Selected geometrical parameters (bond distances in Å), relative energies ∆E (zero-point corrected; kcal mol-1)and relative Gibbs free energies ∆G (kcal mol-1) at 298 K at the M06-L/Def2-SCP level of theory for the optimized stationary points on the oxidative addition reactions (Eq. (1)) [1–30].
The potential energy surfaces of the oxidative addition reactions, L2M + imidazoliumcation → product and CpM′L + imidazolium cation → product (M = Ni, Pd, Pt; M′ = Co, Rh, Ir; Cp = η5-C5H5; L = 1,3-aryl-N-heterocyclic carbene (NHC), aryl = 2,4,6-trimethylphenyl), are studied at the M06-L/Def2-SVP level of theory. The theoretical findings show that the singlet-triplet splitting (∆Est = Etriplet − Esinglet) for the L2M and CpM′L species can be used to predict the reactivity for their oxidative additions. That is to say, current theoretical evidence suggests that both a 14-electron L2M complex and a 16-electron CpM′Lcomplex with a better electron-donating ligand L (such as NHC) result in a reduced ∆Est value and facilitate the oxidative addition to the saturated C─H bond. The theoretical results for this study are in good agreement with the obtainable experimental results and allow a number of predictions to be made.
- oxidative addition reactions
- group 9 elements
- group 10 elements
- imidazolium and density functional theory
Recent studies involving the chemistry of the heterocyclic nitrogen carbene complexes of transition metals have demonstrated that they can act as precatalysts for a variety of reactions [1–11]. These new species offer many opportunities to advance this field of study [12–30]. The use of palladium carbene complexes for the Heck reaction [31–34] and platinum carbene compounds for the C─H activation reactions  has created new opportunities in catalytic chemistry.
Over the last two decades, imidazolium-based ionic liquids have also found many applications in catalysis [35–39], or as nonaqueous alternatives for biphasic catalysis [4, 40–42]. The studies by Cavell and co-workers  showed that the reaction of imidazolium-based ionic liquids with low-valence Ni0 and σ-donor ligands that bear Pd0 is an easy procedure for the production of unusually stable carbene-metal-hydride complexes (see Scheme 1). The major feature of the study was the direct formation of a carbene-metal-hydride, which offers an atom-efficient direct route to an active catalytic species. Besides these experimental facts, it is not surprising that N-heterocyclic carbenes (NHCs) [44–46] have found applications in a series of catalytic reactions, such as amination reactions, the Suzuki-Miyaura and Sonogashira coupling reactions, hydroformylation, hydrosilylation, and polymerization and olefin metathesis [47–50].
The crucial experimental works that are presented in Scheme 1 inspire this study of the potential energy surfaces of these oxidative addition reactions, using density functional theory (DFT). There have been a number of reports concerning the conventional oxidative additions-reductive eliminations of alkanes to low-valence metals, which has led to an understanding of the factors that affect these reactions [51–56]. These studies have mostly focused on the catalytic reactions of saturated hydrocarbons to zerovalent group 10 elements (i.e., Ni, Pd, and Pt). To the authors’ best knowledge, there has been neither experimental nor theoretical study of the catalytic oxidative addition reactions for the group 9 atoms (i.e., Co, Rh, and Ir) or the imidazolium cation. This study gives a thorough understanding of the catalytic reactions for potential transition metal complexes with imidazolium cations (ICs). Accordingly, a study of the important C─H activation reactions, Eqs. (1) and (2), is undertaken:
Since oxidative addition involves charge transfer from the metallic center of both L2M and CpM′L to the approaching IC, an electron-donating L that increases the electron density on the central metal stabilizes its transition state and lowers the barrier height. That is to say, increasing the electron density on the central metal atom of both L2M and CpM′L increases the chance of its triplet participating in the oxidative addition reaction (vide infra). Therefore, the reactivity of both substituted 14-electron L2M and 16-electron CpM′L is verified by the singlet-triplet splitting (∆Est = Etriplet − Esinglet), which can result from several factors, such as the effect of the geometrical structure (i.e., linear or bent for the L2M system) , the nature of electron-withdrawal or electron-acceptance for the ancillary ligand, L, and the character of the central transition metal atom. In the organometallic field, the NHC groups are stronger σ-donors and weaker π-acceptor ligands than the traditional PR3 ligands [47–50]. Therefore, the model systems (both L2M and CpM′L complexes) that are studied in this work use the NHC as the ancillary ligand L.
Since the transition-metal-catalyzed reactions that contain imidazolium salt are both helpful and novel, a comprehensive understanding of the factors that control the magnitude of the activation barriers and the reaction enthalpies allows a greater understanding of their reactivity. Full realization of the factors that influence the reactivities of transition metal complexes with ICs benefits basic science and a continued expansion of their applications.
2. Theoretical methods
The geometries of all of the stationary points are fully optimized at the M06-L level of theory , using the Gaussian 09 program package . These M06-2X calculations are executed using pseudo-relativistic effective core potentials on group 9 and group 10 elements, using the Def2-SVP basis sets [59–63]. These M06-L calculations are denoted as M06-L/Def2-SVP. Frequency computations are accomplished for all structures to verify that the reactants and products have no imaginary frequencies and that the transition states occupy only one imaginary frequency. The relative free energy (∆G) at 298 K is computated at the M06-L/Def2-SVP level of theory.
3. The origin of the barrier and the reaction enthalpy for the oxidative addition of an imidazolium cation to transition metal complexes
In this section, the valence bond state correlation diagram (VBSCD) model [64–68] that was developed by Shaik and Pross is used to interpret the oxidative addition for an imidazolium cation to transition metal complexes. For the σ-bond insertion reaction, the system must have a number of predetermined states, each of which is approximated by an appropriate electronic configuration [64–68]. In particular, there are two important configurations that contribute significantly to the total wave function, Ψ, and change the shape of the potential energy surface. Figure 1 shows the qualitative behavior of the two configurations for the insertion of a transition-metal complex (LnM) into a C(carbenic carbon)─H bond of an IC. The first line shows the reactant ground-state configuration, which connects the excited state for the products, denoted as the reactant configuration (IR). The second line shows the excited configuration of the reactants, which connects the ground state of the products and is marked as the product configuration (IP).
From the valence bond (VB) viewpoint, the reactions for the insertion of LnM fragments into the C─H bond are illustrated in 1 and 2, as shown in Figure 1. In the reactant configuration (IR), which is labeled 1[LnM]1[IC], the two electrons on the LnM moiety are spin-paired to form a lone pair and the two electrons on the CH moiety are spin-paired to form a C─H σ bond. In the product configuration (IP), which is labeled 3[LnM]3[IC], the electron pairs are coupled to allow the formation of both an M─C and an M─H bond and the simultaneous breaking of a C─H bond. From the molecular orbital (MO) viewpoint, the representations of VB configurations 1 and 2 are respectively given in 3 and 4.
It is proposed that the transition state for the reaction that inserts LnM into a C─H bond is regarded as the respective triplet states of the reactants. It is worthy to note that these individual triplets are coupled to an overall singlet state. Since new M─C and M─H covalent bonds are formed in the product LnM(C)(H), the bond-prepared LnM state must have at least two open shells. Therefore, the lowest state for this type is the triplet state. In other words, the bonding in the LnM(C)(H) product is between the triplet LnM state and two doublet radicals (the C radical and the H radical). Similarly to the bonding in a water molecule, from the valence-bond point of view, it is represented as bonding between a triplet oxygen atom and two doublet hydrogen atoms .
As schematically illustrated in Figure 1, the singlet-triplet excitation energy plays a decisive role in the VBSCD model [64–68]. The singlet-triplet excitation energy (i.e., the energy between the IR and the IP) corresponds to the energy gap, S, in the VBSCD model. In terms of the reactants, IR is the ground state and IP is in an excited state whose energy is greater than IR. When the reaction is in progress, the energy of IR increases and that of IP decreases. The transition state occurs at a point along the reaction coordinate where the energy curves for IR and IP cross (see the dotted curve in Figure 1). Finally, in terms of the products, IR assumes the excited-state configuration and IP a ground state. These two configurations cross. This is the simplest description of the ground state energy profiles for the chemical reactions of the related molecular systems [64–68].
Figure 1 shows that the energy of point 2 (left in Figure 1), the anchor point for 3[LnM]3[IC] in the reactant geometry, is governed by the singlet-triplet energy gap for both LnM and C─H; i.e., ∆Est(= Etriplet − Esinglet for LnM) + ∆Eσσ*(= Etriplet − Esinglet for C─H). In other words, the smaller the value of ∆Est + ∆Eσσ*, the lower is the activation barrier and the more exothermic is the reaction [64–68]. If a reactant, LnM, has a singlet ground state with a small triplet excitation energy, there is a greater probability that a triplet LnM contributes to the singlet reaction and the reactions occur readily. Both the order of the singlet and triplet states and the magnitude of the singlet-triplet energy separation also determine the existence and the height of the energy barrier.
Since CH2 and 16-electron CpML and 14-electron L2M are isolobal , each has two valence orbitals with the same symmetry patterns (5), in which each fragment has one orbital of a′ and a″ symmetry.
In this qualitative theoretical treatment, the transition-metal fragment L2M and CpML has an empty electrophilic orbital (i.e., a', as shown in 5) that interacts with a filled hydrocarbon fragment orbital. This facilitates a concerted 1,2-hydrogen migration. In other words, the net molecular result of the insertion of the L2M and CpML complexes into a C─H σ bond of an IC is that a new M─C σ bond and a new M─H σ bond are formed and the C─H σ bond of an IC is broken. This analysis is used to interpret the results in the following section.
4. Results and discussion
4.1. The geometries of the triscarbene-nickel-hydrido complex and the triscarbene-palladium-hydrido complex
The geometrical structures of the triscarbene-nickel-hydrido complex (Pro-Ni) and thetriscarbene-palladium-hydrido complex (Pro-Pd) are firstly determined theoretically. The optimized geometries for these two species are computed at the M06-L/Def2-SVP level of theory. As shown in Figure 2, the M06-L calculations show that the computed M─C bond lengths for both molecules (average 1.924 and 2.089 Å at M06-L) compare favorably with the average M─C bond lengths that are determined from X-ray data (1.907 and 2.057 Å) . Similarly, the average values for the ∠C─M─C and ∠C─M─H angles for these two structures are calculated to be 98.26° and 82.58° (Ni) and 97.41° and 82.23° (Pd), which agrees reasonably well with the experimental data (97.85, 82.00, 95.94, and 84.00°, respectively) , as shown in Figure 2. Given the agreement between the M06-L method using the Def2-SVP basis set and the available experimental data , it is expected that the same relative accuracy is applicable to any discussion of their reactivities and the reaction mechanisms, for which experimental data are still not available.
4.2. The geometries and energetics of the L2M + 1,2-dimethylimidazolium cation
The results for four regions on the potential energy surfaces for L2M (M = Ni, Pd, Pt;L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl) and 1,2-dimethylimidazolium cation (IC) are shown: 14-electron L2M plus free IC (Rea), a precursor complex (Pcx), the transition state (TS), and the oxidative addition product (Pro). The fully optimized geometries for the key points, calculated at the M06-L/Def2-SVP level, are shown in Figure 3. The important geometrical parameters and relative energies and the potential energy profiles at the same level of theory are listed in Table 1 and Figure 4, respectively. Four points are noteworthy.
The C3─H4 bond distance in IC (reactant) is calculated to be 1.090 Å.
The reactants, Rea-Ni, Rea-Pd, and Rea-Pt, are computed as both low-spin (singlet) and high-spin (triplet state) complexes. The M06-L computations demonstrate that these transition metal complexes all adopt the singlet ground state. The computations also show that the singlet-triplet triplet free energy splitting (∆Est; kcal/mol) for these fragments are in the order: Rea-Ni (23.7) < Rea-Pd (50.1) < Rea-Pt (63.9). These values are much greater than those for other previously studied L2M complexes that have various ancillary ligands [51–56]. Therefore, it is possible that the oxidative addition reactions (Eq. (1)) that are studied in this work proceed on the singlet surface. The singlet surface is therefore the focus of this study, from this point.
The optimized transition state structures (TS-Ni, TS-Pd, and TS-Pt) and arrows that indicate the main atomic motion in the transition state eigenvector are shown in Figure 3. These model computations show that the oxidative addition reactions that are studied using these model reactants all proceed in a concerted fashion via a three-center transition state, as shown in Figure 3, and all reactions are exothermic. It is noted that for the oxidative addition reactions involving the group 10 transition metals that are studied in this work, the free energies for the transition states are all less than those for the corresponding reactants. It is theoretically predicted that these oxidative addition reactions proceed readily, even at room temperature. Further supporting evidence comes from the fact that the oxidative additions between Rea-Ni and Rea-Pd species and an imidazolium cation have been experimentally proven to be easy .
According to the theoretical analysis of the VBSCD model that is discussed in Section 3, the smaller the value of ∆Est for L2M, the lower is the barrier height and the more exothermic is the reaction and the faster is the oxidative addition reaction. The model evidence confirms this prediction. For the M06-L calculations for the model systems that have group 10 transition metals, a plot of the activation barrier (∆E‡) versus the ∆Est is shown, for which the best fit is ∆E‡ = 0.518∆Est – 11.2. The linear correlation between ∆Est and the Gibbs free energy (∆G), which is also calculated at the same level of theory, is ∆G = 0.566 ∆Est − 67.5. The theoretical results definitely show that for the facile oxidative addition of C─H bonds, an understanding of the ∆Est of the coordinatively unsaturated 14-electron L2M is crucial, since it can be used to predict the reactivity of the reactants.
4.3. The geometries and energetics of the CpM′+ 1,2-dimethylimidazolium cation
Similarly to the study of the L2M system, the M06-L/Def2-SVP level is also used to study the mechanisms for the oxidative addition reactions for CpM′L (M′ = Co, Rh, Ir; L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl), as shown in Figure 5. The relative M06-L energies and the key geometrical parameters for the stationary points are also listed in Table 2. The corresponding potential energy profiles are given in Figure 6. Three interesting conclusions can be drawn from these figures and the table.
The C2─H3 bond distance in IC (reactant) is calculated to be 1.090 Å.
The M06-L calculations in Table 2 show that the ground states for the CpCoL and CpIrL fragments are triplets, but the CpRhL complex is a singlet. The M06-L results also show that the ∆Est value for the CpCoR and CpIrR fragments are respectively computed to be− 8.3 and − 0.88 kcal/mol and the ∆Est of CpRhR was predicted to be 10.2 kcal/mol. It is worthy to note that whenever a reactant contains a heavy atom that is not necessarily directly included in the reaction, a strong spin-orbit coupling (SOC) can occur [71–75]. That is, because of the presence of the heavy atom, a triplet reactant can cause a spin-inversion process. It transfers to the singlet reactant and then forces the singlet reaction. Since these theoretical calculations show that both the CpCoR and the CpIrR species have a small value for ∆Est and a heavier transition metal is involved, the SOC is expected to be substantial for the oxidative additions and these would eventually proceed in the singlet chemical reactions.
Figure 6 shows that, similar to the case for L2M molecules, the energy of the transition state for Co, Rh, and Ir is less than that for the reactants, which demonstrates that the CpM′L (M′ = Co, Rh, and Ir) complexes readily overcome the energy barrier and then undergo oxidative addition into the C─H bond of IC in a concerted fashion, even at room temperature. The model computations show that the oxidative addition of a CpM′L fragment that has a group 9 metal (M′) decreases in the order: CpCoL > CpIrL > CpRhL. For the reverse process (right to left in Figure 6), the barriers to reductive elimination for the Co, Rh, and Ir systems have much higher energies than those for the corresponding oxidative addition. The theoretical evidence demonstrates that these CpM′L complexes undergo oxidative additions more easily than reductive eliminations, as noted in the introduction. That is to say, because the attached NHC groups readily donate electrons, the electrons in the metal, M′, are abundant and the CpM′L readily allows oxidative additions with the incoming molecules. The theoretical studies suggest that the CpM′L molecules prefer to undergo oxidative addition reactions with the imidazolium cation, even at room temperature.
According to the VBSCD model, the smaller the ∆Est value for CpM′L (if ∆Eσσ* is a constant), the lower is the barrier height, the more exothermic is the reaction and the faster is the oxidative addition reaction [64–68]. The M06-L/Def2-SVP results support this prediction. The M06-L calculations show that value for ∆Est (kcal/mol) increases in the order: CpCoL (−8.3) < CpIrL (−0.77) < CpRhL (+8.0). As shown in Table 2, both the activation energies (∆E‡) and the Gibbs free energies (∆G) follow the same order as the ∆Est value (kcal/mol): Co (+9.28, −62.4) < Ir (+10.8, −46.2 kcal/mol) < Rh (+11.0, −39.1). In order to determine a good model for the facile oxidative addition of 16-electron CpM′L to a C-H bond of an imidazolium cation, an understanding of the ∆Est of the coordinatively unsaturated CpM′L is important.
In summary, the theoretical evidence demonstrates that both a 14-electron L2M complex and a 16-electron CpM′L complex with a better electron-donating ligand, L (such as NHC), result in a smaller value for ∆Est and allow a more facile oxidative addition to the saturated C─H bond. This theoretical study also demonstrates that, in terms of the VBSCD model, the ∆Est value is a useful foundation for predicting the relative magnitude of the activation barriers and the reaction enthalpies for the activation of an imidazolium cation by L2M and CpM′L. Although the computed magnitude of the barrier and the predicted geometry for the transition state for these reactions are dependent on the level of theory that is used, these qualitative predictions are in good agreement with the theoretical results that are presented here and with the available experimental observations.
It is hoped that this study will stimulate for further research into the subject.
The authors are grateful to the National Center for High-Performance Computing of Taiwan for generous amounts of computing time and the Ministry of Science and Technology of Taiwan for the financial support.