**4. Results and discussion**

### **4.1. The geometries of the triscarbene-nickel-hydrido complex and the triscarbenepalladium-hydrido complex**

The geometrical structures of the triscarbene-nickel-hydrido complex (**Pro-Ni**) and the triscarbene-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

**Scheme 4.** 

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) [43]. 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) [43], as shown in **Figure 2**. Given the agreement between the M06-L method using the Def2-SVP basis set and the available experimental data [43], 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.

**Figure 1** shows that the energy of point **2** (left in **Figure 1**), the anchor point for 3

and 16-electron CpML and 14-electron L2

In this qualitative theoretical treatment, the transition-metal fragment L2

is broken. This analysis is used to interpret the results in the following section.

**4.1. The geometries of the triscarbene-nickel-hydrido complex and the triscarbene-**

The geometrical structures of the triscarbene-nickel-hydrido complex (**Pro-Ni**) and the triscarbene-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

the value of ∆*E*st + ∆*Eσσ*\*

Since CH2

**Scheme 4.** 

and a″ symmetry.

molecular result of the insertion of the L2

158 Descriptive Inorganic Chemistry Researches of Metal Compounds

**4. Results and discussion**

**palladium-hydrido complex**

the reactant geometry, is governed by the singlet-triplet energy gap for both LnM and C─H; i.e., ∆*E*st (= *E*triplet − *E*singlet for LnM) + ∆*Eσσ\**(= *E*triplet − *E*singlet for C─H). In other words, the smaller

tion [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.

orbitals with the same symmetry patterns (**5**), in which each fragment has one orbital of a′

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

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

, the lower is the activation barrier and the more exothermic is the reac-

[LnM]3

M and CpML has

M are isolobal [70], each has two valence

M and CpML complexes into a C─H *σ* bond of an IC

[IC] in

**Figure 2.** Selected geometrical parameters (in Å and deg) for the triscarbene-nickel-hydrido complex (**Pro-Ni**) and the triscarbene-palladium-hydrido complex (**Pro-Pd**), calculated at the M06-L/Def2-SVP level of theory and a comparison with the experimental values [43]. Hydrogens are omitted for clarity.

#### **4.2. The geometries and energetics of the L2 M + 1,2-dimethylimidazolium cation**

The results for four regions on the potential energy surfaces for L2 M (M = Ni, Pd, Pt; L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl) and 1,2-dimethylimidazolium cation (IC) are shown: 14-electron L2 M 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.

	- **1.** 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 (∆*E*st; 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 L2 M 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.
	- 2. 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 threecenter 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 [43].
	- 3. According to the theoretical analysis of the VBSCD model that is discussed in Section 3, the smaller the value of ∆*E*st for L2 M, 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 ∆*E*st is shown, for which the best fit is ∆*E*‡ = 0.518∆*E*st – 11.2. The linear correlation between ∆*E*st and the Gibbs free energy (∆*G*), which is also calculated at the same level of theory, is ∆*G* = 0.566 ∆*E*st − 67.5. The theoretical results definitely show that for the facile oxidative addition of C─H bonds, an understanding of the ∆*E*st of the coordinatively unsaturated 14-electron L2 M is crucial, since it can be used to predict the reactivity of the reactants.

The Mechanisms for the Oxidative Addition of Imidazolium Salts to a Group 9 Transition Metal Atom (Co0, Rh0, and... http://dx.doi.org/10.5772/67567 161

**4.2. The geometries and energetics of the L2**

160 Descriptive Inorganic Chemistry Researches of Metal Compounds

shown: 14-electron L2

─H4

**2.** The C3

The results for four regions on the potential energy surfaces for L2

are listed in **Table 1** and **Figure 4**, respectively. Four points are noteworthy.

are much greater than those for other previously studied L2

3, the smaller the value of ∆*E*st for L2

shown, for which the best fit is ∆*E*‡

14-electron L2

singlet surface is therefore the focus of this study, from this point.

L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl) and 1,2-dimethylimidazolium cation (IC) are

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

**1.** For the optimized structures, see **Figure 3**. For the relative free energies, see **Figure 4**.

**1.** 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 (∆*E*st; kcal/mol) for these fragments are in the order: **Rea-Ni** (23.7) < **Rea-Pd** (50.1) < **Rea-Pt** (63.9). These values

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

2. 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 threecenter 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 [43]. 3. According to the theoretical analysis of the VBSCD model that is discussed in Section

thermic 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

and the Gibbs free energy (∆*G*), which is also calculated at the same level of theory, is ∆*G* = 0.566 ∆*E*st − 67.5. The theoretical results definitely show that for the facile oxidative addition of C─H bonds, an understanding of the ∆*E*st of the coordinatively unsaturated

M is crucial, since it can be used to predict the reactivity of the reactants.

have group 10 transition metals, a plot of the activation barrier (∆*E*‡

bond distance in IC (reactant) is calculated to be 1.090 Å.

**M + 1,2-dimethylimidazolium cation**

M plus free IC (**Rea**), a precursor complex (**Pcx**), the transition state (**TS**),

M (M = Ni, Pd, Pt;

M complexes that have

) versus the ∆*E*st is

M, the lower is the barrier height and the more exo-

= 0.518∆*E*st – 11.2. The linear correlation between ∆*E*st

**Figure 3.** M06-L/Def2-SVP optimized geometries for the stationary points for the oxidative addition reactions of **Rea-M** (M = Ni, Pd, and Pt) molecules. For selected geometrical parameters and relative energies for each species, see **Table 1**. The bold arrows denote the main atomic motions in the transition state eigenvector. Some hydrogens are omitted for clarity.


**Table 1.** 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].

**Figure 4.** The reaction energy profile (in kcal/mol) for the oxidative addition reactions: L<sup>2</sup> M + 1,2-dimethylimidazolium cation (M = Ni, Pd, and Pt; L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl). All of the energies are calculated at the M06-L/Def2-SVP level. See also **Table 1** and **Figure 3**.

#### **4.3. The geometries and energetics of the CpM′+ 1,2-dimethylimidazolium cation**

Similarly to the study of the L2 M 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.

	- **1.** 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 ∆*E*st value for the CpCoR and CpIrR fragments are respectively computed to be− 8.3 and − 0.88 kcal/mol and the ∆*E*st 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 ∆*E*st 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.
	- 2. **Figure 6** shows that, similar to the case for L2 M 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.
	- 3. According to the VBSCD model, the smaller the ∆*E*st 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 ∆*E*st (kcal/mol) increases in the order: CpCoL (−8.3) < CpIrL (−0.77) < CpRhL (+8.0). As shown in **Table 2**, both the

**Figure 4.** The reaction energy profile (in kcal/mol) for the oxidative addition reactions: L<sup>2</sup>

M06-L/Def2-SVP level. See also **Table 1** and **Figure 3**.

cation (M = Ni, Pd, and Pt; L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl). All of the energies are calculated at the

**Geometrical structures Energies**

**Table 1.** 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

**Rea-Ni** 1.836 1.836 – – – 0.0 0.0 **Pcx-Ni** 1.938 1.961 – 1.107 2.056 −50.24 −33.65 **TS-Ni** 1.981 1.947 1.886 1.482 1.527 −49.38 −32.26 **Pro-Ni** 1.911 1.904 – 1.985 1.394 −69.31 −54.36 **Rea-Pd** 2.015 2.015 – – – 0.0 0.0 **Pcx-Pd** 2.050 2.053 – 1.115 2.105 −39.69 −23.67 **TS-Pd** 2.159 2.138 2.039 1.437 1.679 −25.99 −8.417 **Pro-Pd** 2.057 2.067 – 2.144 1.572 −55.36 −38.23 **Rea-Pt** 2.003 2.003 – – – 0.0 0.0 **Pcx-Pt** 2.022 2.019 – 1.119 2.134 −41.35 −22.46 **TS-Pt** 2.128 2.064 2.067 1.333 1.797 −16.49 −1.384 **Pro-Pt** 2.054 2.060 – 2.139 1.621 −47.52 −31.98

**-H4 M-H4 ∆***E* **∆***G*

**Systems M-C1 M-C2 M-C3 C3**

162 Descriptive Inorganic Chemistry Researches of Metal Compounds

stationary points on the oxidative addition reactions (Eq. (1)) [1–30].

M + 1,2-dimethylimidazolium

**Figure 5.** M06-L/Def2-SVP optimized geometries for the stationary points for the oxidative addition reactions of **Rea-M**′ (M′ = Co, Rh, and Ir) molecules. For the selected geometrical parameters and relative energies for each species, see **Table 2**. The bold arrows denote the main atomic motions in the transition state eigenvector. Some hydrogens are omitted for clarity.

The Mechanisms for the Oxidative Addition of Imidazolium Salts to a Group 9 Transition Metal Atom (Co0, Rh0, and... http://dx.doi.org/10.5772/67567 165


**Table 2.** Key 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, calculated at the M06-L/Def2-SCP level of theory, for the optimized stationary points on the oxidative addition reactions (Eq. (2)) [1–30].

**Figure 6.** The reaction energy profile (in kcal/mol) for the oxidative addition reactions: CpML + 1,2-dimethylimidazolium cation (M = Co, Rh, and Ir; L = 1,3-aryl-NHC, aryl = 2,4,6-trimethylphenyl). All of the energies are calculated at the M06-L/ Def2-SVP level. See also **Table 1** and **Figure 3**.

**Figure 5.** M06-L/Def2-SVP optimized geometries for the stationary points for the oxidative addition reactions of **Rea-M**′ (M′ = Co, Rh, and Ir) molecules. For the selected geometrical parameters and relative energies for each species, see **Table 2**. The bold arrows denote the main atomic motions in the transition state eigenvector. Some hydrogens are omitted for clarity.

164 Descriptive Inorganic Chemistry Researches of Metal Compounds

activation energies (∆*E*‡ ) and the Gibbs free energies (∆*G*) follow the same order as the ∆*E*st 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 ∆*E*st of the coordinatively unsaturated CpM′L is important.
