Activation of Propane C-H and C-C Bonds by Gas-Phase Pt Atom: A Theoretical Study

Abstract

The reaction mechanism of the gas-phase Pt atom with C₃H₈ has been systematically investigated on the singlet and triplet potential energy surfaces at CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz level. Pt atom prefers the attack of primary over secondary C-H bonds in propane. For the Pt + C₃H₈ reaction, the major and minor reaction channels lead to PtC₃H₆ + H₂ and PtCH₂ + C₂H₆, respectively, whereas the possibility to form products PtC₂H₄ + CH₄ is so small that it can be neglected. The minimal energy reaction pathway for the formation of PtC₃H₆ + H₂, involving one spin inversion, prefers to start at the triplet state and afterward proceed along the singlet state. The optimal C-C bond cleavages are assigned to C-H bond activation as the first step, followed by cleavage of a C-C bond. The C-H insertion intermediates are kinetically favored over the C-C insertion intermediates. From C-C to C-H oxidative insertion, the lowering of activation barrier is mainly caused by the more stabilizing transition state interaction ΔE^≠_int, which is the actual interaction energy between the deformed reactants in the transition state.

1. Introduction

In recent years, the dehydrogenation of lower alkanes has gained great importance in natural and petroleum gas utilization [1,2]. Propane is a cheap and easily available raw material as it is produced through a number of petrochemical processes, while the propylene market demand is rapidly increasing. Accordingly, the dehydrogenation of propane is an interesting alternative route to propylene production. In the catalytic cracking of alkanes and catalytic dehydrogenation of alkanes, platinum based catalysts have received much attention. Elucidation of the role of isolated platinum units in heterogeneous catalysis can be aided by gas-phase study, which can provide insight into the intrinsic properties and reactivities of discrete and well-characterized catalytic species [3].

In particular, the activation of C-H and C-C bonds of propane by transition metals (neutral, cationic, or clusters) in the gas phase has been an active area of research that provides fundamental information on catalytic reaction mechanisms, kinetics, and thermodynamics [4,5]. Of the first-row transition metal series, for the activation of propane, the early members (Sc⁺ [6], Ti⁺ [7], and V⁺ [8]) exhibit efficiency for the dehydrogenation of propane. Co⁺ cation favors H₂ over CH₄ [9,10], whereas Fe⁺ and Ni⁺ cations favor CH₄ over H₂ [9,11]. Cr⁺ cation does not show any efficiency for the activation of propane [12]. Of the second-row transition metal series, for Nb⁺ [13], Mo⁺ [12,14,15], and Rh⁺ cations [16], the dehydrogenation of propane is efficient and the dominant process at low energies, whereas products resulting from both C-H and C-C cleavage processes are observable at high energies. Rh atoms are also effective for the H₂ elimination from ethane and larger alkanes under kinetics technique experiment [17]. For the reaction of Ag⁺ with propane, the dehydrogenation and formation of AgH⁺ + R products are not observed, whereas the C-C bond cleavage is the predominant process [18]. Of the actinide ions, for the activation of propane, Th⁺, Pa⁺ and U⁺ cations are efficient for the dehydrogenation of propane. For the other cations (Np⁺, Pu⁺, Am⁺, and Cm⁺), no reactions are observed experimentally [19]. For Th²⁺ and U²⁺, both C-H and C-C cleavage products are effectively observed [20]. Finally, for [(MgO)_n]⁺ clusters, the higher reactivity with propane is not specific to [(MgO)₂]⁺, but has been also observed for (MgO)⁺ [21,22].

Concerning the 5d-series transition metal Pt (neutral, cationic, or clusters), the reactions with linear alkanes have been extensively explored by means of diverse experimental and theoretical methods [23–29]. It is reported that the transition metal Pt (neutral, cationic, or clusters) are the efficient C-H insertion agents [23–29]. However, as far as we know, although a few investigations of C-H insertion processes have focused on the neutral Pt atom [23–27], the C-C insertion has hardly been investigated in the gas phase.

In the present study, a complete mechanism of neutral Pt atom with propane along with both the C-H and C-C bond activation processes is investigated, which is necessary to enable us to determine the crucial steps and to either block or enhance particular steps to steer the reaction in the desired direction. The goals of the present investigation are as follows: (a) to provide reliable structures and chemically accurate energetics of the reactants, intermediates, transition states (TSs), and products; (b) to elucidate the rate-determining step and the selectivity-controlling step; and (c) to gain a better understanding of the preference of reaction pathway. Particularly, to shed some light on the intrinsic reactivity of platinum atom toward the propane activation, the trends in reactivity and competition among the C-H and C-C bond cleavage mechanisms are analyzed using the activation strain model of chemical reactivity [30,31]. The potential energy profiles on the singlet and triplet states are investigated, because spin crossing is often involved in the transition metal-containing reactions [7,15,20].

2. Computational Details

All calculations were carried out with the Gaussian 03 program [32]. Full geometry optimizations were run to locate all of the stationary points and TSs on the singlet and triplet potential energy surfaces (PESs) for the reactions of Pt atom with C₃H₈, using the BPW91 [33,34] method with 6-311++G(d, p) basis set for the carbon and hydrogen atoms [35,36], and the Lanl2dz basis set and the corresponding effective core potential (ECP) for platinum [37], namely BPW91/6-311++G(d, p), Lanl2dz. Meantime, the stability of the density function theory (DFT) wavefunction was tested [38,39]. If an instability was found, the wavefunction was reoptimized with appropriate reduction in constraints, and the stability tests and reoptimizations were repeated until a stable wavefunction was found [38,39]. Harmonic frequency calculations were run to characterize stationary points and to take corrections of zero-point energy (ZPE) into account. The intrinsic reaction coordinate (IRC) method was performed to track minimum energy paths from transition structure to the corresponding minima [40,41]. The dominant occupancies of natural bond orbitals for some species have been analyzed with the help of the natural bond orbital (NBO) analysis [42,43]. To further determine electron correction energies, the single-point calculation of various species based on the optimized BPW91/6-311++G(d, p), Lanl2dz geometries were then refined using CCSD(T) [44] method with the same basis sets, namely CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz. Unless otherwise mentioned, all energies are relative to the ground-state reactants [Pt(³D) + C₃H₈] at the CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz level, including ZPE correction obtained at the BPW91/6-311++G(d, p), Lanl2dz level.

3. Results and Discussion

Considering the present system, the BPW91/6-311G++(d, p), Lanl2dz level is suitable to reproduce experimental values of geometrical parameters of H₂, Pt₂, and PtH diatomic molecules [45]. Furthermore, the single-point calculation of various species were then refined at the CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz level. Thereupon, the present theoretical method of CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz should be appropriate and reliable for the Pt + C₃H₈ systems.

In this work, we will mainly discuss the following reactions of Pt atom with C₃H₈:

$$\text{Pt}+{\text{C}}_3{\text{H}}_8\to {\text{PtC}}_3{\text{H}}_6+{\text{H}}_2$$

(1)

$$\text{Pt}+{\text{C}}_3{\text{H}}_8\to {\text{PtCH}}_2+{\text{C}}_2{\text{H}}_6$$

(2)

$$\text{Pt}+{\text{C}}_3{\text{H}}_8\to {\text{PtC}}_2{\text{H}}_4+{\text{CH}}_4$$

(3)

The above three product channels were divided into five sections: (i) C-H bond activation: dehydrogenation, (ii) C-C bond activation: deethanization, (iii) C-C bond activation: demethanation, (iv) comparison of C-H with C-C bond activation, and (v) activation strain analysis of the direct C-H and C-C bond cleavage.

3.1. C-H Bond Activation: Dehydrogenation

For the dehydrogenation of C₃H₈ by Pt atom, the reaction pathway and the optimized geometric structures of various species are depicted in Scheme 1.

The triplet state Pt atom, ³D(d⁹s¹), is the ground state. The singlet state Pt atom, ¹S(d¹⁰), lies 59.4 kJ·mol⁻¹ above the ground triplet state ³D(d⁹s¹), in good agreement with the estimated value of 56.6 kJ·mol⁻¹ [26]. The superscript prefixes “¹” and “³” will be used to indicate the singlet and triplet states, respectively. As depicted in Scheme 1, there are two primary (tans-C-H⁽¹⁾ and cis-C-H⁽¹⁾ in the trans and cis position with respect to the CH₃ group, respectively) and one secondary (C-H⁽²⁾) C-H bonds in propane. Then, with regard to the initial interaction between Pt atom and C₃H₈, three molecular complexes are considered: (i) Pt atom attacking the H-end of primary tans-C-H⁽¹⁾ (1-PtC₃H₈), (ii) Pt atom attacking the H-end of secondary C-H⁽²⁾ approaching to Pt atom (2-PtC₃H₈), (iii) Pt atom attacking the H-end of primary cis-C-H⁽¹⁾ (3-PtC₃H₈).

As discussed earlier, Pt atom has a triplet ground state (³D) with excitation energy of 59.4 kJ·mol⁻¹ to the lowest singlet state (¹S). Considering the initial interaction of Pt atom with C₃H₈, only the triplet ground state ³1-PtC₃H₈, ³2-PtC₃H₈, and ³3-PtC₃H₈ molecular complexes are obtained, whereas we failed to locate the corresponding ones on the singlet PES despite extensive attempts. For ³1-PtC₃H₈, ³2-PtC₃H₈, and ³3-PtC₃H₈, the BSSEs [46] by BPW91 are 10.1, 10.5, and 10.3 kJ·mol⁻¹, and the complexation energies corrected by BSSEs are calculated to be 1.6, 15.7, and 3.8 kJ·mol⁻¹ relative to the reactants Pt(³D) + C₃H₈, respectively. It is shown that the complex stability increases along ³1-PtC₃H₈ < ³3-PtC₃H₈ < ³2-PtC₃H₈. For ³1-PtC₃H₈, ³2-PtC₃H₈, and ³3-PtC₃H₈, the C-H bond close to Pt atom is elongated to 1.147, 1.164 and 1.147 Å from the 1.100, 1.103, and 1.101 Å of free C₃H₈, while there is a short Pt-H distance of 2.016, 1.955, 2.023 Å, respectively, indicating some molecular interaction between Pt atom and C₃H₈. The minimal energy reaction pathway (MERP) may start at the triplet molecular complexes (³1-PtC₃H₈, ³2-PtC₃H₈, and ³3-PtC₃H₈) from the corresponding ground triplet reactants.

As shown in Scheme 1, from these molecular complexes (1-PtC₃H₈, and 2-PtC₃H₈, 3-PtC₃H₈), the C-H bond cleavage may lead to the dehydrogenation product PtC₃H₆ (Pt-propene) + H₂ and Pt(CH₂)₃ (Pt-cyclopropane) + H₂. The change of Gibbs free energies (ΔG₂₉₈) for the reactions of Pt(³D) + C₃H₈→¹PtC₃H₆ (Pt-propene) + H₂ and ¹Pt(CH₂)₃ (Pt-cyclopropane) + H₂ are calculated to be −111.6 and −104.5 kJ·mol⁻¹, respectively. Thereby, the dehydrogenation of C₃H₈ is thermodynamically favorable.

For the formation of PtC₃H₆ (Pt-propene) + H₂, there are five reaction pathways beginning at the three kinds of molecular complexes (two from 1-PtC₃H₈, two from 2-PtC₃H₈, and one from 3-PtC₃H₈), respectively, as shown in Scheme 1. Alternatively, for the formation of Pt(CH₂)₃ (Pt-cyclopropane) + H₂, there is an unique reaction pathway starting from 3-PtC₃H₈.

First, from 1-PtC₃H₈, the initial primary C-H bond oxidative insertion via TS1 or TS2 leads to the σ-complex intermediate 1-HPtC₃H₇ or cis-1-HPtC₃H₇, respectively. From 1-HPtC₃H₇, a 1,2-dehydrogenation process takes place via four-center transition state TS3, resulting in a dihydrogen propene complex (H₂)PtC₃H₆. Finally, the molecular complex (H₂)PtC₃H₆ reductively eliminates H₂, leaving PtC₃H₆ behind. Alternatively, from cis-1-HPtC₃H₇, a 1,2-dehydrogenation process occurs via five-center transition state TS4 directly, leading to the dissociation products PtC₃H₆ + H₂.

Second, from 2-PtC₃H₈, the initial secondary C-H bond oxidative insertion via TS5 yields the σ-complex intermediate HPtCH(CH₃)₂. From HPtCH(CH₃)₂, there are two reaction pathways for the formation of PtC₃H₆ + H₂. On the one hand, a 1,2-dehydrogenation process takes place via four-center transition state TS6, producing the dihydrogen propene complex (H₂)PtC₃H₆. On the other hand, from HPtCH(CH₃)₂, a 1,2-dehydrogenation process occurs via five-center transition state TS7, directly resulting in the dissociation products PtC₃H₆ + H₂.

Third, from 3-PtC₃H₈, the initial primary C-H bond oxidative insertion via TS8 or TS9 generates a σ-complex intermediate 3-HPtC₃H₇ or cis-3-HPtC₃H₇, respectively. From 3-HPtC₃H₇, a 1,3-dehydrogenation process takes place via five-member transition state TS10, generating the dihydrogen metallacycle molecular complex H₂Pt(CH₂)₃. Last, the molecular complex dissociates into Pt(CH₂)₃ + H₂. The structure of metallacycle Pt(CH₂)₃ is similar to that of Sc(CH₂)₃⁺ [6], TiC₃H₆⁺ [7], and NiC₄H₈⁺ [47]. Alternatively, from cis-3-HPtC₃H₇, a 1,2-dehydrogenation process occurs via five-center transition state TS11, producing the dihydrogen propene complex (H₂)PtC₃H₆. Finally, (H₂)PtC₃H₆ reductively eliminates H₂, leaving PtC₃H₆ behind.

For the formation of PtC₃H₆ + H₂, from 1-PtC₃H₈, the MERP should proceed via the minimal energy crossing point (MECP) between ¹1-HPtC₃H₇ and ³1-HPtC₃H₇, with the energy height of the highest point (EHHP) of 61.2 kJ·mol⁻¹ at ³TS1. From 2-PtC₃H₈, the MERP should proceed via MECP between ¹HPtCH(CH₃)₂ and ³HPtCH(CH₃)₂, with the EHHP of 69.5 kJ·mol⁻¹ at ³TS5. From 3-PtC₃H₈, the MERP should progress via MECP between ¹cis-3-HPtC₃H₇ and ³cis-3-HPtC₃H₇, with the EHHP of 162.1 kJ·mol⁻¹ at TS11. Since the EHHP at ³TS1 from 1-PtC₃H₈ is the lowest among the three reaction channels, this reaction channel for the formation of PtC₃H₆ + H₂ is the most feasible kinetically. Furthermore, these results reveal a high preference of Pt atom for the attack of primary C-H bonds in propane, which is analogous to that of MgO⁺ cation for the attack of alkanes [21]. This feature represents a notable distinction of the transition-metal atom from various transition-metal oxide cations, which show a clear preference for the attack of secondary C-H bonds [21].

For the formation of Pt(CH₂)₃ + H₂, from 3-PtC₃H₈, the MERP should advance via MECP between ¹3-HPtC₃H₇ and ³3-HPtC₃H₇, with the EHHP of 65.5 kJ·mol⁻¹ at ³TS8.

Moreover, the ¹1-HPtC₃H₇, ¹cis-1-HPtC₃H₇, ¹HPtCH(CH₃)₂, ¹3-HPtC₃H₇, ¹cis-3-HPtC₃H₇, and ¹(H₂)PtC₃H₆ intermediates lie −182.5, −181.6, −192.3, −180.4, −183.3, and −202.9 kJ·mol⁻¹ in a deep energetic well on each MERP, respectively. Then, these intermediates are thermodynamically favored in the dehydrogenation of C₃H₈. For the intermediates containing –PtH and –Pt-alkyl moieties (¹1-HPtC₃H₇, ¹cis-1-HPtC₃H₇, ¹HPtCH(CH₃)₂, ¹3-HPtC₃H₇, and ¹cis-3-HPtC₃H₇), the NBO results show that a complete σ-bond has been formed both in Pt-H and in Pt-C.

From Pt + C₃H₈ to the C-H insertion intermediates (¹1-HPtC₃H₇, ¹cis-1-HPtC₃H₇, ¹HPtCH(CH₃)₂, ¹3-HPtC₃H₇, and ¹cis-3-HPtC₃H₇), only the triplet molecular complexes and the triplet TSs are obtained, while we failed to gain the corresponding singlet ones, despite extensive attempts. Furthermore, for Pt atom (10 valence electrons), Pt(¹S) singlet state, has an empty orbital and five doubly occupied nonbonding orbitals, whereas Pt(³D) triplet state has all of its s and d valence orbitals occupied, with four doubly occupied nonbonding orbitals, and two singly occupied nonbonding orbitals. That is to say, the bonding capacity of Pt(¹S) singlet state to C₃H₈ is stronger than that of Pt(³D) triplet state. Then, the binding of Pt to C₃H₈ in the C-H insertion intermediates (1-HPtC₃H₇, cis-1-HPtC₃H₇, HPtCH(CH₃)₂, 3-HPtC₃H₇, and cis-3-HPtC₃H₇) inverts the energies of the singlet and triplet states from the Pt atom. Therefore, the ground state of the C-H insertion intermediates is the singlet state, as depicted in Scheme 1. The reaction goes forward from the excited state reactants Pt(¹S) + C₃H₈ to the C-H inserted intermediates, without energy barrier. This can be ascribed to the fact that the singlet state Pt(¹S) has an empty orbital, which should greatly facilitate the interaction with propane and its bond activation, leading smoothly to the formation of two covalent bonds to H and C₃H₇. This phenomenon has also appeared in the analogous Pt + CH₄ system [26].

3.2. C-C Bond Activation: Deethanization

For the deethanization of C₃H₈ by Pt atom, the reaction pathway and the optimized geometric structures of various species are depicted in Scheme 2. The change of Gibbs free energies (ΔG₂₉₈) for the reaction of Pt(³D) + C₃H₈→¹PtCH₂ + C₂H₆ is calculated to be −45.9 kJ·mol⁻¹. Thereupon, the deethanization of C₃H₈ is thermodynamically favorable. Then, it is necessary to discuss kinetically the above reaction infra.

As shown in Scheme 2, for the deethanization of C₃H₈ by Pt atom, there are seven reaction pathways, three from 1-PtC₃H₈, one from 2-PtC₃H₈, and three from 3-PtC₃H₈. These seven reaction pathways are separated into two kinds of reaction pathways, one through the initial C-C bond direct cleavage, and another through the σ-complex assisted C-C σ-bond metathesis. For simplicity, we will primarily discuss the three reaction pathways from 1-PtC₃H₈ infra, which are analogous to those from 2-PtC₃H₈ and 3-PtC₃H₈. The nuances in energy mainly stem from their configuration differences among the three kinds of reaction channels.

As mentioned earlier, from 1-PtC₃H₈, there are three reaction pathways for the PtCH₂ + C₂H₆ formation. For the first reaction pathway, Pt atom firstly inserts the C-H bond via five-member TS2, resulting in the intermediate cis-1-HPtC₃H₇. Then, from cis-1-HPtC₃H₇, a σ-complex assisted C-C σ-bond metathesis takes place via a four-member TS12 with both 1,3-H migration and C-C cleavage, yielding the molecular complex, C₂H₆PtCH₂. Finally, C₂H₆PtCH₂ releases C₂H₆ molecule, leaving PtCH₂ behind. The MERP should proceed via the MECP between ¹cis-1-HPtC₃H₇ and ³cis-1-HPtC₃H₇, with the highest energy requirement (HER) of 273.2 kJ·mol⁻¹ at the ¹cis-1-HPtC₃H₇→¹TS12 reaction step and the EHHP of 91.6 kJ·mol⁻¹ at ¹TS12.

For the second and third reaction pathways from 1-PtC₃H₈, there are two reaction pathways to produce cis-CH₃PtC₂H₅. That is, Pt atom directly inserts the C-C bond via three-member TS13, leading to the intermediate cis-CH₃PtC₂H₅. Alternatively, Pt atom firstly inserts the C-H bond via the three-member TS1, resulting in the intermediate 1-HPtC₃H₇. Next, from 1-HPtC₃H₇, a σ-complex assisted C-C σ-bond metathesis occurs via a four-member TS14 with both 1,2-H shift and C-C bond cleavage, also yielding cis-CH₃PtC₂H₅. Then, from CH₃PtC₂H₅, the σ-complex assisted C-H σ-bond metathesis takes place via a four-member TS15 with 1,3-H shift, yielding the molecular complex C₂H₆PtCH₂. As mentioned earlier, C₂H₆PtCH₂ releases C₂H₆ molecule, staying PtCH₂ behind. For the two reaction pathways, each MERP should advance via the MECP between ¹cis-CH₃PtC₂H₅ and ³cis-CH₃PtC₂H₅, with the HER of 299.0 kJ·mol⁻¹ at the ¹cis-CH₃PtC₂H₅→¹TS15 reaction step. The two MERPs involve the EHHP of 156.1 and 120.3 kJ·mol⁻¹ at ³TS13 and ¹TS15, respectively.

Comparing these three reaction pathways, one can conclude that the reaction pathway via TS2 involving the first C-H cleavage and via TS12 involving C-C cleavage with synchronous 1,3-H migration is the gross MERP for the 1-PtC₃H₈→PtCH₂ + C₂H₆ reaction, owing to its comparatively low HER (273.2 vs. 299.0 kJ·mol⁻¹) and low EHHP (91.6 vs. 120.3 and 156.1 kJ·mol⁻¹), with the rate-determining step of ¹cis-1-HPtC₃H₇→¹TS12→¹C₂H₆PtCH₂.

From 2-PtC₃H₈ for the formation of PtCH₂ + C₂H₆, only one reaction pathway is obtained, which includes the initial C-C bond cleavage and σ-complex assisted C-H σ-bond metathesis. This reaction pathway is homologous to that via the initial C-C cleavage from 1-PtC₃H₈ with the HER of 299.0 kJ·mol⁻¹ and the EHHP of 156.1 kJ·mol⁻¹ at ³TS13.

From 3-PtC₃H₈ for the formation of PtCH₂ + C₂H₆, there are also three reaction pathways. These three reaction pathways are similar to those from 1-PtC₃H₈. The reaction pathway of σ-complex assisted C-C σ-bond metathesis via ³TS9 and ¹TS19 is kinetically most preferable in the three reaction pathways, because of its lowest HER (274.9 vs. 298.7 kJ·mol⁻¹) and lowest EHHP (91.6 vs. 120.3 and 156.1 kJ·mol⁻¹).

In summary, for the formation of the C-C cleavage products PtCH₂ + C₂H₆, the optimal pathway proceeds through the σ-complex cis-1-HPtC₃H₇ or cis-3-HPtC₃H₇ from initial C-H bond cleavage, which assists the C-C σ-bond metathesis. This reactivity mode is also complementary for the classical reactivity picture through the direct C-C cleavage intermediate (M = Fe⁺ [48] and Ta⁺ [49]).

3.3. C-C Bond Activation: Demethanation

For the demethanation of C₃H₈ by Pt atom, the reaction pathway and the optimized geometric structures of various species are depicted in Scheme 3. The change of Gibbs free energies (ΔG₂₉₈) for the reactions of Pt(3D) + C₃H₈→1PtC₂H₄ + CH₄ are calculated to be −143.6 kJ·mol⁻¹, which is thermodynamically favorable. Afterwards, we will discuss the kinetics of the above reaction infra. As shown in Scheme 3, there are four kinds of reaction pathways, which are through cis-CH₃PtC₂H₅, CH₃PtC₂H₅, HPtCH(CH₃)₂, and C₂H₄PtH(CH₃) intermediates, respectively.

First, from cis-CH₃PtC₂H₅, a σ-complex assisted C-H σ-bond metathesis takes place via a four-member TS20 with 1,4-H shift, yielding the molecular complex CH₄PtC₂H₄. The molecular complex CH₄PtC₂H₄ releases CH₄ molecule, leaving PtC₂H₄ behind. Through cis-CH₃PtC₂H₅, the MERP should go forward via the MECP between ¹1-HPtC₃H₇ and ³1-HPtC₃H₇, with the HER of 319.0 kJ·mol⁻¹ at the ¹cis-CH₃PtC₂H₅→¹TS20 reaction step and the EHHP of 140.3 kJ·mol⁻¹ at ¹TS20.

Second, from CH₃PtC₂H₅, a σ-complex assisted C-H σ-bond metathesis occurs via a four-member TS27 with 1,3-H shift, yielding a molecular complex CHCH₃PtCH₄. Then, the molecular complex CH₄PtCHCH₃ sets a CH₄ molecule free, leaving PtCHCH₃ behind. Next, from PtCHCH₃, 1,2 H shift occurs via a four-member TS22, staying PtC₂H₄ behind. Through CH₃PtC₂H₅, the MERP should go forward via the MECP between ¹3-HPtC₃H₇ and ³3-HPtC₃H₇, with the HER of 225.8 kJ·mol⁻¹ at the ¹3-HPtC₃H₇→¹TS17 reaction step and the EHHP of 68.9 kJ·mol⁻¹ at ¹TS22.

Third, from HPtCH(CH₃)₂, a σ-complex assisted C-C σ-bond metathesis occurs via a four-member TS21 with 1,3-H shift, also leading to the molecular complex CHCH₃PtCH₄. The MERP should go forward via the MECP between ¹2-HPtC₃H₇ and ³2-HPtC₃H₇, with the HER of 277.4 kJ·mol⁻¹ at the ¹HPtCH(CH₃)₂→¹TS21 reaction step and the EHHP of 85.1 kJ·mol⁻¹ at ¹TS21.

Fourth, from 3-HPtC₃H₇, an oxidative insertion of C-C bond to the platinum center takes place via a four-member TS23, producing a methyl hydrid complex C₂H₄PtH(CH₃). Then, from C₂H₄PtH(CH₃), 1,2-H shift occurs, yielding the molecular complex CH₄PtC₂H₄. Last, the molecular complex CH₄PtC₂H₄ sets a CH₄ molecule free, leaving PtC₂H₄ behind. The MERP should go forward via the MECP between ¹3-HPtC₃H₇ and ³3-HPtC₃H₇, with the HER of 143.1 kJ·mol⁻¹ at the ¹3-HPtC₃H₇→¹TS23 reaction step and the EHHP of 65.5 kJ·mol⁻¹ at ³TS8.

Comparing these four kinds of reaction pathways, one can see that the reaction pathway starting at the 3-PtC₃H₈ involving the crucial intermediate C₂H₄PtH(CH₃) is the most optimal MERP for the Pt + C₃H₈→PtC₂H₄ + CH₄ reaction, thanks to the lowest HER (143.1 vs. 319.0, 225.8, and 277.4 kJ·mol⁻¹) and lowest EHHP (65.5 vs. 140.3, 85.1, and 68.9 kJ·mol⁻¹), with the rate-determining step of ¹3-HPtC₃H₇→¹TS23→C₂H₄PtH(CH₃). Thereby, the optimal pathway proceeds through the σ-complex 3-HPtC₃H₇ from initial C-H bond cleavage, which assists the C-C σ-bond metathesis. That is to say, the optimal C-C bond cleavages are assigned to C-H bond activation as the first step, followed by cleavage of a C-C bond. This reactivity mode is complementary for the classical reactivity picture through the direct C-C cleavage intermediate (M = Fe⁺ [48], and Ta⁺ [49]).

3.4. Comparison of C-H with C-C Bond Activation

As shown in Schemes 1–3, the C-H insertion intermediates (¹1-HPtC₃H₇, ¹cis-1-HPtC₃H₇, ¹HPtCH(CH₃)₂, ¹3-HPtC₃H₇, ¹cis-3-HPtC₃H₇) and the C-C insertion intermediates (¹CH₃PtC₂H₅, ¹cis-CH₃PtC₂H₅, ¹C₂H₄PtH(CH₃), and ¹CH₄PtC₂H₄) deposit in a deep well, respectively. It is indicated that these intermediates are thermodynamically preferred. For the formation of the C-H and the C-C insertion intermediates, the corresponding MERP should involve the HER of about 60~70 and 140~230 kJ·mol⁻¹, respectively. Thereby, the C-H insertion intermediates are kinetically favored, while the C-C insertion intermediates are kinetically hindered by energy barriers. These results are in qualitative agreement with the experimental results, in which the C-H insertion product is experimentally observed and the C-C insertion product is not formed in observable quantity in Pt + C₂H₆ system [27].

For the formation of C-C bond cleavage intermediates ¹CH₃PtC₂H₅ and ¹cis-CH₃PtC₂H₅, one can see that the reaction pathways of the direct C-C activation via ³TS16 and ³TS13 are inferior to those of the σ-complex assisted C-C σ-bond metathesis via ¹TS17 and ¹TS14 from 3-HPtC₃H₇ and 1-HPtC₃H₇, respectively, because of their higher EHHP (156.1 vs. 65.5 and 61.2 kJ·mol⁻¹). This is reminiscent of the important role of σ-complex assistance for the C-C σ-bond metathesis. In other words, the direct C-C bond activation is associated with a sizable barrier, which would prohibit this channel.

A glance to the reaction pathways shown in Schemes 1–3 reveals that two kinds of σ-complexes (1-HPtC₃H₇, HPtCH(CH₃)₂, and 3-HPtC₃H₇) and (cis-1-HPtC₃H₇ and cis-3-HPtC₃H₇) from initial C-H bond cleavage are crucial for the selective formation of the final C-H and C-C cleavage products.

First, from the identical intermediate 1-HPtC₃H₇, the reaction step of ¹1-HPtC₃H₇→¹TS3→¹(H₂)PtC₃H₆ is competitive with that of ¹1-HPtC₃H₇→¹TS14→¹cis-CH₃PtC₂H₅. Because ¹TS3 lies 160.9 kJ·mol⁻¹ below ¹TS14, (H₂)PtC₃H₆ is selectively preferred, whereas cis-CH₃PtC₂H₅ is selectively hampered. In other words, from 1-HPtC₃H₇, the dehydrogenation process dominates.

Second, from the identical intermediate cis-1-HPtC₃H₇, the reaction step of ¹cis-1-HPtC₃H₇→¹TS12→¹C₂H₆PtCH₂ is competitive with that of ¹cis-1-HPtC₃H₇→¹TS4→PtC₃H₆ + H₂. Since ¹TS12 locates 57.3 kJ·mol⁻¹ below ¹TS4, C₂H₆PtCH₂ is selectively favored. That is to say, from cis-1-HPtC₃H₇, the deethanization process predominates.

Third, from the identical intermediate HPtCH(CH₃)₂, these reaction steps of HPtCH(CH₃)₂→¹TS6→(H₂)PtC₃H₆, HPtCH(CH₃)₂→¹TS7→PtC₃H₆ + H₂, and HPtCH(CH₃)₂→¹TS21→CH₃CHPtCH₄ are competitive. As ¹TS6 lies 276.5 and 210.7 kJ·mol⁻¹ below ¹TS7 and ¹TS21, respectively, (H₂)PtC₃H₆ is selectively preferred. Then, from HPtCH(CH₃)₂, the dehydrogenation process dominates.

Fourth, from the identical intermediate 3-HPtC₃H₇, these reaction steps of 3-HPtC₃H₇→¹TS10→(H₂)Pt(CH₂)₃, 3-HPtC₃H₇→¹TS17→CH₃PtC₂H₅, and 3-HPtC₃H₇→¹TS23→C₂H₄PtH(CH₃) are competitive. Because ¹TS10 locates 117.0 and 34.3 kJ·mol⁻¹ below ¹TS17 and ¹TS23, respectively, (H₂)Pt(CH₂)₃ is selectively favored, whereas CH₃PtC₂H₅ and C₂H₄PtH(CH₃) are selectively hindered. Thereby, from 3-HPtC₃H₇, the dehydrogenation process dominates.

Last, from the identical intermediate cis-3-HPtC₃H₇, these reaction steps of cis-3-HPtC₃H₇→¹TS11 →PtC₃H₆ + H₂ and cis-3-HPtC₃H₇→¹TS19→¹C₂H₆PtCH₂ are competitive. Because ¹TS19 lies 70.5 kJ·mol⁻¹ below ¹TS11, ¹C₂H₆PtCH₂ is selectively preferred. Therefore, from cis-3-HPtC₃H₇, the deethanization process predominates.

In summary, once the σ-complex [1-HPtC₃H₇, or HPtCH(CH₃)₂, or 3-HPtC₃H₇] is formed, the major reaction channel results in the dehydrogenations products. Alternatively, as far as the σ-complex [cis-1-HPtC₃H₇ or cis-3-HPtC₃H₇] is concerned, the major reaction channel leads to the deethanization products. Besides, the demethanation process is kinetically ruled out.

To estimate quantitatively the reactivity and selectivity for the two kinds of products [PtC₃H₆ + H₂ and PtCH₂ + C₂H₆], the rate constants have been evaluated according to conventional transition state theory (TST) [50], including tunneling correction based on Winger’s formulation [51]. The formation of rate constant k(T) including tunneling correction coefficient κ(T) in transition state theory is given by

$$k(\text{T})=k^{\prime }(\text{T})*\kappa (\text{T})$$

(4)

The rate constant k′(T) is simply given by

$$k^{\prime }(\text{T})=\frac{k_{B}T}{h{c}^0}{e}^{\frac{-\mathrm{\Delta }{G}^{*}}{RT}}$$

(5)

where k_B is the Bolzmann constant, h is the Planck constant, T is thermodynamic temperature, c⁰ is standard concentration, and ΔG^≠ is Gibbs free energy. The tunneling correction coefficient κ(T) is written in the form of

$$\kappa (\text{T})=1+\frac{1}{24}{\left|\frac{h{\nu }^{\ne }}{k_{B}T}\right|}^2$$

(6)

where k_B is the Bolzmann constant, h is the Planck constant, T is thermodynamic temperature, and v^≠ is the imaginary frequency of the unbound normal mode at the saddle point. The branching ratio (α_i) of product i is calculated by

$${\alpha }_{\text{i}}=\frac{k_i(\text{T})}{\mathrm{\Sigma }{k}_i(\text{T})}$$

(7)

where k_i is the rate constant of product i.

From the identical reactants Pt + C₃H₈, the formation of PtC₃H₆ + H₂ and PtCH₂ + C₂H₆ are competitive, while their selectivity-controlling steps are Pt(³D) + C₃H₈→³TS1→³1-HPtC₃H₇ and Pt(³D) + C₃H₈ → ³TS9→³cis-3-HPtC₃H₇ on their MERPs, respectively. Thereby, the rate constants were taken into account, where Pt(³D) + C₃H₈ were taken as reactants, while ³TS1 and ³TS9 served as TSs, respectively. The rate constants for the formation of ³1-HPtC₃H₇ (k₁) and ³cis-3-HPtC₃H₇ (k₂) calculated over 300–1100 K temperature range can be fitted by the following expressions (in dm³·mol⁻¹·s⁻¹):

$$k_1=6.65\times {10}^8\hspace{0.17em}\text{exp}(-65,855/RT)$$

(8)

$$k_2=2.85\times {10}^8\hspace{0.17em}\text{exp}(-72,999/RT)$$

(9)

The branching ratios for the formation of PtC₃H₆ + H₂ and PtCH₂ + C₂H₆ are calculated to be 97.7~83.6% and 2.3~16.4%, respectively, over 300–1100 K temperature range. In other words, the dehydrogenation channel is predominant, and the deethanization channel is minor, while the demethanation channel is ruled out.

3.5. Activation Strain Analysis of the direct C-H and C-C Bond Cleavage

To gain insight into how the Pt atom affects the activation barriers of the initial C-H and C-C bond cleavage, i.e., insight into how this effect depends on the nature of concomitant geometrical deformation and electronic structures of Pt and C₃H₈, the trends in reactivity and competition among the initial C-H and C-C bond mechanisms are analyzed using the activation strain model of chemical reactivity [30,31]. In this model, activation energies ΔE^≠ of the TS are divided into the activation strain ΔE^≠_strain and the stabilizing TS interaction ΔE^≠_int: ΔE^≠ = ΔE^≠_strain + ΔE^≠_int. The activation strain ΔE^≠_strain is the strain energy associated with deforming the reactants from their equilibrium geometry to the geometry they adopt in the TS. The TS interaction ΔE^≠_int is the actual interaction energy between the deformed reactants in the TS [30,31].

The results of the activation strain analysis are listed in

Table 1. Geometry (in Å) at the BPW91/6-311++G(d, p), Lanl2dz level and activation strain analysis of transition state (in kJ·mol⁻¹) at the CCSD(T)//BPW91/6-311++G(d, p), Lanl2dz level for the C-H and C-C bond cleavage in C₃H₈ by Pt atom.

Activated bond	TS	Length in C3H8	Length in TS	Stretching in TS	Stretching in TS (in %)	ΔE≠strain	ΔE≠int	ΔE≠
C-H	3TS1	1.100	1.947	0.847	77.0	301.2	−240.0	61.2
C-H	3TS2	1.100	1.872	0.772	70.2	289.6	−219.9	69.7
C-H	3TS5	1.103	1.948	0.845	76.6	293.3	−223.8	69.5
C-H	3TS8	1.101	1.879	0.778	70.7	303.8	−238.3	65.5
C-H	3TS9	1.101	1.948	0.847	76.9	290.1	−221.5	68.6
C-C	3TS13	1.535	2.032	0.497	32.4	207.5	−51.4	156.1
C-C	3TS16	1.535	2.032	0.497	32.4	207.5	−51.4	156.1

. The activation energy ΔE^≠ increases from the initial C–H cleavage TSs (³TS1, ³TS2, ³TS5, ³TS9, and ³TS8) of 60~70 kJ·mol⁻¹ to the initial C–C cleavage TSs (³TS13 and ³TS16) of ~160 kJ·mol⁻¹. The activation strain ΔE^≠_strain decreases from the intial C–H cleavage TSs (³TS1, ³TS2, ³TS5, ³TS9, and ³TS8) of 290~300 kJ·mol⁻¹ to the initial C–C cleavage TSs (³TS13 and ³TS16) of ~200 kJ·mol⁻¹. The activation strain appears to be related to the bond strength of the activated bond and with the percentage-wise extent of bond stretching in the TS. Typical strengths and lengths of the C-H and C-C bonds are the following: 414 (C-H) and 347 kJ·mol⁻¹ (C-C), and ~1.1 (C-H) and ~1.5 Å (C-C) [52]. Moreover, we recall that the percentage-wise extent of bond stretching in the TS for oxidative insertion is 70~80% (C-H) and ~30% (C-C). Hence, both the bond strength and the percentage-wise bond elongation in the TS decreases from C-H to C-C. This correlates nearly with the activation strain ΔE^≠_strain, which decreases in the same order. It is indicated that the activation strain prefers the C-C oxidative insertion over the C-H oxidative insertion. That is to say, the activation strain ΔE^≠_strain makes in the reverse order as the activation energy ΔE^≠, for the C–H and C–C oxidative insertion. Alternatively, the strength of the TS interaction increases from ~−50 kJ·mol⁻¹ (C-C) to −220~−240 kJ·mol⁻¹ (C-H). From C-C to C-H bond activation, the strengthening of the TS interaction varies among 170–190 kJ·mol⁻¹, whereas the activation strain changes only by ~90 kJ·mol⁻¹. Thereby, the lowering activation energy from C-C to C-H bond activation stems mainly from the strengthening of the TS interaction.

Thus, the stabilizing interaction ΔE^≠_int prefers C-H oxidative insertion, whereas the activation strain ΔE^≠_strain favors C-C oxidative insertion. From C-C to C-H oxidative insertion, the lowering of activation barrier is mainly caused by the TS interaction ΔE^≠_int becoming more stabilizing.

4. Conclusions

The reaction mechanism of the gas-phase Pt atom with C₃H₈ has been systematically investigated on the singlet and triplet potential energy surfaces. Considering the initial interaction of Pt atom with C₃H₈, Pt atom prefers the attack of primary over secondary C-H bonds in propane. The major and minor reaction channels lead to the dehydrogenation products PtC₃H₆ + H₂ and the deethanization products PtCH₂ + C₂H₆, respectively, whereas the possibility to form the demethanation products PtC₂H₄ + CH₄ is so small it can be neglected. Over the 300–1100 K temperature range, the branching ratios for the formation of PtC₃H₆ + H₂ and PtCH₂ + C₂H₆ are calculated to be 97.7%~83.6% and 2.3~16.4%, respectively. The MERP for the formation of the main products PtC₃H₆ + H₂, involving one spin inversion, prefers to start at the triplet state and afterward proceed along the singlet state. The optimal C-C bond cleavages are assigned to C-H bond activation as the first step, followed by cleavage of a C-C bond. This reactivity mode is complementary for the classical reactivity picture through the direct C-C cleavage intermediate.

Furthermore, both the C-H insertion intermediates [1-HPtC₃H₇, cis-1-HPtC₃H₇, HPtCH(CH₃)₂, 3-HPtC₃H₇, cis-3-HPtC₃H₇] and the C-C insertion intermediates [CH₃PtC₂H₅, cis-CH₃PtC₂H₅, C₂H₄Pt(H)(CH₃), and CH₄PtC₂H₄] are thermodynamically preferred. However, the C-H insertion intermediates are kinetically favored over the C-C insertion intermediates. These results are in qualitative agreement with the experimental results, in which the C-H insertion product is experimentally observed and the C-C insertion product is not formed in observable quantity in Pt + C₂H₆ system.

Unlike the role of the activation strain ΔE^≠_strain, the stabilizing interaction ΔE^≠_int favors the initial C-H oxidative insertion over the initial C-C oxidative insertion. From C-C to C-H oxidative insertion, the lowering of activation barrier is mainly caused by the TS interaction ΔE^≠_int becoming more stabilizing.