The ligand effect on the selective C–H versus C–C bond activation of propane by NiBr⁺: a theoretical study

Abstract

Density functional theory has been employed to investigate the ligand effect in the reaction of ligated NiBr⁺ with propane. Both initial C–H and C–C bond activation mechanisms for losses of HBr, H₂, and CH₄ are analyzed in terms of the topology of the potential energy surface. Losses of HBr and H₂ involve three C–H activation mechanisms, that is, α,β-H, α,γ-H, and β,α-H abstractions, where the last β,α-H abstraction is the most favorable mechanism. Loss of CH₄ involves initial C–C activation, but it is prevented by the high-energy barrier. When propane reacts with the open-shell ligated NiBr⁺, the ligand of Br in the initial C–H activation could direct abstract a H atom from propane substrate via a four-center transition state, without forming multi-σ-type bonding of Ni⁺, whereas the metal center in the initial C–C activation needs to experience an unfavorable three σ-type bonding (with Br, CH₃, and CH₂CH₃), which explains why HBr and H₂ are formed in the reaction of BrNi⁺/C₃H₈ and CH₄ not.

1 Introduction

Transition metal ions are of fundamental interesting in chemical and biology researches in the field of catalytic process. Because transition metal ions contain incompletely filled d or f orbits, they can supply electrons to ligands and accept electrons from ligands and thus have favorably catalytic activity. In order to deeply understand their intrinsic binding properties and reactivities, over the past three decades, a huge number of papers have been devoted to the investigation of the reactions of transition metal ions with organic molecules in the gas phase by using the experimental and theoretical methods [1–7]. In particular, the gas-phase reaction of bare transition metal ions with alkanes has undergone extensive investigation [8–31], which involves in the first three transition periods of metal. Interestingly, further study found that the introduction of ligands could change the reaction activity of metal ion greatly. Closed-shell ligand L (such as carbonyl, alkene, and phosphine) can through the electronic supply or feedback effect change electronic structure of the metal ion and may bring spatial constraints to the metal ions. Open-shell ligand X (such as halogen, hydroxyl, and cyclopentadienyl) can also change the electronic states of the metal ions via formation of the polarized covalent bonds, thereby leading to the change of thermal chemical property, ionization energy, binding energy, and even spin state of the metal ions. Generally, closed-shell ligand L only has an effect on the reaction efficiency of metal ions, whereas the influence of open-shell ligand X is according to the actual situation.

In all kinds of open-shell ligands, halogen X (X = F, Cl, Br, and I) is well known as the prototype of the class of covalent ligands [32–35]. Because of the large electronegativity and poor donor properties, halogen could form strongly polarized covalent bond to metals, and thus, it controls the reaction efficiency largely and even changes the product of the reaction. For example, bare Cr⁺ is one of the least reactive transition metal ions, whereas CrCl⁺ is significantly more reactive [36], and CrF⁺ is even capable of dehydrogenating propane [37]. Under thermal conditions, both PtCl⁺ and PtCl₂ ⁺ could react with methane giving rise to HCl, while in the case of PtBr⁺, formation of the corresponding carbine takes place. In order to understand the influence that ligand X (X = F, Cl, Br, and I) brings to the reactivity of NiX⁺/RH (R = H, C₂H₅, nC₃H₇, and nC₄H₉) system, Schlangen et al. [38] have studied the gas-phase reaction of NiX⁺/RH by using the electrospray ion (ESI) mass spectrum technology. They inferred that the reaction of NiBr⁺/C₃H₈ exclusively involves initial C–H activation for losses of HBr and H₂, rather than initial C–C activation (for formation of CH₄). In this paper, we select the NiBr⁺ + C₃H₈ reaction as a model of our theoretical study to discuss the C–H and C–C bond activation mechanisms (see Scheme 1). We hope to determine the essential factors that ligand controls the selectivity of the NiBr⁺/C₃H₈ reaction.

Scheme 1

Schematic reaction mechanism of C₃H₈ with NiBr⁺

1.1 Computational details

The geometry optimization and frequency calculations were carried out for all the relevant species using the B3LYP [39, 40] functional together with the DZVP(d)(opt + 3f) basis set [41] for Ni⁺ and the 6-311++G(2d,2p) basis set [42] for nonmetal atoms. All the energies are reported with zero-point energy (ZPE) corrections with a scaling factor of 0.961 [43]. The DZVP(d)(opt) sets built up by Chiodo et al. have presented a good reliability for the B3LYP method in predicting transition metal ion ground- and excited-state order and splitting [41, 44]. The selected method has been proven to combine reasonable computational cost with accuracy sufficient for describing open-shell metal systems [43]. The intrinsic reaction coordinate (IRC) was performed to check the pathways between transition states and their connecting minima. Besides, the natural bond orbital (NBO) theory [45, 46] was used to shed new light on the characters of some important species involved. Dispersion energy was calculated to evaluate the dispersion contribution using ωB97X-D method with the DZVP(d)(opt + 3f): 6-311++G(2d,2p) basis set [47–49]. We confirmed the minimum energy crossing point (MECP) via single-point energy calculation of both considered states at the DZVP(d)(opt + 3f): 6-311++G(2d,2p) level for the relevant IRC points along the singlet pathway until they reach an equal energy. All these calculations were performed using the Gaussian 09 package [50].

The calculation methods of spin–orbit coupling (SOC) and crossing probability at the MECP, which has been described previously [51], are presented in detail in supporting information (SI). In brief, by using the GAMESS package [52], CASSCF calculations were first performed for both states at the MECP to get the converged CASSCF wave functions. The SOC value is the matrix element that expresses the coupling of the singlet and triplet states by the operator of Eq. 1 [53],

$$ \left\langle {{\mathbf{H}}_{\text{SO}} } \right\rangle_{{S,S^{{\prime }} }} = \left\langle {{}^{1}\varPsi_{1} ({\mathbf{M}}_{S} )\left| {{\mathbf{H}}_{\text{SO}} } \right|^{3} \varPsi_{2} ({\mathbf{M}}_{{S^{{\prime }} }} )} \right\rangle . $$

(1)

Here, ¹ Ψ ₁ (³ Ψ ₂) is the M _S (M _S′ ) component of the many-body singlet-state (triplet-state) wave function. Considering the generated spin sublevels M _S , a reasonable measure of the SOC-induced triplet–quintet interaction is the root-mean-square coupling constant (SOCC) of Eq. 2.

$$ {\text{SOCC}} = \left[ {\sum\limits_{{S,S^{{\prime }} }} {\left\langle {{\mathbf{H}}_{\text{SO}} } \right\rangle_{{S,S^{{\prime }} }}^{2} } } \right]^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} . $$

(2)

A crude estimation of the crossing probability at the MECP can be done using the Landau–Zener formula [54–56],

$$ \begin{gathered} P = 1 - e^{{ - 2\delta }} , \hfill \\ \delta = \frac{{\pi \left| {V_{{ij}} } \right|^{2} }}{{\hbar \nu \left| {\Delta g_{{ij}} } \right|}} = \frac{{\pi \left| {{\text{SOCC}}} \right|^{2} }}{{(2{\text{min}}(S_{i} ,S_{j} ) + 1)\hbar \nu \left| {\Delta g_{{ij}} } \right|}}, \hfill \\ \end{gathered} $$

(3)

where V _ij is a matrix element of a diabatic operator (SOC in this case) coupling two adiabatic states i and j, Δg _ij is the difference in the gradients of the two adiabatic states i and j, and v is the effective velocity with which the system is passing through the crossing point that can be calculated from the kinetic theory of gases at 298 K.

2 Results and discussion

In the following sections, we will first establish the accuracy that is expected from the chosen level of theory for the NiBr⁺/C₃H₈ system. Then, we will present structures and energies of reactants, products, and encounter complexes. Last, we will examine the title reaction in detail, including geometries of various stationary points and PESs. For simplicity, optimized geometries, selected structural parameters, calculated total energies, zero-point energies as well as 〈S ²〉 values for all the species involved in the reaction are given in SI.

2.1 Calibration

To evaluate the reliability of the level of theory employed, we compare the experimental thermochemical data with the results from the B3LYP approach. Table 1 collects the theoretically predicted adiabatic bond dissociation energies (BDEs) and the most reliable experimental data for some relevant species [57–69].

Table 1 Adiabatic bond dissociation energies (kcal/mol) at 0 K determined by calculations and experiments

As shown in Table 1, the calculated excitation energy of Ni⁺ (²D(d ⁹) → ⁴F(d ⁸ s ¹)) agrees well with the experimental gap value (20.1 vs 24.9 kcal/mol [57]). Moreover, the theoretical BDEs of H–Br and H–C₃H₇ accord well with the experimental findings. Our calculated bonding in Ni⁺–X (X = H, CH₂, CH₄, C₂H₄, and C₂H₆) is overestimated by about 4–7 kcal/mol, which may be considered as a systematic shortcoming of the B3LYP functional. It should be noted that the calculated BDE of Ni⁺–Br is underestimated by 13.4 kcal/mol based on the datum derived by Allison and Ridge [69]. Thus, the relative stability of the HBr + [C₃, H₇, Ni]⁺ asymptote with respect to the remainder of the [C₃, H₈, Br, Ni]⁺ potential energy surface (PES) is probably underestimated by about 13 kcal/mol. However, the relative energies of the other parts of the PES are still described more satisfactorily. Such a situation has also been found for the PESs of the Co⁺/C₂H₆, Co⁺/C₂H₆/N₂O, Fe⁺/C₂H₆, and Fe⁺/C₂H₆/N₂O systems calculated using density functional theory (DFT) [70–73].

To evaluate the dispersion contribution in the NiBr⁺/C₃H₈ system, dispersion energies (DBs) were calculated using ωB97X-D method [47–49]. Calculated DB values for the species involved in the α,γ-H abstraction mechanism are given in Table S2. It is found that the DBs of NiBr⁺, H₂, and HBr are zero nearly, while the values of C₃H₈ and other product ions ([NiCH₂CH₂CH₃]⁺ (¹ Ia) and [NiBrCH₂CH₂CH₂]⁺ (Ja)) are 2.5 and 3.0–3.6 kcal/mol, respectively. For the intermediates and transition states involved, the DBs are calculated to be 3.8–4.6 kcal/mol. All these suggest that the dispersion contribution is relatively small and has a negligible effect on the relative energies of the [C₃, H₈, Br, Ni]⁺ PES.

2.2 Reactants, encounter complexes, and products

In this section, we will discuss the structures and energies of reactants, encounter complexes, and products involved in the reaction of NiBr⁺/C₃H_8. The optimized geometric configurations and structural parameters are shown in Fig. 1.

Fig. 1

Geometries and selected structural parameters optimized at the B3LYP: B3LYP/DZVP(d)(opt + 3f): 6-311++G(2d,2p) level for the reactants, encounter complexes, and some product species involved in the NiBr⁺ + propane reaction. Bond lengths are in angstroms, and bond angles are in degrees

For bare Ni⁺, it has a doublet ground state with the ²D(d ⁹) → ⁴F(d ⁸ s ¹) excitation energy of 20.1 (calcd) and 24.9 (expt) kcal/mol [57]. However, NiBr⁺ bears a high-spin ground state (triplet). NBO analysis suggests that Ni⁺ and Br form strong polarized covalent bonds through the 4s3d(Ni⁺) and 4s4p(Br) orbits. The bond in triplet comprises one σ(Ni⁺Br) and one β–π(Ni⁺Br) binding orbitals, whereas the singlet state only forms one σ(Ni⁺Br) binding orbital, which leads to a short Ni–Br⁺ equilibrium distance [2.156 (triplet) vs 2.188 (singlet) Å] and strong diabatic BDE (74.2 vs 14.8 kcal/mol) of the triplet species and a large triplet → singlet excitation energy of 39.1 kcal/mol.

Three encounter complexes (1a, 1b, and 1c) are formed in the reaction of NiBr⁺/C₃H₈. 1a is featured by a BrNi⁺(η ⁴–C₃H₈) structure, where Ni⁺ is simultaneously coordinated to 2α,2γ-H (noted as BrNi⁺(η ⁴–2α,2γ-H–C₃H₈)). Both ¹ 1b and ¹ 1c possess a BrNi⁺(η ²–α,β-H–C₃H₈) structure, in which the BrNi⁺ axis inclines to H^α and H^β, respectively, while ³ 1b and ³ 1c bear a respective BrNi⁺(η ³–α,2β-H–C₃H₈) and BrNi⁺(η ³–2α,β-H–C₃H₈) structure. Energetically, the diabatic BDEs of 1a, 1b, and 1c are calculated to be in the range of 57.2–59.4 kcal/mol (singlet) and 43.5–41.3 kcal/mol (triplet), indicating the nearly identical stability as well as the coexistence for these isomers in the gas phase.

NBO analysis shows that the association of NiBr⁺ with C₃H₈ (1a, 1b and 1c) is dominated by the electrostatic interaction as well as donor–acceptor stabilization, i.e., electrons donation from the coordinated σ(CH) orbitals to unoccupied 4s3d(Ni⁺) and σ*(Ni⁺Br) orbits as well as the back-donation from the filled 4s3d(Ni⁺) orbit to the σ ^*(CH) orbit [∆E ⁽²⁾ = 148.6 (90.2) (1a), 147.4 (77.7) (1b), and 143.7 (73.1) (1c) kcal/mol in the singlet (triplet)]. This results in the weakening interaction of the corresponding C–H bond and in preparation for the next step of hydrogen transfer. Furthermore, the much stronger donor–acceptor interaction in the singlet explains its stronger diabatic BDE.

Ni(C₃H₇)⁺ is the product of HBr elimination in the reaction of NiBr⁺/C₃H₈. It contains three kinds of isomers, i.e., Ia and Ib via α-H abstraction and Ic via β-H abstraction, respectively. Ia is featured by cis-Ni⁺(η ²–α-C,γ-H–CH₂CH₂CH₃), forming a five-membered structure, while Ib bears a trans-Ni⁺(η ¹–α-C–CH₂CH₂CH₃) structure. For Ic, the metal ion strongly binds to the radical C^β atom of CH₃CHCH₃ (noted as Ni⁺(η ¹–β-C–CH₂CH₂CH₃)). Although the nearest Ni⁺–C distances in ³ Ia − ³ Ic (1.93–1.97 Å) are calculated to be longer than those in the singlet (1.86–1.87 Å), the triplet diabatic BDEs are larger than those of the singlet [84.0 vs 61.4 (Ia), 81.0 vs 63.3 (Ib), 80.5 vs 64.5 (Ic) kcal/mol]. This is because that the diffuse single-occupied 4s orbital in Ni⁺(⁴F(d ⁸ s ¹)) favors forming a relative strong covalent bond with the radical-C atom of C₃H₇. NBO analysis shows that the Ni⁺–(C₃H₇) association is dominated by the covalent interaction via a σ(Ni⁺C) binding orbital, which is consisted by the 2p(radical-C) orbital and the 3d(Ni⁺) orbital in the singlet and the α-4s and β-3d(Ni⁺) orbitals in the triplet.

For the H₂-loss product, two candidates can be envisaged: BrNi(CH₂CH₂CH₂)⁺ complex (Ja) via α,γ-H abstraction and BrNi(CH₂CHCH₃)⁺ complex (Jb) via α,β- and β,α-H abstractions. In ¹ Ja, Ni⁺ of NiBr⁺ simultaneously attacks at both terminal C atoms of CH₂CH₂CH₂ (with Ni⁺–C distance of 1.883 Å), forming a quadrilateral-type structure. In the triplet, however, the C₃H₆ ligand forms a cyclopropane structure and NiBr⁺ is coordinated to one side of cyclopropane. The corresponding diabatic BDE is calculated to be 74.0 and 51.2 kcal/mol in its singlet and triplet states, respectively. NBO analysis suggests that the metal ion in the singlet state forms two strong polarized covalent bonds with two-coordinated C atoms, while the association of NiBr⁺ with C₃H₆ in the triplet state is dominated by electrostatic interaction as well as donor–acceptor stabilization (∆E ⁽²⁾ = 65.3 kcal/mol). The triplet BrNi⁺(CH₂CHCH₃) (Jb) is featured by an alkenyl-CC π-type bound structure (with Ni⁺–C distances of 2.093 and 2.402 Å) (∆E ⁽²⁾ = 70.4 kcal/mol), while the singlet counterpart favors a multicenter association of metal ion with C^α, C^β, and H^γ of C₃H₆ (with distances of 2.053, 1.942, and 1.792 Å, respectively), suggesting the stronger interactions of metal with both the alkenyl-π and σ(C^γH) orbitals (∆E ⁽²⁾ = 115.6 and 41.9 kcal/mol, respectively). Thus, the diabatic BDE of the singlet (81.7 kcal/mol) is stronger than that of the triplet (55.4 kcal/mol).

BrNi(CH₂CH₂)⁺ is the C–C activation product via loss of methane. In both multiplicities, the species have the C _s symmetry and NiBr⁺ attaches the two ethylene C atoms simultaneously through the metal with the difference that the NiBr⁺ bond in the triplet is co-plane with the Ni⁺CC plane, whereas the singlet association favors an out-of-plane location of the NiBr⁺ bond (the dihedral angle of NiBr⁺ with the Ni⁺CC plane is 94.9°). This association results in elongation of the C–C bond as well as distortion of the C–C–H angle (especially for the singlet species). NBO analysis indicates that the complex is stabilized by the electron donor–acceptor interaction, i.e., donation of π(CC) → 4s3d(Ni⁺) and σ*(Ni⁺Br) as well as back-donation of 4s3d(Ni⁺) → π*(CC) (∆E ⁽²⁾ = 149.9 (singlet) and 27.6 (triplet) kcal/mol). Compared to the triplet species, the larger donor–acceptor interaction in the singlet leads to a stronger diabatic BDE [69.8 (singlet) vs 48.2 (triplet)] as well as a larger change of structure.

2.3 Gas-phase reaction mechanism

In this section, we will discuss all possible mechanisms for the H₂, HBr, and CH₄ eliminations in the gas-phase reaction of NiBr⁺ with C₃H₈.

2.3.1 Initial C–H activation

Three possible initial C–H activation pathways for losses of H₂ and HBr have been surveyed, that is, α,β-H, α,γ-H, and β,α-H abstractions. PESs together with the schematic structures involved in the reaction pathways are shown in Figs. 2, 3 and 4.

Fig. 2

Energy profile for the α,γ-H abstraction mechanism involved in the reaction of NiBr⁺ with propane. Numbers refer to the relative stabilities with respect to the separated reactants of ³NiBr⁺ + propane evaluated at the B3LYP/DZVP(d)(opt + 3f): 6-311++G(2d,2p) level including ZPE corrections. Scaling factor for the ZPE is 0.961. Relative energies are in kcal/mol

Fig. 3

Energy profile for the α,β-H abstraction mechanism involved in the reaction of NiBr⁺ with propane. Parameters follow the same notations as in Fig. 2

Fig. 4

Energy profile for the β,α-H abstraction mechanism involved in the reaction of NiBr⁺ with propane. Parameters follow the same notations as in Fig. 2

α,γ-H abstraction As shown in Fig. 2, α,γ-H abstraction starts from encounter complex 1a. 1a could involve into species 2a ((HBr)Ni(CH₂CH₂CH₃)⁺) via a σ-complex-assisted metathesis (σ-CAM) mechanism [74], which experiences a direct H-transfer from the metal-coordinated propane to the Br ligand via a four-center transition state (TS _1a–2a ). In this process, approaching of the metal side of NiBr⁺ to C₃H₈ induces a preferential attack of C^α–H bond and promotes the cleavage of the C^α–H bond, subsequently through direct C^α– to –Br hydrogen transfer 2a is formed. The H–Br–Ni–C^α four-centered structure of TS _1a–2a favors forming the σ(Ni⁺C^α) and σ(HBr) [σ(Ni⁺C^α), σ(HBr), and β-σ(Ni⁺Br)] binding orbitals in the singlet (triplet) state. Furthermore, the system is stabilized by strong electron donation of 4p(Br) and σ(HBr) → 4s*(Ni⁺) and σ*(Ni⁺C^α) and back-donation of 3d(Ni⁺) and σ(Ni⁺C^α) → σ*(HBr) (∆E ⁽²⁾ = 279.1 (singlet) and 69.3 (triplet) kcal/mol). It can be found that Ni⁺ in TS _1a–2a forms one (singlet) and two (triplet) covalent bonds with the ligand and avoids binding with multi (three)-σ-type covalent ligands (for example, (Br)Ni⁺(H)(C₂H₅)). Thus, it is an energetically favorable process (E _rel(TS _1a–2a ) = −11.4 (singlet) and −6.1(triplet) kcal/mol).

Species 2a is featured by a two-coordinated structure ((HBr)Ni⁺(η ²–α-C,γ-H–CH₂CH₂CH₃)). Different with the binding situation in NiBr⁺ and BrNi⁺(C₃H₈) (1a–1c), the metal center in 2a involves two σ-type bonding, for which perfects pairing of electrons in preferred in the low-spin (singlet) ground state. Further NBO analysis shows that Ni⁺ in the singlet forms strong covalent bonds with both C₃H₇ and HBr groups via the σ(Ni⁺C^α) and σ(Ni⁺Br) binding orbitals, respectively, whereas in the triplet, the metal center only forms the covalent bond with C₃H₇ (via σ(Ni⁺C^α)) and the binding of Ni⁺–(HBr) is dominated by donor–acceptor stabilization (∆E ⁽²⁾ = 72.0 kcal/mol). Thus, ¹ 2a is 6 kcal/mol more stable than ³ 2a and 24.9 kcal/mol below the reactants ³NiBr⁺ + C₃H₈.

It can be found from Fig. 2 that a triplet-to-singlet crossing occurs in the ³ 1a → ¹ TS _1a–2a process. For the relevant MECP _1a–2a , the activated C–H bond is stretched to 1.184 Å, and the newly formed H–Br bond length is reduced to 2.237 Å (see Fig. S1). The SOC constant (SOCC) of MECP _1a–2a is calculated to be 133.8 cm⁻¹, and the crossing probability is estimated to be 59 % at the room temperature.

One exit of 2a is the direct dissociation into Ni(CH₂CH₂CH₃)⁺ (Ia) and HBr, with the whole endothermicity of 2.8 (2.5) kcal/mol on the singlet (triplet) PES. The other is yielding 3a via a H^γ transfer to metal center. The corresponding transition state TS _2a–3a is located at −4.0 (19.9) kcal/mol on the singlet (triplet) PES. Species 3a bears a (HBr)Ni⁺(H)(η ²–α,γ-C–CH₂CH₂CH₂) structure, which is located at −4.2 (singlet) and 0.6 (triplet) kcal/mol. NBO analysis shows that Ni⁺ in ¹ 3a forms strong covalent bonds with all three coordinated ligands via the σ(Ni⁺Br), σ(Ni⁺H), σ(Ni⁺C^α), and σ(Ni⁺C^γ) binding orbitals, whereas in ³ 3a, metal center only binds covalently with the H and HBr groups via the σ(Ni⁺H) and β–σ(Ni⁺Br) binding orbitals, respectively, and the association of Ni⁺–(C₃H₆) is stabilized by donor–acceptor interaction (∆E ⁽²⁾ = 46.3 kcal/mol).

Along reaction coordination, 3a could involve into complex 4a ((Br)Ni⁺(H₂)(η ²–α,γ-C–CH₂CH₂CH₂)) via a direct hydrogen coupling between the HBr and Ni⁺H groups. The transition state TS _3a–4a in this process lies at 3.7 (6.8) kcal/mol in the singlet (triplet) state. Both two spin structures of 4a have C _s symmetry, and two H atoms that absorbed on Ni⁺ have formed covalent bond. The difference is that the H–H bond is co-plane with the Br–Ni⁺–C^β symmetry plane in the singlet and perpendicular in the triplet. Different with a low-spin ground state of 3a, ³ 4a (E _rel = −17.5 kcal/mol) is 14.6 kcal/mol more stable than ³ 2a. Subsequently, 4a could form BrNi(CH₂CH₂CH₂)⁺ (Ja) and H₂ via a direct dissociation. The overall reaction is endothermic by 2.5 kcal/mol on the singlet PES and exothermic by 13.9 kcal/mol on the triplet PES.

α,β-H abstraction α,β-H abstraction begins with 1b (see Fig. 3). NiBr⁺ attacks C^α–H bond of C₃H₈ in 1b induces H shift from C^α to Br, yielding 2b. 2b is also featured by a two-coordinated structure [(HBr)Ni⁺(η ¹–α-C–CH₂CH₂CH₃)], which favors a low-spin (singlet) ground state (E _rel = −28.6 (singlet) and −15.5 (triplet) kcal/mol). The corresponding transition state TS _1b–2b is located at −15.2 and −2.5 kcal/mol on the singlet and triplet PESs, respectively. Thus, a triplet-to-singlet crossing is expected to occur immediately before TS _1b–2b . The relevant MECP _1b–2b is located when the activated C–H bond is stretched to 1.204 Å, and the newly formed H–Br bond length is reduced to 2.181 Å. The SOCC of MECP _1b–2b is calculated to be 127.6 cm⁻¹, and the crossing probability is found to be 64 %.

Direct decomposition of (HBr)–Ni⁺(CH₂CH₂CH₃) accounts for Ni(CH₂CH₂CH₃)⁺ (Ib) + HBr, but it is a slight endothermic channel with a reaction heat of 0.9 (3.0) kcal/mol on the singlet (triplet) PES. Alternatively, direct C^β-to-Ni⁺ H-shift from 2b could yield species 3b ((HBr)Ni⁺(H)(η ²–α,β-C–CH₂CHCH₃)). In both multiplicities, the 3d(Ni⁺) and 1s(H) orbitals form a σ(Ni⁺H) binding orbital, while the linkage of metal center with the other two groups (HBr and CH₂CHCH₃) is strengthened by the strong electron donation from the 4s4p(Br) and π(CC) orbitals to 4s4p(Ni⁺) orbitals as well as back-donation from the 3d(Ni⁺) orbital to the π*(CC) orbital (∆E ⁽²⁾ = 256.7 (singlet) and 150.8 (triplet) kcal/mol). Energetically, species 3b is located at −25.1 (−16.2) kcal/mol on the singlet (triplet) PES, while the relevant transition state (TS _2–3b ) lies at −21.8 (−5.1) kcal/mol.

Subsequently, species 3b involves into molecular hydrogen complex 4b ((Br)Ni⁺(H₂)(η ²–α,β-C–CH₂CHCH₃)). Mainly, electrostatic interaction as well as donor–acceptor stabilizations for the (H₂)–BrNi⁺–(CH₂CHCH₃) association results in a triplet ground state for 4b, similar to NiBr⁺ (excitation energy for ³ 4b → ¹ 4b: 17.3 kcal/mol). The situation of transition state TS _3b–4b is a compromise between 3b and 4b, where the triplet transition state lies above the singlet one by 9.2 kcal/mol. Loss of H₂ from 4b accounts for BrNi⁺(CH₂CHCH₃) (Jb), exothermic by 15.9 (28.7) kcal/mol in the singlet (triplet) state.

β,α-H abstraction β,α-H abstraction pathway starts with 1c (see Fig. 4). Direct C^β– to –Br hydrogen shift could carry 1c into 2c ((HBr)Ni⁺(η ¹–β-C–CH₃CHCH₃)), which also favors a singlet ground state [E _rel = −32.7 (singlet) and −22.8 (triplet)]. The relevant transition state TS _1c–2c is located at −17.8 (−3.8) kcal/mol on the singlet (triplet) PES. As shown in Fig. 4, a triplet-to-singlet crossing occurs in the ³ 1c → ¹ TS _1c–2c process. The activated C–H bond and newly formed H–Br bond in the relevant MECP _1c–2c are calculated to be 1.221 and 2.243 Å, respectively (see Fig. S1). The SOCC of MECP _1c–2c is calculated to be 134.3 cm⁻¹, and the crossing probability is estimated to be 73 % at the room temperature, indicating that the β,α-H abstraction accounts for the most large crossing probability in all three H abstraction mechanisms.

Direct loss of HBr from 2c accounts for Ni(CH₃CHCH₃)⁺ (Ic), which is exothermic by 4.2 kcal/mol on the singlet PES and endothermic by 3.0 kcal/mol on the triplet PES. The other exit of 2c is α-H shift to metal center forming 3c. Similar to 3b, 3c is featured by a (HBr)Ni⁺(H)(η ²–α,β-C–CH₂CHCH₃) structure and bears singlet as ground state (E _rel = −25.1 (singlet) and −14.8 (triplet) kcal/mol). The relevant transition state TS _2c–3c is located at −23.5 (−12.1) kcal/mol on the singlet (triplet) PES. Subsequently, direct H coupling between the BrH and Ni⁺H groups carries 3c into 4b via transition state TS _3c–4c (lying at −12.1 (singlet) and −8.9 (triplet) kcal/mol). Direct loss of H₂ from 4b forming BrNi(CH₂CHCH₃)⁺ (Jb) has been discussed above.

From Figs. 2, 3, 4 and 5, we can find that all of the α,β-, α,γ-, and β,α-H abstraction mechanisms could account for losses of HBr and H₂. Two spin crossing occurs in all three mechanisms, that is, initial C–H activation and hydrogen coupling. The probability of the former crossing is calculated to be 64, 59, and 73 % for the α,β-, α,γ-, and β,α-H abstraction mechanisms, respectively, indicating that the triplet pathway can easily proceed to the singlet surface near the intersection, which reduced the reaction energy barrier. In all three H abstraction mechanisms, the most favorable mechanism is the β,α-H abstraction because it is not only energetically favorable but could also take place adiabatically on both the singlet and triplet PESs. If the underestimate of the stability of the HBr + [C₃, H₇, Ni]⁺ exit channel (about 13 kcal/mol) is considered, loss of HBr is also a strong exothermic process for all three H abstraction mechanisms. Furthermore, the HBr-loss pathway is much simple compared to that of loss of H₂. Therefore, the HBr/H₂ branching ratio of 58:42 is determined by the ESI mass spectrum experiment [38].

Fig. 5

Energy profile for the initial C–C activation involved in the reaction of NiBr⁺ with propane. Parameters follow the same notations as in Fig. 2

2.4 Initial C–C activation

We also considered the C–C activation pathway to loss of CH₄. PES together with schematic structures involved in the reaction is shown in Fig. 5. This channel involves encounter complex 1b. Starting with 1b, the nickel ion inserts into one C–C bond of propane forming species 2d ((CH₃)Ni⁺(Br)(CH₂CH₃)) via transition state TS _1b–2d . In this process, metal center involves three σ-type bonding (with Br, CH₃, and CH₂CH₃), which is unfavorable for Ni⁺(²D(d ⁹) and ⁴F(d ⁸ s ¹). NBO analysis indicates that Ni⁺ in both ¹ TS _1b–2d (³ TS _1b–2d ) and ¹ 2d (³ 2d) has a high population of 4p orbital (3d ^8.724s ^0.294p ^0.53 (3d ^8.464s ^0.484p ^0.25) and 3d ^8.724s ^0.354p ^0.39 (3d ^8.594s ^0.364p ^0.43)). Therefore, it is a high-energy pathway [E _rel(TS _1b–2d and 2d) = −2.0 (+8.6) and −20.2 (−3.2) kcal/mol in the singlet (triplet)]. PES shows that a triplet-to-singlet crossing emerges before TS _1b–2d . The relevant SOCC is calculated to be 116.7 cm⁻¹ with the crossing probability of 45 %.

A subsequent β-H shift to methyl could form species 3d via transition state TS _2b–3d (E _rel = −6.4 (singlet) and −1.6 (triplet) kcal/mol). Species 3d bears a (CH₄)Ni⁺(Br)(η ²–C,C–CH₂CH₂) structure, lying at −44.3 and −31.9 kcal/mol on the singlet and triplet PES, respectively. 3d undergoes direct bond cleavage forming CH₄ and BrNi(C₂H₄)⁺, with the whole exothermicity of 15.9 (33.4) kcal/mol on the singlet (triplet) PES.

As shown in Fig. 5, we can found that although loss of CH₄ is an exothermic process, it needs to overcome a high-energy barrier in the initial C–C activation [E _rel(TS _1b–2d ) = −2.0 (+8.6) kcal/mol in the singlet (triplet)], which is 15.8 (12.4) kcal/mol higher than that of the initial C^β-H abstraction (TS _1c–2c ). As it is well known from the Arrhenius formula for the evaluation of kinetics, a difference of about 10 kcal/mol between two barriers implies that rates change by several orders of magnitude. Thus, it is quite clear that why HBr and H₂ are formed in the BrNi⁺/C₃H₈ reaction and CH₄ not.

It is well known that Ni⁺ has a ground and excited electron configuration of ²D(d ⁹) and ⁴F(d ⁸ s ¹), respectively, suggesting that it is unfavorable forming multi-σ-type bonding with other covalent ligands. When introducing an open-shell Br ligand to Ni⁺, the initial C–C activation of propane by BrNi⁺ needs to experience an unfavorable three σ-type bonding (with Br, CH₃, and CH₂CH₃), resulting in the reaction being restrained. However, the initial C–H activation favors a σ-CAM mechanism, where the ligand of Br could direct abstract a H from the propane substrate through a four-center transition state, without forming multi-σ-type bonds of metal center, explaining the favorable C–H activation for the HBr and H₂ losses in the reaction of BrNi⁺/C₃H₈.

3 Conclusions

DFT has investigated the reaction of NiBr⁺/C₃H₈, which add new insight into the experimental observations. We can make a conclusion by summarizing some of the main points in the following: Both HBr and H₂ could be formed via three initial C–H activation mechanisms, that is, α,β-, α,γ-, and β,α-H abstractions, where the most favorable mechanism is the β,α-H abstraction. Losses of HBr and H₂ are favored by undergoing a four-center transition state in the initial C–H activation process, avoiding forming multi-σ-type bonding of metal center. However, loss of CH₄ is prevented by experience unfavorable three σ-type bonding of Ni⁺ (with Br, CH₃, and CH₂CH₃) in the initial C–C activation process.