Theoretical insight into the C–H and C–C scission mechanism of ethane on a tetrahedral Pt₄ subnanocluster

Abstract

The activation mechanism of C₂H₆ on a Pt₄ cluster has been theoretically investigated in the ground state and the first excited state potential energy surfaces at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level. On the Pt₄ cluster, the optimal channel order was kinetically as follows: demethanation > dehydrogenation > deethylenation from C₂H₆. The two-fold dehydrogenation of ethane to acetylene was almost equivalent to its single dehydrogenation to ethylene, both thermodynamically and kinetically. In addition, the C–H cleavage intermediate was kinetically more preferable than the C–C cleavage intermediate, while both the C–H cleavage intermediate and the C–C cleavage intermediate were thermodynamically favoured. Nevertheless, the extremely stable C–H cleavage intermediate was trapped in a deep well, which hindered the release of H₂. Together with the excellent reactivity of the Pt₄ cluster, for the design of an efficient and selective catalyst towards the dehydrogenation of C₂H₆, one can expect that it is necessary to improve the release of H₂ from the C–H cleavage intermediate by introducing some additive or support into the Pt₄ cluster, which decreases the binding of the catalyst towards H₂. Concerning selectivity, the Pt atom was the most favourable for the dehydrogenation, the Pt₂ cluster was the most preferable for deethylenation, and the Pt₄ cluster was the most beneficial for the demethanation. Both Pt₄ and Pt₂ clusters exhibited more promising catalytic performance compared with the mononuclear Pt atom towards C₂H₆ activation.

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Introduction

C–H and C–C scission reactions play an important role in a wide variety of industrial processes, ranging from the dehydrogenation of higher alkanes to the cracking of hydrocarbon fuels.¹ Among the catalysts known for the dehydrogenation of alkane, Pt is one of the most active.^2,3 Small clusters are known to possess reactivity that are not observed in their bulk analogues, which can make them attractive for catalysis.⁴ The under-coordination of Pt atoms in clusters is responsible for the surprisingly high reactivity compared with extended surfaces.⁵ An in-depth knowledge of elementary C–H and C–C scission reactions on its cluster is therefore a welcome addition to existing knowledge.

Experimentally, Cox et al. had previously discovered that the neutral Pt_n clusters (n ≤ 24) can efficiently activate CH₄, and polyatomic clusters Pt_n (n = 2–5) are more reactive than a mononuclear platinum atom for dehydrogenation.^6,7 Later, Andrews et al. experimentally observed CH₃PtH and CH₂PtH₂, and CH₃CH₂PtH species in the reactions of CH₄ and C₂H₆ on a Pt atom.⁸ Theoretically, Carroll⁹ and Wang et al.¹⁰ found that the most stable intermediate is a hydride HPtCH₃ in the reaction of CH₄ on a Pt atom. Cui et al. suggested that the neutral clusters of Pt₂ and Pt₃ can activate the first C–H bond of CH₄ with small barriers.^11,12 Wang et al. found that the breakage of the second C–H bond in CH₄ is the rate-determining step in the reaction of CH₄ on a neutral Pt₄ cluster.¹⁰ Vajda et al. suggested that the breakage of the first C–H bond (on the CH₂ group) is the rate-determining step in the dehydrogenation of propane on a neutral Pt₄ cluster.⁵ More recently, we studied the competitive activation mechanism of C–H and C–C bonds in C₂H₆ and C₃H₈ on a mononuclear Pt atom,^13,14 and explained why the C–H insertion product was experimentally observed, while the C–C insertion product was not formed in an observable quantity.^13,14 In addition, we have explained that Pt₂ cluster exhibits a more promising catalytic performance towards the dehydrogenation of C₂H₆/C₃H₈ compared with Pt atom, in which the synchronous effect of the atoms of Pt₂ cluster makes two C–H bonds of C₂H₆/C₃H₈ to break simultaneously and then kinetically releases C₂H₄/C₃H₆ readily from the C₂H₆/C₃H₈.^15,16 Furthermore, on a Ni₂ cluster, as a Pt^′₂ congener, the dehydrogenation of CH₄ has been theoretically predicted to be favoured thermodynamically.^17,18 On a Pd_n cluster, as a Pt^′_n congener, the reaction mechanisms of C₂H₆ and C₂H₄ have been investigated both experimentally and theoretically.^19–21 Fayet et al. experimentally found that Pd₂ exhibited the highest rate constant toward C₂H₆, compared with the other Pd_n clusters (n = 1, 3–17).¹⁹ Subsequently, Mamaev et al. theoretically proposed that the Pd₂ cluster was a more promising catalyst in the catalytic hydrogenation of ethylene, compared with a Pd atom.^20,21 These experimental and theoretical studies emphasize that the size of transition metal clusters plays an important role in the catalytic reactivity of the dehydrogenation of alkane.

To highlight the reason behind the observed variation of selectivity and reactivity as a function of cluster size, we aimed to study the detailed mechanism of C–H and C–C bond activation of C₂H₆ on a Pt₄ cluster together with a Pt atom and a Pt₂ cluster. The objectives of this study were as follows: (a) to clarify the rate-determining step and the selectivity-controlling step, (b) to obtain a better understanding of the preference of reaction pathway, and (c) to gain a theoretical clue for the design of an efficient and selective catalyst from the facile dissociation of reactants and weak binding of intermediates on the catalytic site.

Computational details

Full geometry optimizations were performed to locate all the stationary points and TSs in the reaction of C₂H₆ on a Pt₄ cluster using the BPW91 method^22,23 with the Lanl2tz basis set and the corresponding effective core potential (ECP) for Pt atoms,²⁴ and the 6-311++G(d, p) basis set for C and H atoms,^25,26 namely, BPW91/Lanl2tz, 6-311++G(d, p). Moreover, the stability of the density function theory (DFT) wavefunction was tested.^27,28 If an instability was found, the wavefunction was reoptimized with an appropriate reduction in constraints, and the stability tests and reoptimizations were repeated until a stable wavefunction was found.^27,28 Harmonic frequency calculations were performed to characterize stationary points and to take corrections of zero-point energy (ZPE) into account. The intrinsic reaction coordinate (IRC) method was run to track minimum energy paths from a transition structure to the corresponding minima.^29,30 The dominant occupancies of natural bond orbitals and dominant stabilization energies E(2) between donors and acceptors for some species have been analysed with the help of the natural bond orbital (NBO) analysis.^31,32 In addition, to determine electron correction energies, the single-point calculation of various species based on the optimized BPW91/Lanl2tz, 6-311++G(d, p) geometries were then refined using the same method with the same Lanl2tz basis set and ECP for Pt atom, and the aug-cc-pvtz for C and H atoms³³ in view of relativistic effects, namely, BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p). Unless otherwise mentioned, all energies are relative to the ground-state reactants [Pt₄ + C₂H₆] at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level, including ZPE correction obtained at the BPW91/Lanl2tz, 6-311++G(d, p) level. All the calculations were carried out with the Gaussian 09 program.³⁴

The rate constants (k) have been evaluated according to conventional transition state theory k(T) (TST),³⁵ including a tunnelling correction κ(T) based on Winger's formulation as follows:³⁶

where k_B is the Boltzmann constant, T is the absolute temperature, h is the Plank constant, c⁰ is the standard concentration (1 mol dm⁻³), and ΔG^≠ is the activation Gibbs free energy barrier. Finally, ν^≠ is the imaginary frequency of the TS. As a result, the rate constants k with Winger's tunnelling correction can be calculated from the expression k(T) × κ(T).

Results and discussion

In particular, the present computational method of BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level has been assessed in our previous studies in the reaction of C₂H₆ on a Pt₂ cluster.¹⁵ Therefore, the present theoretical method should be appropriate and reliable in the reaction of C₂H₆ on a Pt₄ cluster. Moreover, particular attention was devoted to the possible occurrence of a two-state reactivity phenomenon because the spin crossing is often involved in transition-metal-containing reactions.³⁷ Therefore, the potential energy profiles for the ground and the first excited states of platinum-containing reactions were investigated. The superscript prefixes “1”, “2”, “3”, and “5” will be used to indicate the singlet, doublet, triplet, and quintet states, respectively. For a spin-crossing reaction, a minimum energy crossing point (MECP) was calculated using a partial optimization method.^38,39 Some important MECPs are shown in the ESI.†

This study is divided into three sections: (i) formation of C₂H₄ and H₂ from C₂H₆, (ii) formation of C₂H₂ and H₂ from C₂H₄, and (iii) formation of CH₄ from C₂H₆. Moreover, we will compare the reactivity of a Pt₄ cluster with that of a Pt atom and a Pt₂ cluster towards ethane activation.

Formation of C₂H₄ and H₂ from C₂H₆

The geometric structures of various species and the schematic energy diagrams for the formation of C₂H₄ and H₂ from C₂H₆ on Pt₄ cluster are depicted in Fig. 1a and b, respectively.

Fig. 1 The optimized geometric structures of various species and the schematic energy diagrams for the C–H bond activation of C₂H₆ on Pt₄ cluster. Bond lengths are reported in Å and bonds angles are in degree. Relative energies (kJ mol⁻¹) for the corresponding species relative to the ground state reactants ³Pt₄ + C₂H₆ at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level are shown. (a) CH-S1 through one Pt site; (b) CH-S2 through two Pt sites. Blue, red, and black lines represent the singlet, triplet, and quintet states, respectively.

As shown in Fig. 1a, our calculation shows that a triplet state ³Pt₄ is the ground sate with a quintet excitation state at 5.0 kJ mol⁻¹ and a singlet excitation state at 48.2 kJ mol⁻¹. Thus, the minimal energy reaction pathway (MERP) may start at the triplet ground reactants ³Pt₄ + C₂H₆. The dehydrogenation of C₂H₆ (C₂H₆ → C₂H₄ + H₂) was calculated to be endothermic by 125.0 kJ mol⁻¹, indicating this process being thermodynamically unfavourable. However, as indicated in Fig. 1a and b, from the ground reactants ³Pt₄ + C₂H₆, the C–H bond cleavage may lead to both dehydrogenation and deethylenation products, 1-IM6 + H₂, 1-IM10 + H₂, and 1-IM7 + C₂H₄ with the exothermic values of 89.7, 34.3, and 18.6 kJ mol⁻¹ on their MERPs, respectively. It was determined that both the dehydrogenation and deethylenation of C₂H₆ on a Pt₄ cluster are thermodynamically preferable. We will discuss its kinetics from potential energy surfaces (PESs) in subsequent sections.

Initially, when one C₂H₆ molecule is adsorbed on a Pt₄ cluster, there is a molecular complex 1-IM1 through one Pt site with complexation energy of 62.6 kJ mol⁻¹ in its ground state. Such a large complexation energy makes the molecular complex ³1-IM1 stable. For ³1-IM1, the C–H bond close to the Pt atom was elongated to 1.162 Å from the 1.099 Å of free C₂H₆, while the Pt–H distances were 1.889 and 2.048 Å, respectively. These results showed that there exists some interaction between Pt₄ and C₂H₆ in ³1-IM1. For ³1-IM1, a NBO analysis showed there are dominant stabilization energies E(2) of 44.4 kJ mol⁻¹ in BD(σ)C–H → LP*(6)Pt and 20.8 kJ mol⁻¹ in LP(4)Pt → BD*(σ)C–H, which makes the complex stable. Next, the first C–H bond cleavage takes place via a three-membered ring 1-TS1 by a direct oxidative addition of the C–H bond, leading to a tetraplatinum hydride methyl complex 1-IM2 with the energy barrier of only 2.9 kJ mol⁻¹ on its MERP. By a NBO analysis, it was observed that there are about 0.16e migration from Pt to H, which confirmed the oxidative addition of a C–H bond in the reaction stage of ³1-IM1 → ³1-IM2. Then, a [1,2]-H shift occurred via a three-membered ring 1-TS2, leading to a more stable tetraplatinum hydride methyl complex 1-IM3 with the energy barrier of 29.8 kJ mol⁻¹ on its MERP.

As shown in Fig. 1a and b, there are two reaction pathways for the C₂H₄ + H₂ formation from 1-IM3, which can be attributed to the C–H bond cleavage on one Pt site and two Pt sites, respectively, denoted as CH-S1 and CH-S2. On the one hand, as depicted in Fig. 1a, for CH-S1, from 1-IM3, the [1,3]-H shift makes the second C–H bond rupture to a tetraplatinum dihydride ethylene complex 1-IM4 via a four-membered ring 1-TS3 without almost any energy barrier. Then, a [1,2]-H shift takes place via a three-membered ring 1-TS4, resulting in a more stable tetraplatinum dihydride ethylene complex 1-IM5 with an energy barrier of only 1.8 kJ mol⁻¹ on its MERP. From 1-IM5, there are two reaction pathways. First, 1-IM5 sets a H₂ molecule free by a reductive elimination mechanism, leading to 1-IM6 with an energy barrier of 129.3 kJ mol⁻¹ on its MERP. Then, 1-IM6 releases the C₂H₄ molecule, leaving Pt₄ behind with an energy barrier of 214.7 kJ mol⁻¹ on its MERP. Second, 1-IM5 sets the C₂H₄ molecule free with an energy barrier of 200.4 kJ mol⁻¹ on its MERP, resulting in 1-IM7. Subsequently, 1-IM7 releases a H₂ molecule by a reductive elimination mechanism, keeping Pt₄ behind with an energy barrier of 143.6 kJ mol⁻¹ on its MERP. In a word, from 1-IM5, the release of both H₂ and C₂H₄ reduces the Pt₄ cluster and completes the catalytic cycle. By an NBO analysis, it was observed that the –Pt₄ moiety gets about 0.08e, which reduces the Pt₄ cluster in the reaction stage of ³1-IM5 → ³Pt₄ + C₂H₄ + H₂. On the other hand, as depicted in Fig. 1b, for CH-S2, from 1-IM3, a [1,4]-H shift makes the second C–H bond break into a tetraplatinum dihydride ethylene complex 1-IM8 via a five-membered ring 1-TS5 with an energy barrier of 70.8 kJ mol⁻¹ on its MERP. Subsequently, a [1,2]-H shift takes place via a three-membered ring 1-TS6, leading to a tetraplatinum dihydride ethylene complex 1-IM9 with the energy barrier of 53.0 kJ mol⁻¹ on its MERP. From 1-IM9, there are two reaction pathways. First, 1-IM9 sets the H₂ molecule free, leading to 1-IM10 with an energy barrier of 152.1 kJ mol⁻¹ on its MERP. Then, 1-IM10 releases the C₂H₄ molecule, leaving Pt₄ behind with the energy barrier of 159.3 kJ mol⁻¹ on its MERP. Second, 1-IM9 releases the C₂H₄ molecule, resulting in 1-IM7 with an energy barrier of 167.8 kJ mol⁻¹ on its MERP. As mentioned earlier, 1-IM7 sets H₂ molecule free, leaving Pt₄ behind. In short, from 1-IM9, the release of H₂ and C₂H₄ reduces the Pt₄ cluster and completes the catalytic cycle. By an NBO analysis, it can be inferred that the –Pt₄ moiety accepts about 0.19e, which reduces Pt₄ cluster in the reaction stage of ³1-IM9 → ³Pt₄ + C₂H₄ + H₂. In particular, in 1-IM7 → Pt₄ + H₂, 1-IM5 → 1-IM6 + H₂, and 1-IM9 → 1-IM10 + H₂ reaction stages, we failed to locate the corresponding transition state, despite our extensive attempt. This may stem from the strong dissociation capacity of the Pt₄ cluster towards the H₂ molecule. Once H₂ interacts with the Pt₄ cluster, it is spontaneously adsorbed dissociatively onto the Pt₄ cluster.

From Fig. 1a, it can be observed that for the CH-S1, the triplet PES lies below the quintet and singlet ones. One can see that the MERP should advance on the triplet PES. Besides, from Pt₄ + C₂H₆ to 1-TS1 reaction stage, although the quintet PES deposits below the singlet one, the quintet ⁵1-IM2 was located 43.1 kJ mol⁻¹ above the singlet ¹1-IM2. Thus, after 1-IM2, we do not consider the quintet state and consider the singlet first excited state together with the triplet ground state. In C₂H₆, the cleavage of both first and second C–H bonds took place readily. On the MERP, for the deethylenation from C₂H₆, the highest energy barrier (HER) was 200.4 kJ mol⁻¹ for the 1-IM5 → 1-IM7 + C₂H₄ reaction step with the energy height of the highest point (EHHP) of 0.0 kJ mol⁻¹ at the entrance. For the dehydrogenation from C₂H₆, the highest energy barrier (HER) was 129.3 kJ mol⁻¹ at the 1-IM5 → 1-IM6 + H₂ exit with the EHHP of 0.0 kJ mol⁻¹ at the entrance. Thus, the dehydrogenation from C₂H₆ was more preferable than the deethylenation from C₂H₆, both thermodynamically and kinetically. The tetraplatinum dihydride ethylene complex ³1-IM5 was deposited −219.0 kJ mol⁻¹ into a deep well. It was determined that ³1-IM5 was thermodynamically favoured in the reaction of C₂H₆ on the Pt₄ cluster. For ³1-IM5, an NBO analysis showed that there are dominant occupancies of 1.92e in each BD(σ)Pt–H, indicating a complete σ-bond in Pt–H. Furthermore, there are large dominant stabilization energies E(2) of 273.5 kJ mol⁻¹ in BD(π)C–C → LP*(6)Pt and LP*(4)Pt and of 220.1 kJ mol⁻¹ in LP(3)Pt → BD*(π)C–C. It was observed that comparatively strong hyperconjugation interactions existed in the Pt–C–C three-membered ring, which makes the complex extremely stable.

From Fig. 1a and b, it can be observed that for the CH-S2, the triplet PES appears below the quintet and singlet ones. One can conclude that the MERP should proceed along the triplet PES. On the MERP, for the deethylenation from C₂H₆, the HER is 167.8 kJ mol⁻¹ at the 1-IM9 → 1-IM7 + C₂H₄ reaction step with the EHHP of 0.0 kJ mol⁻¹ at the entrance. For the dehydrogenation from C₂H₆, the HER is 152.1 kJ mol⁻¹ at the 1-IM9 → 1-IM10 + H₂ reaction step with the EHHP of 0.0 kJ mol⁻¹ at the entrance. This indicates that the dehydrogenation from C₂H₆ was more preferable than the deethylenation from C₂H₆, both thermodynamically and kinetically. The dihydride–ethene complex ³1-IM8 deposits −188.9 kJ mol⁻¹ into a deep well. Thus, ³1-IM8 was thermodynamically favoured in the reaction of C₂H₆ on a Pt₄ cluster. For ³1-IM8, an NBO analysis showed that there are dominant occupancies of 1.89 and 1.90e in BD(σ)Pt–H(1) and BD(σ)Pt–H(2), respectively, indicating a complete σ-bond in each Pt–H. Furthermore, there were dominant occupancies of 1.90 and 1.83e in BD(σ)Pt–C(1) and BD(σ)Pt–C(2), indicating a complete σ-bond in each Pt–C.

Comparing these two reaction pathways (CH-S1 and CH-S2) for the dehydrogenation from C₂H₆, one can expect that the CH-S1 is kinetically more favourable than the CH-S2 because it possesses a comparatively lower HER (129.3 vs. 152.1 kJ mol⁻¹). Furthermore, for the deethylenation from C₂H₆, one can see that the CH-S2 was kinetically more favourable than the CH-S1 because of its comparatively lower HER (167.8 vs. 200.4 kJ mol⁻¹). Nevertheless, for the deethylenation from C₂H₆, the CH-S1 was thermodynamically more preferable than the CH-S2 because the ³1-IM5 appears 30.1 kJ mol⁻¹ below ³1-IM8. Furthermore, from 1-IM3, the formation of 1-IM8 with a [1,3]-H shift and 1-IM4 with a [1,4]-H shift were competitive. Because ³1-TS3 lies 72.4 kJ mol⁻¹ below ³1-TS5, the CH-S2 via 1-TS5 should be ruled out in selectivity, compared with the CH-S1 via 1-TS3.

As mentioned earlier, on the Pt₄ cluster, the dehydrogenation from C₂H₆ was more favourable than the deethylenation from C₂H₆, both thermodynamically and kinetically. This result was similar to that in the Pt + C₂H₆ system, in which the dehydrogenation channel was kinetically more favourable than the deethylenation one.¹⁴ However, this result was completely different from that in the Pt₂ + C₂H₆ system, in which the deethylenation channel was kinetically more favourable than the dehydrogenation one.¹⁵ This may originate from not only the synchronous effect of the atoms of the Pt₂ cluster, but also a stronger C–H activation capacity of Pt₂ than Pt₄ because of its greater undercoordination number. It is necessary to investigate the dehydrogenation of C₂H₄, i.e., the two-fold dehydrogenation of C₂H₆, on a Pt₄ cluster.

Formation of C₂H₂ and H₂ from C₂H₄

The geometric structures of various species and the schematic energy diagrams for the formation of C₂H₂ and H₂ from C₂H₄ on a Pt₄ cluster are depicted in Fig. 2a and b, respectively. As depicted in Fig. 2a and b, the reaction of C₂H₄ → C₂H₂ + H₂ was calculated to be endothermic by 172.8 kJ mol⁻¹, indicating that it was a thermodynamically impossible process. However, as shown in Fig. 2a, the reactions of ³Pt₄ + C₂H₄ → ³2-IM5 + H₂ and ³1-IM7 + C₂H₂ were calculated to be exothermic by 87.0 kJ mol⁻¹ and endothermic by 29.2 kJ mol⁻¹, respectively. As shown in Fig. 2b, the reactions of ³Pt₄ + C₂H₄ → ³2-IM10 + H₂ and ³1-IM7 + C₂H₂ were calculated to be exothermic by 76.6 kJ mol⁻¹ and endothermic by 29.2 kJ mol⁻¹, respectively. Thus, the dehydrogenation channel was thermodynamically more preferable than the deacetylenation one. Next, we will kinetically discuss the mentioned above reactions.

Fig. 2 The optimized geometric structures of various species and the schematic energy diagrams for the C–H bond activation of C₂H₄ on Pt₄ cluster. Bond lengths are reported in Å and bond angles are in degree. Relative energies (kJ mol⁻¹) for the corresponding species relative to the ground state reactants ³Pt₄ + C₂H₄ at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level are shown. (a) CH2-S1 through one Pt site; (b) CH2-S2 through two Pt sites. Blue and red lines represent the singlet and triplet states, respectively.

As shown in Fig. 2a and b, there are two reaction pathways for the formation of C₂H₂ + H₂ from C₂H₄ with regard to the cleavage of C–H bond on one Pt site and two Pt sites, denoted as CH2-S1 and CH2-S2, respectively. As shown in Fig. 2a, for CH2-S1, first the C₂H₄ molecule is adsorbed on Pt₄ cluster through one Pt site, yielding a top tetraplatinum ethylene complex 1-IM6 with stabilization energies of 214.2 kJ mol⁻¹ and 214.7 kJ mol⁻¹ on the singlet and triplet states, respectively. Second, from 1-IM6, the first C–H bond cleavage with a [1,2]-H shift occurs via a three-membered ring 2-TS1, leading to a tetraplatinum hydride ethenyl complex 2-IM1. Third, a [1,2]-H shift takes place via a three-membered ring 2-TS2, resulting in a more tetraplatinum hydride ethenyl complex 2-IM2. Fourth, from 2-IM2, the second C–H bond cleavage with a [1,3]-β-H shift to the platinum occurs via a four-membered ring 2-TS3, leading to a tetraplatinum dihydride acetylene complex 2-IM3. Fifth, from 2-IM3, a [1,2]-H shift occurs again via a three-membered ring 2-TS4, yielding a more tetraplatinum dihydride acetylene complex 2-IM4. Finally, 2-IM4 reductively eliminates H₂ or C₂H₂, leaving 2-IM5 or 1-IM7 behind, respectively. For the reactions of Pt₄ + C₂H₄ → 2-IM5 + H₂ and 1-IM7 + C₂H₂, the triplet PESs stand below the singlet ones except for 2-IM2 and 2-IM4. Then, the MERPs should involve two MECPs near 2-IM2 and 2-IM4. For the reaction of Pt₄ + C₂H₄ → 2-IM5 + H₂, the MERP includes the HER of 137.2 kJ mol⁻¹ at the reaction step of 2-IM4 → 2-IM5 + H₂ and the EHHP of 0.0 kJ mol⁻¹ at the Pt₄ + C₂H₄ entrance, whereas for the reaction of Pt₄ + C₂H₄ → 1-IM7 + C₂H₂, the MERP involves a HER value of 253.4 kJ mol⁻¹ at the reaction step of 2-IM4 → 1-IM7 + C₂H₂ and the EHHP of 29.2 kJ mol⁻¹ at the 1-IM7 + C₂H₂ exit. This indicates that the dehydrogenation channel is more preferable than the deacetylenation one, both thermodynamically and kinetically. The singlet ¹2-IM4 deposits into the deep well at −224.2 kJ mol⁻¹, indicating that this reaction is thermodynamically favoured. For ¹2-IM4, an NBO analysis showed that there are dominant occupancies of 1.91e in each BD(σ)Pt–H, indicating a complete σ-bond in Pt–H. Furthermore, there are dominant occupancies of 1.70 and 1.79e in BD(σ)Pt–C(1) and BD(σ)Pt–C(2), respectively, indicating a near σ-bond in each Pt–C.

Alternatively, as shown in Fig. 2b for CH2-S2, in the beginning, the C₂H₄ molecule is adsorbed onto a Pt₄ cluster through two Pt sites, forming a bridge tetraplatinum ethylene complex 1-IM10 with the stabilization energies of 169.3 kJ mol⁻¹ and 159.3 kJ mol⁻¹ for the singlet and triplet states, respectively. Subsequently, from 1-IM10, the first C–H bond cleavage with a [1,2]-H shift takes place via a three-member ring 2-TS5, resulting in a tetraplatinum hydride ethenyl complex 2-IM6. Then, a [1,2]-H shift occurs via a three-membered ring 2-TS6, leading to a more tetraplatinum hydride ethenyl complex, 2-IM7. Subsequently, from 2-IM7, the second C–H cleavage with a [1,2]-H shift takes place via a three-membered ring 2-TS7, resulting in a tetraplatinum dihydride acetylene complex 2-IM8. Later, from 2-IM8, a [1,2]-H shift occurs via a three-membered ring 2-TS8, leading to more tetraplatinum dihydride acetylene complex 2-IM9. Finally, 2-IM9 reductively eliminates H₂ or C₂H₂, leaving 2-IM10 or 1-IM7 behind, respectively. For the reactions of Pt₄ + C₂H₄ → 2-IM10 + H₂ and 1-IM7 + C₂H₂, the triplet PESs are located below the singlet ones except for 2-IM6 and 2-TS7. Thus, the MERPs should involve three MECPs near 2-IM6, 2-IM7, and 2-IM8. For the reaction Pt₄ + C₂H₄ → 2-IM10 + H₂, the MERP includes the HER of 151.0 kJ mol⁻¹ at the reaction step 2-IM9 → 2-IM10 + H₂ and the EHHP of 0.0 kJ mol⁻¹ at the Pt₄ + C₂H₄ entrance, whereas for the reaction of Pt₄ + C₂H₄ → 1-IM7 + C₂H₂, the MERP involves a HER value of 256.8 kJ mol⁻¹ at the reaction step 2-IM9 → 1-IM7 + C₂H₂ and the EHHP of 29.2 kJ mol⁻¹ at the 1-IM7 + C₂H₂ exit. This indicates that the dehydrogenation channel is more favourable than the deacetylenation one, both thermodynamically and kinetically. The triplet ³2-IM9 located in the deep well at −227.6 kJ mol⁻¹, indicates it being thermodynamically preferred. For ³2-IM9, an NBO analysis showed that there are dominant occupancies of 1.81 and 1.91e in BD(σ)Pt–H(1) and BD(σ)Pt–H(2), respectively, indicating a complete σ-bond in each Pt–H. Moreover, there are dominant occupancies of 1.89 and 1.91e in BD(σ)Pt–C(1) and BD(σ)Pt–C(2), respectively, indicating a complete σ-bond in each Pt–C.

From Fig. 2a and b, it can be observed that for the dehydrogenation channel, the HER of CH2-S1 was 13.8 kJ mol⁻¹ lower than that of CH2-S2. Furthermore, the top complex ³1-IM6 appears 55.4 kJ mol⁻¹ below the bridge ³1-IM10. One can conclude that the dehydrogenation channel of CH2-S1 is more favourable than that of CH2-S2, both thermodynamically and kinetically.

Comparing the dehydrogenation of ethene with ethane on a Pt₄ cluster, one can see that the dehydrogenation of ethene was kinetically comparable to that of ethane because of their almost equal HERs (137.2 vs. 129.3 kJ mol⁻¹), while both the dehydrogenation of ethene and ethane on a Pt₄ cluster were thermodynamically favourable in virtue of their exothermicities (−76.6 vs. −87.0 kJ mol⁻¹). Thus, the two-fold dehydrogenation of ethane on a Pt₄ cluster was almost equivalent to its single dehydrogenation, both thermodynamically and kinetically. This result is similar to that on a Pt₂ cluster.¹⁵ This result differs from the dehydrogenation of C₂H₆ on a mononuclear Pt atom, where the two-fold dehydrogenation of ethane on Pt atom takes place with more difficulty than the single dehydrogenation.¹⁴

Formation of CH₄ from C₂H₆

The geometric structures of various species and the schematic energy diagrams for the formation of CH₄ from C₂H₆ on Pt₄ cluster are depicted in Fig. 3a–c, respectively. As depicted in Fig. 3a–c, the reaction ³Pt₄ + C₂H₆ → ³3-IM6 + CH₄ was calculated to be exothermic by 74.6 kJ mol⁻¹, indicating that it is thermodynamically preferable. Now, we will kinetically discuss the abovementioned reactions.

Fig. 3 The optimized geometric structures of various species and the schematic energy diagrams for the C–C bond activation of C₂H₆ on Pt₄ cluster. Bond lengths are reported in Å and bonds angles are in degree. Relative energies (kJ mol⁻¹) for the corresponding species relative to the ground state reactants ³Pt₄ + C₂H₆ at the BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) level are shown. (a) CC-S1a through one Pt site; (b) CC-S1b through one Pt site; (c) CC-S2 through two Pt sites. Blue, red, and black lines represent the singlet, triplet, and quintet states, respectively.

As shown in Fig. 3a–c, there are three reaction pathways for the C–C bond activation of ethane on a Pt₄ cluster, two through a direct C–C bond activation on one Pt site, and the other through the indirect C–C bond activation from the two C–H bond cleavage intermediate 1-IM10s on two Pt sites, denoted as CC-S1a, and CC-S1b, and CC-S2, respectively.

As depicted in Fig. 3a for CC-S1a, for the direct C–C bond activation of C₂H₆ on a Pt₄ cluster, from the molecular complex 1-IM1, the oxidative insertion of the initial C–C bond takes place via a three-membered ring 3-TS1, yielding a tetraplatinum dimethyl compound, 3-IM2. By NBO analysis, there is a migration of about 0.27e from the –Pt₄ moiety to two –CH₃ groups, which confirms the oxidative addition of the C–C bond in the reaction stage of ³1-IM1 → ³3-IM2. For ³3-IM2, there are dominant occupancies of 1.91e in each BD(σ)Pt–C, indicating a complete σ-bond in each Pt–C. As shown in Fig. 3a and b, from 3-IM2, there are two reaction pathways for the formation of CH₄, CC-S1a and CC-S1b, respectively. On the one hand, for CC-S1a, from 3-IM2, the C–H bond cleavage takes place with a [1,2]-H shift from the –CH₃ group to the Pt atom via a three-membered ring 3-TS2, leading to a tetraplatinum hydride methyl methylene compound 3-IM3. Then, from 3-IM3, C–H bond formation occurs with a [1,2]-H shift from the Pt atom to –CH₃ group via a three-membered ring 3-TS3, generating a molecular complex 3-IM4. Subsequently, 3-IM4 liberates a CH₄ molecule, leaving a top tetraplatinum methylene compound 3-IM5 behind. Finally, the top 3-IM5 isomerizes to a more stable bridge tetraplatinum methylene compound 3-IM6 via a three-membered ring 3-TS4. For CC-S1a, the triplet PES is below the singlet one. Thus, the MERP should advance on the triplet PES with the HER of 97.1 kJ mol⁻¹ at the ³3-IM2 → ³3-TS2 reaction step with C–H bond cleavage and the EHHP of 17.1 kJ mol⁻¹ at ³3-TS1.

On the other hand, as depicted in Fig. 3b for CC-S1b, from 3-IM2, initially both a [1,3]-H shift and [1,2]-C shift take place simultaneously via a four-membered ring 3-TS5, resulting in a more stable tetraplatinum hydride methyl methylene compound 3-IM7. Second, from 3-IM7, a [1,2]-H shift occurs via a three-membered ring 3-TS6, leading to a more stable tetraplatinum hydride methyl methylene compound 3-IM8. Third, from 3-IM8, a [1,3]-H shift and [1,2]-C shift take place again simultaneously via a four-membered ring 3-TS7, generating a tetraplatinum dihydride dimethylene compound 3-IM9. Fourth, from 3-IM9, both Pt–C bond cleavage and C–H bond formation take place with a [1,2]-H shift from the Pt atom to a –CH₂ group via a four-membered ring 3-TS8, yielding a tetraplatinum hydride methyl methylene compound 3-IM10. Fifth, from 3-IM10, a [1,2]-H shift occurs, leading to a tetraplatinum hydride methyl methylene compound 3-IM11. Sixth, from 1-IM11, C–H bond formation takes place with a [1,2]-H shift from a Pt atom to a –CH₃ group via a three-membered ring 3-TS10, resulting in a molecular complex 3-IM12. Finally, 3-IM12 sets a CH₄ molecule free, leaving a bridge tetraplatinum methylene compound 3-IM6 behind. For CC-S1b, the triplet PES is located below the singlet one except for 3-TS6 and 3-IM9. Because the energy level of the singlet ¹3-IM9 is almost equal to that of the triplet ³3-IM9, we can neglect the spin crossing near 3-IM9. Then, the singlet–triplet spin flip should take place twice with two important MECPs near 3-IM7 and 3-IM8. Thus, the MERP should begin at the triplet PES and end on the triplet one, maintaining the spin multiplicity with the HER value of 102.7 kJ mol⁻¹ at the ¹3-IM9 → ³3-TS8 reaction step with a [1,2]-H shift and an EHHP of 17.1 kJ mol⁻¹ at ³3-TS1, where the spin flip may take place twice near 3-TS3. Besides, ¹3-IM9 deposits −200.9 kJ mol⁻¹ into a deep well. This indicates that the compound ¹3-IM9 is thermodynamically favoured. For ¹3-IM9, an NBO analysis showed that there are dominant occupancies of 1.83, 1.86, 1.85, 1.98, 1.90, 1.86e in BD(σ)Pt(1)–C(1), BD(σ)Pt(2)–C(1), BD(σ)Pt(2)–C(2), BD(σ)Pt(3)–H(1), BD(σ)Pt(4)–C(2), and BD(σ)Pt(4)–H(2), respectively, indicating a complete σ-bond in each Pt–H and an entire σ-bond in each Pt–C.

As shown in Fig. 3a and b, after 3-IM2, CC-S1a and CC-S1b are competitive. Considering their respective MERP values, after 3-IM2, the EHHP for CC-S1a was 17.1 kJ mol⁻¹ at ³3-TS4 + CH₄, whereas the EHHP for CC-S1b was −68.4 kJ mol⁻¹ at ³3-TS5. Furthermore, the singlet ¹3-IM9 at a deep well on CC-S1b appeared 69.4 kJ mol⁻¹ below the triplet ³3-IM2 at a deep well on CC-S1a. One can see that the reaction pathway for CC-S1b was more preferable than that for CC-S1a, both thermodynamically and kinetically.

As shown in Fig. 3c, for CH2-S2, for the indirect C–C bond activation of ethane from 1-IM8, a σ-complex assisted C–C σ-bond metathesis occurs initially via a five-membered ring 3-TS11 with both a [1,2]-H shift and C–C cleavage, leading to a tetraplatinum hydride methyl methylene compound 3-IM13. Subsequently, from 3-IM13, a [1,2]-H shift takes place from the one platinum to the other platinum via a three-membered ring 3-TS12, resulting in a tetraplatinum hydride methyl methylene compound 3-IM14. Then, from 3-IM14, a [1,2]-H shift again occurs from platinum to carbon via a three-membered ring 3-TS13, yielding a molecular complex 3-IM15. Subsequently, 3-IM15 sets a CH₄ molecule free, leaving 3-IM5 behind. Finally, 3-IM5 isomerizes to 3-IM6. As shown in Fig. 3c, the triplet PES stands below the singlet one except for 3-IM13. This indicates that the singlet–triplet spin flip may take place near 3-IM13 with one MECP between ¹3-IM13 and ³3-IM13, from 1-IM8 to 3-IM6 + CH₄. Together with the Pt₄ + C₂H₆ → 1-IM8 reaction stage, as shown in Fig. 1b and 3c, the MERP for CC-S2 includes the HER of 208.7 kJ mol⁻¹ at the ³1-IM8 → ³3-TS11 reaction step with a [1,2]-H shift and C–C bond cleavage and the EHHP of 19.8 kJ mol⁻¹ at ³3-TS11.

Thus, the reaction pathway for CC-S1b was kinetically more preferable than that for CC-S2 because of its comparatively lower HER (102.7 vs. 208.7 kJ mol⁻¹) and lower EHHP (17.1 vs. 19.8). Therefore, for the formation of CH₄, the gross MERP should go forward with the direct C–C bond cleavage channel CC-S1b.

As mentioned earlier, the C–H cleavage products (1-IM6 + H₂) and the C–C bond cleavage products (3-IM6 + CH₄) are competitive. On their MERPs, the HER for the formation of 1-IM6 + H₂ is 129.3 kJ mol⁻¹ at the 1-IM5 → 1-IM6 + H₂ exit, whereas the HER for the formation of 3-IM6 + CH₄ is 102.7 kJ mol⁻¹ at the ¹3-IM9 → ³3-TS8 reaction step. This indicates that the release of H₂ from C₂H₆ on Pt₄ cluster is kinetically more inferior to the release of CH₄. This may be ascribed to the fact that the reaction traps the extremely stable C–H cleavage intermediate 1-IM5 in a deep well, hindering the release of H₂ from 1-IM5.

However, the C–H cleavage intermediate 1-IM5 and the C–C bond cleavage intermediate 3-IM9 were also competitive. Moreover, the two reaction steps 1-IM1 → 1-TS1 → 1-IM2 and 1-IM1 → 3-TS1 → 3-IM2 are the selectively controlling steps for the formation of 1-IM5 and 3-IM9, respectively. To estimate quantitatively the selectivity for the C–H cleavage intermediate 1-IM5 and the C–C bond cleavage intermediate 3-IM9, the rate constants of 1-IM1 → 1-TS1 → 1-IM2 and 1-IM1 → 3-TS1 → 3-IM2 were taken into account. Over the 300–1100 K temperature range, the rate constants for 1-IM5 (k_CH) and 3-IM9 (k_CC) formation could be adapted by the following expression (in s⁻¹):

k_CH = 5.436 × 10¹² exp(−4165/RT)

k_CC = 1.131 × 10¹² exp(−80 998/RT)

The branching ratio of the C–H cleavage intermediate 1-IM5 and the C–C bond cleavage intermediate 3-IM9 were calculated to be 100% and 0.0%, respectively, over the 300–1100 K temperature range. One can conclude that for the reaction of C₂H₆ on a Pt₄ cluster, the C–H cleavage intermediate 1-IM5 was kinetically more preferable than the C–C cleavage intermediate 3-IM9.

To compare the observed variation of selectivity and reactivity as a function of platinum cluster size toward ethane activation, Table 1 lists the HERs for the deethylenation, dehydrogenation, and demethanation and the EHHP for the C–H and C–C bond cleavage on their MERPs of the Pt atom,¹⁴ Pt₂ cluster,¹⁵ and Pt₄ cluster.

Table 1 The HERs (kJ mol⁻¹) for the deethylenation, dehydrogenation, and demethanation and the EHHP (kJ mol⁻¹) for the C–H and C–C bond cleavage on their MERPs of Pt atom, Pt₂ cluster, and Pt₄ cluster toward ethane activation

Cluster	HER (kJ mol^−1) for deethylenation	HER (kJ mol^−1) for dehydrogenation	HER (kJ mol^−1) for demethanation	EHHP (kJ mol^−1) for C–H bond cleavage	EHHP (kJ mol^−1) for C–C bond cleavage
a From ref. 14.b From ref. 15.
Pt^a	99.2	90.9	314.3	63.4	140.8
Pt2^b	6.3	129.9	119.4	0.0	43.2
Pt4	200.4	129.3	102.7	0.0	17.1

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As shown in Table 1, first, for the mononuclear Pt atom, the HERs were 99.2, 90.9, and 314.3 kJ mol⁻¹ for the deethylenation, dehydrogenation, and demethanation, respectively.¹⁴ Therefore, the kinetically optimal channel order was as follows: dehydrogenation > deethylenation > demethanation from C₂H₆ on mononuclear Pt atom. Second, for a Pt₂ cluster, the HERs were 6.3, 129.9, and 119.4 kJ mol⁻¹ for the deethylenation, dehydrogenation, and demethanation, respectively.¹⁵ Then, the optimal channel order was kinetically as follows: deethylenation > demethanation > dehydrogenation from C₂H₆ on a Pt₂ cluster. Third, for a Pt₄ cluster, the HERs were 200.4, 129.3, and 102.7 kJ mol⁻¹ for the deethylenation, dehydrogenation, and demethanation, respectively. This indicated that the optimal channel order is kinetically as follows: demethanation > dehydrogenation > deethylenation from C₂H₆ on a Pt₄ cluster. In view of selectivity, Pt atom is the most favourable for the dehydrogenation, Pt₂ cluster is the most preferable for the deethylenation, and Pt₄ cluster is most beneficial for the demethanation.

As shown in Table 1, for ethane activation on the MERPs, the EHHPs for the C–H and C–C bond cleavage are 63.4 and 140.8 kJ mol⁻¹ on a mononuclear Pt atom,¹⁴ 0.0 and 43.2 kJ mol⁻¹ on a Pt₂ cluster,¹⁵ and 0.0 and 17.1 kJ mol⁻¹ on a Pt₄ cluster. This indicated that both Pt₄ and Pt₂ clusters exhibit a higher reactivity towards ethane than the mononuclear Pt atom. Thus, both the Pt₄ and Pt₂ clusters exhibit a more promising catalytic performance compared with mononuclear Pt atom. However, on a Pt₄ cluster, the extremely stable C–H cleavage intermediate 1-IM5 was trapped in deep well, hindering the release of H₂ from 1-IM5. Together with the excellent reactivity of a Pt₄ cluster, for the design of an efficient and selective catalyst toward the dehydrogenation of C₂H₆, one can expect that it is necessary to improve the release of H₂ from the C–H cleavage intermediate by introducing some additive or support into the Pt₄ cluster, which decreases the binding of catalyst toward H₂.

Conclusions

The activation mechanism of C₂H₆ on a Pt₄ cluster has been theoretically investigated for the ground state and the first excited state potential energy surfaces. The following conclusions may be drawn from the results presented here.

On a Pt₄ cluster, the optimal channel order is kinetically as follows: demethanation > dehydrogenation > deethylenation from C₂H₆. The two-fold dehydrogenation of ethane to acetylene was almost equivalent to the single dehydrogenation of ethylene, both thermodynamically and kinetically.

In addition, in the reaction of C₂H₆ on a Pt₄ cluster, the C–H cleavage intermediate 1-IM5 was kinetically more preferred than the C–C cleavage intermediate 3-IM2, while both the C–H cleavage intermediate 1-IM5 and the C–C cleavage intermediate 3-IM2 were thermodynamically favoured. Nevertheless, the extremely stable C–H cleavage intermediate 1-IM5 deposited in deep well and impeded the release of H₂ from 1-IM5.

Together with excellent reactivity of the Pt₄ cluster, for the design of an efficient and selective catalyst towards dehydrogenation of C₂H₆, one can expect that it is necessary to improve the release of H₂ from a C–H cleavage intermediate by introducing some additive or support into the Pt₄ cluster, which decreases the binding of catalyst toward H₂.

In view of selectivity, Pt atom is the most favorable for the dehydrogenation, Pt₂ cluster is the most preferable for the deethylenation, and Pt₄ cluster is most beneficial for the demethanation. Both Pt₄ and Pt₂ clusters exhibit a more promising catalytic performance compared with a mononuclear Pt atom toward C₂H₆ activation. Furthermore, both Pt₄ and Pt₂ clusters exhibit more efficient two-fold dehydrogenation of ethane, compared with a mononuclear Pt atom.

Acknowledgements

The authors are grateful for financial support by the National Natural Science Foundation of China (no. 21343001 and 20976109) and the Applied Foundation Research of Sichuan Province (no. 2011JY0024 and 2014JY0218).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Zero-point energies (ZPE) (hartree), total energies (E_c) (hartree) corrected by ZPE, and relative energies (E_r) (kJ mol⁻¹) with respect to the ground state reactants (Pt₄ + C₂H₆) of the species at the BPW91/Lanl2tz, 6-311++G(d, p) and BPW91/Lanl2tz, aug-cc-pvtz//BPW91/Lanl2tz, 6-311++G(d, p) levels. The standard orientations of various species in the Pt₄ + C₂H₆ reaction calculated at the BPW91/Lanl2tz, 6-311++G(d, p) level. Some important minimum energy crossing points (MECPs) in the Pt₄ + C₂H₆ reaction calculated at the BPW91/Lanl2tz, 6-311++G(d, p) level. See DOI: 10.1039/c5ra06550j

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