DFT Study on the Germanium Ion Activated C–H Bond in Methane①

HOU Xiu-Fang FU Feng CHANG Qing ZHANG Wen-Lin

(Laboratory of Analytical Technology and Detection,College of Chemistry and Chemical Engineering, Yan’an University, Yan’an 716000, China)

Density functional calculations show that the GeO+and [OGeOH]+can activate the H3C-H bond, in contrast to the inertness of Ge+and GeOH+.

1 INTRODUCTION

Methane is the smallest saturated hydrocarbon and the principal component in natural gas.It is characterized by the absence of a dipole moment, the extremely high pKa value, the rather small polarizability, the modest proton affinity, an anomalously high ionization energy (12.61±0.01 eV)[1], and a negative electron affinity or the significant energies required for both the homo- and heterolytic cleavage of the C–H bond[2].These properties lead to the lower reactivity of methane relative to desired products such as ethylene or methanol.How to activate methane C–H bonds into value-added products like methanol, acetic acid, hydrogen cyanide and so on under a less expensive and cleaner process is a major problem and a “grand challenge”[3]nowadays.The first thought is metal-mediated dehydrogenation of methane.Bohme’s[4]research indicates that only As+, Nb+, Ta+, W+, Os+, Ir+, and Pt+can bring dehydrogenation of methane to generate metal carbenes in 59 atomic cations, while Ge+and methane only form addition [Ge(CH4)][5].

How can we improve the reactivity and selectivity of metal-mediated bond activation processes? There are chiefly changes of cluster size, charge state and ligands effect.Firstly, the cluster size is one of the most important factors in metal-mediated bond activation processes[5].The catalytic properties of small clusters show large variations with cluster size[6].For example, Pd8and Pd10are the most reactive clusters in Pd clusters activating CH4, while Pd3and Pd9are slower[7].Secondly, generally the cationic metals, owing to their electrophilic nature,are more reactive than their anionic and neutral counterparts, so the main group metal cluster cations Ge+, GeO+, GeOH+and OGeOH+are our objects of study.Thirdly, when the ligand attaches to the metal ion M+, it will affect the electronic character of metal centers, then the chemistry of [ML]+complexes may change greatly.Two or more ligands may tune the chemical features of cationic metal better.

In the Periodic Table, the germanium lies on a special place that the non-metal As is situated at the top, Sn at the bottom, Ga on the left, and the nonmetal As on the right.The electronic structure of the germanium element is 4s24p2, with unfilled shells or unpaired electrons in p orbitals which may lead to special metal-ligand interactions.Benzi[8,9]reported the reactions of monogermane with O2, NH3, CO,CO2, and C2H4under high pressure using Fourier transform mass spectrometry.Tang and co-workers[10]investigated the reactions between M+(M = Si, Ge,Sn and Pb) and benzene in the gas phase using a laser ablation/inert buffer gas ion source coupled with a reflection time-of-flight mass spectrometer.Power[11]indicated that the main-group compounds generally do not interact strongly with CO, C2H4or H2.Ge+and methane only form addition [Ge(CH4)] with the reaction efficiency (2 × 10-4) using an inductivelycoupled plasma/selected-ion flow tube (ICP/SIFT)tandem mass spectrometer[5].These survey results suggest that the Ge chemical property is inactive and requires ligand to tune the reactivity.

In the recent paper, Sun and co-workers[12]have investigated the metal free cluster OSiOH+activation methane system, and the present study is a logical extension to the OGeOH+and CH4system.By electrospray ionization, it failed to generate GeO+,while large amount of GeOH+was produced due to the rather high hydrogen-atom affinities of GeO+.A solid-state-based laser-ablation method can produce GeO+[13].Herein we present the gas-phase reactions of the main group metal Ge+, GeO+, GeOH+and OGeOH+with methane by state-of-the-art quantum chemical calculations so as to explore the origin of the ligand effect.

2 COMPUTATIONAL DETAILS

Full optimization of geometries for all stationary points involved the reaction underlying the main group metal Ge+, GeO+, GeOH+and OGeOH+mediating the methane activation process using the density functional theory (DFT) method[14-16]based on the hybrid of Becke’s three-parameter exchange functional and the Lee, Yang, and Parr correlation functional (B3LYP)[17-19].The 6-311++G** basis set was performed for hydrogen, carbon, nitrogen and germanium.Frequency analysis was calculated at the same theoretical level.Frequency analysis was carried out for all stationary points for two purposes.The first one was to check whether the optimized geometry corresponds to a minimum or a transition state, and the second was to obtain the zero-point vibrational energies and Gibbs free energies.Relative energies were corrected for unscaled zero-point vibrational energy contributions.Furthermore, the intrinsic reaction coordinate (IRC) calculations[20]were performed to confirm that the optimized transition states correctly connect the relevant reactants and products.To check the reliability of our theoretical geometrical and energetic results obtained at the B3LYP/6-311++G** level of theory, we optimized all the complexes with the highly accurate theoretical method.Optimization calculations were done at the CCSD and MP2 levels with 6-311++G**basis set.Besides, the relativistic effective core potential (ECP) of Stuttgart/Dresden (Lanl2dz) was adopted to describe the metal Ge with the label MP2①in Tables S1 and S2 (We mark MP2①to discriminate ECP (Lanl2dz) for Ge from that of 6-311++G** in the MP2 level.).As shown in the supplementary information, there was a good agreement between the geometrical parameters and relative energy calculated with B3LYP, CCSD and MP2, though individual data have big difference.It illustrated that the results are reliable.Furthermore,we should underline the complexation energy calculated with the B3LYP method.The Cartesian coordinates of all stationary points under B3LYP/6-311++G** had be provided in SI.The natural population analysis had been made with the natural bond orbital (NBO) analysis[21,22].We had plotted the map of electrostatic potential surface at 0.001 a.u.isosurface contours by using GaussView software.Furthermore, Multiwfn software was used for quantitative analysis of molecular surfaces[23].All computations reported here are carried out using the GAUSSIAN 09 program suit[24].

3 RESULTS AND DISCUSSION

3.1 Reaction of Ge+ with CH4

We start to discuss the reaction between Ge+and CH4, with the potential energy profiles depicted in the supporting information Fig.S1.The electronic configuration of the ground state Ge+may be written as [Ar]3d104s24p1.For CH4, the C–H bond lengths are 1.09 ?, with the H–C–H angle of 109.5°.The doublet ground state of Ge+is 634.56 kJ/mol more stable than the quartet excited state, so we only take into account the ground state situation, marked 2 at the top left corner of the complex.For example, the methane coordinates to the metal center leading to the encounter complex2GeCH4+, which is –50.95 kJ/mol relative to the reactant asymptote.However, a H-atom transfer happens via transition state to form the complex2HGeCH3+.This step has high activation barrier (49.87 kJ/mol) and therefore is unlikely to happen at room temperature.Bohme’s[4]inductivelycoupled plasma/selected-ion flow tube (ICP/SIFT)tandem mass spectrometer research and Schwarz[25]DFT-based calculation results indicate that Ge+and methane only form the structural association product[Ge(CH4)]+.The Ge+(4s24p1) is incapable of activating CH4since it lacks electrons to donate to the C–H antibonding orbital of CH4in terms of the donoracceptor model.

3.2 Reaction of GeO+ with CH4

In order to improve the Ge+reactivity, we then study the reaction between GeO+and methane.The electronic configuration of the ground state GeO+may be written as(1σ)2(2σ)2(1π)4(3σ)2(4σ)2(5σ)2(2π)4(6σ)2(7σ)2(1δ)4(3π)4(8σ)2(9σ)2(10σ)2(4π)32?+.The equilibrium structure is determined to be re(GeO) = 1.67 ?.Hydrogenatom transfer (HAT) constitutes a key process in methane activation by metal-oxo species.The doublet ground state GeO+is more stable than the quartet excited state, so we only account the ground state situation.Regarding the mechanistic details of HAT, there are two modes.One is the direct HAT from CH4to the oxygen atom of MO+, and the other involves several steps, in which an empty coordinate site at the metal atom is required.The Ge in GeO+has no vacant coordination site, so we only consider the first situation.The direct HAT process prevails mainly for the open shell metal oxide and the high spin located at the terminal oxygen atom (0.72 spin density in O of GeO+).In the C–H bond activation of CH4by GeO+, the reaction proceeds barrier-free,directly to the complex [GeOH]+??CH3˙(0.85 spin density in CH3).In this HAT-product the methyl group loosely coordinates to the H of the newly formed hydroxyl group.The exothermic reaction is completed by liberation of the CH3˙ radical, resulting in the formation of [GeOH]+.This barrier-free step is exothermic by 169.9 kJ/mol.An alternative pathway is that a CH4molecule interacts with the terminal Ge in GeO+, thus forming an electrostatic complex[GeOCH4]+.Then the hydrogen transfer from carbon to Ge via the transition state2TS1/2 to form[HOGeCH3]+.The2TS1/2 lies 99.8 kJ/mol above the reactants, so the path does not occur under ambient conditions.In contrast to the bare metal cation Ge+,which exhibits no activity towards methane according to the above calculation, the reaction of metal monoxide GeO+due to the high spin density at the O atom (0.72) is efficient.In order to explore if the product GeOH+can further react with CH4, the following study is performed.

Fig.1.Schematic potential-energy profiles from GeO+/CH4

3.3 Reaction of GeOH+ with CH4

The GeOH+species is linear and its electronic configuration is described as (1σ)2(2σ)2(1π)4(3σ)2(4σ)2-(5σ)2(2π)4(6σ)2(7σ)2(1δ)4(3π)4(8σ)2(9σ)2(10σ)2(4π)41?+.The equilibrium structure is determined to be re(GeO)= 1.68 ? and re(OH) = 0.97 ?, which are basically consistent with Yamaguchi’s[26]results.The GeO bond length in GeOH+is 0.01 ? longer than that of diatomic GeO+.It is seen that the hydrogen atom destabilizes the Ge–O bond in GeOH+.The single ground state GeOH+is more stable than the triplet excited state, so we only take into account the ground state situa- tion, marked 1 at the top left corner of the complex, for example ‘1M1’.The potential energy profiles are drawn in the supporting information (Fig.S2).The hydrogen atom in CH4transfers to Ge in GeOH+in the transition state1TS1/2.The1TS1/2 lies 341.6 kJ/mol above the reactants, so the path doesn’t occur under ambient conditions.

3.4 Reaction of OGeOH+ with CH4

In OGeOH+, we mark the terminal oxygen atom as*O to distinguish the two oxygen atoms.The equilibrium structure is determined to be re(*OGe) = 1.61 ? and re(GeO) = 1.69 ?, in which oxygen atom lies in the OH group, and re(OH) = 0.98 ?, ∠ OGeO =172° and ∠G eOH = 121°.The four atoms are in the same plane.The oxygen atom adds to the other side of GeOH+; the Ge–O and O–H bonds in OGeOH+are also 0.01 ? longer than that of GeOH+.It is seen that the O atom destabilizes the Ge–O and O–H bonds.The cluster ion OGeOH+is generated in the reaction of [GeO2]+with water based on DFT.Full details of the process are provided in the support information(Fig.S3).Then mechanistic insight into the details of the methane activation step by OGeOH+has been discussed.The most favorable pathways for the reactions of OGeOH+/CH4couple are located on the singlet potential energy surface (PES), as shown in Fig.2.In the first case, an encounter complex (1M1)is initially formed from the reactants.This step is exothermic by 61.9 kJ/mol, thus indicating a rather stronger interaction between the positively charged germanium atom and methane (the charge on the germanium atom of OGeOH+amounts to 2.2 |e|based on a natural bond orbital (NBO) analysis).Subsequently, one C–H of the incoming methane substrate is activated and a hydrogen atom is transferred to the terminal *O atom of OGeOH+via transition state TS1/2 to form the rather stable germanium cation compound M2.In the latter, the positive charge at the germanium atom amounts to 2.1 |e|, and the formations of strong Ge–C and *O–H bonds account for the high stability of M2.Next, the methyl group can migrate via TS2/3 to one of the hydroxide ligands, thus forming complex M3.For the latter route, OGeOH+may be attacked by me-thane at the terminal oxygen atom *O to give directly the intermediate complex M3.To clarify the reaction mechanism of the directly formed intermediate complex M3 by the terminal oxygen atom *O attacking the C–H bond of methane, the energy changes and selected structures have been given in Fig.3.First of all, the terminal oxygen atom *O is close to the C–H bond of methane, with the *O??H bond to be 2.50 ?.Secondly, the activated C–H bond is increased from 1.11 to 1.57 ?, and the *O–H bond(1.01 ?) is nearly formed.And then, the *O–C bond distance is 1.52 ?, and the *O–Ge bond is increased from 1.81 to 2.03 ?.Finally, the Ge–*O bond continues to lengthen to 2.04 ?.The analysis indicates that the process is barrier-free to yield M3.This intermediate then serves as a branching point to either produce CH3OH and [GeOH+] or generate[GeOCH3]+accompanied by the loss of H2O.

Fig.2.Schematic potential-energy profiles from OGeOH+/CH4

Fig.3.Changes of the potential energy along the OGeOH+ + CH4 reaction pathway, where the selected geometry is given

Color-filled maps of the electron localization function along OGeOH++ CH4reaction pathway are presented in Fig.4.In M1, the absence of a disynaptic valence basin between Ge and the CH4carbon and hydrogen atoms confirms that interaction could be an electrostatic interaction.The first C–H bond breaking takes place due to the appearance of V(H,O*) basin in TS1/2.There is strength of disynaptic V(H,O*) basin, indicating that the H atom has shifted to *O completely in M2.As for TS2/3,the analysis reveals the weakening of disynaptic V(C,Ge) basin and the forming of disynaptic V(C,O)basin.There are two paths to form M3.One is[OGeOH+] + CH4→ M1 → TS1/2 → M2 → TS2/3→ M3, and the other is [OGeOH+] + CH4→ M1(Fig.2), which is obviously favorable.The ELF of M3 shows that CH3transfers to *O entirely.At the same time, the Ge–O bond breaks accompanied by the formation of a new *O–H bond.As for TS3/4, the appearance of H–O··H··*O bond by V(H,O,H,O)basin clearly proves the trend of H transferring into O of the OH.In the case of M4, a trisynaptic V(H,O,H) basin takes the place of V(H, O, H, O)basin, which indicates the formation of H2O.At the moment, the M4 intermediate dissociates into GeOCH3+and H2O.The energies of the intermediates and products are below the entrance channel,so the reaction can occur under ambient conditions.

Fig.4.(Color online) ELF projection map of the key points on the OGeOH+ + CH4 reaction pathway

3.5 Comparison of the four systems

The reaction mechanism of the four main group metal cations towards methane can be explained in NBO charge distribution.The charge at the terminal oxygen atom in GeO+and OGeOH+are –0.72 and–0.83 |e| respectively, which reveals that the terminal oxygen atom is the active site.The interaction of terminal oxygen atom and the hydrogen atom in methane leads to the translocation of H to *O atom.In conclusion, the ligands affect the local charge distribution in the main group germanium metal cation compounds.

Molecular electrostatic potential is another influence factor.The molecular electrostatic potential surface maps of the four metal ions and CH4are shown in Fig.5, which is drawn at 0.001 a.u.isosurface contours using GaussView software.The electron density distributions reveal the interaction between molecules.As shown in MEP map, due to electrostatic potential, there is a tendency between terminal oxygen *O in GeO+and OGeOH+and H in CH4to get close to each other.That explains the reason of GeO+and OGeOH+activate H3C–H bond.

Fig.5.Map of molecular electrostatic potential surface of the four metal ion and CH4 plotted by GaussView software using the B3LYP/6-311++G** wave functions

4 CONCLUSION

The methane activation mechanistic by the main group metal Ge+, GeO+, GeOH+and OGeOH+have been studied by the density functional theory method.The main reaction channel of GeO+/CH4is that the H in CH4is abstracted by the O in GeO+to form GeOH+and CH3˙.The fast and efficient reaction is barrier-free process along with exothermicity, which is in agreement with literature.For the OGeOH+and CH4system, the optimal path is that OGeOH+reacts with methane to form M3 firstly, and then, M4, the transformation product of M3, decomposes into[GeOCH3]+and H2O.However, as for Ge+and GeOH+, the activation reaction is difficult to carry out under ambient temperature.Therefore, the ligands affect the main group germanium metal cation compounds reactivity to a certain extent.The results provide effective information for more sophisticated research in the future.

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