Activation of C2H6 by Gas-Phase Ta+: Potential Energy Surfaces

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Organometallics 2009, 28, 6160–6170 DOI: 10.1021/om900360z

Activation of C2H6 by Gas-Phase Taþ: Potential Energy Surfaces, Spin-Orbit Coupling, Spin-Inversion Probabilities, and Reaction Mechanisms Ling-Ling Lv,†,‡ Yong-Cheng Wang,*,† Zhi-Yuan Geng,† Yu-Bing Si,† Qiang Wang,† and Hui-Wen Liu† †

College of Chemistry and Chemical Engineering, Northwest Normal University, LanZhou, Gansu 730070, People’s Republic of China, and ‡College of Life Science and Chemistry, Tianshui Normal University, Tianshui, Gansu 741001, People’s Republic of China Received May 7, 2009

The spin-forbidden reaction mechanism of Taþ(5F, 5d36s1) with C2H6 on the quintet, triplet, and singlet potential energy surfaces has been investigated at the density functional level of theory using the hybrid exchange correlation functional B3LYP. Crossing points between the potential energy surfaces are located using different methods, and possible spin inversion processes are discussed by means of spin-orbit coupling (SOC) calculations. As a result, there is a crossing seam from 3-5CPmin to 3-5CPmax between the quintet and the triplet state surfaces. The reacting system will change its spin multiplicities from the quintet state to the triplet state near this crossing seam, leading to a significant decrease in the barrier height of 5TS1-2 from 34.0 to 15.1 kcal/mol, and then move on the triplet potential energy surface as the reaction proceeds. The minimum energy crossing point (3-5MECP) is located by using the methods of Harvey et al. The probability values of the single (P1ISC) and double (P2ISC) passes estimated at 3-5MECP are approximately 9.39 10-2 and 0.17, respectively. After the C-H insertion intermediate 2, two distinct reaction paths have been found, a H2 elimination path and a CH4 elimination path. The former is found to be the lowest energy path on the triplet PES, while a high C-C insertion barrier of the latter prevents observation of this species under thermal conditions. These conclusions are consistent with the experimental observations.

1. Introduction The chemistry of transition metals and their compounds is strongly influenced by the availability of multiple low-lying electronic states in these species.1-3 This phenomenon particularly often occurs when the formal d electron count on the metal is intermediate (e.g., 2-8), when the ligand field is weak due to the nature or the number of the ligands, and there are higher exchange interactions between compact d orbitals. This means that even thermal chemical reactions of transition-metal compounds are often spin-forbidden in that the reactants and products involved have different overall electronic spin states. During the process of a chemical reaction, the ability of the metal center to access these states and adapt to different bonding situations may enable the *To whom correspondence should be addressed. Fax: þ86-09317971989. E-mail: [email protected]/[email protected]. (1) Heinemann, C.; Cornehl, H. H.; Schr€ oder, D.; Dolg, M.; Schwarz, H. Inorg. Chem. 1996, 35 (9), 2463–2475. (2) Armentrout, P. B. Science 1991, 251 (11), 175–179. (3) Rue, C.; Armentrout, P. B. J. Chem. Phys. 1999, 110 (16), 7858– 7870. (4) (a) Fiedler, A.; Schroder, D.; Shaik, S.; Schwarz, H. J. Am. Chem. Soc. 1994, 116 (23), 10734–10741. (b) Poli, R.; Harvey, J. N. Chem. Soc. Rev. 2003, 32, 1–8. (c) Hirao, H.; Kumar, D.; Que, L.; Shaik, S. J. Am. Chem. Soc. 2006, 128 (26), 8590–8606. (5) Harvey, J. N.; Poli, R.; Smith, K. M. Coord. Chem. Rev. 2003, 238239, 347–361. pubs.acs.org/Organometallics

Published on Web 10/15/2009

system to find low-energy reaction pathways that would not be accessible otherwise.4,5 Thus, a reaction possibly occurs on two or more potential energy surfaces (PESs) under thermal conditions, and therefore it has to involve the electronic process of radiationless transition from one potential energy surface to another surface. However, reactions that involve a change in the spin state and occur on two or more PESs are known to be important in determining the outcome of chemical processes.2-6 In particular, this type of chemical reaction has been emphasized by Schr€ oder, Shaik, and Schwarz7 in recent reviews of “two-state/multiple-state” reactivity and spin-forbidden chemical reactions in organometallic chemical reaction pathways. A large number of recent studies have established the combination of experiment and electronic structure theory as a powerful approach to the elucidation of reaction mechanisms of gas-phase transition-metal cations with hydrocarbons, because these studies can provide fundamental information about bond activation.8-10 These reactions (6) Yarkony, D. R. J. Phys. Chem. 1996, 100 (48), 18612–18628. (7) Schroder, D.; Shaik, S.; Schwarz, H. Acc. Chem. Res. 2000, 33 (3), 139–145. (8) Freiser, B. S., Ed. Organometallic Ion Chemistry; Kluwer Academic: Dordrecht, The Netherlands, 1996. (9) Eller, K.; Schwarz, H. Chem. Rev. 1991, 91 (6), 1121–1177. (10) Weisshaar, J. C. Acc. Chem. Res. 1993, 26 (4), 213–219. r 2009 American Chemical Society

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often involve C-H or C-C bond activation by the metal followed by elimination of hydrogen or small alkane groups. In order to develop practical alkane conversion processes, the process and factors controlling the activity and selectivity of alkane activation need to be better understood. Methane and ethane are useful starting points because they are the simplest hydrides of carbon. Thus, the activation of them by a transition-metal cation, Mþ, or a neutral transition metal, M, has been the subject of a number of studies. For example, the first- and second-row metals Mþ (M = Ti, V, Cr, Fe, Co, Ni, Mo, Nb) and the third-row metals Mþ (M=W, Os, Ir, Pt)11-24 have all been studied experimentally and/or theoretically. The mechanistic details of the CH4 activation brought about by a Taþ ion, which was observed in the gas phase, have been computationally investigated using density functional theory by Armentrout and Koch.25 The overall reaction is computed to be exothermic by ca. 14 kcal/mol. In 2008, a guided ion beam mass spectroscopy study combining theoretical calculation of Ta2þ þ CH4 was reported by Armentrout and co-workers.26 For a Taþ ion with C2H6, an early experiment by the Freiser group27 was performed on a prototype Nicolet FTMS-1000 Fourier transform mass spectrometer. Under single-/cool-collision conditions, the C-H insertion leads to the primary H2 elimination products, TaC2H4þ þ H2. The most recent experimental study of the gas-phase reaction of Taþ with C2H6 employed Fourier transform ion cyclotron resonance mass spectrometry (FTICR/MS) by Gibson and co-workers.28 The results are consistent with the findings of the Freiser group; the primary products observed by Gibson were the elimination products TaC2H4þ þ H2, followed by the double-elimination products TaC2H2þ þ 2H2, with reaction efficiencies (11) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1991, 113 (7), 2769–2770. (12) Yoshizawa, K.; Suzuki, A.; Yamabe, T. J. Am. Chem. Soc. 1999, 121 (22), 5266–5273. (13) (a) Irikura, K. K.; Goddard, W. A. J. Am. Chem. Soc. 1994, 116 (19), 8733–8740. (b) Heinemann, C.; Hertwig, R. H.; Wesendrup, R.; Koch, W.; Schwarz, H. J. Am. Chem. Soc. 1995, 117 (1), 495–500. (14) Ranasinghe, Y. A.; MacMahon, T. J.; Freiser, B. S. J. Phys. Chem. 1991, 95 (20), 7721–7726. (15) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1989, 111 (1), 75–85. (16) Irikura, K. K.; Beauchamp, J. L. J. Phys. Chem. 1991, 95 (21), 8344–8351. (17) Holthausen, M. C.; Fiedler, A.; Schwarz, H.; Koch, W. J. Phys. Chem. 1996, 100 (15), 6236–6242. (18) Holthausen, M. C.; Koch, W. J. Am. Chem. Soc. 1996, 118 (41), 9932–9940. (19) Armentrout, P. B. Organometallics 2007, 26 (23), 5486–5500. (20) Abashkin, Y. G.; Burt, S. K. J. Phys. Chem. A 1997, 101 (43), 8085–8093. (21) Holthausen, M. C.; Fiedler, A.; Schwarz, H.; Koch, W. Angew. Chem., Int. Ed. Engl. 1995, 34 (20), 2282–2285. (22) Guo, Z.; Ke, Z. F.; Phillips, D. L.; Zhao, C. Y. Organometallics 2008, 27 (2), 181–188. (23) Moc, J.; Gordon, M. S.; Fedorov, D. G. J. Chem. Phys. 2000, 112 (23), 10247–10257. (24) Yoshizawa, K.; Shiota, Y.; Yamabe, T. J. Chem. Phys. 1999, 111 (2), 538–544. (25) (a) S€ andig, N.; Koch, W. Organometallics 1997, 16 (24), 5244– 5251. (b) Parke, L. G.; Hinton, C. S.; Armentrout, P. B. J. Phys. Chem. C 2007, 111 (48), 17773–17787. (26) Parke, L. G.; Hinton, C. S.; Armentrout, P. B. J. Phys. Chem. A 2008, 112 (42), 10469–10480. (27) Buckner, S. W.; MacMahon, T. J.; Byrdt, G. D.; Freiser, B. S. Inorg. Chem. 1989, 28 (18), 3511–3518. (28) Gibson, J. K.; Haire, R. G.; Marc€ ualo, J.; Santos, M.; Matos, A. P.; Mrozik, M. K.; Pitzer, R. M.; Bursten, B. E. Organometallics 2007, 26 (16), 3947–3956.

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k/kCOL =0.3. The reactions involve several electronic states that may also have different spins, which should involve spin-conserving and spin-inversion processes. Spin-inversion, one of nonadiabatic processes, can generally occur in the vicinity of a crossing seam of two potential energy surfaces of different spin multiplicities.24 Therefore, detailed analyses of the crossing seam between the different potential energy surfaces are important in order to better understand the mechanism of the Taþ and C2H6 reaction. To our knowledge, a detailed theoretical study for the activation of C2H6 by Taþ ion has not been reported. In the present paper we discussed crossing seams, spin-orbit coupling (SOC), and possible spin-inversion processes in this intriguing chemical reaction by the methods of the intrinsic reaction coordinate (IRC)24 and Harvey et al.29 In addition, it was also concluded that only the H2 elimination products (without the TaCH2þ and CH4 elimination products) occur at low energies.

2. Computational Details 2.1. Geometrical Optimization. Computations were carried out using the Gaussian 03 ab initio program package.30 Energies and geometries of the reaction intermediates and the transition states were calculated with density functional theory (DFT) using the B3LYP level. The triple-ζ 6-311þþG(d,p) basis set of Pople and co-workers31 was used for carbon and hydrogen, and the (8s7p6d) primitive set32 resulting in a (311111|31111|411)[6s5p3d] contraction was used for Taþ. To accurately evaluate thermochemical properties and describe the potential energy surfaces for the title reactions, single-point calculations were performed at the B3LYP level, using the 6-311þþG(3df,3pd) basis set for C and H and for Taþ the (8s7p6d) primitive set supplemented with one polarization f function (R = 0.79),25a resulting in a (311111|31111|411|1)[6s5p3d1f] contraction, which is expressed as 6-311þþG(3df,3pd)∪SDDþf. To confirm the accuracy of the B3LYP calculations in the Taþ/C2H6 system, the splitting energy of the Taþ ion and the overall energy for the reaction Taþ þ C2H6 f TaC2H4þ þ H2 were compared with experimental predictions. The computed splitting energy 5 F(5d36s1) - 3F(5d26s2) (10.7 kcal/mol) and the overall energy (23.0 kcal/mol) are in good agreement with experimental values 9.9 kcal/mol and above 15.0 kcal/mol, respectively.33 Previous investigations of transition-metal compounds employing the B3LYP functional by other groups34-36 and us37,38 indicated that this approach shows a very promising performance to predict properties such as bond dissociation energies, geometries, harmonic frequencies, and electronic details with an accuracy comparable to that obtained from highly correlated, wave function based ab initio methods. (29) Harvey, J. N.; Aschi, M.; Schwarz, H.; Koch, W. Theor. Chem. Acc. 1998, 99 (2), 95–99. (30) Frisch, M. J., et al. Gaussian 03 (Revision-E.01); Gaussian Inc., Pittsburgh, PA, 2003. (31) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80 (7), 3265–3272. (32) Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1989, 90 (3), 1730– 1736. (33) Moore, C. E. Atomic Energy Levels; National Standard Reference Data Series ; National Bureau of Standards: Washington, DC, 1995. (34) Cho, H. G.; Andrew, L. J. Phys. Chem. A 2006, 110 (11), 3886– 3902. (35) Straub, B. F. J. Am. Chem. Soc. 2002, 124 (47), 14195–14201. (36) Filatov, M.; Shaik, S. J. Phys. Chem. A 1998, 102 (21), 3835– 3846. (37) Wang, Y. C.; Zhang, J. H.; Geng, Z. Y. Chem. Phys. Lett. 2007, 446 (1-3), 8–13. (38) Liu, Z. Y.; Wang, Y. C.; Geng, Z. Y.; Yang, X. Y. Chem. Phys. Lett. 2006, 431 (4-6), 223–226.

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Lv et al. Scheme 1

All stationary points were characterized by vibrational analysis, and the zero-point energy (ZPE) was calculated. The transition -state structures all represent saddle points, characterized by one negative eigenvalue of the Hessian matrix. The intrinsic reaction coordinate (IRC) was then calculated and used to track the minimum energy path from transition states to the corresponding minima, to probe the reaction path, and to check if the correct transition state was located. The natural bond orbital (NBO) and natural resonance theory (NRT) analyses were also carried out using the NBO 5.0 procedure.39 To locate the crossing seam between the two PESs of different spin states, we have carried out single-point energy calculations (in the triplet state) as a function of the structural change along the IRC of the quintet state, and vice versa,22-24 and in this way we have obtained the CPs. The minimal energy crossing point (MECPs) between triplet and quintet PESs was identified by using the procedure of Harvey et al.29 2.2. Spin-Orbit Coupling Calculations. The spin-orbit coupling (SOC) between the triplet and quintet states was calculated with the GAMESS program package.40 We carried out multiconfiguration self-consistent-field (MCSCF) wave function calculations along the IRC of the quintet state, corresponding to the 6-311G(d,p) basis set used for C and H and the SBKJC ECP basis set used for Taþ (in order to be consistent with the Zeff parameter given by Koseki et al.41,42), and then we computed the SOC matrix elements using the SO-CI method43 with the converged MCSCF wave function. The MCSCF wave function of the Taþ/C2H6 system contains an active space of 10 electrons in 8 orbitals, as indicated in Scheme 1. Since the orbital sets of the triplet and quintet states must share a common set of core orbitals to calculate the SOC matrix (39) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.;. Bohmann, J. A ; Morales, C. M.; Weinhold, F. NBO 5.0; Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001. (40) The version for personal computers was compiled by A. A. Granovsky, Moscow State University. (41) Koseki, S.; Schmidt, M. W.; Gordon, M. S. J. Phys. Chem. A 1998, 102 (5), 10430–10435. (42) Koseki, S.; Fedorov, D. G.; Schmidt, M. W.; Gordon, M. S. J. Phys. Chem. A 2001, 105 (35), 8262–8268. (43) Koseki, S; Schmidt, M. W.; Gordon, M. S. J. Phys. Chem. 1992, 96 (26), 10768–10772.

element, we employed the converged MCSCF wave function of the quintet state as a reference state for the triplet CI wave function as well as the quintet one. We estimated the SOC with the approximate one-electron spin-orbit Hamiltonian44 given by

HSO ¼ ¼

X R2 X X Z k R2 hi ðZ Þ ðSi 3 Lik Þ ¼ 3 2 i k rik 2 i e2 h 4πme 2 c2

in which the neglect of the two-electron terms is compensated by introducing a semiempirical parameter, here the effective nuclear charge (Zeff). R is the fine structure constant, Lik and Si are the orbital and spin angular momentum operators for electron i in the framework of the nuclei indexed k, respectively, and Z*k is the effective nuclear charge. In the SOC matrix, we used 3.9 and 1049.7 for C and Taþ, according to the analysis of Koseki, Schmidt, and Gordon.45 To calibrate the effective charge of Ta, we calculated the SOC splitting of the Ta (4F) atom. The calculated splitting, 2174.2 cm-1 (4F3/ 4 42 value 2- F5/2), is in good agreement with an experimental -1 of 2010.1 cm . Thus, the effective charge is accurate enough to calculate the SOC value in the Taþ/C2H6 system.

3. Results and Discussion 3.1. Initial Complexes. The optimized geometries and energetic data in the singlet, triplet, and quintet electronic states are depicted in Figures 1 and 2 and Table S1 (see the Supporting Information), respectively, where the superscripts denote the spin multiplicities. A stabilized reactantlike intermediate, denoted as 1, is initially formed as Taþ and (44) Danovich, D.; Shaik, S. J. Am. Chem. Soc. 1997, 119 (7), 1773– 1786. (45) Fedorov, D. G.; Koseki, S.; Schmidt, M. W.; Gordon, M. S. Int. Rev. Phys. Chem. 2003, 22 (3), 551–592.

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Figure 2. Structures of several intermediates and transition states relevant to C-C bond activation along the singlet, triplet, and quintet surfaces of the Taþ þ C2H6 system calculated at the B3LYP/6-311þþG(d,p) level of theory (bond lengths in A˚ and bond angles in deg).

Figure 1. Structures of several intermediates and transition states relevant to C-H bond activation along the singlet, triplet, and quintet surfaces of the Taþ þ C2H6 system calculated at the B3LYP/6-311þþG(d,p) level of theory (bond lengths in A˚ and bond angles in deg).

C2H6 collide side-on with each other. This ion/molecule complex has Cs/C2 geometry. However, only C2 structures involving η2 coordination appear to be minima on three surfaces, while η3-coordinated structures with Cs symmetry produced one imaginary frequency with the eigenvector clearly indicating distortion to 1(C2), such as 477.65i for the 5A0 state. The 31 species (C2,3B) is calculated to be more stable than 31(Cs,3A00 ) by 2.6 kcal mol/mol. The Taþ has a quintet ground state, and so does the initial complex 5 1(C2,5B). As expected, the initial interaction of Taþ with ethane is attractive because of the ion-induced dipole potential. The bond order analysis using NBO 5.0 shows that the hyperconjugative interaction (which is often called “covalent component”) is very weak in the initial complexes, 51(C2,5B) and 31(C2,3B), corresponding to the results calculated: Ta-H (0.0002 covalent þ 0.0103 ionic = 0.0105 total) and Ta-C (0.0003 covalent þ 0.0149 ionic=0.0152 total) in the 5 1 complex; for the 31 complex, Ta-H (0.0002 covalent þ 0.0103 ionic = 0.0105 total) and Ta-C (0.0003 covalent þ 0.0149 ionic = 0.0152 total). In contrast, the percentage contribution of the ionic component is much higher than that of the covalent component, corresponding to 98.44% and 97.78% in the 51 and 31 complexes, respectively. The

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Figure 3. Diagram of molecular orbital interaction and orbital occupancy for coordination of C2H6 to the metal fragment. Spin density distributions at the transition states as calculated by B3LYP/ 6-311þþG(d,p)∪SDD are inserted at the bottom of the diagrams.

geometries and NBO data of complex 1 indicate that the interaction between Taþ and C2H6 is an electrostatic interaction in nature. As can be seen from Table S1, 51(C2,5B) is predicted to be more stable than the Taþ(5F) þ C2H6 entrance channel by 28.8 kcal/mol at the B3LYP/6-311þþG(d,p)∪SDD level due to the ligand-metal weak interactions and the d-d electron exchange interaction (30.6 kcal/mol on Ta), which favors a high-spin situation. 11(C2,1A) is 34.8 and 25.4 kcal/mol higher in energy than 51(C2,5B) and 31(C2,3B), respectively. 3.2. Insertion Transition State TS1-2. Structural parameters of the transition state (TS1-2) on the singlet, triplet, and quintet surfaces are collected in Figure 1. To gain a deep understanding of the activation of the C-H bond of C2H6 by Taþ, we have derived useful information about 5TS1-2 and 3 TS1-2 from molecular orbital analysis, as shown in Figure 3. Figure 3 shows the singly occupied MO (SOMO) of Taþ for 5 TS1-2 on the quintet surface, which is primarily a hybrid mix of the Taþ dyz and dz2 orbitals, interacting with the C-H bonding orbital; this interaction is a three-electron interaction that is maximized in a interaction of the C-H bond on the C2H6 to form one of the φ1, φ2, and φ6 orbitals of 5TS1-2. Thus, the orbital interaction involves donation of electrons from the φCH orbital to the Taþ orbital, resulting in a weakening of the C-H bond (bonding electrons are decreased). At the same time, a σ interaction occurs between the Taþ ion dyz and the in-plane C2H6 φCH orbital; there is a strong bonding interaction φ2 on the C1 side of C2H6, which can lead to the shift of spin electrons on Taþ ion onto the C1 atom. The key features can be understood by inspecting the spin density distributions near the transition state, as inserted in the bottom of Figure 3. The quintet state reveals

Lv et al.

that the C2H5 fragment develops a radical character so that the spin density of the C1 atom reaches 0.78 near the transition state, 5TS1-2. Simultaneously, the spin density on the Taþ ion decreases from 4.0 to 3.29. For the triplet surface, the empty dz2 orbital of Taþ interacts with the C-H bonding orbital to form one of the φ1 bonding orbitals of 3TS1-2. Therefore, the orbital interaction involves donation of electrons from the C2H6 φCH orbital to the metal dz2 orbital, leading to the weakening of the C-H bond. We know that the orbital energy gap and the geometric variations favor the triplet transition state, while the exchange energy would prefer the quintet state. For the C-H bonding insertion process, the orbital energy gap (0.041 au for 3TS1-2; 0.076 au for 5TS1-2) and the geometric variations (see Figure 1) lowers the triplet barrier below the quintet state. The energy of 3TS1-2 is 19.6 kcal/mol lower than that of 5TS1-2. The net barrier (4.0 kcal/mol) on the triplet surface is extremely small (see Table S1), and the corresponding 3TS1-2 is also very early (observe the RC1-H2 distance in Figure 1), while 5TS1-2 is an obvious late transition state. 3.3. Surface-Crossing Behavior. Crossing seams and spin inversion processes are the subject here. The transition of spin multiplicity may be expected to occur from the quintet state to the triplet state near 3TS1-2. Spin inversion is a nonadiabatic process, and we need to inspect a crossing seam on the quintet, triplet, and singlet potential energy surfaces to know the mechanism of the reaction of Taþ with C2H6. Two different approaches were taken to locate the crossing of the different surfaces: (1) an approach suggested by Yoshizawa24 for approximately locating the crossing points of two PESs with different multiplicities. The main idea for this method is to perform a series of single-point states and vice versa. Such an analysis will help locate approximate energy-minimum and -maximum crossing points. (2) The minimum energy crossing point (MECP) is identified by using the methods of Harvey et al.29 and the CASSCF method with the GAMESS program package.40 We first tried to locate the crossing points between the quintet and triplet (or singlet) surfaces in the region from complex 1 to TS1-2. Thus, we performed single-point computations of the triplet and singlet states as a function of the structural change along the IRC of the quintet state (from complex 51 to transition state 5TS1-2) in Figure 4a, and single-point computations of the quintet state along the IRC of the triplet state (from complex 31 to transition state 3 TS1-2) are shown in Figure 4b. As detailed in Figure 4b, the crossing seam point 3-5CPmin is located at IRC=-0.499 with an energy of 15.1 kcal/mol relative to that of 51. The complex at this point has a approximate Cs geometry, in which the dissociating C1-H2 bond distance is 1.2981 A˚ and the forming Ta-H bond distance is 1.8592 A˚. The quintet and triplet potential energy surfaces can begin to touch at this point because the IRC valley of the quintet state still lies below that of the triplet state in this region of the reaction pathway. That is, 3-5CPmin is the energy-minimum crossing point between the quintet and the triplet potential energy surfaces from complex 1 to transition state TS1-2. In Figure 4a, another crossing point 3-5CPmax is found near TS1-2 (IRC=-2.44), the relative 51 energy being 23.7 kcal/ mol. The bond distance of C1-H2 is about 1.5758 A˚, and the Ta-H distance is 1.8107 A˚. This is the energy-maximum crossing point; therefore, there is a crossing seam between 3-5CPmin and 3-5CPmax. The reacting system should

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Figure 4. Potential energy curve-crossing diagrams for the different spin state PESs along the quintet IRC (a) and the triplet IRC (b) at the B3LYP level.

change its spin multiplicities from the quintet state to the triplet state in this crossing region and then move on the triplet potential energy surface as the reaction proceeds. This crossing seam plays the most important role in this reaction pathway because the molecular system should change its spin multiplicity from the quintet state to the triplet state near this crossing region, leading to a significant decrease in the barrier height of 5TS1-2 from 34.0 to 15.1 kcal/mol at the B3LYP/6-311þþG(d, p)∪SDD. The minimum energy crossing point (MECP), 3-5MECP, is identified by using the methods of Harvey et al.29 and the CASSCF method with the GAMESS program package.40

The structure of 3-5MECP is shown in Figure 4a. The 3-5 MECP has a Cs geometry, in which the dissociating C1-H2 bond distance is 1.5303 A˚ and the forming Ta-H bond distance is 1.7779 A˚. The 3-5MECP is located after the transition state 3TS1-2 (RC1-H2 = 1.4063 A˚) and falls between 3-5CPmin (RC1-H2 = 1.2981 A˚) and 3-5CPmax (RC1-H2=1.5758 A˚), with an energy of 16.4 kcal/mol relative to that of 51. Within the seam, the 3-5MECP point is a minimum; the spin hopping easily takes place because the Franck-Condon principle requires that both have the same energies and geometries. Thus, the reaction system will access a lower energy pathway by changing its spin multiplicities via the 3-5MECP point.

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In addition, analysis of the quintet and the singlet state potential energy profiles from complex 1 to TS1-2 shows that there is also a crossing seam; 1-5MECP is located by using the methods of Harvey et al. (see Figure 4a) with an energy about 27.6 kcal/mol higher than 51, the bond distance of C1-H2 is about 1.6487 A˚, and the Ta-H distance is 1.7530 A˚. However, according to Yoshizawa,24 one can see that before the crossing point of the quintet and the singlet potential surfaces occur, the molecular system would preferentially move to the triplet PES from the quintet PES. Hence, this crossing would not likely play a significant role in the most probable reaction pathway from complex 1 to complex 2; therefore, this crossing point is not considered carefully here. 3.4. Spin-Orbit Coupling (SOC) Calculation along the IRC of the Transition State, 5TS1-2. A spin-forbidden transition requires an effect of spin-orbit coupling (SOC) that provides a major mechanism for intersystem crossing in the gas phase.46,47 SOC induces a spin-multiplicity mixing that allows the wave function to break spin symmetry, and the magnitude of the spin-multiplicity mixing increases in a small energy gap between high- and low-spin states due to perturbation theory. Therefore, spin inversion can generally occur in the vicinity of a crossing seam of two potential energy surfaces of different spin multiplicities,48 and the strength of SOC and the energy gap are keys to understanding the mechanism of the reaction of Taþ with C2H6. We next turn our attention to SOC computations. Figure 5 shows computed single-point potential energy surfaces in the triplet state and SOC values between the quintet and the triplet state along the IRC of the transition state, 5TS1-2. The three triplet states, 3(1), 3(2), and 3(3), have a gradual and smooth change in potential energies, as indicated in Figure 5a. The potential energies of the 3(1), 3(2), and 3(3) states are close-lying prior to TS1-2, corresponding to the energy different values of about 5 kcal/mol, respectively. Once the reaction passes through TS1-2, the 3(2), and 3(3) states get unstable in energy, and the 3(2) and 3(3) states lie about 30 kcal/mol above the 3(1) state. Moreover, the activation barriers in both the 3(2) and 3(3) states are more than 40 kcal/mol. Therefore these high-lying states are unlikely to contribute to the spin inversion through the SOC effect after TS1-2; thus, the 3(2) and 3(3) states can be reasonably neglected in the spin inversion after TS1-2 and therefore we considered only the SOC matrix element before TS1-2. Let us look at the electronic structures; the quintet ground states are shown in Scheme 1. The φ1(σ), φ2(σ), and φ3(δ) orbitals are doubly occupied and the φ8(σ*) orbital is vacant, whereas the φ4(σ), φ5(π), φ6(δ), and φ7(δ) orbitals are occupied selectively. Therefore, the selective occupation of the φ4(σ), φ5(π), φ6(δ), and φ7(δ) orbitals determines the electronic state of the excited triplet state. Thus, under approximate Cs symmetry, the three low-lying triplet states are respectively generated from the quintet ground state by the electron shift from φ6(δ) to φ4(σ), from φ6(δ) to φ5(π), and from φ5(π) to φ4(σ), resulting in the electronic configurations of φ4(σ)2φ5(π)1φ6(δ)0φ7(δ)1(3A0 ), φ4(σ)1φ5(π)2φ6(δ)0φ7(δ)1(3A00 ), and φ4(σ)2φ5(π)0φ6(δ)1φ7(δ)1(3A0 ), respectively, corresponding (46) Lower, S. K.; El-Sayed, M. A. Chem. Rev. 1966, 66 (2), 199–241. (47) Richards, W. G.; Trivedi, H. P.; Cooper, D. L. Spin-orbit Coupling in Molecules; Oxford University Press: New York, 1981. (48) Shiota, Y.; Yoshizawa, K. J. Chem. Phys. 2003, 118 (13), 5872– 5879.

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Figure 5. (a) Potential energies at the CASSCF level and (b) SOC values along the quintet IRC. The IRC connects the reaction pathway from the reactant complex to the quintet transition state, TS. Scheme 2

to the electronic shifts shown in Scheme 2. In view of the symmetry selection rules, the direct product of the orbital symmetry labels must contain the irreducible representation to which the rotation operators belong in order to give nonzero SOC values.44 From the character table of the Cs point group, we see that the rotation operators belong to A0 (Rx and Ry) and A00 (Rz), the spin transitions from the 5A00 state to the 3A0 state and from the 5A00 state and 3A00 state should occur, which contains the irreducible representation of the rotation operators (a00 X a0 is A00 , a00 X a00 is A0 ), and spin-orbit coupling is allowed. To further understand the SOC efficiency between the quintet and triplet states, symmetry analysis by itself is insufficient, and we must inspect the orbital relationships which promote the SOC matrix element. We know that a nonzero maximum angular momentum expectation value is obtained when the orbitals are mutually perpendicular. The 3(1)(3A0 )

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state is generated from the 5A00 state by electron shifts from dyz(a00 ) to dx2-y2(a0 ), which lead to the d-AO matrix elements, Ædyz|Lx|dx2-y2æ. The d-AO relationships lead to x components of the angular momentum. As a result, dyz and dx2-y2 are allowed to transform properties of the d-AO0 s under the operation of the Lx operators and therefore we expect that the SOC matrix element should be large. In a similar way, Ædyz|Lz|dxzæ of the 3(2)(3A00 ) state and Ædyz|Ly|dx2-y2æ of the 3(3)(3A0 ) state are allowed under the operation of the Lz and Ly operators, respectively. They should generate large SOC values. The SOC values between the three triplet states and the quintet state are indicated in Figure 5b. The SOC before TS12 is a key to understanding the spin-forbidden transition that takes place in the vicinity of the crossing seam,in which the spin multiplicity of the ground state is changed from the quintet state to the triplet state. Starting from 87.15 cm-1 at RC1-H2 =1.26 A˚, the 3(1)-5 SOC values increase to 336.29 cm-1 at RC1-H2 = 1.68 A˚. The strength of the 3(1)-5 SOC increases and the energy gap between the 3(1) and the quintet state (5) decreases as the reaction coordinate progresses. Thus, the 3(1)-5 SOC is very effective in the spin transition. The 3(2)-5 and 3(3)-5 SOC values start from 228.01 and 250.80 cm-1 at RC1-H2 = 1.26 A˚, resulting in 893.46 and 562.31 cm-1 at RC1-H2 =1.68 A˚, respectively. These values are also large enough to contribute to the spin transition; moreover, these large SOC values fall in the crossing region, between 3-5CPmin (RC1-H2 = 1.2981 A˚) and 3-5CPmax (RC1-H2 = 1.5758 A˚). Therefore, we expect that the 3(1)-5, 3(2)-5, and 3(3)-5 transitions should occur efficiently near the crossing seam before TS1-2. 3.5. Estimation of Probability for Intersystem Crossing (ISC). The probability of ISC for a molecule passing through a quintet-triplet crossing can be calculated from Landau-Zener theory.49 The Landau-Zener equations for the probability of single (P1ISC) and double (P2ISC) passes through the crossing point are shown in eqs 1 and 2:50-52

P1 ISC ¼ 1 - PLZ

ð1Þ

P2 ISC ¼ 2PLZ ð1 - PLZ Þ

ð2Þ

where

2πH12 2 P ðE - Ec Þ ¼ exp pΔF LZ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! μx 2ðE - Ec Þ

Here, H12 is the spin-orbit coupling-derived off-diagonal Hamiltonian matrix element between the two electronic states, and ΔF is the relative slope of the two surfaces at the crossing seam. The reduced mass of the system as it moves along the hopping coordinate x is μx, Ec is the energy of the 3-5MECP relative to complex 51, and E is the total internal energy.53 (49) (a) Zener, C. Proc. R. Soc. London, Ser. A 1932, 137 (833), 696. (b) Zener, C. Proc. R. Soc. London, Ser. A 1933, 140 (842), 660. (50) Harvey, J. N. Phys. Chem. Chem. Phys. 2007, 9, 331–343. (51) Harvey, J. N.; Aschi, M. Phys. Chem. Chem. Phys. 1999, 1, 5555– 5563. (52) Harvey, J. N.; Aschi, M. Faraday Discuss. 2003, 124, 129–143. (53) Lorquet, J. C.; Leyh-Nihant, B. J. Phys. Chem. 1988, 92 (16), 4778–4783.

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Figure 6. Two- and three-dimensional plots with the σH-HfLP*Ta and σTa-Hfσ*H-H interactions in 3TS3-4 from B3LYP/6-311þþG(d,p)∪SDD.

The spin hopping easily takes place in this 3-5MECP. The MECP provides a natural choice for the hopping coordinate, as the gradients on the two surfaces at the MECP are either parallel or antiparallel and are orthogonal to the seam of crossing. Within the seam, the MECP is a minimum. Thus, using Landau-Zener theory, the calculated values of ΔF and μx are 0.1077 hartree bohr-1 and 2001.89 au for 3-5MECP, respectively. The probability of 3-5MECP is sensitive to the SOC matrix element; therefore, the calculated SOC values from 87.15 cm-1 at RC1-H2 = 1.26 A˚ to 180.48 cm-1 at 3-5 MECP are estimated at the lowest and the highest probability. The probabilities of single (P1ISC) and double (P2ISC) passes estimated at the start of the reaction (SOC = 87.15 cm-1) are approximately 1.89 10-3 and 3.77 10-3, respectively, while the values of the P1ISC and P2ISC passes estimated at 3-5MECP are approximately 9.39 10-2 and 0.17, respectively. The calculations show that the 3-5MECP will have a significant influence on the efficiency of the C-H bond activation, and the high probability in the crossing region indicates that the quintet surface intersystem crossing to the triplet state would be clearly very efficient. 3.6. C-H and C-C Bond Activation. The calculated potential energy profiles for the quintet, triplet, and single states are shown in Figures 7 and 8, and the optimized geometries for all of the crucial points on the corresponding three potential energy profiles are shown in Figures 1 and 2. The energies, including the zero-point energies (ZPE) for the reaction pathways, are collected in Table S1. As shown in Figures 7 and 8, forming the C-H bond inserted complex 2 is common to both branches, which then fork into the C-C bond activation route via TS2-5 and the C-H bond activation regime through TS2-3. From the discussion above, it is clearly shown that the quintet surface intersystem crossing to the triplet state to form complex 32 would be very efficient. Next, we will discuss the process of the C-H and the C-C bond activations from complex 2. 3.6.1. H2 Elimination Path. On the triplet surface, the Ta-H bond of the C-H insertion complex 32 rotates via 3 TS2-3 to the rotamer 33, the latter having a planar structure

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Figure 7. Potential energy diagrams (including zero-point energy) along the reaction pathway Taþ þ C2H6 f TiþC2H4 þ H2 in the singlet, triplet, and quintet states. Relative energies are given in kcal/mol. The potential energy surfaces provide a lower energy pathway, which is indicated by the blue line. The high-energy quintet spin surfaces are indicated by the red lines.

Figure 8. Potential energy diagrams (including zero-point energy) along the reaction pathway Taþ þ C2H6 f TiþCH2 þ CH4 in the singlet, triplet, and quintet states. Relative energies are given in kcal/mol. Singlet spin surfaces are indicated by the black line and triplet and quintet spin surfaces by the blue and red lines.

(3A00 ) with a Ta-H bond slightly longer than that in 32 (Figure 1). Two distinct rotamers, 32 and 33, resulting from these calculations, are identified as true minima by the frequency analysis. Species 32, resulting from the C-H insertion process starting from 31, is characterized by an agostic stabilization54 through the appropriate hydrogen at the adjacent methyl group. The presence of the agostic interaction of this hydrogen with the Taþ ion is best seen in the respective C3-H4 bond, which is elongated to 1.1519 A˚, and the C-C-Ta angle, which has decreased to 86.82, and the overall effect results in a rather short nonbonded H4-Ta distance of 2.1111 A˚. The rotamer 33, which differs from 32 (54) Dimitrios, A.; Pantazis, J. E.; McGrady, F. M.; Michel, E. J. Chem. Theory Comput. 2007, 3 (4), 1329–1336.

by the orientation of the methyl group and of the C1-Ta-H2 moiety, does not profit from such an agostic stabilization. However, the activation barrier for the isomerization 32 f 33 as well as the energy difference between the rotamers 32 and 33 is negligibly small, 4.52 kcal/mol, and hence, the rotation around the Ta-C1 bond is virtually free. For the singlet surface, all molecular geometries are similar to the corresponding ones on the triplet PES. However, unlike the triplet and singlet states, the quintet Taþ apparently cannot form stable insertion products; therefore we will not discuss this species any longer. In the next step on the triplet surface, the HTaC2H5þ rotamer 33 can undergo reductive elimination via the planar H2 elimination 3TS3-4 to form the molecular complex TaC2H4þ 3 3 3 H2(4). We located the saddle point 3TS3-4

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directly connecting the rotamers of 33 with the complex 34. This transition structure has an imaginary frequency of 474.83i cm-1, and the transition vector confirms the concerted nature of this four-center H2 activation saddle point. The NBO analysis shows that the doubly occupied σ orbital at H2 donates charge (0.16 e) to the empty 6s5d1.96 hybridization orbital of Taþ, while back-donation involves charge transfer of 0.14 e from the σ Ta-C bond orbital to the antibonding σ* orbital at H2, weakening the H-H bonding (see Figure 6). The strengths of these interactions are estimated by second-order perturbation theory55 (ΔE(2) = ^ -2Æσ|E|σ*æ/ε σ* - εσ). It is found that the interaction second-order perturbation energies, ΔE(2), are 71.14 and 40.3 kcal/mol, respectively. Thus, this H-H bond is elongated by 0.2287 A˚, and the stretching mode decreases from 4418 to 2030 cm-1. Therefore, as compared with the C-C bond activation transition state 3TS5-6, the height of the lower activation barrier with respect to the entrance channel amounts to -32.5 kcal/mol; relative to the starting point of the rearrangement, 33, the barrier is 10.3 kcal/mol high (11.9 kcal/mol at the B3LYP/6-311þþG(3df,3pd)∪SDDþf level). In the final step the H2 molecule is eliminated, yielding the TaC2H4þ product. According to DFT, the latter is left in the triplet state at a net cost of 8.8 kcal/mol, and the overall H2 elimination reaction starting with the C2H6 þ Taþ(5F) reactants is exothermic, by 23.0 kcal/mol. 3.6.2. CH4 Elimination Path. There are indirect and direct C-C bond insertion mechanisms leading to elimination of CH4 from the complex 1. For the indirect mechanism, on the triplet and singlet surfaces, the C-H insertion step is common for H2 and CH4 elimination paths (Figures 7 and 8). However, all our attempts to locate such a direct C-C bond insertion transition state for the triplet and singlet surfaces failed. In the next step on the triplet surface, the HTaC2H5þ intermediate 32 can be transformed to the Ta(CH3)2þ dimethyl cation 35 via the four-center 3TS2-5. The latter 3TS2-5 with features of partially broken C-C and C-H bonds leads to the C-C insertion product from the C-H insertion product, in which the activation barrier is 29.9 kcal/mol with respect to 32. 3TS2-5 is characterized as a transition structure by one imaginary frequency of 687.94i cm-1, and the vibrational vector corresponds to the expected components of the reaction coordinate: i.e., breaking of the C-H and C-C bonds. The optimal structure of Ta(CH3)2þ 35 is bent and has Cs symmetry (3A00 ) with the two methyls eclipsed and the two in-plane hydrogens nearer each other than the four out-ofplane hydrogens. Proceeding along the C-C bond activation reaction coordinate, 35 is converted into 36, which serves as the direct precursor for loss of methane. The saddle point 3TS5-6 for the [1, 3]-H shift directly joining 35 and 36 is characterized by an imaginary frequency of 1277.54i cm-1, and the transition vector clearly identifies the [1,3]-H shift. The relative energy of 3TS5-6 with respect to the dimethyl structure is 42.61 kcal/ mol. Hence, it is this large activation barrier that represents the origin for the failure to observe TaCH2þ and the energetic bottleneck of the reaction process. The final step for this mechanism is release of a CH4 molecule at the cost of 19.9 kcal/mol (DFT). The overall CH4 elimination reaction starting with the C2H6 þ Taþ(5F) reactants is exothermic, by 20.7 kcal/mol. (55) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88 (6), 899–926.


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The quintet surface of the direct C-C bond insertion mechanism has also been obtained (Figure 8); on the quintet surface, the intermediate 51 can be transformed to the Ta(CH3)2þ dimethyl cation 55 via the three-center 5TS1-5. The latter 5TS1-5 with features of partially broken C-C bonds leads to the C-C insertion intermediate 55, in which the activation barrier is 34.0 kcal/mol with respect to 51. 5TS1-5 is characterized as a transition structure by one imaginary frequency of 369.44i cm-1, and the vibrational vector corresponds to the expected components of the reaction coordinate: i.e., breaking of the C-C bond. This is in contrast to the triplet state, where the activation energy is too high to play a significant role in the C-C bond activation processes. Our calculated results are in good agreement with the experimental observations of Gibson et al.28 and the proposed reaction mechanism of the Beauchamp group, further enhancing the level of confidence that can be attributed to our computational approach. A similar conclusion was recently drawn by Koch17,18 and Armentrout,19 in the context of the reactions of the Tiþ, Feþ, Coþ, and Moþ ions with C2H6.

4. Conclusions The reactions of the Taþ ion with the C2H6 molecule have been studied using theoretical calculations. All structures of the quintet, triplet, and singlet potential energy surfaces have been determined and characterized at the DFT-B3LYP level. The SOC between the quintet and triplet states was calculated using the SO-CI method with the converged MCSCF wave function along the IRC of the transition state 5TS1-2 with the GAMESS program package. From the calculations the following conclusions emerged. (i) The Taþ þ C2H6 f TaC2H4þ þ H2 and Taþ þ C2H6 f TaCH2þ þ CH4 elimination reactions are initiated with the formation of the η2-coordinated 51 ion-induced dipole complex in the quintet state. Due to the instability of the quintet C-H bond insertion product relative to the triplet counterparts, there is thus a crossing seam from 3-5CPmin to 3-5 CPmax between the quintet and the triplet state surfaces. The reacting system will change its spin multiplicities from the quintet state to the triplet state near this crossing seam, leading to a significant decrease in the barrier height of 5TS12 from 34.0 to 15.1 kcal/mol at the B3LYP/6-311þþG(d, p)∪SDD, and then move on the triplet potential energy surface as the reaction proceeds. The minimum energy crossing point (MECP), 3-5MECP, is located by using the methods of Harvey et al. The probability values of the single (P1ISC) and double (P2ISC) passes estimated at 3-5MECP are approximately 9.39 10-2 and 0.17, respectively. (ii) The overall H2 elimination reaction is calculated to be exothermic, by 23.0 kcal/mol. Our calculations show that the quintet surface intersystem crossing to the triplet state would be clearly very efficient. The H2 loss transition state, TS3-4, is the rate-determining step at thermal energies; the results presented here suggest that the H2 elimination mechanism is most likely. However, for the CH4 elimination path, although the C-C insertion product Ta(CH3)2þ is a lowenergy intermediate, a high C-C insertion barrier prevents observation of this species under thermal conditions. These results are consistent with the experimental observations of Gibson et al. and the proposed reaction mechanism of the Beauchamp group.

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Acknowledgment. We thank the National Natural Science Foundation of China (Grant No. 20873102) for support of this research and also thank TianShui Normal University for granting “QingLan” talent engineering funds.

Lv et al. Supporting Information Available: Table S1, giving total energies Etot (au) and relative energies ΔErel (kcal/mol) for the optimized species calculated at the B3LYP/6-311þþG(d, p)∪SDD//6-311þþG(3df,3pd)∪SDDþf level. This material is available free of charge via the Internet at http://pubs.acs.org.

Activation of C2H6 by Gas-Phase Ta+: Potential Energy Surfaces

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