On the Intrinsic Reactivity of Diatomic 3d Transition-Metal Carbides in

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On the Intrinsic Reactivity of Diatomic 3d Transition-Metal Carbides in the Thermal Activation of Methane: Striking Electronic Structure Effects Caiyun Geng, Thomas Weiske, Jilai Li, Sason Shaik, and Helmut Schwarz J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b11739 • Publication Date (Web): 06 Dec 2018 Downloaded from http://pubs.acs.org on December 6, 2018

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Journal of the American Chemical Society

On the Intrinsic Reactivity of Diatomic 3d Transition-Metal Carbides in the Thermal Activation of Methane: Striking Electronic Structure Effects Caiyun Geng,† Thomas Weiske,† Jilai Li,‡,†,* Sason Shaik,§,* and Helmut Schwarz†,* ‡Institute

of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of

China †Institut für Chemie, Technische Universität Berlin, Straße des 17. Juni 115, 10623 Berlin, Germany §Institute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel ABSTRACT: Mechanistic aspects of the C-H bond activation of methane by metal-carbide cations MC+ of the 3d transition-metals Sc - Zn were elucidated by NEVPT2//CASSCF quantum-chemical calculations, and verified experimentally for M = Ti, V, Fe and Cu by using Fourier transform ion-cyclotron resonance mass spectrometry. While MC+ species with M = Sc, Ti, V, Cr, Cu, and Zn activate CH4 at ambient temperature, this is prevented with carbide cations of M = Mn, Fe, and Co by high apparent barriers; NiC+ has a small apparent barrier. Hydrogen-atom transfers from methane to metal-carbide cations were found to proceed via a proton-coupled electron transfer mechanism for M = Sc - Co; wherein the doubly-occupied πxz/yz-orbitals between metal and carbon at the carbon site serve as electron donors and the corresponding metal-centered vacant π*xz/yz-orbitals as electron acceptors. Classical hydrogen-atom transfer transpires only in case of NiC+, while ZnC+ follows a mechanistic scenario, in which a formally hydridic hydrogen is transferred. CuC+ reacts by a synchronous activation of two C-H bonds. While spin density is often so crucial for the reactions of numerous MO+/CH4 couples, it is much less important for the C-H bond activation by carbide cations of the 3d transition-metals, in which one notes large changes in bond dissociation energies, spin states, number of d-electrons, and charge distributions. All these factors jointly affect both the reactivity of the metal carbides and their mechanisms of C-H bond activation.

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1. INTRODUCTION Methane constitutes the major component of natural gas and has the potential to serve as an attractive building block for large-scale C(1) chemistry; the selective cleavage of its thermodynamically strong and kinetically inert C-H bond under ambient conditions is viewed as a crucial step in the valorization of this hydrocarbon.1-9 While the progress made over the last few decades is undeniable, still a complete understanding of the various facets is far from being achieved, and this holds also true for a coherent mechanistic description of the elementary steps involved in the reaction.10-14 For example, in a recent JACS Pespective15 the dizzying mechanistic landscape of methane activation by simple metal oxides and carbides was discussed; a summary is depicted in Scheme 1. One of the possible mechanisms is hydrogen-atom transfer (HAT) which occurs whenever the metal oxides possess a localized oxyl radical, M–O•. If the radical is delocalized, e.g. in oligomeric [MgO]n•+ (n ≥ 2), the HAT apparent barrier increases due to the penalty of intracomplex radical localization.16 Adding an electrophilic dopant, e.g. Ga2O3 to [MgO]2•+, localizes the radical and HAT transpires at ambient temperature (Scheme 1, path a).17 If the radical resides on the metal centers as for example in oxygen-deficient Al2O2•+, the mechanism of C-H bond activation switches to proton-coupled electron transfer (PCET).13,16,18-39 In this case, the positively charged Al center of Al2O2•+ acts as a strong Lewis acid that coordinates the incoming methane molecule. One of the bridging oxygen atoms of the cluster abstracts a proton, and the incipient, negatively charged CH3– fragment relocates to the metal center (Scheme 1, path b).18 In some heteronuclear cluster oxides, a competition between PCET and HAT has been observed (Scheme 1, path c).40 Similarly, pristine ZnO•+ activates methane by PCET generating quite a few products. Adding a single CH3CN molecule to form (CH3CN)ZnO•+ leads to a single HAT product.41 The CH3CN···Zn linkage is of electrostatic nature and the CH3CN dipole moment42 acts as an oriented electric field (OEF) that switches off PCET (Scheme 1, path d) and creates selectivity.42-48


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Scheme 1. Mechanistic variants of the thermal C-H bond activation of methane by metal oxides or carbides. Adapted with the permission from ref. 43. Copyright 2018 Royal Society of Chemistry.

Already known since the 19th century,49 transition-metal carbides (TMCs) have attracted much attention over time, particularly in the field of industrial heterogeneous catalysis such as hydrodenitrogenation,50-53 hydrogenation54-59 and Fischer-Tropsch synthesis.60-65 This is mainly due to the fact that some of these affordable TMCs, such as WC,66-74 have similar properties to elements from the expensive platinum group. In addition to the replacement of typical platinum functions, TMCs are regarded as novel materials for CO2 capture, storage, and activation75 and have been proposed as a new type of chemical entities to activate inert hydrocarbons in both gas-phase and condensed-phase studies.76-78 The rather complex


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electronic structures of simple metal carbides in different charge states have been investigated previously using different levels of theory.79-85 While TMCs with high surface areas exhibit excellent catalytic activity comparable to that of noble metals or metal oxides,86,87 a few diatomic MC+ metal carbides were found to operate by unique pathways or distinctly different mechanisms, dictated by the electronic structure of the carbide center.46,76,78,88 For example, in the AuC+/CH4 couple, a rather lowlying empty π-orbital serves as a formal hydride acceptor in the initial phase of thermal bond activation (Scheme 1, path e).88 In contrast, CuC+ brings about - with an unprecedented atomic choreography - the simultaneous transfer of two hydridic hydrogen atoms and coupling of the two CH2 fragments (Scheme 1, path f).46 Since the Cu+-C linkage is mostly electrostatic, much of this mechanistically unique chemistry imparted by Cu+ can be modeled by varying the direction and intensity of OEFs caused by a positive point charge.43,46,47 This Cu+-centered field effect is so strong at the carbide position that it draws significant electron density from CH4. Here, we report a systematic theoretical investigation of the complete row of the 3d transition-metal carbides MC+ (M = Sc - Zn) to develop a conceptual framework aimed at a deeper understanding of their reactions with methane. As shown earlier, the crucial step in the thermal activation of CH4 nearly always concerns the cleavage of the first C-H bond and not so much the ensuing coupling processes, e.g. the generation of C2H4.46,78,88 Therefore, the present study addresses in detail primarily the initial phase of methane activation by diatomic MC+. Where technically possible, the theoretical work was complemented by appropriate gasphase experiments. 2. EXPERIMENTAL AND COMPUTATIONAL METHODS 2.1. Experimental Methods As reported earlier for M = Cu and Au,46,88 here too the diatomic metal-carbide cations MC+ (M = Ti, V, Fe) were generated by laser ablation/ionization of a target consisting of a compressed layer of a metal/graphite powder in the external cluster ion source of a Fourier


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transform ion cyclotron resonance mass spectrometer (FT-ICR MS). For technical details, see the Supporting Information (SI). After transfer of the ions into the ICR cell, their mass-selection and thermalization, the ions were reacted with methane under thermal, near single-collision conditions as described elsewhere.89-91 In addition to exact mass measurements, the identity of the ionic product species has been confirmed by labeling experiments. 2.2. Computational Methods Mechanistic aspects as well as the intrinsic reactivity patterns towards the first C-H bond cleavage of methane mediated by the ten MC+/CH4 (M = Sc - Zn) couples were elucidated by high-level computational methods, which are capable of treating multi-reference species. It is well known that single-determinant wave functions augmented by minimal inclusion of electronic correlation often fail, if strong static electron correlations (SECs) are involved in molecular systems. This holds true, for example, for species with multiple bonds, bi-radicals, some transition-metal atoms, the breaking of covalent bonds, or the proper description of transition-state structures.92-96 In addition, the presence of 3d-electrons and hence the manifold of low-lying electronic states creates enormous challenges for meaningful theoretical investigations. Although CCSD(T) calculations were feasible for the MC+/CH4 systems reported herein, the results may not be sufficiently reliable, as the required T1 diagnostic values are not always met.97 As an accurate account of SECs is challenging in wave function theory (WFT) as well as in density functional theory (DFT),94,98 we have chosen a multi-reference (MR) approach. Besides, some of the employed functionals of DFT gave extremely large deviations for some of the systems investigated (See Table S1).99 As one of the conclusions of this study, we should like to emphasize that results based on singledeterminant calculations should be viewed with extreme caution, especially whenever these systems possess multi-reference character (see Table S1). The following five steps were employed during the computations: (1) Stationary structures along the reaction coordinates were optimized by using the double-hybrid density functional B2PLYP100 with the def2-TZVP101,102 (TZ) basis set. (2) In addition, 18 functionals


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(the local density approximation (LDA), the generalized gradient approximation (GGA), and hybrid (hGGA) rungs), as well as the Møller–Plesset second perturbation method (MP2)103 were applied to perform single-point energy calculations in order to get an overview of the energetic requirements during C-H bond activation. (3) Elaborate coupled-cluster calculations were performed on these cationic diatomic metal carbides to obtain the common global measure of the T1 diagnostics (Table S2). (4) Complete active space self-consistent field (CASSCF)104 calculations were conducted in order to determine the multi-reference character. It became obvious that, except for CuC+, the remaining nine carbides have T1 values indicative of serious multi-reference effects (Table S2). (5) Consequently, a CASSCF structural optimization was augmented by NEVPT2 single-point energy calculations for the cleavage of the first C-H bond of methane.105 Note that NEVPT2 is an efficient perturbative method that treats dynamic correlation without the problems of intruder states or level shifts.106 For further details, see the SI. 3. RESULTS 3.1. Experimental Results The FT-ICR mass spectra, Figure 1, show the results of the reactions of mass-selected, thermalized precursor ions of TiC+ (m/z = 60), VC+ (m/z = 63), and FeC+ (m/z = 68) with isotopologues of methane. To differentiate between reactions of the parent ions with methane and with background gases, reference spectra were recorded with the inert gas argon as well. We also considered the experimental study of other carbides (M = Sc, Cr, Mn, Co, Ni, Zn); however, despite enormous efforts, for these six metals we did not succeed to produce their carbides in amounts sufficient to perform ion/molecule reactions with methane. TiC+ reacts with methane at thermal conditions to form TiC2H2+, accompanied by the liberation of H2 (eq. 1, Figures 1a-c), with a rate constant k(TiC+/CH4) of 2.8×10-10 cm3 molecule-1 s-1; this corresponds to a collision efficiency ϕ of 26%.107-109 The intermolecular kinetic isotope effect (KIE) derived from TiC+/CH4/CD4 amounts to KIEH/D = 2.2 after taking into account the contribution of reactions with background gases. We should mention that due


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to the rather low abundance of the precursor ion, some minor reaction products may have escaped experimental detection; also, the error bar may be larger than the usually reported ±30%.90 Figure 1. Mass spectra resulting from ion/molecule reactions of mass selected thermalized transition-metal carbide cations: 1. TiC+ with a) Ar at 6.0×10-10 mbar, b) CH4 at 4.0×10-9 mbar, c) CD4 at 9.0×10-9 mbar after a reaction time of 5s; 2. VC+ with d) Ar at 6.0×10-10 mbar, e) CH4 at 1.5×10-9 mbar, f) CH2D2 at 3.0×10-9 mbar, g) CD4 at 3.0×10-9 mbar after a reaction time of 5s; 3. FeC+ with h) Ar at 1.0×10-7 mbar, i) CH4 at 1.0×10-7 mbar after a reaction time of 10s. All x-axes are scaled in m/z, and the y-axes represent normalized relative ion abundances. a) TiC+ + Ar

b) TiC+ + CH 4

A

c) TiC+ + CD4

A

A

A = TiC+

B = TiC2H 2+

C = TiC2D2+

C

B 45

60

80 45

60

d) VC+ + Ar

80 45

e) VC+ + CH 4

60 f) VC+ + CH 2D2

D

D

80

D

D = VC+ E = V+ F = VO+

H = VC2HD+

G = VC2H 2+ E E

E 40

F

F 90 40

63 g) VC+ + CD4 D

F

G

63

90 40

H

63

h) FeC+ + Ar

h) FeC+ + CH 4

J

J

I = VC2D2+

90

J = FeC+

E F 40

I

63

90 50

TiC+ + CH 4 VC+

+ CH4

68

85 50

TiC2H 2+ + H 2 V+

+ C2H 4

VC2H 2+ + H 2

FeC+ + CH 4

68

85

(1) (2a) (2b) (3)

As indicated in the reference spectrum, Figure 1d, both carbon-atom transfer (CAT) and oxygen-atom transfer (OAT) take place in the reaction of VC+ with background gases.


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However, when treating VC+ with CH4, CH2D2 or CD4, Figures 1e-g, the signal corresponding to CAT is significantly enhanced, eq. (2a). On thermochemical ground, in this reaction a coupling of the carbide carbon atom with CH4 must have occurred to form C2H4. Moreover, a new signal (m/z = 77) appears, which represents the formal uptake of a CH2 unit from methane accompanied by the liberation of H2, eq. (2b). VC2HD+ and VC2D2+ are generated in the reactions of VC+ with CH2D2 and CD4, respectively, as shown in Figures 1f, g. We mention in passing that in the reaction of VC+ with CH2D2 very weak signals due to the product ions VC2H2+ and VC2D2+ are present; owing to their low intensity, however, they do not appear in Figure 1f. For the VC+/CH4 couple, the rate constant k(VC+/CH4) for the reaction in eq. 2 is estimated to 8.3×10-10 cm3 molecule-1 s-1 (ϕ = 78%). The intermolecular KIE derived from the VC+/CH4/CD4 systems amounts to KIEH/D = 1.1 after considering the possible contribution of reactions with background gases. Finally, for the FeC+/CH4 couple at the detection limit we did not observe any reactions at ambient temperature (eq. 3, Figures 1h,i). Experimental results about the CuC+/CH4 couple have already been reported previously,46 and this late transition-metal carbide brings about efficient C–C coupling with CH4 to form directly Cu(C2H4)+. 3.2. Results from Quantum Chemical Calculations The major results obtained by quantum chemical calculations of the initial phase of the methane activation by the 3d transition-metal carbide cations are summarized in Figure 2.

Figure 2. Structures of the encounter complexes (ECs) and transition states (TSs) calculated with CASSCF/TZ for the energetically most favorable H-abstraction process in the reaction of the 3d transition-metal carbide cations MC+ with methane. Interatomic distances are given in [Å]. The apparent barriers (∆E‡), activation energies (∆Ea), and reaction energies (∆Er) are given in kJ mol-1. ∡CMC bond angles of the TS’s are given in [°]. The next row displays the orbital evolution diagram (OED) for each MC+/CH4 couple. Note, the values for 1[CuC]+, calculated at the B2PLYP level of theory, are taken from ref. 46.


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3.2.1. Mechanistic Aspects For a mechanistic classification, we found it essential to consider the distributions of the charge and spin densities of the hydrogen atom in transit, as well as performing a detailed frontier orbital analysis along the reaction coordinates.110-112 As a result, three different mechanisms were identified for the reactions of the ten 3d transition-metals carbide cations


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with methane (Figure 2, row OED), i.e. proton coupled electron transfer (PCET), hydrogen atom transfer (HAT), and hydride transfer (HT). From row TS in Figure 2, it is immediately apparent that for the first seven elements of the 3d period (M = Sc - Co) the geometries of the transition states are very similar. With one exception, this also applies to their encounter complexes in which the interacting particles are already arranged in such a way that only a slight movement of the reactants towards each other is necessary to arrive at the respective transition state geometry. Only in case of the CoC+/CH4 couple a geometrically more demanding travel is required. This suggests that the underlying mechanism appears to be the same for all of these seven metal carbides which is also corroborated by the respective orbital evolution diagrams (OED). As outlined in more detail further below, these seven carbide cations react via PCET, in which the - and *- orbitals of MC+ and the C-H)-orbital of CH4 play a major role. Only in case of the NiC+/CH4 couple, a classical HAT process takes place in which the single occupied pz-orbital on the carbide acts as the H-abstractor; finally, the carbides of the late transition metals Cu and Zn react via a HT scenario. 3.2.2. Energetic Considerations The different reaction mechanisms tell us on the manners by which the reactions may take place. However, whether they do so at room temperature depends on the energetics of the processes. Thus, what matters in gas phase ion/molecule studies, are the energy differences between the transition states and the separated reactants, i.e. the apparent barriers (∆E‡). Whether a reaction can transpire under thermal conditions depends on the relative energy of the rate-limiting transition state along the reaction coordinate compared to the entrance asymptote. The activation energy (∆Ea), i.e. the energy difference between the encounter complex and the transition state, which matters in homogenous catalysis, is not directly relevant in gas-phase processes, although the ∆Ea and ∆E‡ values may exhibit mutual correlation. The calculated results in Figure 2 indicate that the various MC+/CH4 couples should exhibit quite distinct reactivity patterns. Thus, the apparent barriers for the metal carbide


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cations of Sc, Ti, V, and Cr on the left side of the period, are all negative (-15, -43, -23, -39 kJ mol-1, respectively). As such, these four MC+ carbides are all able to mediate methane activation at ambient temperature. In contrast, the metal carbides of Mn, Fe, and Co in the mid-range should be reluctant to do so since their apparent barriers are positive and prohibitively high (60, 69, and 76 kJ mol-1, respectively). NiC+ has a low apparent barrier of 8 kJ mol-1 and, at ambient temperature, is predicted to sluggishly cleave the C-H bond of methane, perhaps under multiple collision conditions. The unprecedented, synchronous double hydrogen transfer initiated by CuC+ has already been described elsewhere.46 Finally, also ZnC+ is predicted to be a good candidate for methane activation. Its transition state for hydrogen abstraction appears quite late, is placed 67 kJ mol-1 below the entrance channel (∆E‡ < 0) and separated only by 1 kJ mol-1 from the encounter complex. A comparison between the experimentally observed with the predicted reactivities for the four carbide cations of Ti, V, Fe, and Cu shows excellent agreement. Thus, the trends predicted by theory for the whole series of the ten 3d transition-metal carbides deem reliable. 3.3. Detailed Descriptions for Selected MC+/CH4 Couples Even though the heterolytic dissociation of a C-H bond in methane into the formal pairs H+/CH3− and H−/CH3+ requires much more energy than is necessary to bring about a homolytic cleavage,95,96,113 nine carbides start by splitting the C-H bond heterolytically. A typical example is represented by the VC+/CH4 couple; the TiC+ and FeC+ cases are described briefly. 3.3.1. VC+/CH4 For VC+ the ground state corresponds to a triplet (3∆) with a bond length of 1.69 Å; its lowest excited singlet state (1Σ+) lies 3.1 kJ mol-1 higher in energy.83 As shown in Figure 3, the reaction of VC+/CH4 commences on the triplet surface to form an encounter complex 31 by coordinating the incoming ligand to the bare metal center in an η2 mode. The electrostatic interaction, which is also accompanied with charge transfer from methane to VC+ (Table S3), stabilizes the system by as much as 81 kJ mol-1 in energy. Subsequently, a hydrogen atom migrates to the carbon site of VC+ via a tight four-membered, metathesis-like transition state (TS) 3TS1/2.


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Significant structural reorganization happens at this stage. For instance, the V-C bond length increases by 0.04 Å to 1.72 Å and the C-H bond of methane is stretched by as much as 0.56 Å to 1.67 Å, while the bond length of V-Cmet is shortened by 0.36 Å. After the transit of the hydrogen atom to form a new C-H bond, intermediate 32 is generated (-94 kJ mol-1). As the rate-limiting apparent barrier (∆E‡) lies below the entrance asymptote and in the absence of efficient energy dissipation, 3[VC]+ can promote the abstraction of hydrogen from methane at ambient temperature. Figure 3. a) NEVPT2//CASSCF-calculated potential energy profile (ΔH298K) for the initial phase of the reaction of the cationic vanadium carbide VC+ with CH4. Key ground-state structures are depicted with selected geometric parameters. The curve given in black refers to the triplet and the one in blue to the singlet surface. Charges are omitted for the sake of clarity; bond lengths are given in Å, and relative energies in kJ mol-1. b) Schematic natural orbital diagram for 3TS1/2. Note that the label πx(V-C) involves contributions from the hydrogen in transit and the carbon atom of methane. a)

1.58 1SR

+ CH4

3.1

3SR

0.0 1.69 + CH4

1.68 1.60 2.51 2.55

1.72 1.66

1.10 1.12

11

-78

31

-81

= 3[VC]+ + CH4 1SR = 1[VC]+ + CH4

1.43 1.42 1.56 1.67 2.15 2.19

3TS1/2

-23

1TS1/2

-49

1.82 1.70

3SR

C

2.08 2.07 32

MECP

V

1.08 1.07

12

H

-94

-171

b) 3TS1/2

σ(C-H-C)

πx(V-C)

πy(V-C)

dxy

σ(V-C)

σ*(C-H)

As shown in Figure 3, on the singlet surface the transition state 1TS1/2 corresponding to the breaking of the C-H bond of CH4 lies even below the triplet transition state 3TS1/2. Since the two states differ mainly by the occupancy of largely two d-orbitals on the V atom, the spinorbit coupling (SOC) should be rather efficient. Consequently, the system may in fact follow a


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two-state reactivity (TSR) scenario.114-123 However, the corresponding minimum-energy crossing point (MECP)124 was not located due to convergence difficulties with CASSCF. Subsequent reaction steps for the VC+/CH4 couple involve sequential C-C coupling and multiple hydrogen migrations to finally arrive at the product pairs V+/C2H4 and VC2H2+/H2. Several energetically feasible pathways, which also include inter system crossings (ISC) between the singlet and triplet states, are reported in the SI (5→6→7, Figure S1). According to the theoretical analysis, under ambient temperature there exist quite a few routes to form the final products. These channels turned out to be rather complex mechanistically, and as they do not constitute the main target of our investigations, they are not discussed here any further. As to the actual mechanism operating in the 3[VC]+/CH4 couple, a careful analysis of the electronic structures reveals that the first and rate-determining step in the overall process best can be described in terms of a PCET.13,16,18-39 As shown in Figure 3b, the doubly-occupied π-orbital at the terminal carbon moiety in VC+ abstracts a proton, while the ensuing CH3– fragment moves with its electron pair to form a covalent bond with the positively charged, Lewis acidic vanadium atom. In addition, the two unpaired electrons occupy the singlyoccupied spectator orbitals dxy and σpz(V-C). While the carbon atom in 3[VC]+ carries some spin density (0.45, see Table S3 in the SI), the reaction does not involve a classical HAT mechanism since the σ*(C-H-C)-orbital, with a node on the H atom in transit, is vacant.13,14,16,23,125 The reaction on the singlet state surface 1[VC]+/CH4, can also be described as PCET, or equivalently, as a cycloaddition of the πxV-C)+ bond across the σ(C-H)-orbital of CH4 (see caption to Figure 3b). 3.3.2. TiC+/CH4 TiC+, like VC+, based on the NEVPT2//CASSCF calculations (see Figure S2), in its doublet ground state (2Σ+)85 approaches methane forming an η2 complex (-84 kJ mol-1); subsequently, this “hot” encounter complex surmounts transition state 2TS1/2 (-43 kJ mol-1), at which the C-H bond is broken, to form intermediate 22 (-120 kJ mol-1). As the energy of 2TS1/2 is much


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lower than the entrance asymptote, in line with the experimental findings (Figures 1e-g), TiC+ is able to mediate methane activation at ambient temperature. 3.3.3. FeC+/CH4 For diatomic FeC+ the electronic ground state corresponds to the doublet state (2∆);82 its first excited state is a quartet and located 75 kJ mol-1 above the ground state. The NEVPT2//CASSCF results for the C-H bond cleavage of CH4 by FeC+ show that both the doublet and the quartet transition states are located well above the entrance asymptote, by 69 and 100 kJ mol-1, respectively (Figure 4). Thus, they render impossible methane activation at ambient temperature, as confirmed experimentally (Figures 1h,i). A TSR scenario for this system does not play a role.

Figure 4. NEVPT2//CASSCF-calculated potential energy profile (ΔH298K in kJ mol-1) for the initial phase of the reaction of the cationic iron carbide 2,4[FeC]+ with CH4. Key structures with selected geometric parameters are also provided. Charges are omitted for the sake of clarity; bond lengths are given in Å, angles in degree. 1.44 1.68

1.57

1.72

2.14

1.68 2.37

2.44 4[FeC]+

100

+ CH4

2TS3/4

75

69

1.59 2[FeC]+

4TS3/4

43

28

+ CH4

0.0

1.38 2.04

1.66

2.13

24

-14 101.6

23

-84 1.59

2.15

2.22

2.42


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3.4. Remark on Kinetic Isotope Effects Time-honored kinetic isotope effect studies are often insightful for a classification of reaction mechanisms. As mentioned above, for the carbide cation/methane couples of Ti, V and Cu,46 the KIEH/D have been determined experimentally to amount to 2.2, 1.1 and 1.2, respectively. If the KIEH/D were indeed indicative for the mechanisms involved, for the carbides of V and Cu the mechanisms should be similar and in case of Ti and V different. However, this is not the case. Most likely, this finding reflects the fact that for the MC+/CH4 couples, one is dealing with a cascade of reaction steps, and the observed KIE’sH/D do not reflect one step only but represent averages; this topic has been addressed in detail recently by Neese.126 4. DISCUSSION 4.1 Mechanistic Considerations The first seven metal carbides (M = Sc - Co) follow the same PCET route in their reactions with CH4, as described above in some detail for the VC+/CH4 couple. CuC+ and ZnC+ prefer a mechanistic scenario in which a formal hydridic hydrogen atom is transferred, and only NiC+ reacts via a classical HAT path. A closer look at the PCET mechanism reveals additional factors that influence the reaction barrier. For example, the acceptance of a proton from methane is facilitated the more π-electron density is available at the carbon center of the MC+ π-bond, and vice versa. As the π-electron density on the carbon center continuously decreases from ScC+ to CoC+ (Figure 5), the ability of the carbide carbon to accept a proton diminishes, thereby resulting in higher energy barriers. We should mention in passing that the 2s-orbital of the hydrogen-acceptor carbon atom is also involved in the initial stage of the C-H bond activation for the carbides of Sc and Ti. The second factor concerns the CH3– affinity of the transition-metal center. The crucial orbital which will accept the emerging CH3– group during the PCET mechanism, is the empty antibonding π*xz/yz-orbital. However, the ability of this metal-based orbital to accept the CH3–group is counteracted by the electron populations of the metal's dxy- and dx2-y2-orbitals. As


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these orbitals get filled, starting from MnC+ on, the Pauli repulsion and electron-electron repulsion with the electron pairs of the developing CH3– moiety increases, thus the M-CH3 bond is weakened, and consequently, the PCET barrier increases. Indeed, as may be seen from Figure 2, the apparent barrier ∆E‡ jumps up from -39 to +60 kJ mol-1 during the transit from Cr to Mn. The particular importance of the occupation of the d-orbitals is also reflected by the geometry of the transition states involved: As shown in Figure 2, in going from ScC+ to CoC+ the length of the C-H bond to be cleaved increases from 1.57 Å to 1.98 Å, and the ∡CMC bond angle gradually opens from 91° to 112°. Figure 5. Graphical representation of the distribution of the electron density [%] between the metal (red) and the carbon (black) of the π-bond, which is best suited to take over the proton transferred during the reaction of MC+ (M = Sc - Zn) with CH4.

Finally, as a result of the increasing M···CH3– repulsion during the PCET mechanism, as we reach the NiC+/CH4 couple the PCET transition state becomes energetically disfavored, and a mechanistic switch from PCET to HAT13,16,23 takes place (Figure S4). According to the orientation of the singly-occupied 2pz-orbital at the carbon center, which extends along the M-


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C axis, the methane C-H bond approaches the carbon center from the top position in order to engage in an optimal orbital overlap (Figure S4). During the transit of the hydrogen atom, the -electron from the C-H σ-bond is partially shifted to the singly-occupied carbon 2pz-orbital. This is in good agreement with the nearly collinear C-H-C arrangement in the TS and the significant spin density (0.39 |e|) at the carbon atom of the incipient methyl radical. In addition, the transition state is characterized by a singly-occupied antibonding σ*(C-H-C)-orbital, with a node on the hydrogen atom in transit (Figure S4). In 1[CuC]+, the two unpaired electrons of the ground state carbon atom (3P) couple and form a dative bond to Cu, resulting in two vacant 2px/y-orbitals at the carbon center (Figure 2).46 This renders the carbon atom highly electrophilic and facilitates its simultaneous insertion into two C-H bonds. Moreover and as described earlier,46 the non-covalent and mainly electrostatic Cu+-C interaction in CuC+ forms the root cause for the nearly barrier-free, synchronous insertion of the electrophilic carbide carbon atom into the two C-H bonds of methane. For 2[ZnC]+, the CASSCF calculations show that the 4s electrons of Zn and one unpaired electron of the ground state carbon atom (3P) couple to form a dative bond (Figure S5). One unpaired electron still remains on the carbon atom.84 In the competition between the empty 2px- and the singly-occupied 2py-orbital at the carbon center in ZnC+ for the electrons originating from the C-H σ-bond in methane, the empty 2px-orbital emerges as the ‘winner’ even though it lies higher in energy than the 2py-orbital (Figure S4). This can be ascribed to the polarization effect exerted by the Zn+ species; therefore, an intramolecular “hydride” transfer (HT) mechanism is operative as was observed for AuC+ and CuC+.46,88 However, in contrast to CuC+, which is equipped with two empty 2p-orbitals, the carbon center in ZnC+ only possesses one vacant 2p-orbital. This, we suggest, is the root cause that in the latter case only a single and not a concerted double hydrogen-atom transfer occurs as has been observed for CuC+/CH4.46 Thus, the presence of two empty 2p-orbitals at the carbon center


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appears to be an electronic prerequisite for a concerted transfer of two formally hydridic hydrogen atoms.46,88 4.2. Energetic Considerations Understanding the mechanistic variants as depicted in Figure 2, requires some understanding of the change of the energies of the frontier orbitals. These factors will affect the polarization of the M-C bond orbitals and the charge transfer interaction from methane to MC+. As shown in Table 1, the energies of the d-orbitals of the metal cations decrease in the direction from Sc to Zn. Concurrently with the energy lowering, the d-orbitals will also shrink in size and will be less and less able to overlap with the carbon orbitals. Table 1. The canonical orbital energies (in au) of the metal d-block of MC+ obtained at the CASSCF/TZ level of theory. ‘↑↓’ refers to doubly-occupied, ‘↑’ for singly-occupied, and ‘‒’ for vacant orbitals. M Sc Ti V Cr Mn Fe Co Ni Cu Zn

↑↓ -0.442 -0.507 -0.527 -0.576 -0.545 -0.616 -0.656 -0.679 -0.821 -1.084

↑ -0.299 -0.317 -0.328 -0.387 -0.387 -0.372 / / / /

‒ -0.030 -0.011 -0.051 -0.046 -0.136 -0.108 -0.106 -0.180 / /

The early transition metals Sc, Ti, and V possess high-lying d-orbitals, and this corresponds to higher energies of the doubly-occupied p-orbitals on the carbon center in the corresponding MC+ complexes (Table 2). These conditions render a PCET mechanism possible at ambient temperature. As the energy of the doubly-occupied p-orbitals at carbon decreases, its readiness to accept a proton diminishes. The turning point is reached at Ni. In this case, the energy (Table 2) of the doubly-occupied p-orbital is already lowered to such an extent that proton abstraction from methane is no longer an option. Instead, the energetically


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higher and therefore more favorably located, singly-occupied p-orbital ensures that a hydrogen atom is transferred from methane to the carbon atom of the carbide cation via a HAT process. In ZnC+, possessing the energetically lowest lying d-orbitals, the positive charge on the metal center polarizes the orbitals and lowers the energy of the carbon 2p-orbitals, so much so, that the vacant p-orbitals of the carbon moiety of the carbide cation can serve as hydride acceptors (see Table 2). Table 2. The canonical orbital energies (in au) of the carbon p-block of MC+ involved in the reaction of the C-H bond cleavage in CH4 as obtained at the CASSCF/TZ level of theory. ‘↑↓’ refers to doubly-occupied, ‘↑’ for singly-occupied, and ‘‒’ for vacant orbitals. M Sc Ti V Cr Mn Fe Co Ni Cu Zn

↑↓ -0.442 -0.507 -0.627 -0.576 -0.545 -0.616 -0.656 -0.679 -0.616 -0.533

↑ -0.298 -0.317 -0.336 / / / / -0.400 / -0.369

‒ -0.030 -0.011 -0.051 -0.046 -0.136 -0.108 -0.106 -0.180 -0.142 -0.231

4.3. Factors Determining the Barriers – There is No Simple Answer! While the above MC+/CH4 series seems to constitute a perfectly behaving family with perturbations caused mostly due to the change of the metal, this conjecture is far from being the case. Actually, this series involves quite enormous changes in e.g. bond dissociation energies (BDEs) of MC+ (Figure 6, Table S4), relative energies of encounter complexes, transition states and intermediates (Table S5), carbon p-orbital (Table 2) and the metal dorbital energies (Table 1), the atomic charges, the different spin states (Table S3), a variable number of d-electrons, the polarization of M-C bonds, the frontier orbitals energy change (Tables 1 and 2),127-134 and a partial electrostatic catalysis due to the positive charge of M+, as described before.46 All these factors affect the reaction barriers in a convoluted manner and,


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as shown above, they also lead to distinctly different mechanistic scenarios of C-H bond activation.

Figure 6. Plot of apparent barriers for the initial C-H bond activation (∆E‡, black), bond dissociation energies of MC+ (BDE, red), activation energies (∆Ea, blue), and reaction energies (∆Er, brown). Energies are given in kJ mol-1.

As clearly evidenced by the data given in Figure 6, there is no single factor that alone can explain the experimentally observed findings in a satisfactory manner. Thus, the BellEvans-Polanyi principle cannot be applied,135,136 and also no other simple principle alone can explain the graphical patterns shown in Figure 6. Briefly, i) there is no direct correlation between the experimental findings and the bond dissociation energies of MC+ (BDE), the apparent barrier (∆E‡), the activation energies (∆Ea), or the reaction energies (∆Er), i.e. the energy difference between the encounter complex and the intermediate, for the whole 10 transition-metals (Figure 6). ii) While the d-orbital energies of MC+ invariably decrease in going from Sc to Zn (Table 1), again a valid correlation cannot be established. This also holds true for the carbon p-orbital energies of MC+ (Table 2). Thus, the importance of frontier orbitals must not be overestimated.128 Clearly, chemical processes reflect both the frontier- and


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charge-controlled mechanisms.131,132 In a different context, this was recognized by Klopman as early as in 1968.137 No doubt, the same atom located in a different environment can well exhibit a rather different behavior.128 4.4. Localized Spin Density Does Not Always Promote HAT – The PCET/HAT Dichotomy An additional problem concerns the effect and role of spin density at the abstractor site. As shown previously, experimental and theoretical findings for numerous metal oxides have led to a rule of thumb stating that whenever the spin density is highly localized at a hydrogenacceptor site the most favorable pathway for cleavage of a C-H bond often - but not always proceeds via classical HAT.10-16,23 However, this rule does not apply for the metal-carbide cations studied in the present work. An inspection of the orbital occupancy-evolution diagrams (Figure 2, OED row) reveals that the spin density is highly localized on the carbon sites of the corresponding carbide cations of, for example, Sc, Ti, V, Ni, and Zn. Yet, only for NiC+ a standard HAT transpires involving the singly-occupied σpz-orbital to accept the hydrogen atom being accompanied by a homolytic C-H bond cleavage of methane. The carbide cations of Sc, Ti and V cleave the C-H bond at ambient temperature and those of Mn, Fe, and Co could do this at elevated temperatures heterolytically via a PCET. As analyzed in great detail previously,16,23 a prerequisite for a PCET to take place is the presence of a relatively basic electron pair at the acceptor site and a highly Lewis-acidic center. For the MC+ species, these conditions are provided by a doubly-occupied πxz/yz-orbital between the metal and carbon centers of the carbide cation and the corresponding empty π*xz/yz-orbital located at the metal center. While the proton from methane is accepted by the carbon site of the doubly-occupied πxz/yz-orbital the resulting electron pair, localized at the CH3– moiety, is injected into the corresponding empty antibonding π*xz/yz-orbital localized at the metal center. The combination of a singly-occupied πxz/yz-orbital and its associated empty π*xz/yz-orbital seems not to be sufficient for a successful PCET. A different case, where HAT is avoided and replaced by an intramolecular transfer of “hydride” hydrogen atom, is represented by the MC+/CH4 couples with M = Cu and Zn, where electrostatic catalysis no doubt plays a substantial role.46


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5. CONCLUSION In summary, mechanistic features of the C-H bond activation of methane by the diatomic, bare 3d transition-metal carbides MC+ (M = Sc - Zn) have been explored in a combined experimental/computational study. The ten metal carbides demonstrate rather distinct reactivities toward C-H bond activation of methane; in addition, three different mechanistic scenarios, i.e. PCET, HAT and HT are encountered.15 Electronic structure analysis reveals that for diatomic metal carbides, in contrast to metal oxides, a high spin-density at the hydrogen-acceptor carbide site does not necessarily result in classical HAT from methane. Rather, a combination of more subtle effects, e.g. bond dissociation energy, d-orbital occupancy, Pauli repulsion, and electrostatic catalysis, contribute and give rise to a mechanistically rich landscape of the 3d transition-metal mediated C-H bond activation of methane by diatomic MC+.15,69 Resolution of all the contributing factors and the construction of a coherent model of reactivity are needed to cope in a more quantitative fashion with the fascinating challenges offered by these structurally simple but electronically complex metal carbides – their seemingly simple chemistry with methane and the associated reaction mechanisms are all but boring.


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.xxx Experimental and computational details, additional potential energy surfaces, intermediates, energetic information, schematic molecular orbital diagrams, B2PLYP calculated TS structures, the orbital composition of the active space for MC+ obtained by CASSCF, and Cartesian coordinates for key calculated species (PDF)

ACKNOWLEDGEMENTS This research was sponsored by the Deutsche Forschungsgemeinschaft (DFG), in particular the Cluster of Excellence "Unifying Concepts in Catalysis", and the Fonds der Chemischen Industrie. The work at Jilin University has been supported by the National Natural Science Foundation of China (No. 21473070 and 21773085). The research at the Hebrew University of Jerusalem has been sponsored by the Israel Science Foundation (ISF grant 520/18). We thank Dr. Jun Zhang, University of Illinois, for helpful discussions. We are grateful to the reviewers for their thorough reviews, valuable comments, and helpful suggestions. DEDICATION

This article is dedicated to President Dr. Drs. h.c. Wolfgang A. Herrmann on the occasion of his 70th birthday and to his alma mater, the TU München, celebrating “150 years of culture of excellence”.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected]

ORCID Jilai Li: 0000-0002-3363-9164 Sason Shaik: 0000-0001-7643-9421 Helmut Schwarz: 0000-0002-3369-7977

NOTES The authors declare no competing financial interest.


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On the Intrinsic Reactivity of Diatomic 3d Transition-Metal Carbides in

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