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A Theoretical Study on Methane C–H Bond Activation by Bare [FeO] Yang Wang, Xiaoli Sun, Jun Zhang, and Jilai Li
J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b13113 • Publication Date (Web): 24 Mar 2017 Downloaded from http://pubs.acs.org on March 27, 2017
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A Theoretical Study on Methane C–H Bond Activation by Bare [FeO]+/0/– Yang Wang,1, Xiaoli Sun,1,* Jun Zhang,2,* Jilai Li,1,3 1
Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of
China 2
Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA. 3
Institut für Chemie, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin,
Germany *Correspondence and requests for further materials should be addressed to X.S. (
[email protected]), or to J.Z. (
[email protected]) ABSTRACT The first C−H bond activation of methane by bare diatomic FeO in different charge states (cationic +, neutral 0, and anionic –) have 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 subject to single point energy (SPE) 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 least sensitive to the density functionals. The electronic structure analysis demonstrates that the cationic and neutral systems proceed by 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.
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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 which may prove helpful in the development of new concepts for the design of catalysts.1,12,16-18 Even
though
there
are
experimental/computational studies,
numerous
1,19-23
successful
examples
we have to face failure sometimes.
of
combined
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 hydrogen-atom 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 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 a lot of literature.44-46 Actually, hybrid DFT methods with 20–25 percent of the HF exchange weight, especially B3LYP, seem proper for iron-containing 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
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catalysis, i.e., the so-called “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 coworkers 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 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 method, then they are subjected to single point energy calculations at both DFT level and CCSD(T) level. 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 to 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 oxide cluster [Fe–O]+/0/–. The triplet (LS) and quintet states (HS) for neutral species [Fe–O], quartet (LS) and sextet states (HS) for both [Fe–O]+ and [FeO]– were considered for the reactions of [Fe–O]+/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 second-row 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, B3LYP was found to perform best both in accuracy and error distributions in a recent benchmark study. used the def2-TZVP
82
81
We
(TZ) basis set in combination with the density functional method. In
the previous study, we have shown that the smaller basis sets, such as def2-SVP, are completely useless.83 Further increasing the basis set to quadruple zeta level has a smaller effect on the energies.83 The B3LYP functional combined with at least a triple zeta level basis set can reach the quality of the gold-standard CCSD(T) method in our recent studies.83,84
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Harmonic vibrational frequencies were computed to verify the nature of the stationary points. Each minimum structure reported possesses a positive-definite Hessian matrix, whereas each transition state (TS) has only one negative eigenvalue. To corroborate the correct link between the minima and the transition state TSs, intrinsic reaction coordinate (IRC)85-88 calculations were performed. Unscaled vibrational frequencies (obtained for each DFT method) were used to calculate zero-point energy (ZPE) contributions and thermal corrections to the enthalpy (∆H) within the ideal-gas, rigid-rotor, harmonic-oscillator approximation at a temperature of 298 K and a pressure of 1 atm. It is well known that it is quite challenging for some DFT methods to describe a wide range of metal-containing systems.81 Therefore, mechanistic conclusions based on a single DFT method should be viewed with caution.8,84 Therefore, all structures obtained at the B3LYP level were further re-optimized with nine DFT methods: the pure functionals BP86,89 TPSS,90 and hybrid functionals with different amount of Hartree-Fock (HF) exchange (indicated in parentheses after each method), TPSSh (0.1),90 PBE1PBE (0.25),91 M06 (0.27),92 BMK (0.42),93 BH&HLYP (0.5),94 wB97(1.0),95 and M11(0.428/1.0).96 Subsequently, DFT single-point energy (SPE) calculations on each DFT-optimized structures were performed. Furthermore, CCSD optimization for reactants and transition states was also used to define a “correct” answer for geometries, then high-level energetic refinement was performed at coupled-cluster 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 (< 5.5 kJ/mol) and geometries (
