**2. Theoretical methods**

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 [43] showed that the reaction of imidazolium-based

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

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)

(M = Ni, Pd, Pt; L = 1, 3 - aryl-NHC, aryl = 2, 4, 6 - trimethylphenyl) (1)

and *σ*-donor ligands that bear Pd0

is an easy procedure

ionic liquids with low-valence Ni0

154 Descriptive Inorganic Chemistry Researches of Metal Compounds

olefin metathesis [47–50].

**Scheme 1.** 

and (2), is undertaken:

The geometries of all of the stationary points are fully optimized at the M06-L level of theory [57], using the Gaussian 09 program package [58]. 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.
