (Cs)

Fig. 5. The optimized structures of (C4H6)Cr(CO)n (n = 5, 4).

The predicted dissociation energy (Table 7) for the loss of one CO group from (C4H6)2Cr2(CO)7 (27-S1) to give (C4H6)2Cr2(CO)6 (26-S1) is 26.2 kcal/mol (B3LYP) or 26.7 kcal/mol (BP86). This carbonyl dissociation energy is similar to the related experimental CO dissociation energies [39] of 27, 41 and 37 kcal/mol for Ni(CO)4, Fe(CO)5, and Cr(CO)6, respectively. However, further dissociation of a CO group from (C4H6)2Cr2(CO)6 (26-S1) to give (C4H6)2Cr2(CO)5 (25-S1) requires significantly less energy of 11.0 kcal/mol (B3LYP) or 19.2 kcal/mol (BP86). This lower CO dissociation energy of (C4H6)2Cr2(CO)6 relative to (C4H6)2Cr2(CO)7 is consistent with the exothermic disproportionation of (C4H6)2Cr2(CO)6 to give

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3

2

O

2

1.862 1.832

Cr

1.893 1.840 C 1.164 1.183

1.924 1.879

C

O

O

12-S1 (C1)

3

4

1

1 Cr

C

4

4

1

1.169 1.186

3

2

1.935 1.896

Cr

C 1.161 1.178

1.162 1.180

C

2.002 1.937

2.053 1.990

1.155 C 1.175

O 1.154 1.174

O

12-T1 (C1)

O

12-Q1 (Cs, C1)

Fig. 7. The optimized (C4H6)Cr(CO)2 structures.

Table 5 Total energies (E in hartree) and relative energies (DE in kcal/mol) of the (C4H6)Cr(CO)2 structures. None of the structures has any imaginary vibrational frequencies. 12-S1 (C1)

E DE

12-T1 (C1)

12-Q1 (Cs, C1)

B3LYP

BP86

B3LYP

BP86

B3LYP

BP86

1427.21114 12.6

1427.39167 7.7

1427.23119 0.0

1427.40391 0.0

1427.22970 0.9

1427.38976 8.9

Table 6 Atomic charges and Wiberg bond indices for the (C4H6)2Cr2(CO)n structures by the BP86 method.

(C4H6)2Cr2(CO)7 (C4H6)2Cr2(CO)6 (C4H6)2Cr2(CO)6 (C4H6)2Cr2(CO)5 (C4H6)2Cr2(CO)5 (C4H6)2Cr2(CO)5

(27-S1) (26-S1) (26-S2) (25-S1) (25-S2) (25-S3)

Natural charge on Cr1/Cr2

Wiberg bond index

Cr–Cr distance (Å)

Formal Cr–Cr bond order

1.714/1.798 1.420/1.420 1.450/1.450 0.907/1.547 0.678/1.686 0.811/1.525

0.26 0.74 0.61 0.88 0.55 0.76

3.089 2.689 2.732 2.361 2.750 2.652

1 2 2 3 2 2

(C4H6)2Cr2(CO)7 + (C4H6)2Cr2(CO)5 by 15.2 kcal/mol (B3LYP) or 7.5 kcal/mol (BP86). The homoleptic binuclear chromium carbonyl Cr2(CO)11 has never been synthesized and is predicted theoretically to be disfavored with respect to dissociation into Cr(CO)6 + Cr(CO)5 [13]. The heptacarbonyl (C4H6)2Cr2(CO)7 may be derived from Cr2(CO)11 by replacement of two CO groups on each chromium atom by a butadiene ligand. Similar to Cr2(CO)11, the butadiene derivative (C4H6)2Cr2(CO)7 is predicted to be disfavored with respect to the mononuclear derivatives (C4H6)Cr(CO)4 + (C4H6)Cr(CO)3 by 18.7 kcal/mol (B3LYP) or 11.7 kcal/mol (BP86) (Table 7). In addition, the dissociation of (C4H6)2Cr2(CO)6 into 2 (C4H6)Cr(CO)3 fragments is an exothermic process. However, (C4H6)2Cr2(CO)5 is predicted to be viable with respect to dissociation into mononuclear fragments and thus represents the most promising synthetic target among the binuclear derivatives.

4. Discussion The low-energy structures of the binuclear butadiene chromium carbonyl complexes (C4H6)2Cr2(CO)n studied in this work can be compared with the low-energy structures of the previously studied isomeric trimethylenemethane chromium carbonyl complexes [(CH2)3C]2Cr2(CO)n (n = 7, 6, 5). Only single low-energy singlet structures were found for the isomeric heptacarbonyls (C4 H6)2Cr2(CO)7 and [(CH2)3C]2Cr2(CO)7. These structures are quite similar with essentially identical predicted Cr–Cr distances of 3.18 Å (B3LYP) or 3.09 Å (BP86) corresponding to the formal single bonds required to give each chromium atom the favored 18-electron configuration. In this (C4H6)2Cr2(CO)7 structure one of the CO groups is a bridging group but the remaining six CO groups are terminal CO groups. The low energy [(CH2)3C]2Cr2(CO)7 structure has a similar bridging CO group. However, one of the

Table 7 Bond dissociation energies (kcal/mol) for removal of one carbonyl group and disproportionation energies of the (C4H6)2Cr2(CO)n (n = 7, 6, 5) derivatives.

(C4H6)2Cr2(CO)7 (27-S1) ? (C4H6)2Cr2(CO)6 (26-S1) + CO (C4H6)2Cr2(CO)6 (26-S1) ? (C4H6)2Cr2(CO)5 (25-S1) + CO 2 (C4H6)2Cr2(CO)6 (26-S1) ? (C4H6)2Cr2(CO)7 (27-S1) + (C4H6)2Cr2(CO)5 (25-S1) (C4H6)2Cr2(CO)7 (27-S1) ? (C4H6)Cr(CO)4 (14-S1) + (C4H6)Cr(CO)3 (13-S1) (C4H6)2Cr2(CO)6 (26-S1) ? 2(C4H6)Cr(CO)3 (13-S1) (C4H6)2Cr2(CO)6 (26-S1) ? (C4H6)Cr(CO)4 (14-S1) + (C4H6)Cr(CO)2 (12-S1) (C4H6)2Cr2(CO)5 (25-S1) ? (C4H6)Cr(CO)3 (13-S1) + (C4H6)Cr(CO)2 (12-S1) (C4H6)Cr(CO)5 (15-S1) ? (C4H6)Cr(CO)4 (14-S1) + CO (C4H6)Cr(CO)4 (14-S1) ? (C4H6)Cr(CO)3 (13-S1) + CO (C4H6)Cr(CO)3 (13-S1) ? (C4H6)Cr(CO)2 (12-S1) + CO

B3LYP

BP86

26.2 11.0 15.2 18.7 16.4 6.4 23.9 17.4 28.5 51.2

26.7 19.2 7.5 11.7 2.8 22.9 39.3 17.6 35.7 61.3

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remaining six CO groups is a weakly semibridging CO group with a long Cr–C distance of 2.98 Å (B3LYP) or 2.78 Å (BP86). Both (C4H6)2Cr2(CO)7 and [(CH2)3C]2Cr2(CO)7 are predicted to be thermochemically disfavored with respect to dissociation into mononuclear fragments similar to the experimentally unknown Cr2(CO)11 from which they are derived. The lowest energy (C4H6)2Cr2(CO)6 and [(CH2)3C]2Cr2(CO)6 structures are both singlet spin state structures having Cr@Cr distances ranging from 2.69 to 2.84 Å interpreted as the formal double bonds required to give each chromium atom the favored 18-electron configuration. In this (C4H6)2Cr2(CO)6 structure all six CO groups are terminal CO groups. However, in the lowest energy [(CH2)3C]2Cr2(CO)6 structure one of the six CO groups is a bridging CO group. Higher energy singlet (C4H6)2Cr2(CO)6 and [(CH2)3C]2Cr2(CO)6 structures are found with similar Cr@Cr double bond distances but with two bridging or semibridging CO groups. In this doubly bridged (C4H6)2Cr2(CO)6 structure these bridging CO groups are symmetrical bridges whereas in the otherwise corresponding [(CH2)3C]2Cr2(CO)6 structure these bridging CO groups are actually only weakly semibridging with long Cr–C distances of 2.7 Å. Both (C4H6)2Cr2(CO)6 and [(CH2)3C]2Cr2(CO)6 are disfavored with respect to disproportionation into the corresponding hepta- and pentacarbonyls. For (C4H6)2Cr2(CO)6 related triplet spin state structures are found within 3 kcal/mol of the global minimum using the BP86 method, which normally favors low-spin states. However, for [(CH2)3C]2Cr2(CO)6 the lowest lying triplet spin state structure lies 14 kcal/mol above the global minimum using the BP86 method. The lowest lying (C4H6)2Cr2(CO)5 and [(CH2)3C]2Cr2(CO)5 structures are unbridged structures suggested to have formal Cr„Cr triple bonds thereby giving each chromium atom the favored 18electron configuration. The Cr„Cr triple bond distance is 2.37 Å in this (C4H6)2Cr2(CO)5 structure, whereas in the corresponding [(CH2)3C]2Cr2(CO)5 structure the Cr„Cr triple bond distance is significantly longer at 2.509 Å (B3LYP) or 2.424 Å (BP86). However, for [(CH2)3C]2Cr2(CO)5 a slightly higher energy structure was found with a Cr„Cr distance of 2.391 Å (B3LYP) or 2.304 Å (BP86) closer to the Cr„Cr distance for the (C4H6)2Cr2(CO)5. For (C4H6)2Cr2(CO)5 a structure with a four-electron donor g2-l-CO group and a Cr@Cr double bond of length 2.853 Å (B3LYP) or 2.753 Å (BP86) was found in contrast to the isomeric [(CH2)3C]2Cr2(CO)5. In summary, the differences between isomeric (C4H6)2Cr2(CO)n and [(CH2)3C]2Cr2(CO)n (n = 7, 6, 5) are predicted to be rather subtle ones, mainly involving bridging and semibridging CO groups rather than the chromium–chromium bonding. These differences may be related to the different geometries of the isomeric hydrocarbon ligands, namely linear for the butadiene ligand and branched for the trimethylenemethane ligand. 5. Summary The lowest energy (C4H6)2Cr2(CO)7 structure is a singlet singly bridged structure with a Cr–Cr distance of 3.1 Å corresponding to a formal single bond. This structure is predicted to be disfavored with respect to dissociation into the mononuclear fragments (C4H6)Cr(CO)4 + (C4H6)Cr(CO)3. The lowest energy singlet (C4H6)2 Cr2(CO)6 structure is an unbridged structure with a Cr@Cr distance of 2.7 Å corresponding to a formal double bond. However, a doubly bridged isomeric singlet (C4H6)2Cr2(CO)4(l-CO)2 structure with two bridging CO groups and a similar Cr@Cr double bond lies only slightly higher in energy. Related triplet (C4H6)2Cr2(CO)6 with longer Cr–Cr distances of 3.0 Å corresponding to formal single bonds are comparable in energy to the singlet structures. The hexacarbonyl (C4H6)2Cr2(CO)6 is predicted to be disfavored with respect to disproportionation into (C4H6)2Cr2(CO)7 + (C4H6)2Cr2(CO)5.

The pentacarbonyl (C4H6)2Cr2(CO)5 appears to be the most promising synthetic objective. The lowest energy (C4H6)2Cr2(CO)5 structure has all terminal CO groups and a short Cr„Cr distance of 2.4 Å interpreted as a formal Cr„Cr triple bond. A higher energy (C4H6)2Cr2(CO)5 structure by 4 kcal/mol has a four-electron donor g2-l-CO group and a Cr@Cr distance of 2.7 Å corresponding to a formal double bond. Acknowledgments This study was supported by the National Natural Science Foundation of China (Grant Nos. 11204244 and 11074204), the Program for New Century Excellent Talents in University (Grant No. NCET10-0949), the Youth Foundation (Grant No. 2012JQ0055) of the Department of Science and Technology, the Fund of Key Laboratory of Advanced Scientific Computation, Xihua University, China, and the US National Science Foundation (Grant CHE-1057466). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ica.2013.07.042. References [1] O. Reihlen, A. Gruhl, G. Hessling, O. Pfrengle, Liebigs Ann. Chem. 482 (1930) 161. [2] B.F. Hallam, P.L. Pauson, J. Chem. Soc. (1958) 642. [3] T.J. Kealy, P.L. Pauson, Nature 168 (1961) 1039. [4] S.A. Miller, J.A. Tebboth, J.F. Tremaine, J. Chem. Soc. (1952) 632. [5] N.V. Sidgwick, R.W. Bailey, Proc. R. Soc. London, A 144 (1934) 521. [6] P. Pyykkö, J. Organomet. Chem. 691 (2006) 4336. [7] O.S. Mills, G. Robinson, Acta Crystallogr. 16 (1963) 758. [8] E.O. Fischer, P. Kuzel, H.P. Fritz, Z. Naturforsch. 16b (1961) 138. [9] I. Fischler, M. Budzwait, E.A. Koerner von Gustorf, J. Organomet. Chem. 105 (1976) 325. [10] G.J. Reiss, M. Finze, Acta Crystallogr., Sect. E 67 (2011) m333. [11] J. Nasielski, P. Kirsch, L. Wilputte-Steinert, J. Organomet. Chem. 27 (1971) C13. [12] M. Wrighton, M.A. Schroeder, J. Am. Chem. Soc. 95 (1973) 5764. [13] N.A. Richardson, Y. Xie, R.B. King, H.F. Schaefer, J. Phys. Chem. A 105 (2001) 11134. [14] S. Li, N.A. Richardson, Y. Xie, R.B. King, H.F. Schaefer, Faraday Discuss. 124 (2003) 315. [15] S. Li, N.A. Richardson, R.B. King, H.F. Schaefer, J. Phys. Chem. A 107 (2003) 10118. [16] Q. Fan, H. Feng, W. Sun, H. Li, Y. Xie, R.B. King, J. Organomet. Chem. 730 (2013) 69. [17] Q. Fan, H. Feng, W. Sun, H. Li, Y. Xie, R.B. King, Comput. Theor. Chem. 999 (2012) 129. [18] T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [19] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [20] A.J.H. Wachters, J. Chem. Phys. 52 (1970) 1033. [21] D.M. Hood, R.M. Pitzer, H.F. Schaefer, J. Chem. Phys. 71 (1979) 705. [22] T. Ziegler, J. Autschbach, Chem. Rev. 105 (2005) 2695. [23] M. Bühl, H. Kabrede, J. Chem. Theory Comput. 2 (2006) 1282. [24] M. Brynda, L. Gagliardi, P.O. Widmark, P.P. Power, B.O. Roos, Angew. Chem., Int. Ed. 45 (2006) 3804. [25] N. Sieffert, M. Bühl, J. Am. Chem. Soc. 132 (2010) 8056. [26] P. Schyman, W. Lai, H. Chen, Y. Wang, S. Shaik, J. Am. Chem. Soc. 133 (2011) 7977. [27] R.D. Adams, W.C. Pearl, Y.O. Wong, Q. Zhang, M.B. Hall, J.R. Walensky, J. Am. Chem. Soc. 133 (2011) 12994. [28] R. Lonsdale, J. Olah, A.J. Mulholland, J.N. Harvey, J. Am. Chem. Soc. 133 (2011) 12994. [29] S. Ye, T. Tuttle, E. Bill, L. Simkhorich, Z. Gross, W. Thiel, F. Neese, Chem. Eur. J. 14 (2008) 10839. [30] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [31] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [32] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [33] J.P. Perdew, Phys. Rev. B 33 (1986) 8822. [34] M.J. Frisch et al., GAUSSIAN 09, Revision A.02, Gaussian Inc., Wallingford, CT, 2009. [35] M. Reiher, O. Salomon, B.A. Hess, Theor. Chem. Acc. 107 (2001) 48. [36] O. Salomon, M. Reiher, B.A. Hess, J. Chem. Phys. 117 (2002) 4729. [37] J. Potenza, P. Giordano, D. Mastropaolo, A. Efraty, Inorg. Chem. 13 (1974) 2540. [38] H. Wang, Y. Xie, R.B. King, H.F. Schaefer, J. Am. Chem. Soc. 128 (2006) 11376. [39] L.S. Sunderlin, D. Wang, R.R. Squires, J. Am. Chem. Soc. 115 (1993) 12060.