**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 (Ln M) 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 (*I* <sup>R</sup>). 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 (*I* P).

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 (*I* R), 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 (*I* P), which is labeled 3 [LnM]3 [IC], the electron pairs are coupled to

**Figure 1.** The energy diagram for an oxidative addition reaction, showing the formation of a state curve (Ψ) by mixing two configurations: the reactant configuration (*I* <sup>R</sup>) and the product configuration (*I* P). The reactants are separated by an energy gap, S. Configuration mixing near the crossing point causes an avoidance crossing (dotted line). For details see the text.

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**.

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

M) 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 configu-

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

a lone pair and the two electrons on the CH moiety are spin-paired to form a C─H *σ* bond. In

**Figure 1.** The energy diagram for an oxidative addition reaction, showing the formation of a state curve (Ψ) by mixing two

<sup>R</sup>) and the product configuration (*I*

gap, S. Configuration mixing near the crossing point causes an avoidance crossing (dotted line). For details see the text.

ground state of the products and is marked as the product configuration (*I*

P), which is labeled 3

<sup>R</sup>). The second line shows the excited configuration of the reactants, which connects the

[LnM]3

[IC], the two electrons on the LnM moiety are spin-paired to form

P).

[IC], the electron pairs are coupled to

P). The reactants are separated by an energy

(Ln

(*I*

ration (*I*

R), which is labeled 1

the product configuration (*I*

configurations: the reactant configuration (*I*

[LnM]1

156 Descriptive Inorganic Chemistry Researches of Metal Compounds

It is proposed that the transition state for the reaction that inserts Ln M 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 Ln M(C)(H), the bond-prepared Ln M 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 Ln M(C)(H) product is between the triplet Ln M 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 [69].

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 *I* R and the *I*P) corresponds to the energy gap, S, in the VBSCD model. In terms of the reactants, *I* R is the ground state and *I*P is in an excited state whose energy is greater than *I* R. When the reaction is in progress, the energy of *I* R increases and that of *I*P decreases. The transition state occurs at a point along the reaction coordinate where the energy curves for *I* R and *I* <sup>P</sup> cross (see the dotted curve in **Figure 1**). Finally, in terms of the products, *I* R assumes the excited-state configuration and *I* <sup>P</sup> 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., ∆*E*st (= *E*triplet − *E*singlet for LnM) + ∆*Eσσ\**(= *E*triplet − *E*singlet for C─H). In other words, the smaller the value of ∆*E*st + ∆*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 L2 M are isolobal [70], 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 L2 M 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 L2 M 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.
