Methane Activation by MH+ - American Chemical Society

Article pubs.acs.org/JPCA

Methane Activation by MH+ (M = Os, Ir, and Pt) and Comparisons to the Congeners of MH+ (M = Fe, Co, Ni and Ru, Rh, Pd) Shaoli Liu, Zhiyuan Geng,* Yongcheng Wang, and Yunfeng Yan Gansu Key Laboratory of Polymer Materials, College of Chemistry and Chemical Engineering, Key Laboratory of Eco-environment-related Polymer Materials, Ministry of Education, Northwest Normal University, Lanzhou, Gansu 730070, P.R. China S Supporting Information *

ABSTRACT: The mechanism of ligated-transition-metal- [MH+ (M = Os, Ir, and Pt)] catalyzed methane activation has been computed at the B3LYP level of density functional theory. The B3LYP energies of important species on the potential energy surfaces were compared to CCSD(T) single-point energy calculations. Newer kinetic and dispersioncorrected methods such as M05-2X provide significantly better descriptions of the bonding interactions. The reactions take place more easily along the low-spin potential energy surface. The minimum-energy pathway proceeds as MH+ + CH4 → M(H)2(CH3)+ → TS → MH(CH2)(H2)+ → MH(CH2)+ + H2. The ground states are 5Π, 4Σ−, and 1Σ+ for OsH+, IrH+, and PtH+, respectively. The energy level differences of the reactants between the high- and low-spin states gradually become smaller from OsH+ to PtH+, being 30.66, 9.17, and 0.09 kcal/mol, respectively. The CH bond can be readily activated by MH+ (M = Os, Ir, and Pt) with a negligible barrier in the low-spin state; thus, OsH+, IrH+, and PtH+ are likely to be excellent mediators for the activition of the CH bond of methane. H2 elimination is quite facile without barriers in the presence of excess reactants. The products of the reactions of MH+ (M = Os, Ir, and Pt) + methane are all carbene complexes MH(CH2)+. The exothermicities of the reactions are 3.99, 15.66, and 12.14 kcal/mol, respectively. The results for MH+ (M = Os, Ir, and Pt) are compared with those for the first- and second-row congeners, and the differences in behavior and mechanism are discussed. first and second rows can be rationalized by the increasing strengths of MH, MCH3, and MCH2 bonds from the first to the third row.20 Alkanes interact very weakly with transition metals for several reasons: Alkanes are relatively nonpolarizable, electrically neutral, and very poor electron donors and electron acceptors, so that charge-transfer, electrostatic, and covalent interactions with metals are weak.1j An alternative way to probe the activation of the CH bond in methane is to start with ligated transition-metal ions.21,22 The addition of a single ligand to the metal center has been employed either to alter electronic structure of the metal center through selective tuning of the electronic states or to prepare reactive centers. Bare Cr+, for example, is one of the least reactive transition-metal cations, whereas CrCl+ is already significantly more reactive.23 Extraordinary ligand effects have also been reported for diatomic MH+ ions. For example, Zhang et al.15 reported an experimental and theoretical investigation of methane dehydrogenation by MH+ (M = Fe, Co, Ni) (eq 1)

1. INTRODUCTION Methane, CH4, one of the most important chemicals, has been widely used in chemical industry, such as in hydrogen production and energy production. In particular, the cleavage of the CH bond in methane is an industrial process of great interest because it is the first step in converting natural gas into a transportable liquid feedstock. Therefore, methane activation has been studied extensively by both experimentalists and theorists.1 Several studies of atomic transition-metal ions with small alkanes have provided a wealth of insight concerning the intrinsic interactions of metal ions with bonds composed of carbon and hydrogen atoms.2−15 Experimental and density functional theory (DFT) studies performed on first-row transition-metal ions (Cr, V, Fe, Co, and Ni) showed that methane molecules sequentially cluster to the ionic metal centers, leaving the CH bonds intact.14 Second-row transition-metal cations have been found to be more reactive toward methane than their first-row counterparts but much less reactive than their third-row counterparts, and activation of methane by second-row species is rarely observed.16 Additional studies have demonstrated that methane can be spontaneously activated by third-row transition-metal ions such as Os+, Ir+, and Pt+, yielding the metallic carbene cations and H2.17−20 The higher reactivity of the third-row metal ions over those in the © 2012 American Chemical Society

Received: November 14, 2011 Revised: April 20, 2012 Published: April 23, 2012 4560

dx.doi.org/10.1021/jp210924a | J. Phys. Chem. A 2012, 116, 4560−4568

The Journal of Physical Chemistry A

Article

Table 1. Computed Bond Distances [r(MH)], Vibrational Frequencies (ν), Bond Dissociation Energies (BDEs), and Electron Excitation Energies (Eex) for the MH+ Complexes species OsH

+

Π Π 2 Δ 4 − Σ 1 + Σ 3 Δ 3

5

IrH+ PtH+ a

ν (cm−1)

r(MH) (Å)

state

1.575 1.602 1.540 1.556 1.514 1.542

2293 2194 2402 2318 2465 2319

(1.605)a (1.560)a (1.519)a (1.518)b (1.544)b

(2244)a (2372)a (2399)a (2403)b (2275)b

BDE (kcal/mol)

Eex (kcal/mol)

57.8 66.3 (56.2)a 66.8 72.7 (65.8)a 68.0 (62.9)a 85.5

−22.18 −3.25 18.41

Calculated values from ref 33a in parentheses. bCalculated values from ref 33g in parentheses.

MH+ + CH4 → MCH3+ + H 2

(1)

MH+ + CH4 → MHCH 2+ + H 2

(2)

double and perturbative triple excitations [CCSD(T)] approach, as well as the kinetic- and dispersion-corrected M05-2X32a method, at the B3LYP geometries. The M05-2X32a method provides a significantly better description of the bonding interactions. All computations reported here were carried out using the Gaussian 0332b and 0932c program suites.

The results showed that, whereas the naked metal ions M+ do not bring about thermal CH bond cleavage, NiH+ activates methane at temperatures as low as 80 K, CoH+ reacts at room temperature, and for FeH+ temperatures above 600 K are required for the H/CH3 ligand exchange. We extended these studies and described the reaction of methane catalyzed by ligated transition-metal ions MH+ (M = Ru, Rh, Pd).15 The results clearly demonstrated that MH+ (M = Ru, Rh, and Pd) can efficiently convert methane to metal methyl. Recently, an experimental investigation of methane dehydrogenation by PtH+ was reported by Schröder et al.24 Their results showed that CH4 activation by PtH+ is slightly endothermic by 3.00 ± 2.08 kcal/mol. To our knowledge, the detailed potential energy surfaces for the dehydrogenation of methane by MH+ (M = Os, Ir, and Pt) have not been reported. To gain systematic insight into the mechanism of the reaction with methane of third-row transition-metal ions ligated by hydrogen, we have carried out a theoretical study at the DFT level on the reaction MH+ (M = Os, Ir, Pt) + CH4 (eq 1 or 2).

3. RESULTS AND DISCUSSION 3.1. Structures of MH+ (M = Os, Ir, and Pt). The structures of OsH+, IrH+, and PtH+ were reported previously,33 and our main goal here is to compare our results with the reported values (Table 1). For OsH+, the ground electronic state is 5Π, which is mainly derived from the 5d66s1 (6D) state of atomic Os+, with nonbonding configuration (dσ)1(dπ)3(dδ)2. It has an NBO population of 5d6.186s0.826p0.01. The triplet electronic excitation state of OsH+ has a relative energy 30.66 kcal/mol higher than that of the ground-state reactant, with a valence NBO population of 5d6.726s0.226p0.01. For IrH+, the ground state is 4 − Σ (σ1π4δ2) due to the 5d76s1 (5F) configuration of Ir+, with an NBO population of 5d7.266s0.796p0.01. The low-spin doublet state lies 9.17 kcal/mol higher in energy than the ground state and has a valence electron population of 5d7.876s0.186p0.01. Because Pt+ has a d9 configuration, the singly occupied dx2 orbital combined with the 1s orbital of H leads to a 1Σ+ ground state for PtH+. The triplet electronic excitation state, 3Δ, is only 0.09 kcal/mol higher than the ground state, which indicates that the 1Σ+ and 3Δ states of PtH+ are practically isoenergetic. These results agree well with previous experimental24 and theoretical33b results. The energy level difference between the high- and low-spin states becomes gradually smaller from OsH+ to IrH+ and PtH+. As has been well established by now, this is due to the combined action of the excitation energy of M+ and the bonding energies of M+H. The calculated excitation energies are 22.18, 3.25, and 18.41 kcal/mol, respectively, corresponding to ground states of 6D for Os+, 5F for Ir+, and 2D for Pt+. The differences of the bonding energy (ΔBDE) between the high- and low-spin states were calculated to be 8.49, 5.92, and 17.50 kcal/mol for OsH+, IrH+, and PtH+, respectively. Thus, this combined action between the excitation energy and ΔBDE results in the energy level differences between the lowand high-spin states of MH+. The equilibrium distances of the ground-state M+H ions were calculated to be 1.602, 1.556, and 1.514 Å for Os, Ir, and Pt, respectively, which agree well with the previous results (1.605, 1.560, and 1.519 Å).33 The change in the bond distance of MH+ can be rationalized by the fact that the atomic radius decreases from Os to Pt. From Table 1, one can see that the bond distances of the low-spin-state MH+ ions are shorter than those of the high-spin states and that the dissociation energies

2. METHODS OF CALCULATION Full optimization of geometries for all stationary points involved in methane dehydrogenation by MH+ (M = Os, Ir, Pt) was performed using the density functional theory (DFT) method based on the hybrid of Becke’s three-parameter exchange functional and the Lee, Yang, and Parr correlation functional (B3LYP).25−27 The B3LYP functional was used for all calculations performed in this work because it provides reasonable results for the analogous MH+ ions of the first- (Fe, Co, Ni) and second- (Ru, Rh, Pd) row transition-metal ions with CH4 systems.2,15 For carbon and hydrogen, the large 6311+G** basis set was used, whereas the Stuttgart/Dresden relativistic effective core potentials (ECPs), designated as SDD, were employed to describe the metals Os, Ir, and Pt.28 For each optimized stationary point, vibrational analysis was performed at the same level of theory to determine the character (minimum or saddle point) of the stationary point and to evaluate the zero-point vibrational energy (ZPVE) corrections, which were included in all relative energies. Furthermore, intrinsic reaction coordinate (IRC) calculations29 were performed to confirm that the optimized transition states correctly connect the relevant reactants and products. Natural population analysis was performed with natural bond orbital (NBO) analysis30,31 to obtain further insight into the bonding properties. Single-point energy calculations were performed using the highly correlated coupled-cluster with single and 4561



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Table 2. Relative Energies (kcal/mol) of the Species on the Potential Energy Surfaces of the Reactions MH+ (M = Os, Ir, and Pt) + CH4 Obtained Using the B3LYP Functional Os species +

MH MH(CH4)+ TS1 MH2(CH3)+ TS2 M(CH3)(H2)+ TS3 MH(CH2)(H2)+ MHCH2++H2 MCH3++H2 a

Π

3

30.66 −13.39 −14.20 −32.01 −11.06

−16.10 −3.99

Ir Π

5

0.00 −11.98 7.15 3.89 6.89 −9.91 22.23 16.62 23.92 −3.32

2

Δ

9.17

−43.78 −21.13

−27.06 −15.66

Pt 4 −

Σ

Σ

1 +

0.00 −17.14 4.12 2.88 3.20 −13.58 13.14 11.33 20.39 −5.48

0.00

−51.00 −17.31 (−9.75)a (−10.64)a −18.73 −12.14 (1.16)a

Δ

3

0.90 −13.43 3.92 −0.86 −0.34 −5.96 12.85 11.34 21.37 2.52

Relative energies of the species for the reaction PtH+ + CH4 → PtCH3+ + H2 in parentheses.

approach propsed by Zhang et al.19 and Yoshizawa et al.34 for locating the crossing point of two PESs of different multiplicities. As shown in Figure 2, the minimum on the seam of the crossings has an OsC distance of 2.90 Å. After the molecular complex, the global-minimum structure on the triplet potential energy surface was found to be 3 Os(H)2(CH3)+, where H1 (H1 is the activated hydrogen of CH4) has been transferred to Os from C, which adopts Cs symmetry. As shown in the Supporting Information, the Os C and OsH bond lengths in 3Os(H)2(CH3)+ are 1.991 and 1.587 Å, respectively, shorter than those in 5Os(H)2(CH3)+ (2.029 and 1.691 Å, respectively). The results listed in Table 2 show that 3Os(H)2(CH3)+ (which is 32.01 kcal/mol below the ground-state reactants) is 35.90 kcal/mol lower in energy than 5 Os(H)2(CH3)+. This is because of the difference in binding of the low- and high-spin states of Os(H)2(CH3)+. The low-spin state allows Os+ to form a covalent bond with both H atoms and the methyl group (i.e., there are six electrons in these bonding orbitals), whereas a high-spin state requires that one of these electrons must be moved to a nonbonding orbital. Hence, the bonding is stronger in the low-spin state. TS1 is the transition state of the oxidative addition of the CH1 bond on the reaction path. Bonding in the low-spin 3 TS1 is illustrated in Figure 3. Key orbitals involved in the cleavage of the CH bond are displayed. The singly occupied 1s orbitals from the hydrogen atom and a singly occupied sp3hybridized orbital from the methyl group contribute to the formation of a σ-bonding orbital and an antibonding orbital. For Os of OsH+, one of its two singly occupied d orbitals forms a nonbonding orbital, and the second one pairs with the empty antibonding orbital from HCH3, forming a singly occupied πbonding orbital, bridging the carbon in the methyl group and the hydrogen atom, and an empty π*-antibonding orbital. This is the reason for the low energy of 3TS1. On the low-spin potential energy surface, the energy and geometry obtained for transition state 3TS1 are all very close to those of the complex 3 OsH(CH4)+. These results indicate that no true minimum was found for 3OsH(CH4)+ and that the transition state might be negligible on the overall low-spin reaction path. In 5TS1, the activated CH1 bond is almost broken, and the OsH1 bond is nearly formed, indicating that this transition state, 5TS1, is a typical three-centered late transition state, which is 19.13 kcal/ mol above the encounter complex 5OsH(CH4)+, but only 3.26 kcal/mol above 5Os(H)2(CH3)+.

of the low-spin states are lower than those of the high-spin states. The trends in bond distances for MH+ are dominated by the spatial extents of the valence orbitals (6s and 5d). Orbital sizes scale as a0(n2/Zeff), where a0 is the Bohr radius, n is the principal quantum number, and Zeff is the effective nuclear charge felt by the electron. The valence s orbital has a value of n that is one unit larger than the valence d orbital (6s versus 5d), making it significantly more diffuse than the d orbital. NBO analysis indicates that, in the high-spin state, the s electron of H binds with the outer s core orbital of the metal. However, in the low-spin state from OsH+ to PtH+, because of the absence of an s electron in the outer core orbitals, the bonding orbital involved on the metal is the σ (dx2) orbital to bind with the s orbital of H, making the H core closer to the metal core and leading the bond distance of MH in the low-spin state to be shorter than that in the high-spin state. 3.2. Reactivities of MH+ (M = Os, Ir, and Pt) with CH4. In this section, we discuss the reactivities of MH+ in the activation process of CH4. Both low- and high-spin states were considered, and the energetics of intermediates and transition states relative to ground-state MH+ + CH4 are summarized in Table 2. CCSD(T) single-point energies and M05-2X dispersion-corrected energies based on the B3LYP geometries, as well as the geometries of these structures, are listed in the Supporting Information. The potential energy surfaces of the reaction MH+ + CH4 in the low- and high-spin states are presented in Figure 1. 3.2.1. OsH+ + CH4. The reaction starts with the formation of the methane complex OsH(CH4)+. In the triplet state, the molecular complex 3OsH(CH4)+ lies 13.39 kcal/mol below the ground-state reactants. This complex has a tilted η 3 coordination in Cs symmetry, similar to those in the reaction systems of Os+ and Rh+ with methane.16,19 The NBO population of the valence electrons is 5d6.826s0.486p0.01 for the Os center in 3OsH(CH4)+. The calculated ligand association energy of CH4 to 3OsH+ is 44.05 kcal/mol. The activated C H1 (CH1 represents the activated CH bond) distance was calculated to be 1.290 Å, and the corresponding OsH1 and OsC distances are 1.665 and 2.203 Å, respectively, indicating a large agostic interaction. The high-spin 5OsH(CH4)+ complex was found to have η2 coordination with Cs symmetry, with an OsC distance of 2.675 Å and a 1.41 kcal/mol higher energy than triplet 3OsH(CH4)+. The low-spin 3OsH+ forms a more tightly bound complex than the high-spin (quintet) state. It can be seen from the energies that a curve crossing is required from the quintet state to the triplet state. Thus, we chose an 4562



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Figure 2. Quintet and triplet potential energies of the reactant complex as a function of the distance between Os+ and the carbon atom of CH4.

Figure 3. Molecular orbital diagram of 3TS1 on the triplet potential energy surface of the reaction OsH+ + CH4.

9.91 kcal/mol in energy below the ground-state reactants. As for 5Os(CH3)(H2)+, which has a valence electron population of 5d6.306s0.636p0.01, the bond between Os and the methyl radical can be visualized as spin pairing of an electron in an sdσ orbital of Os with the unpaired electron in the spσ orbital of CH3. Later, the migration of a second hydrogen occurs to give the H2 molecule complex 5OsH(CH2)(H2)+. Because of the high barrier of 32.14 kcal/mol, we do not discuss this path further. The reductive elimination transition state 3TS2 connecting 3 Os(H)2(CH3)+ and 3OsH(CH2)(H2)+ was located as the Cs structure shown in the Supporting Information. 5TS2 has a C1 structure and connects 5Os(H)2(CH3)+ and 5Os(CH3)(H2)+. From the structures of TS2, one can see that 3TS2 is a very late transition state, but the quintet transition state 5TS2 is an early transition state. Because the triplet transition state 3TS2 is preferred for 3OsH(CH2)(H2)+ but less favorable for 3Os(H)2(CH3)+, 5TS2 is consistent with the relatively large exothermicity (16.80 kcal/mol) of the step from 5Os(H)2(CH3)+ to 5Os(CH3)(H2)+. This shows clearly that the barrier for the quintet state (3.00 kcal/mol) is considerably smaller than that for the triplet state (20.95 kcal/mol). However, because of the global minimum of 3Os(H)2(CH3)+, 3 TS2 is 17.95 kcal/mol lower in energy than 5TS2, and the reaction of this step is exothermic relative to the ground-state reactants on the triplet surface.

Figure 1. Potential energy surfaces of the reactions (a) OsH+ (b) IrH+ and (c) PtH+ + CH4 in both the low- and high-spin states.

The next step is a reductive elimination step to form a H2 molecule complex. On the triplet surface, there is in concert a migration of a second hydrogen from the CH3 group to the metal, leading to the carbene complex 3OsH(CH2)(H2)+, which lies 16.10 kcal/mol below the ground-state reactants. The natural population analysis of 5d6.676s0.606p0.01 indicates that, in 3OsH(CH2)(H2)+, the sdσ orbital makes a large contribution to two normal covalent bonds with hydrogen and carbon and the dπ orbital of Os and the pπ orbital of carbene are involved in a πOsC bond. In the quintet state, the product of the reductive elimination step is 5Os(CH3)(H2)+, which lies 4563



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Table 3. Valence NBO Populations for the 5d/6s/6p Orbitals of M+ (M = Os, Ir, and Pt) in the Stationary Points Os species +

MH MH(CH4)+ TS1 MH2(CH3)+ TS2 M(CH3)(H2)+ TS3 MH(CH2)(H2)+ MHCH2++H2 MCH3++H2 a

3

Π

6.72/0.22/0.01 6.82/0.48/0.01 6.83/0.49/0.01 6.56/0.71/0.01 6.73/0.62/0.01

6.67/0.60/0.01 6.63/0.64/0.01

Ir Π

5

6.18/0.82/0.01 6.18/0.80/0.01 6.18/0.71/0.02 6.06/0.72/0.02 6.04/0.75/0.02 6.30/0.63/0.01 6.41/0.59/0.02 6.24/0.65/0.02 6.16/0.68/0.02 6.25/0.71/0.01

Pt

Δ

4 −

7.87/0.18/0.01

7.26/0.79/0.01 7.36/0.73/0.01 7.43/0.67/0.01 7.36/0.74/0.01 7.36/0.75/0.01 7.48/0.57/0.01 7.53/0.56/0.01 7.58/0.60/0.01 7.43/0.65/0.01 7.34/0.67/0.01

Σ

2

7.81/0.65/0.01 7.90/0.57/0.01

7.86/0.57/0.01 7.81/0.61/0.01

Σ

1 +

8.99/0.15/0.01

8.89/0.69/0.01 8.92/0.69(9.02/0.18/0.01)a (9.06/0.07/0.01)a 8.88/0.72/0.01 8.86/0.72/0.01 (9.05/0.07/0.01)a

Δ

3

8.41/0.70/0.01 8.51/0.69/0.02 8.66/0.63/0.02 8.67/0.69/0.01 8.76/0.57/0.01 8.68/0.50/0.01 8.67/0.53/0.01 8.61/0.57/0.01 8.58/0.59/0.02 8.44/0.64/0.01

Valence NBO populations for the reaction PtH+ + CH4 → PtCH3+ + H2 in parentheses.

the methyl group is easier. The occupied π-bonding orbital in Figure 3 has two electrons in the IrH+/CH4 system, leading to a lower energy for the transition state TS1 on the low-spin surface of the IrH+ + CH4 system. The activation of the CH bond and the formation of the MH bond are easier. No activation transition state was found on the doublet surface. The activation of the first CH bond is without barriers. These results can be understood similarly to the OsH+ + CH4 system and indicate that CH is activated spontaneously on the doublet surface. The structure of 2Ir(H)2(CH3)+ is nonplanar, with a H1IrH2C dihedral angle of 103°, indicating that the sdδ orbitals of Ir make a large contribution to the metalH bonds. On the quartet surface, there exists only the loosely bound complex 4IrH(CH4)+, in which the IrC distance is 2.582 Å. Because the quartet state is the ground state of IrH+, CH4 activation starting from the ground-state reactants again requires an intersystem crossing mechanism as described in the case of OsH+ + CH4. As shown in Figure 4, the minimum on the seam of crossings is close to the reactants (the IrC distance is 3.15 Å).

As to the final products, the ground electronic state of OsH(CH2)+ has a triplet low-spin configuration, which has a H2 association energy of 12.11 kcal/mol. The structures and the bonding modes of the 3OsH(CH2)+ product are very much like those of the HOsCH2 part in the corresponding intermediate 3 OsH(CH2)(H2)+ species. The product of the high-spin state is 5 Os(CH3)+, which is only weakly bound to the H2 molecule by 6.59 kcal/mol. An interesting phenomenon in this region is that triplet 3OsH(CH2)+ and quintet 5Os(CH3)+ have completely different structures from each other, but the energy of the quintet 5Os(CH3)+ is only 0.67 kcal/mol higher than that of the ground-state 3OsH(CH2)+. As a short summary, we see that the CH bond is readily activated by OsH+ with a negligible barrier in the low-spin state. The global-minimum structure on the potential energy surface was found to be 3Os(H)2(CH3)+, which has a nonplanar structur,e indicating that the sdδ orbitals of Os makes a large contribution to the OsH bonds. Afterward, although the reductive elimination step of H2 has a distinct barrier in the low-spin state for reaction starting from the global-minimum intermediate, it is exothermic relative to the ground-state reactants on the overall reaction path. The final product is the carbene complex OsH(CH2)+. 3.2.2. IrH+ and PtH+ toward CH4. For CH4 activation by IrH+ and PtH+, the mechanisms are very similar to those for OsH+ discussed in the preceding section. Indeed, some geometrical parameters in M(H)2(CH3)+, TS, MH(CH2)(H2)+, and MH(CH2)+ are all very similar to the corresponding structures in the case of OsH+, as can be seen clearly by comparing parts a−c of S.Figure 1 in the Supporting Information. As seen from Table 3, the changes of the valence NBO populations of M+ of the species for the reactions of MH+ (M = Os, Ir, and Pt) and methane are also very similar, clearly indicating the similarity in bonding nature. Therefore, we do not discuss their geometries in further detail but show some differences. For IrH+ + CH4, as calculated results, the low-spin 2IrH+ with methane tends to form an 2Ir(H)2(CH3)+ intermediate directly. No encounter complex was found (similar to the PtH+/CH4 system in the low-spin state). To confirm the calculated results, MP2/sdd/6-311+G** was used to calculate the encounter complex 2IrH(CH4)+, but we could not find it. According to the analysis of 3TS1 in the OsH+/CH4 system and Figure 3, the d orbitals are tighter to the core from Os to Pt, and the energies of the d orbitals of Ir+ and Pt+ are lower than that of the Os+, so the bonding between the d orbital of metal and the orbitals of

Figure 4. Quartet and doublet potential energies of the reactant complex as a function of the distance between Ir+ and the carbon atom of CH4.

Energetically, the reactions proceed in a rather parallel fashion in both the low- and high-spin states of OsH+ and IrH+, as illustrated in Figure 1a,b. In the step of the oxidative addition of the CH1 bond, there is no activation barrier on the doublet 2IrH+ + CH4 reaction potential surface, whereas the barrier height is 4.12 kcal/mol on the quartet surface, measured from the ground-state 4IrH+ + CH4. The intermediate 2Ir4564



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(H)2(CH3)+ is the global minimum, which is 43.78 kcal/mol below the reactants, whereas 4Ir(H)2(CH3)+ is 2.88 kcal/mol higher relative to the ground-state reactants. After overcoming a large barrier of 22.65 kcal/mol in the doublet state or a small barrier of 0.32 kcal/mol in the quartet state, the stable complex 2 IrH(CH2)(H2)+ or 4Ir(CH3)(H2)+ is formed. The products 2 IrH(CH2)+ and H2 are 15.66 kcal/mol below the ground-state 4 IrH+ + CH4, whereas the quartet products 4Ir(CH3)+ and H2 are 5.48 kcal/mol below the ground-state reactants. Unlike OsH+ and IrH+, the ground state of PtH+ is the lowspin singlet state. Because the 1Σ+ and 3Δ states of PtH+ are practically isoenergetic, one can expect that, starting from the singlet PtH+, CH4 activation proceeds rather quickly on the singlet electronic state; alternatively, the system might also cross over to the singlet electronic state from the triplet state around the reactants. Schröder et al.24 reported experiments on the reaction of PtH+ with CH4. They reported that CH4 activation to PtCH3+ by PtH+ is slightly endothermic by 3.00 ± 2.08 kcal/mol. Our calculation for the formation of PtCH3+ is endothermic by 1.16 kcal/mol, in close agreement with the experimental works on the reaction of PtH+ + CH4 → PtCH3+ + H2. However, what we found interesting is the other path obtained in the current work. In this path, the product 1 PtH(CH2)+ lies 13.30 kcal/mol lower in energy than 1Pt(CH3)+ on the low-spin reaction path. In fact, Schröder et al. pointed out that, with regard to the low kinetic isotope effect observed, the mechanism of the gas-phase processes described is most likely difficult to assess by experimental means for the time being. Therefore, we conjecture that the favorable groundstate product should be 1PtH(CH2)+. As mentioned in the Introduction, the activation of methane by Os+, Ir+, and Pt+ has been the subject of previous studies,17−19 in which Os+ and Ir+ were found to be able to activate CH4 effectively and the overall reactions were calculated to be exothermic. However, the reacting system of M+ (M = Os and Ir) + CH4 should change its spin multiplicity three times in the overall reaction processes. (As pointed out in ref 17, the reaction of Ir+ + CH4 can also occur with only a single spin change.) In other words, Os+/Ir+ activation of CH4 is not spontaneous starting from the ground-state M+ and might actually be rather slow because of the necessary intersystem crossing. For the OsH+/IrH+ + CH4 systems, although there is also a two-state reactivity similar to that in the Os+/Ir+ + CH4 system, there is only one crossing point around OsH(CH4)+ where the triplet and quintet states become close in energy on the overall reaction path. In short, because of the transformation probabilities, CH4 activation proceeds faster with OsH+/IrH+ than with Os+/Ir+. For Pt+ or PtH+, the reaction in the ground low-spin state is more exothermic and more favorable with a lower barrier, and the reaction is a spinallowed reaction. Thus, it is expected that PtH+ activates the CH bond in CH4 with a similar activition as in the Pt+ system. From the general energy profiles of the reaction pathways, the MH+ (M = Os, Ir, and Pt) complexes are expected to activate CH4 efficiently, and OsH+, IrH+, and PtH+ are likely to be excellent mediators for CH4 activation. Initially, one can see that one of the H atoms migrates to the metal atom, forming the intermediate M(H)2(CH3)+. Then, a reductive elimination step to form a H2 molecule complex in concert with the migration of a second hydrogen from CH3 to the metal yields MH(CH2)(H2)+. The products of the reaction of MH+ and

methane are all the carbene complex MH(CH2)+. The exothermicities of the reactions are 3.99, 15.66, and 12.14 kcal/mol for Os, Ir, and Pt, respectively. 3.3. Crossing Points between PESs of Different Multiplicities. For electron spin to be conserved in H2 elimination reactions with CH4 where ground-state products are formed, the spin multiplicities of M+ and MCH2+ must be the same according to the Wigner−Witmer spin conservation rules because the ground states of CH4(1A1) and H2(1Σg) are both singlets.35 As discussed above, one can see that the minimum-energy path is not one of a certain spin state. To better understand the spin inversion processes, it is instructive to locate the crossing points between the high- and low-spin states on the reaction path. For OsH+ and CH4, the OsH+ quintet state is lower than the OsH+ triplet state by 30.66 kcal/ mol, but the quintet complex OsH(CH4)+ lies 1.41 kcal/mol higher than the triplet one. These results indicate that the spin crossing occurs before the complex region. One can see from Figure 1a that, for the later parts of the reaction path, if intersystem crossing to the excited potential energy surface is involved, the energy barrier is significantly reduced. First, the computed potential energy profiles of the triplet and quintet states, as functions of the distance between Os and C of CH4, are shown in Figure 2. For a given OsC bond length, all other geometrical degrees of freedom were optimized for each spin state. As shown in Figure 2, as CH4 approaches Os, the energy of the complex decreases monotonically for the triplet state, but the energy of the quintet complex increases after decreasing. The triplet and quintet curves cross near the bottom of the quintet well, at which point the OsC bond length is 2.45 Å. As same-row counterparts, Os, Ir, and Pt atoms should have some similar properties. In this case, we also scanned the IrC and PtC bonds to verify whether the spin crossing point exists before the complex region. As CH4 approaches Ir, as shown in Figure 4, the differences between the potential energies of the reactant complexes decrease until the distance of IrC bond reaches 3.15 Å, where the energy-minimum crossing point occurs between the doublet and quartet paths; that is, the spin crossing occurs in this region, making the doublet state lower for the later parts of the reaction. For the scan of the PtC bond, one can see from Figure 5 that the energies of the complex in the triplet state are always above those in the singlet state, until the PtC bond become long enough (as the reactants), at which point the PtH(CH4)+

Figure 5. Triplet and singlet potential energies of the reactant complex as a function of the distance between Pt+ and the carbon atom of CH4. 4565



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Table 4. Single-Point Energies (kcal/mol) of the Species on the Potential Energy Surfaces of the Reactions MH+ (M = Os, Ir, and Pt) + CH4 from DFT-Optimized Structures Os

Ir

Π

Π

3

species

CCSD(T)

M052X

MH(CH4)+ TS1 MH2(CH3)+ TS2 M(CH3)(H2)+ TS3 MH(CH2) (H2)+

16.11 16.00 2.86 18.06 − − 12.38

2.00 1.88 −17.03 7.27 − − 4.39

a

Pt 4 −

Δ

5

Σ

2

CCSD(T)

M052X

0.00 24.73 22.54 25.91 10.62 46.77 37.89

0.00 23.87 21.45 25.49 4.91 41.72 37.36

CCSD(T)

M052X

− − −16.17 −8.46 − − 1.94

− − −25.94 9.07 − − −1.77

Σ

1 +

3

Δ

CCSD(T)

M052X

CCSD(T)

M05-2X

CCSD(T)

M052X

0.00 27.59 27.89 28.53 12.45 40.77 39.80

0.00 27.57 26.71 26.47 6.36 39.03 37.59

− − −33.87 12.35 (3.69)a (9.37)a − 2.07

− − −42.38 2.39 (−1.24)a (71.97)a − −2.86

0.00 23.86 17.19 20.32 16.16 34.16 31.90

0.00 17.26 24.50 20.52 8.92 28.31 27.64

Relative energies of the species for the reaction PtH+ + CH4 → PtCH3+ + H2 in parentheses.

complexes are practically isoenergetic. Thus, no crossing point between the triplet and singlet paths occurs. Schwarz et al.24 predicted that a multitude of both single- and multistate reactivity routes are accessible in the course of Pt-mediated H/ CH3 ligand exchange. On this point, the calculated results indicate that the reaction of PtH+ + CH4 is single-state reactivity on the singlet potential surface. As discussed above, the MC distances of the MH(CH4)+ complex at the crossing point become longer from Os to Pt, as the OsC distance is 2.45 Å [shorter than the OsC bond of the stationary point OsH(CH4)+ in the high-spin (quintet) state]; the IrC distance is 3.15 Å [longer than the IrC bond of IrH(CH4)+ in the high-spin (quartet) state]; and although the PtC distance is longer than 4 Å, the PtH(CH4)+ molecule complex of the singlet and triplet state are practically isoenergetic. Under this position of the crossing point, if one supposes that the ground state of PtH+ is the high-spin (triplet) state, the PtC distance is much longer than that in the highspin intermediate PtH(CH4)+. That is, the crossing point becomes gradually closer to the reactant from Os to Pt. 3.4. Single-Point Energies. In this section, we report the results of single-point energy calculations that were performed using the highly correlated CCSD(T) approach, as well as the kinetic- and dispersion-corrected M05-2X method at the B3LYP geometries. The energies relative to high-spin MH(CH4)+ are reported in Table 4; the absolute energies can be found in the Supporting Information. The CCSD(T) and M05-2X results show that the energy of activation for the first CH bond in the OsH+/CH4 system is negligible, 0.11 kcal/mol for CCSD(T) and 0.12 kcal/mol for M05-2X; these calculated energies are in good agreement with B3LYP result of 0.81 kcal/mol. Likewise, the calculated singlepoint energies from M05-2X are in good agreement with the B3LYP energies. For example, the calculated energy of the transition state 3TS1 in the OsH+/CH4 system, 1.88 kcal/mol relative to 5OsH(CH4)+ from M05-2X, compares well with the −2.22 kcal/mol energy of 3TS1 relative to 5OsH(CH4)+ for B3LYP. The agreement between the B3LYP energies and the results obtained using the dispersion-corrected M05-2X functional suggests that B3LYP is practicable for modeling this class of reactions such as MH/CH4 systems. 3.5. Comparison to MH+ (M = Fe, Co, Ni and Ru, Rh, Pd) + CH4. In this section, we summarize the findings of both our work and previous studies concerning the behavior of the PESs for the dehydrogenation reaction of methane by first-row (M = Fe, Co, Ni),15,33c−e second-row (M = Ru, Rh, Pd),2,33f

and third-row (M = Os, Ir, Pt) metal hydride diatomic cations. As can be seen in Figure 1 and in the structures in the Supporting Information and on the basis of previous results,2,15,33 the reaction paths and the geometric structures of key points have many features in common, especially along the low-spin-state PESs. Despite the qualitative similarities among the reaction paths, there are significant differences in some aspects. Previous studies2,15,33 have reported differences among the metal hydride diatomic cations. First, differences exist with regard to the details of orbital configurations of MH+. For Fe+, Co+, and Ni+, the best bonds are obtained by using the s1dn−1 excited states. The result is 5Δ for FeH+, 4Φ for CoH+, and 3Δ for NiH+.15,33c−e The second transition row differs from the firstrow counterparts, where stabilization of dn is so strong that RuH+, RhH+, and PdH+ are all based on dn rather than s1dn−1, leading to 3Σ−, 2Δ, and 1Σ+, respectively.2,33f In the third row, the dominant feature is the extra stabilization of s1dn−1 over dn, associated with the much larger relativistic effects after the lanthanides. The NBO analysis indicates that the hydrides OsH+ and IrH+ have one electron in the nonbonding s orbital, except for PtH+. The ground states are 5Π, 4Σ−, and 1Σ+ for OsH+, IrH+, and PtH+, respectively. Because of the above discussions, fundamental differences exist with regard to the details of the potential energy surfaces and thus the actual reaction mechanisms. As already shown by Zhang et al.,15 Fe-, Co-, and Ni-mediated H/CH3 ligand exchange is a spin-accelerated process (or two-state reactivity) because two crossings between the high-spin and low-spin potential energy surfaces take place at both the entrance and the exit channels of the reaction. The reaction of MH+ (M = Ru, Rh, and Pd) with methane can be fully explained without invoking a multistate pattern; instead, the overall reaction proceeds on the ground-state potential energy surface in a spinconserving manner, as shown by our laboratory.2 In the processes of the reactions of first- and second-row MH+ and methane, one of the hydrogen atoms from methane shifts to the metal, and the molecule H2 is formed simultaneously through a four-membered transition state, giving rise to the MCH3(H2)+ molecule complex.2,15 The MH+/CH4 (M = Os, Ir and Pt) couple also involves two-state reactivity, but only one crossing takes place at the entrance channel between the highand low-spin potential energy surfaces of the reaction and thus occurs in a diabatic way on two or more potential energy surfaces. In distinct contrast, the migration of a second hydrogen to the metal from carbon occurs, with the elimination 4566



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of a molecule of H2 through a concerted reaction to give the MH(CH2)(H2)+ complex, in which M+ is capable of forming three covalent bonds including an MC double bond (in which the formal oxidation state of M is IV). These results indicate that the higher oxidation state of the third-row transition metals is more stable.

AUTHOR INFORMATION

Corresponding Author

*Fax: +86 0931 7971989. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Natural science foundation of Gansu province (Grant No.10710RJZA114), the Natural Science Foundation of Gansu province education office (Grant No.10801-10).These grants are gratefully acknowledged. We would like to show our deepest gratitude to Haijun Jiao (Institute of Coal Chemistry, Chinese Academy of Sciences), who has provided us with the calculations to CCSD(T) and M05-2X using the Gaussian 09 program and with valuable guidance of the writing of this thesis.

4. CONCLUSIONS The dehydrogenation reaction mechanisms of methane catalyzed by the ligated transition-metal ions MH+ (M = Os, Ir, and Pt) have been investigated theoretically at the DFT (B3LYP) level, by considering both the low- and high-spin potential energy surfaces, and some comparisons with their first- and second-row congeners and the reactions of their cations with methane have been performed. The following conclusions can be drawn from the present work: Using arguments based on energetics, we suggest that the reaction takes place more easily along the low-spin potential energy surface. Because the ground states of OsH+ and IrH+ are high-spin states (5Π and 4Σ−, respectively), a curve crossing to the low-spin state is required, and the minimum crossing point can be approximately viewed as the reactants. In contrast, the PtH+/CH4 couple proceeds on the ground-state potential energy surface in a spin-allowed manner. Because of the combined action of the excitation energy of M+ and ΔBDE of the MH bond, the energy level differences gradually become smaller from OsH+ to PtH+, being 30.66, 9.17, and 0.09 kcal/mol, respectively. The CH bond can be readily activated by MH+ with a negligible barrier in the low-spin state, as the relative energies of the intermediate M(H)2(CH3)+ are −32.01, −43.78, and −51.00 kcal/mol for Os, Ir, and Pt, respectively. The structure of M(H)2(CH3)+ is nonplanar, which indicates that the sdδ orbitals make a large contribution to the metalH bonds. The reductive elimination step of H2 has a distinct barrier (20.95, 22.65, and 33.69 kcal/mol, respectively) for reactions starting from the global minimum M(H)2(CH3)+. However, because of the lowest energy of M(H)2(CH3)+, the reductive elimination step of H2 is exothermic relative to the ground-state reactants. The products of the reaction of MH+ and methane are all the carbene complex MH(CH2)+. The exothermicities of the reactions are 3.99, 15.66, and 12.14 kcal/mol for Os, Ir, and Pt, respectively.

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ASSOCIATED CONTENT

S Supporting Information *

Selected output files from DFT calculations listing the Cartesian coordinates, zero-point energies (au), sums of electronic and zero-point energies (au), structures, and frequencies of the reactants, transition states, and products reported herein. CCSD(T) single-point energies (Hartree) and dispersion-corrected energies (Hartree) based on the B3LYP geometries. Geometry optimizations for all of the reactants, intermediates, transition states, and products were carried out with the 6-311+G** basis set for the carbon and hydrogen atoms of the reactions investigated, and Stuttgart/Dresden relativistic effective core potentials (ECPs), designated as SDD, were employed to describe the metals Os, Ir, and Pt. This material is available free of charge via the Internet at http:// pubs.acs.org. 4567



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