Theoretical study on the activation of C-H bond in ethane by PdX⁺ (X = F, Cl, Br, H, and CH₃) in the gas phase

Abstract

The mechanism of C-H bond activation of ethane was catalyzed by palladium halide cations (PdX⁺ (X = F, Cl, Br, H, and CH₃)), which was investigated using density functional theory (DFT) at B3LYP level. The reaction mechanism was taken into account in triplet and singlet spin state potential energy surfaces. For PdF⁺, PdCl⁺, and PdBr⁺, the high spin states were the ground states, whereas the ground states were the low spin states in PdH⁺ and PdCH₃⁺. The reaction of PdF⁺, PdCl⁺, and PdBr⁺ with ethane occurred via a typical “two-state reactivity” mechanism. In contrast, for PdH⁺ and PdCH₃⁺, the overall reaction performed on the ground state PESs in a spin-conserving manner. The crossing points between two potential energy surfaces were observed and effectively decreased the activation barrier in PdX⁺/C₂H₆ (X = F, Cl, and Br). The minimum energy crossing points (MECP) were obtained used the algorithm in Harvey method. The natural valence electron configuration calculations were analyzed by natural bond orbital. The distribution and contribution of the front molecular orbital of the initial complexes could be further understand by the density of states. The feature of the bonding evolution in the main pathways was studied using topological analysis including localized orbital locator and atoms in molecules.

Introduction

In the past few decades, the activation of the C-H and C-C bonds in alkanes catalyzed by transition metal ions has attracted considerable attention, due to its importance and widespread application in the energy transform, organic synthesis, and catalytic researches [1,2,3,4]. In the previous studies, chemists have discovered that some mononuclear transition metal ions M⁺ can activate the C-C and C-H bonds of alkanes. For example, methane could be activated by first-row and second-row transition metal cations [5, 6], C-C and C-H bonds of ethane activation by Fe⁺ [7], etc. However, some mononuclear transition metal ions were not or low reactivity to the C-H bonds of alkanes. To solve this problem, chemists have attempted adding ligands to increase the catalytic efficiency of these metal ions. The catalytic efficiency of the metal was effectively enhanced by the synergy between the transition metal ion and the ligand. For instance, Cr⁺ does not have any reactivity with small alkanes, whereas the diatomic CrCl⁺ does [8]; and CH₄ cannot be activated by bare Ni⁺, but NiH⁺ brings about thermal bond activation [9]. Obviously, the metal combined with the ligand L by covalent bond changes considerably the catalytic activity of metals, and a suitably chosen ligand L can improve the reactivity of a reagent.

In 2007 and 2011, Schlangen et al. reported the reaction mechanism in gas-phase reactions of NiX⁺/RH couples (X = F, Cl, Br; R = CH₃, C₂H₅, C₃H₇, n-C₄H₉) in experimental section and theoretical aspects, respectively [10, 11]. As Ni congener, palladium is a precious metal, 0.0000015% abundance of palladium in the Earth’s crust [12]. The reactivity of atomic palladium with alkanes was very low in the gas phase because its ground state cannot accomplish oxidative insertion, and its lowest excited state was also quite high in energy to deal with C-H bond activation [13]. Therefore, the addition of an appropriate ligand to enhance the catalytic activity of palladium had become an important issue. Compared with atomic Pd, theoretical studies and experiments have shown that the cationic palladium hydride has high activity toward C-H bonds of methane in the gas phase [14, 15]. Simultaneously, the dehydrogenation reaction of methane activation by [Pd(H)(OH)]⁺ has been theoretically investigated at our lab [16]. Theoretical studies on the activation of C-H bonds by PdX⁺ (X = F, Cl, Br, H, and CH₃) had not been reported. To further insight into how halogen ligands affect the activity of palladium and the reaction mechanism with target molecules, in this paper, the reaction mechanism of PdX⁺-activated ethane C-H bond was systematically studied theoretically.

Computational methods

Theoretical calculation for all stationary points involved in the reaction of PdX⁺(X = F, Cl, Br, H, and CH₃) with C₂H₆ has been surveyed by the density functional theory (DFT) [17,18,19,20]. For C, H, F, Cl, and Br, the large 6-311+G (d, p) basis set was applied [21]. The Pd atom was described by using the Stuttgart/Dresden relativistic effective core potentials (ECP) of SDD [22]. The vibrational frequency was calculated for each stationary point to confirm whether it was minima structure or transition state (TS). The minimum structure had only positive eigenvalues and TS had only one negative eigenvalue. Intrinsic reaction coordinate (IRC) calculations were performed to determine the correct link between the minima and the transition states (TS) [20]. The natural population analysis and the bonding properties for some structures have been made with natural bond orbital (NBO) analysis [23]. Density of states (DOS) of initial complexes was analyzed using the Multiwfn package [24, 25]. We used the single-point energy of the DFT to roughly locate crossing points (CPs) between two potential energy surfaces (PESs). The minimum energy crossing point (MECP) was obtained using the mathematical algorithm proposed by Harvey et al. [26]. In addition, the bonding evolution of the main reaction pathways was studied by localized orbital locator (LOL) [27] analysis and atoms in molecules (AIM) [28] analysis using the Multiwfn program. All of the theoretical calculations were implemented using the Gaussian 09 program [29].

Results and discussion

The mechanism of ethane activated by PdX⁺ has been considered in singlet and triplet state. The superscript prefixes “1” and “3” were defined as the singlet and triplet states, respectively. The structures of stationary points in the high and low spin states and the corresponding PESs are depicted in Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 (Fig. S1-S5 in support information). The scenario of the reaction paths is depicted in Scheme 1.

Fig. 1

Optimized geometries for the stationary points of the first α-C-H bond activation of ethane in the singlet state (a) ¹PdF⁺, (b) ¹PdCl⁺, and (c) ¹PdBr⁺ (bond lengths unit Å)

Fig. 12

Orbital interaction diagram at the four-membered ring (Pd-C1-C2-H4) in intermediate ¹IM2 (a) ¹PdF⁺, (b) ¹PdCl⁺, and (c) ¹PdBr⁺

Fig. 2

Potential energy profiles of reactions of ethane with PdF⁺

Fig. 3

Potential energy profiles of reactions of ethane with PdCl⁺

Fig. 4

Potential energy profiles of reactions of ethane with PdBr⁺

Fig. 5

Optimized geometries for the stationary points of the β-C-H bond activation of ethane in the singlet state (a) ¹PdF⁺, (b) ¹PdCl⁺, and (c) ¹PdBr⁺ (bond lengths unit Å)

Fig. 6

Optimized geometries for the stationary points of the second α-C-H bond activation of ethane in the singlet state (a) ¹PdF⁺, (b) ¹PdCl⁺, and (c) ¹PdBr⁺ (bond lengths unit Å)

Fig. 7

Optimized geometries for the stationary points of the first α-C-H bond activation of ethane in the singlet state (d) ¹PdH⁺ and (e) ¹PdCH₃⁺ (bond lengths unit Å)

Fig. 8

Potential energy profiles of reactions of ethane with PdH⁺

Fig. 9

Potential energy profiles of reactions of ethane with PdCH₃⁺

Fig. 10

Optimized geometries for the stationary points of the β-C-H bond activation of ethane in the singlet state (d) ¹PdH⁺ and (e) ¹PdCH₃⁺ (bond lengths unit Å)

Fig. 11

Optimized geometries for the stationary points of the second α-C-H bond activation of ethane in the singlet state (d) ¹PdH⁺ and (e) ¹PdCH₃⁺ (bond lengths unit Å)

Scheme 1

The scenario of the reaction paths

Electronic structures of reactants

The calculated results showed that ³PdX⁺ was ground state and the energy of ³PdX⁺ (X = F, Cl, and Br) was 24, 57 and 102 kJ/mol lower than ¹PdX⁺, respectively. In contrast, ¹PdX⁺ was the ground state for PdX⁺ (X = H and CH₃). The energy of the triplet state ³PdX⁺ was 82 and 88 kJ/mol higher than the ground state, respectively. The energy level differences of the reactants between the singlet and triplet state became gradually bigger from PdF⁺ to PdCl⁺ and PdBr⁺, while PdH⁺ was very close to those of the PdCH₃⁺. The natural valence electron configuration calculations were performed for PdX⁺ (X = F, Cl, Br, H, and CH₃), which is shown in Table 1. From F to CH₃, the electronic number of the 4d orbital was increased significantly, and the 5s orbit had almost no changed in the singlet state. In contrast, the number of 5s orbital electrons was changed obviously, whereas the 4d orbital did not in the triplet state.

Table 1 Valence natural bond orbital population of Pd on the PdX⁺ complexes

As shown in Fig. 1 and Fig. S1, the bond distances of PdX⁺ (X = F, Cl, Br, H, and CH₃) were 1.83, 2.19, 2.33, 1.48, and 1.99 Å (in the singlet state) and 1.88, 2.22, 2.32, 1.58, and 2.15 Å (in the triplet state), respectively. From H to Br, the distance of the Pd-X (H < F < CH₃ < Cl < Br) bond gradually increased. The change in the bond distance of PdX⁺ was explained by the atomic radius increase from H to Br. From Figs. 1 and 7 (Fig. S1-S5), one can see that the bond distances of the low spin state PdX⁺ ions were shorter than the high spin state. The bond distance for PdX⁺ was determined by the spatial extent of the valence orbit (5s and 4d) [30]. The NBO analysis results indicated that the Pd-X bond was mainly composed of the p orbital of X with the 5s and 4d orbitals of palladium. However, since the less electron in 5s orbital of Pd in ¹PdX⁺, the bond distance of Pd-X in the low spin state was shorter than that in the high spin state.

Initial complexes

The reaction started from catalyst PdX⁺ (X = F, Cl, Br, H, and CH₃) combined with ethane to yield initial complexes IM1, in which the primary C-H bond was elongated (1.09 Å for free ethane), as shown Table 2. The binding energies of the formation of the initial complexes were 170, 153, 191, 102, and 70 kJ/mol (in singlet states) and 136, 99, 101, 62, and 77 kJ/mol (in triplet states), respectively. The initial complexes IM1 was found to had a η³ coordination, as seen Figs. 1 and 7, and Fig. S1-S5. Based on the distance of the activated C-H and the corresponding Pd-C in the initial complexes IM1 (see Table 2), it was concluded that there was an agostic Pd···H-C interaction prior to C-H cleavage.

Table 2 Computed bond distances r(C-H), r(Pd-H), and r(Pd-C) for the PdX(C₂H₆)⁺ complexes

To better understand the molecular orbital composition, we performed DOS analysis of initial complexes M1 (see Fig. S6) [31]. In the picture, fragment 1, fragment 2, fragment 3, and fragment 4 represented carbon, hydrogen, palladium, and ligand, respectively. The vertical dashed line indicated the position of HOMO level. The height of black curve represented the total density of states (TDOS), and we could clearly see the density of the energy levels distributed and strength everywhere. The curve of the partial density of states (PDOS) was valuable for visualizing the contribution of each atomic orbital (AO) to the molecular orbital (MO). For example, the PDOS-Pd curve was relatively high and close to the TDOS in the region of HOMO level, respectively. Therefore, we concluded that the d orbital of palladium had great contribution to the HOMO orbits.

Reaction mechanisms

Reactivities of PdX⁺ (X = F, Cl, and Br) with C₂H₆

Before the transition state ³TS1/2, there was a crossing phenomenon between the two PESs, as show in Figs. 2, 3, and 4. After the cross points, the reaction was carried out along the single PES in a spin-conserving manner. Since the stationary points of the triplet state were higher in energy than those of the singlet state, we were not going to discuss the triplet state PES further. Starting with the initial complexes IM1, the hydrogen atom H1 transferred from the α-carbon of ethane to PdX⁺ and afforded an intermediate ¹IM2. In this process, H1 was transferred in two different ways (see Fig. 1).

In one, H1 shifted to palladium from ethane via the three-centered late transition state ¹TS1/2, resulted the high-energy intermediate ¹IMa in ¹PdX⁺/C₂H₆ (X = F, Cl) system. In ¹IMa, the distance of the Pd-H bond was 1.50 Å, and NBO analysis revealed that the Pd-H1 bond was formed from 5s and 4${\mathrm{d}}_{{\mathrm{z}}^2}$ orbital of palladium and 1s orbital of hydrogen (see Fig. S7). After this oxidation addition (OA) reaction, the hydrogen atom migrated from palladium to halogen through reductive elimination (RE), and the stable intermediate ¹IM2 (FHPd(C₂H₅)⁺ and ClHPd(C₂H₅)⁺) was formed. The exothermicity of the whole OA/RE process was 210 and 131 kJ/mol, respectively. In addition, the transition state ¹TSa was − 114 kJ/mol lied below intermediate ¹IMa by 2 kJ/mol when the zero-point energy correction was taken into account in ¹PdCl⁺/C₂H₆ (see Fig. 3), indicated that the process was a low-barrier or even barrier-free transformation on the overall low spin reaction path. Another way, in ¹PdBr⁺/C₂H₆, the hydrogen atom H1 shifted directly to form the intermediate ¹IM2 via transition state ¹TS1/2 with a barrier of 25 kJ/mol; this step was exothermic by 112 kJ/mol. In the process of σ-CAM, the Pd-X and C1-H1 bonds are concurrently broken, and two σ-bonds of Pd-C1 and X-H1 were formed simultaneously. In ¹IM2, the Pd-C1 and C1-C2 bond lengths were 2.04 and 1.46 Å, respectively. This variation remained almost constant across from F to Br. But the Pd-X bond trends to lengthen along from F to Br. The intermediate ¹IM2 was the global minimum structure on the singlet potential energy surface, and the energy of ¹IM2 relative to the ground state reactants was − 356, − 230 and − 201 kJ/mol, respectively. As shown in Fig. 12, the π orbital of the four-membered ring was formed from p orbital of two C atoms and d orbital of Pd in ¹IM2. This interaction results in increased stability of the intermediate ¹IM2. After intermediate ¹IM2, the reaction was divided into three paths, as shown in Scheme 1. Path 1, the loss of HX directly in the intermediate ¹IM2 required energy of 63, 83, and 99 kJ/mol, respectively, yielded metal ethyl ions ¹Pd(C₂H₅)⁺. The exothermicity of the loss of HX gradually decreased from F to Br relative to ground state reactants. Path 2 and 3 channels were distinguished based on the reaction mechanism of 1, 2- and 1, 1-elimination of hydrogen. The following reaction mechanism of path 2 and 3 was discussed in detail.

1, 2-Elimination mechanism

The second hydrogen atom H4 from β-carbon on the ethyl ligand shifted to the palladium via a four-member (Pd-C1-C2-H4) transitional structure ¹TS2/3, given rise to the hydride complex ¹IM3 (see Fig. 5). The second C-H activation energy barriers were 23, 27, and 28 kJ/mol, respectively. In intermediate ¹IM3, the Pd, C₁, and C₂ atom formed an isosceles triangle. In the step, the distance of the C-C was shortened from 1.53 Å in an isolated ethane molecule to 1.38 Å. The changed of distance suggested that the C-C double bond has been formed (the distance of C-C bond in ethylene molecules was 1.33 Å). This step was endothermic by 9, 16, and 18 kJ/mol, respectively.

After the formation of the intermediate ¹IM3, the reaction bifurcated to two routes (see Scheme 2). One route was the expulsion of HX directly from the newly formed complex ¹IM3 with an activation barrier of 67, 80, and 95 kJ/mol, respectively. Another route was H1 back transfer from HX to the hydride ligand via transitional structure ¹TS3/4 to afford the ¹IM4 molecular complexes, as path ②. The energy barrier value in this step was 229, 136, and 109 kJ/mol, respectively. Compared with the loss of HX, dehydrogenation was relatively difficult. The reason was that the d orbital of the Pd in PdX⁺ interacted with the π orbital of the C=C bond and formed π bond in intermediate ¹IM3 (see Fig. S9). In order to reach ¹TS3/4, the intermediate ¹IM3 needed to overcome more energy. And the energy barrier gradually decreased from F to Br relative to ¹IM3. In the reaction mechanism of σ-CAM, Pd-H4 and X-H1 bonds were concurrently broken and then H-H and Pd-X bonds were formed simultaneously. The H₂ elimination process was endothermic by 212, 132, and 108 kJ/mol, respectively. Finally, the elimination of H₂ from the newly yielded ¹PdX(H₂)(C₂H₄)⁺ complex terminated this reaction pathway. In this process, it is necessary to overcome the dissociation energies of 72, 86, and 85 kJ/mol, respectively. Dehydrogenation was the rate-determining step of path 2. The final products of the reaction of PdX⁺ with ethane were the mixture of HX and H₂.

Scheme 2

1, 2-Elimination reaction paths

1, 1-Elimination mechanism

In the second hydrogen transfer process, there was competition between α-hydrogen and β-hydrogen on the ethane. For the path 3, starting from the intermediate ¹IM2, the second hydrogen atom H2 from the α-carbon migrated to palladium via transition state ¹TS2/5, which lead to intermediate ¹IM5 (see Fig. 6). H2 transfer occurred with the activation barrier of 113, 123, and 129 kJ/mol, respectively. The step was endothermic by 101, 117, and 125 kJ/mol, respectively.

Subsequently, the reaction was divided into two paths (see Scheme 3). In path ③, HX was liberated directly and ¹Pd(H)(CHCH₃)⁺ was formed by overcoming an activation barrier of 69, 75, and 83 kJ/mol, respectively. In path ④, H1 from HX back transferred to the hydride ligand via transition state ¹TS5/6, and then an intermediate ¹IM6 was formed. Corresponded activation barriers were 229, 136, and 109 kJ/mol, respectively. We noted in particular the features of the transition structure ¹TS5/6 in which the migrated H1 atom interacted with three centers simultaneously, that is, the palladium, halogen, and H2 atoms. As required for an σ-CAM process, the atoms H1, H2, Pd, and X (X=F, Cl, Br) were coplanar in ¹TS5/6. A similar trend was seen in the ¹BrPd(C₂H₆)⁺ → ¹(HBr)Pd(C₂H₅)⁺ and ¹IM3 → ¹IM4 transformation. Here, the H-H bond distance was 0.85 Å, which was very close to H-H bond distance (0.74 Å) of free H₂. It was suggested that the Pd-H2 and H1-X bonds were broken and H-H bond was formed. During this reaction, dehydrogenation was the rate-determining step. In the last step, H₂ and ¹XPd (CHCH3)⁺ were formed by overcoming 66, 49, and 57 kJ/mol dissociation energy, respectively. In the following section, we would discuss the reaction of PdH⁺ and PdCH₃⁺ with C₂H₆ in detail.

Scheme 3

1, 1-Elimination reaction paths

Reactivities of PdX⁺ (X = H and CH₃) with C₂H₆

In the reaction of PdH⁺ and PdCH₃⁺ with C₂H₆, the reaction mechanism and optimized structures on the two PESs were very similar to those for the reaction of PdX⁺/C₂H₆ (X = F, Cl, and Br) discussed above. Unlike PdF⁺, PdCl⁺, and PdBr⁺, the whole reaction of PdH⁺ and PdCH₃⁺ with C₂H₆ proceeded on the ground state PES in a spin-conserving manner. Similar to PdX⁺ (X = F, Cl, and Br), we only discuss the reaction mechanism on the ground state PESs. Starting with the initial complexes ¹IM1, the hydrogen atom H1 transferred from ethane to PdX⁺ in two ways and to yield an intermediate ¹IM2. In the process of the C-H1 bond activation, there was no low energy barrier ¹IMa → ¹TSa → ¹IM2 process on the ¹PdH⁺/C₂H₆, whereas the barrier was 6 kJ/mol on the ¹PdCH₃⁺/C₂H₆. H1 transferred in ¹PdCH₃⁺ was very similar to that of ¹PdF⁺ and ¹PdCl⁺, with a total exothermicity of 76 kJ/mol, while ¹PdH⁺ and ¹PdBr⁺ were similar, this process exothermic 67 kJ/mol.

The intermediate ¹IM2 was the global minimum structure on the whole PESs, which was 169 and 146 kJ/mol below the ground state reactants, respectively. After overcoming 61 kJ/mol in the ¹PdH⁺ and 60 kJ/mol in the ¹PdCH₃⁺, H₂ and CH₄ were liberated. For the second C-H bond activation in the ¹PdH⁺/C₂H₆ and ¹PdCH₃⁺/C₂H₆, there was also competition between α-H and β-H similar to that in the reaction of ¹PdF⁺, ¹PdCl⁺, and ¹PdBr⁺ with ethane (path 2 and 3).

The β-C-H and the second α-C-H bond activation occurred in the same way as that of ¹PdF⁺, ¹PdCl⁺, and ¹PdBr⁺. ¹IM2 → ¹TS2/3 → ¹IM3 was the β-C-H bond activation process with the activation barrier of 56 and 29 kJ/mol, respectively. The step was endothermic by 52 for ¹PdH⁺ and 14 kJ/mol for ¹PdCH₃⁺. Similar to ¹PdX⁺/C₂H₆ (X = F, Cl, and Br), the Pd, C1, and C2 atom was an isosceles triangle in intermediate ¹IM3. Finally, H₂ and CH₄ were liberated from ¹IM3 with an activation barrier of 23 and 59 kJ/mol, respectively.

¹IM2 → ¹TS2/4 → ¹IM4 was the second α-C-H bond activation process. The C-H activation occurred with the activation barrier of 136 and 120 kJ/mol, respectively. The step was endothermic by 130 and 116 kJ/mol, respectively. Subsequently, H₂ and CH₄ were liberated directly, and ¹Pd(H)(CHCH₃)⁺ was formed by overcoming dissociation energy of 40 and 53 kJ/mol, respectively. Similarly, the activation of β-C-H bond was also easier than that of the second α-C-H bond in ¹PdH⁺ and ¹PdCH₃⁺. However, for PdX⁺/C₂H₆ (X = H and CH₃), the hydrogen atom H1 back transfer from HX to the hydride ligand and combined with H2 or H4 on Pd to afford H₂ was not observed. In paths 1 and 2, the energy of all points on the singlet state was lower than those of the reactants, indicated that these reactions were a barrier-free transformation. In path 3, the whole reaction was only endothermic 1 kJ/mol for ¹PdH⁺ and 2 kJ/mol for ¹PdCH₃⁺. The final product was H₂ for PdH⁺ and CH₄ for PdCH₃⁺.

Rate constant

From the potential energy profiles in Figs. 2, 3, and 4, it could be seen that the rate-determining transition ¹TS3/4 was located below ¹TS5/6 in the process of 1, 2-elimination in reaction of ¹PdX⁺ (X = F, Cl, Br) with ethane. Compared with β-hydrogen transfer in pathway 2, the process of α-hydrogen in the pathway 3 had less competitive ability. And the process of HX loss was relatively easier than H₂ elimination in the whole pathway 2. In ¹PdX⁺/C₂H₆ (X = H, CH₃) system, path 2 was also more favorable than path 3, as shown in Figs. 8 and 9. To estimate quantitatively the reactivity for several product formation processes of path 2 (Pd-X bond cleavage products, ¹Pd(C₂H₅)⁺ + HX and ¹PdH(C₂H₄)⁺ + HX, and without apparent Pd-X bond cleavage products ¹PdX(C₂H₄)⁺ + H₂), the rate constants have been evaluated based on conventional transition state theory (Eq. (1)) [32].

$$ k(T)=\frac{k_BT}{h}\exp \left(-\frac{\Delta {G}^{\ne }}{RT}\right) $$

(1)

where k_B is the Boltzmann constant, T is the thermodynamic temperature, h is the Plank constant, and ∆G^≠ is the activation Gibbs free energy barrier. In T = 298 K, the rate constants of the rate-determining step in several products formation process have been calculated in Table 3.

Table 3 The rate constants of rate-determining step at 298 K

Compared with the rate constants in several product formation processes, we concluded that the rate constant gradually decreased in the loss HX while gradually increases in the H₂ elimination from F to Br. The results showed that the loss of HX was most favorable for ¹PdF⁺/C₂H₆, but the elimination of H₂ was easier for ¹PdBr⁺/C₂H₆. In ¹PdX⁺/C₂H₆ (X = H and CH₃), only the products of Pd-X bond cleavage were observed. Also, the dissociation of product ¹PdH (C₂H₄)⁺ + HX was easier than that of product ¹Pd (C₂H₅)⁺ + HX.

To intuitively illustrate the efficiency of HX and H₂ elimination, branching ratios of all products were presented. As shown in Fig. 13, the loss of HX was abundant for all systems, whereas the elimination of ¹PdX(C₂H₄)⁺ + H₂ was relatively most effective for ¹PdBr⁺/C₂H₆. This was consistent with the results of the discussion above.

Fig. 13

Branching ratios for product (a) ¹Pd(C₂H₅)⁺ + HX(), (b) ¹PdH(C₂H₄)⁺ + HX (), and (c) ¹PdX(C₂H₄)⁺ + H₂ ()

Gas-phase reactions proceed in closed containers, and all of these reactions occur at constant energy and angular momentum. Depuy reports, in the gas phase, the reaction that occurred through an ion-dipole complex that contains high energy [33]. In the reaction of PdX⁺ with ethane, the formation of encounter complex IM1 in the minimal energy reaction pathways (MERPs) contributed 146, 99, 101, 102, and 70 kJ/mol (for F, Cl, Br, H, and CH₃) of heat to the closed system, respectively. And all energies were retained within the encounter complex IM1 since there were no solvent molecules to transfer it. This indicated that there was enough energy to overcome the reaction barrier. Therefore, we concluded from the above calculation results that ethane was effectively activated by PdX⁺ at room temperature.

MECP between PESs of different multiplicities

As shown in Figs. 2, 3, and 4, the crossing phenomenon between two PESs was observed at both the entrance and exit channels of reaction of PdX⁺ (X = F, Cl, and Br) with ethane. In PdF⁺/C₂H₆, the energy of ³IM1 was higher than ¹IM1 by 10 kJ/mol, which implied that CPs existed at the entrance channel of reaction. For PdCl⁺ and PdBr⁺, the energy of ³IM1 was 3 and 12 kJ/mol lower than that of ¹IM1, while ³TS1/2 was higher than ¹TS1/2 by 115 and 99 kJ/mol, respectively, which indicated that CPs existed between ³IM1 and ³TS1/2. From Br to F, CPs was gradually close to the reactants. In order to locate the CPs between two PESs, we used the method of partial geometry optimization to calculate single-point energy. To more accurately locate the CP, the method of Harvey et al. was used to obtain the actual MECP, as shown in Fig. 14. This change of spin states between two PESs effectively avoided the energetically inaccessible transition structure ³TS1/2 on the ground state surface. This spin-crossing phenomenon could be called a “two-state reaction” in the organometallic chemistry [34]. After the systems crossing, the whole reaction on the singlet PESs proceeded in a spin-conserving manner. The minimal energy reaction pathway (MERP) started from the triplet state reactants via intersystem crossing mechanism, then proceeded along the low spin PESs to liberate HX and H₂. For PdX⁺/C₂H₆ (X = H, CH₃), the whole reaction proceeded in a spin-conserving manner on the singlet PESs, and there was no crossing phenomenon, as shown in Figs. 8 and 9.

Fig. 14

Potential energy curve-crossing diagrams. a PdF⁺. b PdCl⁺. c PdBr⁺

Bonding evolution analysis

To further understand bond evolution of the main reaction pathways, LOL and AIM analyses were investigated. LOL was a function for locating high localization regions, defined by Schmider and Becke. Compared with the electron localization function (ELF) [35], LOL has similar description. Jacobsen reported that LOL could exhibit more accurate and clearer picture than ELF [36]. The value range of LOL is (0, 1). The LOL pictures for the stationary points in main paths were described in Fig. 15 and Fig. S11–12. The regions of white in pictures indicated that electron density exceeded the upper limit of color scale (0.8). In AIM analysis, the chemical bonding was described by the bond critical point (BCP) [37]. The bond strength and the atomic interaction at BCP were estimated by the electron density (ρ_b) and the Laplacian electron density (▽²ρ_b), respectively. BCP has been analyzed in terms of the values of ρ_b and ▽²ρ_b at the (3, − 1) critical points. The values of ρ_b and ▽²ρ_b were listed in Table S1–5. Positive and negative values of ▽²ρ_b indicated that electron density was depleted and concentrated.

Fig. 15

Localized orbital locator (LOL) map of stationary points on the main path

As shown in Fig. 15 and Fig. S11-S12, the low LOL value indicated that there was no covalent bond between Pd and H1 atom in ¹IM1. This conclusion was confirmed by the AIM analysis; result showed that ρ_b between Pd and H1 atom was very low (ρ_b = 0.078, 0.088, 0.088, 0.079, and 0.70 au, respectively), and ▽²ρ_b value was positive. The first C-H bond was activated in two different ways. For F, Cl, and CH₃, the LOL of ¹TS1/2 showed that C1-H1 bond was broken and Pd-H1 bond begins to form. In ¹TS1/2, the ρ_b of Pd-H1 bond significantly increased (ρ_b = 0.152, 0.150, and 0.152 au, respectively), and ▽²ρ_b of Pd-H1 bond was negative value, but the Pd-H1 bond was not yet formed. In intermediate ¹IMa, Pd-H1 bond was completely formed. This is consistent with the AIM analysis, which showed that ρ_b values of Pd-H1 bond were 0.171, 0.166, and 0.166 au respectively. Compared with ¹IMa, the ρ_b value of Pd-H1 and Pd-X was decreased while Pd-C1 increased in ¹TSa, indicated that H1 was transferred from Pd to ligand. In ¹TSa, AIM analysis showed that the ρ_b value of Pd-H1 bond was 0.152, 0.157, and 0.158, respectively; this result indicated that the Pd-H1 bond was broken. Another for Br and H, H1 was transferred directly from C1 to Br and H, respectively. AIM analysis showed that the ρ_b (0.148 and 0.151 au) of Pd-H1 in ¹TS1/2 increased obviously compared with that in ¹IM1. Subsequently, the second C-H bond was activated. In ¹TS2/3, the ρ_b value of Pd-H4 increased obviously compared with ¹IM2, and ▽²ρ_b was negative value, suggested that H4 atom was gradually transferred from C2 to Pd. In addition, the weak interaction between Pd and H4 also was observed in ¹IM2, which was confirmed by the small ρ_b value (ρ_b = 0.087, 0.079, 0.075, 0.072, and 0.078 au, respectively). In ¹PdX⁺/C₂H₆ (X = H and CH₃), the reaction was terminated after the formation of intermediate ¹IM3. In the ¹PdX⁺/C₂H₆ (X = F, Cl, and Br) system, the ρ_b value of the H1-H4 bond was 0.180~0.186 au, indicated that H₂ was formed in stage of ¹TS3/4. The H1-H4 bond was formed completely in ¹IM4; this was also confirmed by the AIM analysis.

Comparison the reactivity of PdX⁺(X = F, Cl, Br, H, and CH₃) with atomic Pd and Pd⁺ toward C₂H₆ activation

In order to compare the reactivity of Pd, Pd⁺, and PdX⁺ with ethane, we theoretically studied the reaction mechanism of Pd and Pd⁺ with ethane at the same level as PdX⁺. The optimized structure of stable point on PESs of two spin states is shown in Fig. S13-S14. The calculated results showed that the ground states were ¹Pd and ²Pd⁺, respectively. The energy of the excited state ³Pd and ⁴Pd⁺ was 79 and 277 kJ/mol higher than the ground states, respectively. The NBO valence electron populations of the high spin were calculated to be 5s^1.004d^9.00 and 5s^1.004d^8.00 for ³Pd and ⁴Pd⁺, respectively. In the reaction of atom Pd with C₂H₆, C₂H₆ cannot been activated by triplet ³Pd, because of its lowest excited state was quite high in energy to deal with C-H bond activation [30]. As shown in Fig. S13-S14, the whole reaction of ¹Pd and ²Pd⁺ with ethane performed on the ground state PESs in a spin-conserving manner. Therefore, we only discussed the reaction mechanism Pd and Pd⁺ with ethane on the ground state PESs. The reaction was divided into the following three steps. Firstly, the first C-H bond of ethane was activated by ¹Pd and ²Pd⁺ with the energy barriers of 50 and 67 kJ/mol, respectively. Our calculation for the formation of ¹IM2 was endothermic by 19 and 64 kJ/mol, respectively. For the second C-H bond activation in the ¹Pd/C₂H₆ and ²Pd⁺/C₂H₆, there was also competition between α-H and β-H similar to that in the reaction of ¹PdX⁺ with ethane. ¹IM2 → ¹IM3 was the process of β-C-H bond activation; the energy barrier heights (relative to ¹IM2) were 122 and 71 kJ/mol, respectively. The exothermicities of the step were 52 and 135 kJ/mol for ¹Pd and ²Pd⁺, respectively. Finally, H₂ was liberated by overcoming the dissociation energies of 54 and 26 kJ/mol, respectively. The α-C-H bond was activated in ¹IM2 → ¹IM4; the C-H bond activation barriers were 293 and 126 kJ/mol, respectively. The step was exothermic by 118 and 53 kJ/mol, respectively. Subsequently, H₂ was liberated by overcoming the dissociation energies of 41 (for ¹Pd) and 39 kJ/mol (for ²Pd⁺), respectively. Compared with β-C-H bond activation, the α-C-H bond activation has less competition ability in the reaction of ¹Pd and ²Pd⁺ with ethane. We concluded that the main reaction path was 1¹IM1 → ¹TS1/2 → ¹IM2 → ¹TS2/3 → ¹IM3 in the reaction of ¹Pd and ²Pd⁺ with ethane. The highest energy relative to the ground state reactants was 123 and 33 kJ/mol in the whole ¹Pd and ²Pd⁺ with ethane reaction. Comparing the reactivity of atomic Pd and Pd⁺ with ethane, the highest energy in ¹Pd/C₂H₆ was 90 kJ/mol higher than that of ²Pd⁺/C₂H₆. It was indicated that the ²Pd⁺ was easier to activate the C-H of C₂H₆ than the neutral atomic Pd.

Despite the qualitative similarities among the reaction paths, there were significant differences in some aspects. NBO calculations showed that the ground states ¹Pd and ²Pd⁺ had a valence electron population of 4d¹⁰ and 4d⁹ on Pd atom, respectively. Compared with atomic ¹Pd, the population of the 4d orbitals of Pd in cations ²Pd⁺ and ¹PdX⁺ was unfilled. For PdF⁺, PdCl⁺, and PdBr⁺, the high spin states were the ground states, while the ground states were the low spin states in Pd, Pd⁺, PdH⁺, and PdCH₃⁺. In the ground states of PdF⁺, PdCl⁺, and PdBr⁺, the valence electron population of the 4d orbitals of Pd from F to Br gradually increased; similarly from Pd⁺ to PdH⁺, PdCH₃⁺, and atomic Pd, the valence electron population of the 4d orbitals on Pd also increased in the ground states of Pd⁺ to PdH⁺, PdCH₃⁺, and atomic Pd. The reaction of PdX⁺ (X = F, Cl and Br) with ethane started from triplet state and then through CPs point; the final proceeded in the singlet state PESs. This reaction was typical “two-state reaction.” In contrast, for ¹Pd, ²Pd⁺, and PdX⁺ (X = H and CH₃) with C₂H₆, the overall reaction was performed on the ground state PESs in a spin-conserving manner. In ¹PdX⁺/C₂H₆ (X = F, Cl, and CH₃), the first hydrogen atom H1 was transferred through the OA/RE reaction mechanism, whereas for ¹PdX⁺/C₂H₆ (X =H and Br), H1 was transferred via the σ-CAM mechanism. Before intermediate ¹IM3, the reaction mechanism of ¹Pd, ²Pd⁺, and ¹PdX⁺ ethane was very similar. In reaction of PdX⁺ (X = F, Cl, and Br) with C₂H₆, the hydrogen atom H1 back transfer combined with H2 or H4 on Pd to afford H₂, whereas those of PdH⁺ and PdCH₃⁺ were not observed. In the reaction of ¹PdX⁺ with ethane, the activation of the first C-H bond was exothermic, and the second C-H bond was endothermic, whereas for ¹Pd and ²Pd⁺, the first C-H bond activation was endothermic and the second C-H bond activation was exothermic. For PdX⁺/C₂H₆ (X = F, Cl, and Br), the main products were HX with a small amount of H₂. In the reaction of Pd, Pd⁺, and PdH⁺ with C₂H₆, only H₂ was liberated. For PdCH₃⁺, only CH₄ was produced. Dehydrogenation was the rate-determining step of reaction ¹PdX⁺/C₂H₆ (X = F, Cl, and Br), the rate constants gradually increased from F to Br. In ¹Pd, ²Pd⁺, and ¹PdH⁺, the activation of the second C-H bond was the rate-determining step. From ¹Pd to ²Pd⁺ and ¹PdH⁺, the rate constants also gradually increased (rate constants were 1.08 × 10⁻⁹ for ¹Pd and 0.45 for ²Pd⁺). The rate-determining step was the release of CH₄ molecule at the PdCH₃⁺/C₂H₆ system. Based on the above data, the order of reactivity of atomic Pd-, Pd⁺-, and PdX⁺-activated C-H bond of ethane has been listed as PdH⁺ > PdF⁺ > PdCH₃⁺ >PdCl⁺ > PdBr⁺ > PdCH₃⁺ > Pd⁺ >Pd.

The above mentioned was the activation process of C-H bond in all systems, while the activation of C-C bond was only observed in the ¹Pd/C₂H₆ system, as shown in Fig. S15. In the activation of the C-C bond process, it was observed that no methane was formed while formation the complex CH₃-Pd-CH₃. The barrier height of the TS in C-C bond activation was 26 kJ/mol lower than that of C-H bond. It is indicated that the reaction efficiency of atomic Pd activation C-H bond of ethane was lower than that of activated C-C.

Conclusions

The reaction mechanism of PdX⁺ activation C-H bond of C₂H₆ was investigated by B3LYP method under DFT theory. The front molecular orbital of the initial complexes was analyzed by density of states (DOS). The d orbital of palladium and the p or s orbital of ligand had significant contribution to the HOMO orbits. The first hydrogen atom can be transferred in two different ways, OA/RE (for F, Cl and CH₃) and σ-CAM (for Br and H). During the second hydrogen transfer, the cations PdX⁺ exhibited high bond selectivity for the activation of α-C-H and β-C-H bonds in ethane. In the second hydrogen transfer process, the α-hydrogen transfer process had less competitive abilities than that of β-hydrogen. CPs between the two PESs could be observed and effectively decreased the activation barrier in PdX⁺ (X = F, Cl, and Br). The most favorable reaction pathway started from triplet PESs and then proceeded through the singlet PESs to liberate HX and H₂. In PdX⁺ (X = H and CH₃) system, the whole reaction proceeded on the ground state PESs in a spin-conserving manner. Theoretical studies on the reactions PdX⁺ (X = F, Cl, and Br) with ethane had showed that the loss of HX was more facile than dehydrogenation. The final main products of the reaction of PdX⁺ (X = F, Cl, and Br) with ethane were HX and small amount of H₂. In the reaction of PdH⁺ with C₂H₆, only H₂ was liberated. For PdCH₃⁺, only CH₄ was produced. Adding appropriate ligands could enhance the catalytic efficiency of palladium; the order of reactivity of atomic Pd-, Pd⁺-, and PdX⁺-activated C-H bond of ethane has been listed as PdH⁺ > PdF⁺ > PdCH₃⁺ >PdCl⁺ > PdBr⁺ > PdCH₃⁺.