ARTICLE pubs.acs.org/JPCA
Nickel-Catalyzed Alkyl Coupling Reactions: Evaluation of Computational Methods Lawrence M. Pratt,* Stewart Voit, and Fabian N. Okeke Department of Chemistry, Fisk University, 1000 17th Avenue North, Nashville, Tennessee 37208, United States
Nobuaki Kambe* Department of Applied Chemistry, Osaka University, Suita, Osaka 565-0871, Japan
bS Supporting Information ABSTRACT: The B3LYP, M06, M06L, M062X, MPW1K, and PBE1PBE DFT methods were evaluated for modeling nickel-catalyzed coupling reactions. The reaction consists of a nucleophilic attack by a carbanion equivalent on the nickel complex, SN2 attack by the anionic nickel complex on an alkyl halide, and reductive elimination of the coupled alkane product, regenerating the nickel catalyst. On the basis of CCSD(T)//DFT single-point energies, the B3LYP, M06, and PBE1PBE functionals were judged to generate the best ground state geometries. M06 energies are generally comparable or superior to B3LYP and PBE1PBE energies for transition state calculations. The MP2 and CCSD methods were also evaluated for single-point energies at the M06 geometries. The rate-determining step of this reaction was found to be nucleophilic attack of a L2NiR anion on the alkyl halide.
’ INTRODUCTION Synthesis of natural products frequently involves coupling of two organic fragments, and metal coupling reactions are of prime importance in synthetic organic chemistry. A few recent examples include synthesis of etnangien, heterocycles, sporolides, and halicholactone and their derivatives.1-4 Coupling reactions fall into a few broad categories. Suzuki coupling and related reactions are used primarily for the synthesis of functionalized aromatic rings and generally involve oxidative addition of an aryl or vinyl halide or pseudohalide to the metal catalyst, a ligand exchange reaction, and reductive elimination of the product.5 However, cross-coupling using alkyl halides has been extensively studied during the past decade.6 Examples of asymmetric palladium and nickel coupling reactions have also been reported.7-10 Most of the cross-coupling reactions require the use of expensive palladium catalysts; however, Ni, Co, Fe, Ag, as well as Cu also catalyze coupling using alkyl halides.11,12 Although there are minor variations, these palladium-catalyzed coupling reactions go through catalytic cycles similar to the one illustrated in Scheme 1. A common feature of these reactions is that the electrophile adds to the metal first, followed by ligand exchange by the nucleophile, often a main group organometallic compound. A complementary set of coupling reaction to efficiently join sp3-sp3 carbon fragments with copper and nickel catalysts begin with a nucleophilic addition of a main group metal alkyl to a transition metal complex, followed by reaction with an electrophile, and, finally, reductive elimination of the product. The bestknown example is Gilman coupling. An alkyllithium or Grignard reagent reacts with a Cu(I) salt, forming a dialkylcopper(I) anion unit. That anion may exist as a solvent-separated ion pair or an aggregate, as shown in Scheme 2 for a lithium cuprate. Oxidative r 2011 American Chemical Society
addition of the electrophile, usually an alkyl halide or pseudohalide, can occur by several mechanisms, including both radical and nonradical mechanisms.13-17 That step is followed by a reductive elimination from the Cu(III) intermediate. The overall mechanism is illustrated in Scheme 3. We have previously shown that the cuprate coupling reaction mechanism is highly dependent on the aggregation state,13 which is, in turn, dependent on solvation and other factors. A new type of nickel-catalyzed coupling reaction is complementary scope to cuprate coupling.18,19 It is mechanistically similar to the Gilman coupling mechanism, with a main group metal alkyl adding to the bis-allylnickel reagent in the first step. That is followed by SN2 attack by the nucleophilic nickel on an alkyl halide or pseudohalide electrophile, followed by reductive elimination of the product, as illustrated in Scheme 4. Other examples of nickel-catalyzed coupling reactions have been reported.6,20,21 A significant difference between the Cu(I) and the Ni(II) coupling reactions is the coordination sphere of the metal. The copper nucleophile is a R-Cu-R- or R-Cu-Y- unit, where Y is a dummy ligand like cyanide. In contrast, the reactive nickel species contains two allyl-type ligands or two allyl groups in a single polydentate ligand. This ligand pair presents an opportunity to modulate the reactivity of the complex. Another advantage of the nickel-catalyzed coupling is the greater nucleophilicity of the nickel species, compared to copper. That is likely to result in milder conditions, lower reaction temperatures, and, therefore, greater tolerance to functional groups in the reactants.19 Unlike most Received: August 15, 2010 Revised: February 4, 2011 Published: February 25, 2011 2281
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The Journal of Physical Chemistry A Scheme 1. Generalized Mechanism of Palladium-Catalyzed Coupling Reactions
Scheme 2. Possible Structures of Lithium Cuprate Reagents
Scheme 3. Mechanism of Cuprate Coupling Reactions
Scheme 4. Mechanism of Diallylnickel Coupling Reactions
Gilman coupling reactions, the nickel-catalyzed reaction works well with alkyl chlorides at 298 K, eliminating the need for more expensive alkyl bromides or iodides.12 The first step in Scheme 4 may be quite complex in solution, as the main group organometallic compound M-R may exist in several aggregation and/or solvation states. In addition, the anionic intermediate may exist as a contact ion pair or a solvent-separated ion pair, depending on the solvent and metal counterion. Those complications are relatively unimportant for the purpose of evaluating computational methods, so some simplifying assumptions have been made. The organometallic nucleophile M-R was replaced by a gas-phase methyl anion. Although that will make the calculated energies of the first step much too exergonic compared to what happens in solution, it is a valid approach for comparing the methods, since the same type of “error” will be introduced in each calculation. The anionic intermediate will also be assumed to exist as a solvent-separated ion pair, and calculations will be performed only on the anionic intermediate. This avoids the complication of different computational methods predicting different cation-anion interactions and also makes higher level calculations tractable on this system. In this study we used compounds in which the allyl ligands are completely flexible (1),18 rigid (2), or of intermediate
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flexibility (3).12 During the reaction, the allyl ligands alternate between 3η and 1η bonding, as illustrated in Scheme 4. The orbital overlap in both bonding modes may be affected by the rigidity of the ligand pair, thus affecting the relative energies of the catalyst and intermediates.
’ COMPUTATIONAL METHODS All calculations were performed using the Gaussian 09 set of programs.22 Geometry optimizations were performed with the B3LYP,23 M06. M06L, M062X, MPW1K, and PBE1PBE DFT functionals24 and the 6-31þG(d) basis set, followed by frequency calculations at the same level of theory. Geometry optimizations were initially attempted with the MP2 method, but problems of wave function RHF-UHF instability were encountered. The wave function stability was optimized using the stable=opt keyword, but after one optimization cycle, the wave function again became unstable. Therefore, MP2 optimizations were not included in this study. CCSD(T)/6-31þG(d)25 single-point energies were calculated at each DFT-optimized geometry using an initial guess from the stabilized Hartree-Fock wave function and the frozen core option. For the smallest system involving the bis-allylnickel complex (1), CCSD(T)/augcc-pvdz//M06/6-31þG(d) single-point energies were also calculated.26 The free energies of each species were calculated from the DFT energy at the optimized geometry and the thermal correction to the free energies, obtained from frequency calculation. The DFT-calculated thermal corrections were also added to the CCSD(T) electronic energies to obtain approximate free energies at the CCSD(T) level. ’ RESULTS AND DISCUSSION The results are presented in three components. First, a qualitative description of the species along the reaction coordinate is presented. Second, the computational methods are evaluated. The evaluation includes the four DFT functionals under consideration for their ability to produce accurate geometries for the system of interest. The DFT energies are also compared to those obtained from single-point post-HartreeFock energy calculations at the DFT geometries. Finally, the effect of the catalyst structure is evaluated by comparison of calculated energies and available experimental data. Description of Reactive Species. Compounds 1-3 are believed to react according to the mechanism depicted in Scheme 4. The geometries of each of the reactants, intermediates, transition states, and products were optimized with the 4 DFT functionals. All 4 functionals generated qualitatively similar optimized geometries unless otherwise indicated. Compounds 1 and 3 can exist as syn and anti isomers, as can the anionic intermediates. The M06-optimized geometries of those compounds are shown in Figure 1. In compounds 1 and 3, the nickel atom is sandwiched between the two allyl groups, which are not quite parallel to each other. The two-carbon tether in compound 3 restricts the mobility of the allyl groups. In contrast, catalyst 2 is unable to exist in a geometry in which the metal is sandwiched 2282
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Figure 3. M06-optimized geometries of the SN2 transition states resulting from reaction of 4 with chloromethane.
Figure 1. M06-optimized geometries of catalysts 1-3.
Figure 4. M06- and B3LYP-optimized geometries of the SN2 transition states resulting from reaction of 5 with chloromethane.
Figure 2. M06-optimized geometries of anions 4-7.
between the allyl ligands, and the ligands are constrained so that a syn arrangement is not possible. This has a significant effect on the reaction and activation energies via catalyst 2, as will be seen shortly. The optimized geometries of the L2NiMe- anions are shown in Figure 2. The anti isomer of anion 4 exists with one allyl group η3 bonded to the nickel and the other allyl group η1 bonded. The
syn isomer has both allyl groups η3 bonded, as optimized with all DFT functionals except M062X. This and other discrepancies in the M062X geometries, described below, are not too surprising because that functional was optimized for main group chemistry. The anion derived from catalyst 3 can exist as two pairs of syn/ anti isomers, labeled 6 and 7. The syn and anti isomers of anions 6 and 7 each have one allyl group η3 bonded and the other one η1 bonded to nickel. anti-6 and syn-6 have the η1 allyl group bonded to nickel via the internal sp2 carbon atom, while 7 is bonded to nickel at the terminal sp2 carbon. The nickel atom in anions 4-7 is sufficiently nucleophilic to undergo an SN2 reaction with alkyl halides, and several different transition states are possible. The anti isomer of anion 4 reacts via two different transition states, labeled TS 8 and TS 9 in Figure 3. Likewise, the syn isomer reacts via TS 10 and TS 11. Anion 5 reacted via a single transition state, TS 12. In this case, the B3LYP functional generated a different transition state geometry than the other functionals. The M06, M06L, M062X, MPW1K, and PBE1PBE functionals optimized the transition state to a geometry in which the anionic ligand assisted the expulsion of the chloride leaving group and the nickel nucleophile attacked the methyl carbon at an angle rather than head on. The M06- and B3LYP-optimized transition states are shown in Figure 4. The anti isomer of anion 6 reacted with chloromethane via transition states TS 13 and TS 14 (Figure 5. The syn isomer reaction proceeded via transition state TS15 and TS 16 to generate the C8H12NiMe2 intermediate. The B3LYP, M06, M06L, MPW1K, and PBE1PBE functionals generated similar transition state geometries, but the M062X functional produced an optimized transition state corresponding to the direct coupling of the two methyl groups with the anti isomer of 6, without going through the C8H12NiMe2 intermediate. A similar situation was encountered with TS 15 via the syn isomer. Subsequent 2283
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Figure 5. M06-optimized geometries of the SN2 transition states resulting from reaction of 6 with chloromethane.
Figure 7. M06-optimized geometries of L2NiMe2 20-23.
Figure 6. M06-optimized geometries of the SN2 transition states resulting from reaction of 7 with chloromethane.
CCSD(T) single-point calculations showed those unusual M062X transition states to be high-energy points on the PES, and those species were not further investigated. The transition states for the SN2 reactions of anti- and syn-7 are shown in Figure 6. Nucleophilic attack on chloromethane from the top or bottom side of anti-7 resulted in identical structures, TS 17. The M06, M062X, B3LYP, MPW1K, and PBE1PBE functionals optimized the transition state to the geometry shown in the top left of Figure 6, but the M06L functional optimized to the structure shown in the upper right, with one allyl ligand η1 bonded to nickel. The transition states from reaction of syn-7 are illustrated as TS 18 and TS 19. The SN2 reaction of the anions with chloromethane generate the L2NiMe2 intermediates 20-23, which then undergo reductive elimination of ethane, via transition states 24-30, reforming the catalytic species 1-3. The intermediates 20-23 are shown in Figure 7, and the transition states are shown in Figure 8. Catalyst 3 resulted in the formation of intermediates 22 and 23 from the SN2 reaction of anions 6 and 7, respectively. Evaluation of Computational Methods. Evaluation of the performance of the various DFT methods examined two issues:
Figure 8. M06-optimized geometries of the transition states corresponding to reductive elimination of ethylene.
How well each method predicted the ground state and transition state geometries, and how well each method performed in calculating the reaction and activation free energies. The first 2284
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Table 1. Differences in the CCSD(T) Energies (kcal/mol) at DFT-Optimized Geometries Relative to the B3LYP Geometry molecule
Table 2. Calculated Free Energies of syn-1 and syn-3 Relative to the Anti Isomers
M06
M06L
M062X
MPW1K
PBE1PBE
method
1-anti
0.925
1.05
1.59
2.01
1.01
B3LYP
1.41
3.09
1-syn 4-anti
0.561 -0.265
0.650 -0.215
2.09 2.77
1.89 1.28
0.615 -0.161
M06 M06L
1.01 0.762
3.38 3.69
1
3
2.62
2.76
2.53
4.00
2.67
MPW1K
1.87
3.69
TS 8 (anti)
-0.0688
0.653
3.04
1.45
0.208
PBE1PBE
1.50
3.38
TS 10 (syn)
2.82
0.420
4.69
3.25
CCSD(T)//B3LYP
0.409
3.94
TS 9 (anti)
-0.725
0.552
2.34
0.898
-0.19
CCSD(T)//M06
0.0451
3.96
TS 11 (syn)
-0.737
0.151
2.78
0.998
-0.106
CCSD(T)//M06L
0.0100
4.04
20-anti
-1.92
-1.90
1.08
-0.350
-1.91
CCSD(T)//MPW1K
0.216
3.16
20-syn TS 24 (anti)
-1.92 -1.63
-1.88 0.360
1.20 3.62
-0.167 1.08
-1.86 0.125
CCSD(T)//PBE1PBE
0.0671
3.09
TS 25 (syn)
-1.85
0.458
-1.29
0.916
0.0442
2.78
1.36
4-syn
2
0.761
1.45
5
0.412
TS 12
4.65
-2.42
0.528
14.1
0.264 1.53
1.92
-1.53
8.85
-3.47
0.421 -0.862
-0.628
-0.563
0.050
0.808
TS 26
0.805
0.952
0.199
2.15
0.667
3-anti 3-syn
0.435 0.454
0.490 0.583
1.10 1.41
1.74 1.90
0.440 0.476
0.00678
21
0.154
2.89
1.59
-0.0112
-0.0162
0.124
2.88
1.58
-0.0199
TS 13 (anti)
3.60
0.573
11.9
5.55
3.61
TS 15 (syn)
0.536
0.764
10.8
3.56
0.377
TS 14 (anti)
0.00471
0.914
12.0
2.25
0.173
6-anti 6-syn
TS 16 (syn)
-0.192
0.620
3.21
1.60
0.120
7-anti 7-syn
-0.506 -0.071
-0.484 -0.105
1.77 2.78
0.784 1.57
-0.461 -0.0717
TS 17 (anti)
-0.698
0.522
0.951
4.66
-0.0588
TS 18 (syn)
2.81
0.394
3.85
5.09
-0.00307
TS 19 (syn)
-0.594
0.256
2.30
1.30
-0.0516
22-anti
-0.650
-0.476
-0.0350
0.940
-0.720
22-syn
2.13
2.02
5.81
4.62
1.72
TS 27(anti)
5.20
7.11
5.94
7.13
6.22
TS 28(syn) 23-anti
5.93 -0.717
7.17 -0.659
6.25 -0.607
7.62 0.534
6.49 -0.798
-1.18
-1.18
23-syn
-1.24
-0.44
0.524
TS 29 (anti)
-0.765
0.649
-2.59
1.16
TS 30 (syn)
-1.00
0.308
-0.966
1.61
0.208
MeCl
-0.0434
-0.0155
-0.0124
0.160
-0.0155
CH3-
-0.0031
0.0773
0.0451
0.0916
0.00314
ethane
0.0556
0.0855
0.0444
0.282
0.0416
0.345
task was performed by performing geometry optimizations with the B3LYP, M06. M06L, M062X, MPW1K, and PBE1PBE functionals, followed by CCSD(T) single-point energy calculations at the optimized geometry from each functional. The results, shown in Table 1, are presented as the difference in CCSD(T) energies at each geometry relative to those at the B3LYP geometry. A positive number means that the B3LYP geometry was the lower energy geometry at the CCSD(T) level. For ground state species, the most accurate DFT geometry will be the one that generates the lowest CCSD(T)//DFT energy. That will not necessarily be the case for transition state geometries. Considering only the ground state species (no transition states)
of the metal-containing compounds, the average difference between the CCSD(T)//B3LYP and the CCSD(T)//M06 energies was 0.019 kcal/mol, indicating that M06, on average, is essentially equivalent to B3LYP for obtaining ground state geometries. The average difference between CCSD(T)//B3LYP and CCSD(T)//PBE1PBE energies was only slightly larger at 0.035 kcal/mol. The average CCSD(T)//B3LYP-CCSD(T)// M06L, CCSD(T)//M062X, and CCSD(T)//MPW1K differences were 0.12, 1.61, and 1.58 kcal/mol, respectively. Because of the poorer overall performance in ground state energies and the significant deviations in transition state geometries described earlier, the M062X functional was not further considered in this work. This is also consistent with other published results on the performance of M062X with transition metals.24 The first reaction step in the catalytic cycle is formation of the anions 4-7 from the catalysts 1-3 and a Grignard reagent or other main group organometallic. The relative free energies of the two isomers of catalysts 1 and 3 are shown in Table 2, calculated at the DFT and CCSD(T)//DFT levels. At the CCSD(T) level, it was found that the anti isomer of catalyst 1 is favored by less than 1 kcal/mol and the anti isomer of catalyst 3 is favored by between 3 and 4 kcal/mol. The calculated free energies of addition of a methyl anion to the catalyst are shown in Table 3. The CCSD(T)/6-31þG(d) single-point energies at the five DFT geometries were within about 2 kcal/mol of each other for all 3 catalytic systems. The DFT reaction energies for this step were less consistent between the different functionals. These results suggest that the B3LYP, M06, and M06L functionals all generate good optimized geometries for this system, but they each have shortcomings in predicting the reaction energy. The M06 and M06L functionals generally performed better than the other functionals in predicting the reaction energy for this step. For comparison, CCSD(T)/ aug-cc-pvdz//M06/6-31þG(d) energies were calculated for methyl anion addition to anti- and syn-1, and the calculated energies were within 3-4 kcal/mol of those calculated at the CCSD(T)/6-31þG(d) level. The energies of the syn isomers of anions 4-7, relative to the anti isomers, are shown in Table 4. Anion 4, derived from catalyst 1, favored the anti isomer, although the DFT methods predicted a greater energy difference than CCSD(T). Catalyst 3 could potentially generate anions 6 and 7, each with syn and anti isomers. The syn isomer was slightly favored for anion 6 and favored by more than 10 kcal/mol for anion 7. At the CCSD(T)//M06 level of theory, syn-7 was found to be more stable than syn-6 by 5.64 kcal/mol. At the same level of theory, anti-6 was 2285
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Table 3. Calculated Free Energies of formation (kcal/mol) of L2NiMe Anion from L2Ni and Methyl Anion L2Ni
B3LYP
M06
M06L
MPW1K
PBE1PBE
1 f 4 anti
-39.7
-42.5
-41.1
-41.7
-40.2
1 f 4syn
-26.6
-31.2
-35.7
-29.0
-31.9
2f5
-71.5
-79.4
-79.5
-79.3
-77.7
3 f 6 anti
-45.6
-47.7
-45.9
-47.5
-45.8
3 f 6 syn
-49.2
-52.0
-49.9
-52.0
-50.0
3 f 7 anti
-43.0
-43.9
-41.2
-43.1
-41.5
3 f 7 syn
-55.0
-57.9
-55.3
-57.9
-55.6
CCSD(T)//B3LYP
CCSD(T)//M06
CCSD(T)//M06L
CCSD(T)//MPW1K
CCSD(T)//PBE1PBE
1 f 4 anti
-43.1
-43.7
-44.0
-43.8
-44.0
1 f 4syn
-42.7
-40.2
-40.0
-40.1
-40.1
2f5
-75.4
-75.5
-76.2
-75.9
-76.2
3 f 6 anti
-50.0
-50.2
-50.4
-50.1
-50.2
3 f 6 syn
-54.0
-54.3
-54.7
-54.3
-54.5
3 f 7 anti
-44.4
-44.1
-44.4
-44.6
-44.3
3 f 7 syn
-58.1
-58.7
-59.2
-58.4
-58.6
Table 4. Calculated Free Energies of syn-4, syn-6, and syn-7 Anions Relative to the Anti Isomers method
4
6
B3LYP
14.5
-0.555
M06
12.3
-0.903
M06L MPW1K
6.10 14.6
7 -8.98 -10.6
-0.567
-10.7
-0.803
-11.1
PBE1PBE
9.83
-0.812
-10.6
CCSD(T)//B3LYP
0.693
-1.00
-12.3
CCSD(T)//M06
3.57
-1.03
-11.9
CCSD(T)//M06L CCSD(T)//MPW1K
3.66 0.216
-1.03 -1.07
-12.0 -10.6
CCSD(T)//PBE1PBE
0.0671
-1.18
-11.2
more stable than anti-7 by 5.24 kcal/mol. Thus, in the absence of kinetic effects, the syn isomer of 7 will be the dominant species derived from catalyst 3. The second step in the catalysis is an SN2-like reaction by the anionic nickel species on an electrophile, which was modeled by chloromethane in this study. The calculated activation free energies are shown in Table 5 and the reaction free energies in Table 6. The CCSD(T)/6-31þG(d) single-point energies at the geometries of the five DFT functionals were all within 4 kcal/mol of each other, except for TS 12, and some of the transition structures optimized with the MPW1K functional. The DFT activation energies were much less consistent, sometimes predicting higher activation energies than CCSD(T) and sometimes lower. The M06L functional predicted barrier heights lower than the CCSD(T)//M06L values. The CCSD(T) calculations predicted the overall energy of this reaction step to be endergonic except for the bridged system 5. For the smallest system derived from anion-4, CCSD(T)/aug-cc-pvdz//M06/6-31þG(d) single-point energies were also calculated, and the activation energies with the larger basis set were within 4-5 kcal/mol of those obtained with the 6-31þG(d) basis set, as is further described in the comparison of DFT and post-Hartree-Fock methods below.
The activation and reaction free energies for the reductive elimination of ethane from L2NiMe2 are shown in Tables 7 and 8, respectively. The activation energies calculated by CCSD(T)// DFT are all within 3 kcal/mol of each other, except for the B3LYP-optimized structure of anti-22. The latter case with the apparent negative activation energy illustrates a case where the DFT and CCSD(T) methods would predict different transition state geometries, perhaps as a result of different metal-ligand interactions. Another example is found in TS 30, in which the CCSD(T)//B3LYP and CCSD(T)//M06 calculations predicted an apparent negative activation energy. We conclude that except for intermediate 21, the barrier heights for the reductive elimination step are quite small and the elimination step will be quite fast. The DFT-calculated activation energies were less consistent than those predicted by the CCSD(T) single points. The differences between the DFT methods and between the DFT and the CCSD(T) methods exceeded 10 kcal/mol in some cases. The reaction free energies of this step were all within 4 kcal/mol of each other at the CCSD(T) level but less consistent between the DFT methods. Although CCSD(T) calculations can be performed on this system, it is desirable to determine whether the less expensive MP2 and CCSD methods can generate comparable results for single-point energies at DFT geometries. It is also desirable to know how coupled cluster energies will be affected by larger basis sets. The latter calculations were only tractable for the smallest system. For the bis-allylnickel systems, CCSD(T)/aug-cc-pvdz// M06/6-31þG(d) calculations were performed. Tables 9-13 provide a comparison of M06, MP2//M06, CCSD//M06, CCSD(T)//M06, and, where possible, the CCSD(T)/aug-ccpvdz//M06/6-31þG(d) energies for ground and transition state energies along the reaction coordinate. The data in Table 9 shows a reasonable agreement between the M06-, CCSD-, and CCSD(T)-calculated reaction energies, but the MP2 energies were in poor agreement with the coupled cluster energies. The CCSD(T) energies showed a difference of 3-4 kcal/mol with the two basis sets. The data in Table 10 shows the CCSD calculations to consistently overestimate the barrier heights of the SN2 reactions 2286
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Table 5. Calculated Activation Free Energies (kcal/mol) for Reaction of L2NiMe- with Chloromethane L2NiMe-
B3LYP
M06
M06L 10.7
4 anti TS 8
19.6
18.5
4 anti TS 9
16.7
15.5
MPW1K 28.0
21.0
7.86
25.2
17.9 11.0
4 syn TS10
4.94
6.32
4.67
13.4
4 syn TS 11
3.18
4.38
2.80
11.6
2.13
24.7
5 TS 12
12.5
12.8
PBE1PBE
10.4
9.32 12.3
6 anti TS 13
19.5
17.8
27.6
21.0
6 anti TS 14
18.7
16.6
9.71
26.3
19.7
6 syn TS 15 6 syn TS 16
20.8 18.0
18.7 16.4
11.7 9.08
28.7 26.2
22.1 19.5
7 anti TS 17
15.3
15.0
6.81
24.5
17.2
7 syn TS 18
17.1
15.9
8.02
25.5
18.4
7 syn TS 19
17.2
16.4
8.48
25.6
18.7
CCSD(T)//B3LYP
CCSD(T)//M06
CCSD(T)//M06L
CCSD(T)//MPW1K
CCSD(T)//PBE1PBE
4anti TS 8
16.4
16.4
16.8
16.9
16.9
4 anti TS 9
12.9
12.0
12.6
12.9
13.1
4 syn TS10 4 syn TS 11
14.6 13.8
14.7 10.5
11.6 10.0
15.2 10.8
15.1 10.8
5 TS 12
6.20
11.2
4.02
14.5
3.68
6 anti TS 13
15.3
18.5
15.2
19.3
19.0
6 anti TS 14
14.1
13.8
14.2
14.8
14.4
6 syn TS 15
15.9
16.3
16.4
18.3
16.7
6 syn TS 16
14.2
14.0
14.2
14.6
14.7
7 anti TS 17
13.7
12.0
12.9
16.9
13.3
7 syn TS 18 7 syn TS 19
12.7 14.5
15.5 13.9
12.8 14.1
16.5 14.6
13.0 14.7
Table 6. Calculated Reaction Free Energies (kcal/mol) for Reaction of L2NiMe Anion with Chloromethane L2NiMe4 anti
B3LYP
M06
15.3
14.4
-0.0502 -1.61
4 syn 5
M06L 4.38 -2.67 -12.8
1.13 -1.85
MPW1K
PBE1PBE
20.5
14.0
4.85 6.66
3.15 -1.68
6 anti
15.1
16.2
9.44
21.7
16.5
6 syn
12.2
14.2
5.19
19.6
14.5
7 anti
12.1
16.8
7.32
20.8
14.6
7 syn
12.1
15.2
5.87
19.6
13.9
CCSD(T)//B3LYP
CCSD(T)//M06
CCSD(T)//M06L
CCSD(T)//MPW1K
CCSD(T)//PBE1PBE
4 anti
13.0
11.6
11.4
12.2
12.1
4 syn 5
10.8 -2.18
6.58 -3.12
5.72 -3.00
7.16 -3.12
6.75 -3.04
6 anti
17.9
6 syn
7.41
17.1
16.2
17.5
17.2
11.4
11.6
12.1
12.1
7 anti
20.3
18.3
18.7
19.3
18.8
7 syn
15.9
14.8
14.9
15.2
15.0
with chloromethane, compared to CCSD(T). A similar trend was noted in a recent study of lithium cuprate coupling reactions.7 Although the M06 calculations sometimes underestimated the activation energies, it performed better than MP2. The MP2 activation energies were remarkably close to the CCSD(T) values in some cases, but in other cases MP2 either greatly overestimated or underestimated the barrier height. For the reaction free energies, presented in Table 11, the M06, CCSD, and CCSD(T)
values were in reasonably good agreement with each other. In contrast, the MP2-calculated reaction free energies were erratic and predicted the reaction to be too endergonic by as much as 20 kcal/mol. The CCSD(T) barrier heights showed a difference of 4-5 kcal/mol with the two basis sets but only a 1-2 kcal/mol difference in reaction energies. A similar trend was observed for the activation and reaction energies of the reductive elimination step. Except for the reaction 2287
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ARTICLE
Table 7. Calculated Activation Free Energies (kcal/mol) for Reductive Elimination of Ethane from L2NiMe2 L2NiMe2
B3LYP
M06
M06L
MPW1K
PBE1PBE
20 anti TS 24
5.22
4.61
10.3
4.02
5.79
20 syn TS 25
6.03
5.56
11.1
5.13
21 TS 26
21.8
17.4
23.0
6.77
18.9
19.5
22 anti TS 27
3.49
0.624
3.57
0.736
0.875
22 syn TS 28
7.34
3.93
9.37
4.29
4.83
4.53
8.90
5.58
7.22
2.52
7.31
3.07
4.17
CCSD(T)//M06
CCSD(T)//M06L
CCSD(T)//MPW1K
CCSD(T)//PBE1PBE 3.73
23 anti TS 29
10.4
23 syn TS 30
6.78 CCSD(T)//B3LYP
20 anti TS 24
2.83
2.09
4.42
3.23
20 syn TS 25
4.13
3.10
5.78
4.12
21 TS 26
22.0
23.9
22 anti TS 27
-3.97
1.68
22 syn TS 28
7.84
9.46
23 anti TS 29
2.57
2.58
23 syn TS 30
-1.18
-1.07
23.8
4.95
23.4
4.14 10.4
23.6
1.86
2.30
9.15
9.73
3.77
2.92
3.86
0.179
-0.373
4.94
Table 8. Calculated Reaction Free Energies (kcal/mol) for Reductive Elimination of Ethane from L2NiMe2 L2NiMe2
B3LYP
M06
M06L
MPW1K
PBE1PBE
20 anti
-65.8
-62.3
-54.8
-74.0
-65.6
20 syn
-63.5
-60.3
-53.1
-71.1
-63.1
21
-17.0
22 anti 22 syn
-59.6 -53.1
-9.08
0.779
-58.9 -52.5
-55.0 -46.8
-22.6
-12.5
-69.4 -62.8
-62.6 -56.3
23 anti
-59.3
-63.2
-57.6
-73.0
-65.0
23 syn
-47.2
-47.6
-42.1
-57.0
-50.3
CCSD(T)//B3LYP
CCSD(T)//M06
CCSD(T)//M06L
CCSD(T)//MPW1K
CCSD(T)//PBE1PBE
20 anti
-59.8
-57.9
-57.3
-58.2
-58.0
20 syn
-58.0
-56.3
-55.6
-56.8
-56.6
21
-12.4
-11.3
-10.7
-10.8
-10.7
22 anti 22 syn
-57.9 -43.4
-56.8 -47.1
-55.8 -46.9
-57.2 -47.6
-56.8 -47.5
23 anti
-65.9
-64.1
-64.2
-64.5
-64.4
23 syn
-47.8
-46.1
-45.5
-46.6
-46.3
Table 9. Comparison of DFT and Post-HF Methods for Free Energies of Formation (kcal/mol) of L2NiMe Anion from L2Ni and Methyl Anion [aug-cc-pvdz basis set] L2Ni
M06
MP2//M06
CCSD//M06
CCSD(T)//M06
1 f 4 anti
-42.5
-30.5
-43.2
-43.7 [-40.7]
1 f 4 syn
-31.2
-11.1
-34.4
-40.2 [-36.3]
2f5
-79.4
-84.0
-76.6
-75.5
3 f 6 anti
-47.7
-36.7
-49.7
-50.2
3 f 6 syn
-52.0
-37.1
-53.6
-54.3
3 f 7 anti 3 f 7 syn
-43.9 -57.9
-30.8 -44.7
-42.9 -58.3
-44.1 -58.7
of 21, the M06, CCSD, and CCSD(T) activation barriers were within 4 kcal/mol of each other. The MP2 calculations predicted negative barrier heights in two cases and generally predicted barrier heights in poor agreement with the CCSD(T) calculations. The reaction free energies of this step were calculated to be too
exergonic by CCSD, compared to CCSD(T). In general, the M06 reaction energies were in much better agreement with the CCSD(T) calculation than were the MP2 energies. For the reductive elimination step, the CCSD(T) barrier heights were within 2 kcal/mol of each other for the two basis sets. That difference was less than 1 kcal/mol for the CCSD(T)-calculated reaction energies. From comparison to the CCSD(T) energies, the B3LYP and M06 functionals were comparable in performance for this system. Both appear to be somewhat better than M06L and considerably better than M062X, which was parametrized for main group chemistry. This study involved gas-phase species, but future studies will include THF solvation. When solvation with explicit solvent ligands is included, M06 has proven superior to B3LYP,27,28 and that functional will be used for future work on this and similar systems. Compared to CCSD(T)//M06 singlepoint energies, the M06 energies are generally superior to CCSD and far superior to MP2 energies. Effects of Catalyst Structure. The first step of the catalytic cycle is addition of a metal alkyl nucleophile to the L2Ni catalyst. 2288
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ARTICLE
Table 10. Comparison of DFT and Post-HF Methods for Activation Free Energies (kcal/mol) of Reaction of L2NiMe with Chloromethane [aug-cc-pvdz basis set] L2Ni
M06
MP2//M06
CCSD//M06
CCSD(T)//M06
Table 13. Comparison of DFT and Post-HF Methods for Reaction Free Energies (kcal/mol) of Reductive Elimination of Ethane from L2NiMe2 [aug-cc-pvdz basis set] L2NiMe2
M06
MP2//M06
CCSD//M06
CCSD(T)//M06
TS 8
18.5
18.4
24.3
16.4 [11.5]
20 anti
-62.3
-93.7
-64.6
-57.9 [-57.2]
TS 9
15.5
13.8
20.3
12.0 [8.03]
20 syn
-60.3
-93.4
-63.0
-56.3 [-55.5]
TS 10
6.32
18.2
15.2
14.7 [10.1]
21
-16.2
-14.9
-11.3
TS 11
4.38
-1.74
13.2
10.5 [5.29]
22 anti
-58.9
-9.08
-89.4
-60.4
-56.8
TS 12 TS 13
12.8 17.8
41.3 40.1
22.7 24.8
11.2 18.5
22 syn 23 anti
-52.5 -63.2
-87.7 -102.6
-53.7 -67.7
-47.1 -64.1
TS 14
16.6
12.1
21.2
13.8
23 syn
-47.6
-79.8
-50.1
-46.1
TS 15
18.7
16.0
23.6
16.3
TS 16
16.4
21.9
14.0
TS 17
15.0
21.2
20.6
12.0
TS 18
15.9
34.8
21.5
15.5
TS 19
16.4
17.2
21.8
13.9
1.63
Table 11. Comparison of DFT and Post-HF Methods for Free Energies (kcal/mol) of Reaction of L2NiMe- with Chloromethane [aug-cc-pvdz basis set] L2NiMe-
M06
4 anti
14.4
4 syn
1.12
5 6 anti
MP2//M06 32.9
CCSD//M06 16.6
CCSD(T)//M06 11.6 [10.9]
13.3
6.18
-1.85 16.2
8.96 34.9
0.283 18.8
6.58 [4.88]
6 syn
14.2
33.5
16.1
11.4
7 anti
16.8
42.3
19.4
18.3
7 syn
15.2
33.3
17.2
14.8
-3.12 17.1
Table 12. Comparison of DFT and Post-HF Methods for Activation Free Energies (kcal/mol) for Reductive Elimination of Ethane from L2NiMe2 [aug-cc-pvdz basis set] L2NiMe2
M06
MP2//M06
CCSD//M06
20 anti TS 24
4.61
-8.92
2.36
20 syn TS 25
5.56
-7.27
3.43
21 TS 26
17.4
22 anti TS 27
0.624
22 syn TS 28
3.93
23 anti TS 29
4.53
23 syn TS 30
2.52
35.2 2.62 10.9 0.250 -10.8
26.0 1.73
CCSD(T)//M06 2.09 [0.503] 3.10 [1.23] 23.9 1.68
7.06
7.84
7.10
2.58
1.88
-1.07
The calculations for each diallylnickel species predict that step to be highly favorable. While the use of Grignard, alkyllithium, or other organometallic species will make the reaction less exergonic than is predicted by use of the hypothetical methyl anion in the calculations, the first step is likely to take place in quantitative yield. The second step is an SN2-like reaction by the nickel nucleophile on an alkyl halide. For each catalyst system, this step is predicted to be rate determining. This is in accord with the evidence that primary alkyl bromides react with alkyl Grignard reagents within 30 min at 0 °C in Ni/butadiene system to give cross-coupling products quantitatively but alkyl chlorides required 20 h at room temperature and that secondary alkyl halides are much less reactive than primary alkyl halides.12 The
nucleophilic substitution is endergonic for the anions 4 and 6 and slightly exergonic for anion 5. The L2NiMe2 species 20 and 22 will probably not be observable under normal conditions, because they undergo a highly exergonic reductive elimination of ethane to regenerate the catalysts 1 and 3, respectively. The calculated activation free energy of the reductive elimination step was calculated to be on the order of 1-8 kcal/mol, making that reaction step extremely rapid even at low temperatures. Although anion 5 reacts with an alkyl halide to from the L2NiMe2 species 21, the dimethyl intermediate is predicted to be far more stable than 20 or 22, as indicated by the calculated activation free energy of over 20 kcal/mol. A possible reason for that higher barrier height is the inflexibility of the two allyl groups in the rigid bicyclic ligand. Although the reductive elimination step is still calculated to be exergonic, it is much less so compared to the reaction of 20 and 22.
’ CONCLUSIONS The challenges of computational chemistry on a transition metal system were overcome by a combination of modern DFT geometry optimizations and CCSD(T) single-point energies. The M06 functional appears to generate the best geometries of the six functionals considered, and the M062X functional, optimized for main group compounds, performed poorly for the transition metal system. The MP2 method also performed quite poorly and was unsuitable for geometry optimizations because of instability in the Hartree-Fock wave function. Stabilized wave functions were used as the initial guess for MP2 and coupled cluster single-point energies. The CCSD method generated reaction energies qualitatively similar to the CCSD(T) method, but it sometimes overestimated activation barrier heights. The calculations predicted the nucleophilic attack of the L2NiMe- anion to be rate determining. The resulting Li2NiMe2 species would be fleeting in the case of simple diallyl ligands, reductively eliminating ethane with a very low activation barrier. For the bridged system 21, the activation barrier was calculated to be much higher, and that may affect the effectiveness of compounds like 2 as coupling catalysts. ’ ASSOCIATED CONTENT
bS
Supporting Information. Tables of M06-optimized geometries and M06, MP2//M06, CCSD//M06, and CCSD(T)// M06 energies of all structures; sample input file provided for CCSD(T)//aug-cc-pvdz calculations with first-row transition metals. This material is available free of charge via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail: lpratt@fisk.edu (L.M.P.);
[email protected]. ac.jp (N.K.).
’ ACKNOWLEDGMENT This work was supported through TeraGrid resources provided by NCSA under grant no. TG-CHE090139. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC0376SF00098. Thanks to Fernando R. Clemente and Douglas J. Fox of Gaussian, Inc., for technical assistance. ’ REFERENCES (1) Li, P.; Arikan, F.; Ahlbrecht, W.; Dieckmann, M.; Menche, D. J. Org. Chem. 2010, 75, 2429–2444. (2) Zhang, X.; Lu, Z.; Fu, C.; Ma, S. J. Org. Chem. 2010, 75, 2589–2598. (3) Bonazzi, S.; Binaghi, M.; Fellay, C.; Wach, J.-Y.; Gademann, K. Synthesis 2010, 631–642. (4) Bischop, M.; Doum, V.; Nordschild, A. C. M.; Pietruszka, J.; Sandkuhl, D. Synthesis 2010, 527–537. (5) (a) Metal-Catalyzed Cross-Coupling Reactions, 2nd ed.; De Meijere, A., Diederich, F., Eds.; Wiley-VCH: Weinheim, 2004. (b) Phapale, V. B.; Cardenas, D. J. Chem. Soc. Rev. 2009, 38, 1598–1607. (6) (a) Rudolph, A.; Lautens, M. Angew. Che. Int. Ed. 2009, 48, 2656–2670. (b) Frisch, A. C.; Beller, M. Angew. Chem., Int. Ed. 2005, 44, 674–688. (c) Furstner, A.; Martin, R. Chem. Lett. 2005, 34, 624–629. (d) Netherton, M. R.; Fu, G. C. Adv. Synth. Catal. 2004, 346, 1525–1532. (7) Hayashi, T. J. Organomet. Chem. 2002, 653, 41–45. (8) Glorius, F. Angew. Chem., Int. Ed. 2008, 47, 8347–8349. (9) Node, M.; Ozeki, M.; Planas, L.; Nakano, M.; Takita, H.; Mori, D.; Tamatani, S.; Kajimoto, T. J. Org. Chem. 2010, 75, 190–196. (10) Yoo, K. S.; O’Neill, J.; Sakaguchi, S.; Giles, R.; Lee, J. H.; Jung, K. W. J. Org. Chem. 2010, 75, 95–101. (11) Recent reviews. For Fe: (a) Sherry, B. D.; Fuerstner, A. Acc. Chem. Res. 2008, 41, 1500–1511. For Co: (b) Gosmini, C.; Begouin, J.M.; Moncomble, A. Chem. Commun. 2008, 3221–3233. For Ag: (c) Someya, H.; Yorimitsu, H.; Oshima, K. Tetrahedron Lett. 2009, 50, 3270–3272. (12) Terao, J.; Watanabe, H.; Ikkumi, A.; Kuniyasu, H.; Kambe, N. J. Am. Chem. Soc. 2002, 124, 4222–4223. (13) Pratt, L. M.; Voit, S.; Mai, B. K.; Nguyen, B. H. J. Phys. Chem. A 2010, 114, 5005–5015. (14) Ashby, E. C.; Coleman, D. J. Org. Chem. 1987, 52, 4554–4565. (15) Yoshikai, N.; Iida, R.; Nakamura, E. Adv. Synth. Catal. 2008, 350, 1063–1072. (16) Yoshikai, N.; Nakamura, E. J. Am. Chem. Soc. 2004, 126, 12264–12265. (17) Yamanaka, M.; Kato, S.; Nakamura, E. J. Am. Chem. Soc. 2004, 126, 6287–6293. (18) Terao, J.; Kambe, N. Acc. Chem. Res. 2008, 41, 1545–1554. (19) Singh, S. P.; Terao, J.; Kambe, N. Tetrahedron Lett. 2009, 50, 5644–5646. (20) Gonzales-Bobes, F.; Fu, G. C J. Am. Chem. Soc. 2006, 128, 5360–5361. (21) Strotman, N. A.; Sommer, S.; Fu, G. C. Angew. Chem., Int. Ed. 2007, 46, 3556–3558. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.;
ARTICLE
Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision A.1; Gaussian, Inc.: Wallingford, CT, 2009. (23) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (24) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215–241. (25) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968–5975. (26) The original aug-cc-pvdz basis set in Gaussian 09 had an error that affected the first-row transition metals. That error has been corrected in revision B1, but it is necessary to add the diffuse functions using the general basis set option. They are available for download at http://tyr0.chem.wsu.edu/∼kipeters/basissets/tm3dbasis.html. A sample input file is included in the Supporting Information. (27) Pratt, L. M.; Tran, P. T. T.; Nguyen, N. V.; Ramachandran, B. Bull. Chem. Soc. Jpn. 2007, 9, 1107–1125. (28) Ramachandran, B.; Kharidehal, P.; Pratt, L. M.; Voit, S.; Okeke, F. N.; Ewan, M. J. Phys. Chem. A 2010, 114, 8423–8433.
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