A Theoretical Study on Methane C H Bond Activation

Article pubs.acs.org/JPCA

A Theoretical Study on Methane CH Bond Activation by Bare [FeO]+/0/− Yang Wang,† Xiaoli Sun,*,† Jun Zhang,*,‡ and Jilai Li†,§ †

Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China Department of Chemistry, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States § Institut für Chemie, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany ‡

S Supporting Information *

ABSTRACT: The first CH bond activation of methane by bare diatomic FeO in different charge states (cationic + , neutral 0, and anionic − ) has been studied by means of density functional theory (DFT) and CCSD(T) methods. The structures were optimized by using 10 popular different density functionals (DFs) with different Hartree−Fock exchange fractions, as well as the CCSD method and then were subjected to single point energy calculations at both the DFT level and the CCSD(T) level. The performance of these methods on the energies and structures in different charged states of the systems was discussed. The results show that the cationic system has lower barrier than the neutral and anionic systems. In most cases, the impact of density functionals is larger than that of structures on energies. Among the three charged states, the anionic system is the least sensitive to the density functionals. The electronic structure analysis demonstrates that the cationic and neutral systems proceed by either hydrogen-atom transfer (HAT) or proton-coupled electron transfer (PCET), while the anionic system only employs the proton transfer (PT) mechanism. Knowledge from this study is of value for further studies on methane activation. error can be removed by solvent correction and counterion,40,41 or reduced to a certain extent by using hybrid or double hybrid functional methods instead of pure DFT methods.40−43 However, the former option by using counterion or solvent seems improper when dealing with isolated reactants in gas-phase experiments. On the other hand, pure DFT methods have been employed to study gas-phase charged systems with a combined experimental/computational approach in most literature.44−46 Actually, hybrid DFT methods with 20−25% of the HF exchange weight, especially B3LYP, seem proper for ironcontaining systems. This is probably because Kohn−Sham orbitals obtained from B3LYP calculations are a good choice as a basis for CCSD(T) calculations and may offer better convergence and much smaller single excitation amplitudes than Hartree−Fock orbitals.47 Our previous study also confirmed this.48 CH bond activation of methane in a controlled fashion still constitutes a central challenge, whereas the search for catalysts capable of directly transforming methane to more value-added commodities has been pursued for over a century.49,50 Metal oxides, being capable of bringing about activation of methane under (quasi-) thermal conditions in the gas phase,15,51 have served as prototypical systems to probe the active sites in heterogeneous catalysis, that is, the so-called

1. INTRODUCTION Using density functional theory (DFT), electronic structure calculations of elementary processes can be done with reasonable accuracy and on a time-scale competitive with experiments.1,2 As a result, it is now commonplace for DFT to complement experimental studies in order to elucidate mechanistic insights by obtaining the atomistic interactions of chemical phenomena.3 The interplay of well-designed experimental studies with a rapid computational workflow has enriched the mechanistic understanding of some seemingly simple but actually complicated bond-activation reactions.4−14 Actually, numerous gas-phase studies have been performed to reveal mechanistic aspects by employing well-defined cluster oxides and subjecting them to state-of-the-art experiments over the last years.15 Thus, molecular level-based knowledge has been provided that may prove helpful in the development of new concepts for the design of catalysts.1,12,16−18 Even though there are numerous successful examples of combined experimental/computational studies,1,19−23 we have to face failure sometimes.24−30 Sometimes computational prediction might be biased by using an inappropriate DFT method. An artificial “direct” hydrogen-atom abstraction from methane serves as a remarkable example in this context; in fact, a hydrogenatom abstraction transition state should be expected when an intermolecular primary kinetic isotope effect (KIE)31 amounting to KIE = kH/kD > 1 was observed experimentally.7,32−37 The self-interaction error (SIE) is regarded as the most severe shortcoming of the DFT methods for charged systems;38,39 this © 2017 American Chemical Society

Received: December 31, 2016 Revised: March 15, 2017 Published: March 24, 2017 3501

DOI: 10.1021/acs.jpca.6b13113 J. Phys. Chem. A 2017, 121, 3501−3514

The Journal of Physical Chemistry A

Article

Table 1. Key Bond Lengths (in Å) of [FeO]+/0/−a +

0

−

method

4

6

BP86 TPSS TPSSh B3LYP PBE1PBE M06 BMK BH&HLYP wB97 M11

1.56 1.56 1.55 1.69 1.55 1.67 1.56 1.57 1.68 1.73 3 FeO

1.63 1.64 1.63 1.64 1.62 1.66 1.62 1.63 1.62 1.61 5 FeO


1.60 1.60 1.59 1.58 1.57 1.67 1.57 1.58 1.69 1.78 4 FeO

1.60 1.60 1.60 1.61 1.60 1.64 1.61 1.61 1.61 1.62 6 FeO


1.62 1.62 1.62 1.64 1.63 1.68 1.64 1.64 1.62 1.67

1.70 1.69 1.69 1.70 1.69 1.71 1.72 1.71 1.67 1.71

FeO

Table 2. Key Geometric Parameters of Various Reaction States of the [FeO]+/0/− + CH4 Reactions at the B3LYP/ def2-TZVP Level of Theory

FeO

species +

4

RC TS1 4 IM1 4 TS2 4 IM2 6 RC 6 TS1 6 IM1 6 TS2 6 IM2 3 RC 3 TS1 3 IM1 3 TS2 3 IM2 5 RC 5 TS1 5 IM1 5 TS2 5 IM2 4 RC 4 TS1a 4 IM1 6 RC 6 TS1 6 IM1 4

0

−

FeO

OH

CH

∠FeOH

1.57 1.69 1.70 1.62 1.69 1.64 1.71 1.71 1.72 1.73 1.59 1.74 1.78 1.66 1.73 1.61 1.73 1.79 1.71 1.78 1.64 1.85 1.87 1.71 1.78 1.90

2.57 1.60 1.00 1.36 0.97 3.79 1.45 0.99 1.30 0.97 2.71 1.21 0.97 1.38 0.97 2.63 1.08 0.97 1.35 0.96 2.14 1.06 0.96 2.08 1.21 0.96

1.13 1.15 1.89 1.34 3.12 1.10 1.19 1.99 1.42 4.12 1.09 1.29 2.39 1.31 3.51 1.09 1.50 2.18 1.37 4.56 1.10 1.48 4.33 1.10 1.45 3.03

47.6 99.7 142.2 71.3 132.6 22.8 115.2 148.5 71.9 148.1 109.9 120.0 118.1 70.5 125.7 109.4 180.0 139.2 69.5 139.1 124.2 71.0 108.6 119.0 83.1 107.9

a4

TS1 is the top point on the relaxed the minimum energy paths MEP scan.

a

The superscript m in mX represents the spin multiplicity of the species.

Scheme 1

“aristocratic atoms”.52,53 In addition, metal-oxide mediated hydrogen-atom transfer (HAT) generating CH3• from CH4 is viewed as a decisive step in the oxidative coupling of methane (OCM).54−60 Among metal oxide mediated methane activation, the reaction of [FeO]+ with methane has attracted much attention.61−71 The pioneering work by Shaik, Schwarz, and co-workers on the gas-phase reaction of [FeO]+ with CH4 and H2, as a prototype model, has laid out the concept of two-state reactivity as an important motif in transition-metal oxidation chemistry.72−74 In addition, the structures of [FeO]0/− as well as their reactivity, was also reported.75−77 Herein, we study the reactions of [FeO]+/0/− with methane to test the performance of 10 popular DFT methods, including pure, hybrid, as well as range-separated DFT methods. We optimize the structures with DFT and CCSD methods, then they are subjected to single point energy calculations at both the DFT and CCSD(T) levels. We discuss the performance of these methods on the energies, structures, as well as charged states of the systems. We also investigate whether the problem can be reduced by performing the calculations at the CCSD(T) level of theory. Note that we concentrate our attention on the first CH bond activation step in these reactions, which is regarded as the decisive step in the oxidative coupling of methane to ethane via recombination of two CH3• radicals.57

2. METHOD There are several accessible spin states for the diatomic ions [FeO]+/0/−. The triplet (low spin) and quintet states (high spin) for neutral species [FeO] and quartet (low spin) and sextet states (high spin) for both [FeO]+ and [FeO]− were considered for the reactions of [FeO]+/0/− with methane herein. Initially, we used the B3LYP78,79 hybrid density functional for geometry optimization without symmetry constraints. It is the most widely used density functional and has a welldocumented accuracy. For molecules containing first- and secondrow atoms, the error bars only rarely exceed ±13 kJ/mol; for transition metal containing systems, the accuracy is normally around ±21 kJ/mol.80 Even for highly ligand-deficient systems, 3502

DOI: 10.1021/acs.jpca.6b13113 J. Phys. Chem. A 2017, 121, 3501−3514

The Journal of Physical Chemistry A

Article

Figure 1. FeO (Δ), CH (∇), OH (○), bond distances (a, c, e) and ∠FeOH (☆) (b, d, f) of the transition states (TS1) correlated with the fraction of exact exchange (X) of the functional for the cationic (a,b), neutral (c,d) and anionic (e,f) systems.

then high-level energetic refinement was performed at coupledcluster singles, doubles, and perturbative triples approximation (CCSD(T))97 with def2-QZVPP82 (QZ) basis set level of theory on each DFT-optimized and CCSD structure in order to calibrate the DFT performance. We should mention in passing that benchmark studies show that CCSD gives reliable results both on the energies (