Dehydrogenation of Methane by Gas-Phase Th, Th+ - American

Organometallics 2010, 29, 3735–3745 DOI: 10.1021/om100156r

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Dehydrogenation of Methane by Gas-Phase Th, Thþ, and Th2þ: Theoretical Insights into Actinide Chemistry K. J. de Almeida* and H. A. Duarte Departamento de Quı´mica, Universidade Federal de Minas Gerais, Avenida Antonio Carlos, 6627, CEP-31270-901, Belo Horizonte, Minas Gerais, Brazil Received February 25, 2010

Unrestricted density functional theory calculations have been carried out to investigate the reactivity of Th, Thþ, and Th2þ toward the methane dehydrogenation process. A close description of the reaction mechanisms together with the analysis of the electronic factors offer insights into the reactivity of the thorium species. All possible spin states of the metal centers were considered as well as the effect of spin-orbit interactions on the transition-state barrier heights. The three reactions investigated are found to be exothermic, with the best thermochemical conditions observed for Th2þ around 105 kJ mol-1. The Thþ þ CH4 reaction is found to be kinetically more favorable than that for the neutral Th atom. The DFT results indicate a direct participation of 5f electrons/orbitals in the reactivity of thorium species. The presence of electrons in 5f orbitals has an important effect on the insertion activation barrier, providing an electrostatic repulsion toward the closed-shell methane. The NBO results show that 5f orbitals play an important role in the overall strengths of the Th-C and Th-H chemical bonds, favoring thermochemical conditions of these reactions.

I. Introduction Natural gas, which is composed primarily of methane, is one of the most abundant, low-cost, carbon-based feedstocks. However, the use of this energy resource is still limited since an efficient technology has not yet been developed to economically convert methane to useful liquid products. Given the potential for high payoff, the design of new and selective catalysts for specific molecular targets is an important challenge in chemistry today.1-5 In this respect, the actinide thorium arises as a very promising catalyst due to its high reactivity toward inert molecules such as CO2, NO, CH4, and small alkanes.6-9 The reaction products of the gas-phase Th atom and Thþ ion with methane, as outlined in eqs 1 and 2, have been studied by using different experimental techniques.9-12 In *To whom correspondence should be addressed. E-mail: julia@ dedalus.lcc.ufmg.br. (1) Periana, R. A.; Mironov, O.; Taube, D.; Bhalla, G.; Jones, C. J. Science 2003, 301, 814–818. (2) Das, S.; Incarvito, C. D.; Crabtree, R. H.; Brudvig, G. W. Science 2006, 312, 1941–1943. (3) Mas-Balleste, R.; Que, L. Science 2006, 312, 1885–1886. (4) Shilov, A. E.; Shul’pin, G. B. Chem. Rev. 1997, 97, 2879–2932. (5) Fokin, A. A.; Schreiner, P. R. Chem. Rev. 2002, 102, 1551–1593. (6) Gibson, J. K. Int. J. Mass Spectrom. 2002, 214, 1–21. (7) Gibson, J. K.; Marc-alo, J. Coord. Chem. Rev. 2006, 250, 776–783. (8) Wang, X; Andrews, L.; Marsden, C. J. Chem.;Eur. J. 2007, 13, 5601–5606. (9) Andrews, L.; Cho, H. J. Phys. Chem. A 2005, 109, 6796–6798. (10) Marc-alo, J.; Leal, J. P.; Matos, A. P. Int. J. Mass Spectrom. Ion Processes 1996, 158, 265–274. (11) Gibson, J. K. Int. J. Mass Spectrom. 2002, 216, 185–202. (12) Gibson, J. K.; Marc-alo, J.; Haire, R. G.; Santos, M.; de Matos, A. P.; Mrozik, M. K.; Pitzer, R. M.; Bursten, B. E. Organometallics 2007, 26, 3947–3956. r 2010 American Chemical Society

particular, Marc-alo et al.10 carried out the first FTICR-MS study on the reactions of the Anþ actinide ions with small hydrocarbons. In this study, it was found that only Thþ effectively reacts with all hydrocarbons including methane, presumably in an exothermic process. Later, Gibson et al.11,12 reported two studies of the Thþ þ CH4 reaction. In the first experiment, the laser ablation with prompt reaction and detection (LAPRD) technique was employed, and the carbene cationic ThCH2þ product was observed, but quantitative results were not given.11 In the second study using FTICR-MS experiments, these authors stated that the Thþ þ CH4 reaction is indeed exothermic and proceeds at a rate of 0.10 10-10 cm-1 s-1.12 From another front, the reaction of laser-ablated Th atoms with CH4 was investigated, and the actinide methylidene CH2dThH2 product was characterized by infrared spectrum.9 Gas-phase studies of the d-block transition elements have shown that only some of the third-row transition metal (TM) ions (Taþ, Wþ, Osþ, Irþ, and Ptþ) dehydrogenate methane at thermal energies, while the ground-state Pt is unique among the neutral transition metal atoms able to react with methane at 300 K.13-15 However, experimental and theoretical studies indicate that the gas-phase Pt þ CH4 reaction is thermodynamically unfavorable and the intermediate CH3-PtH complex is the only stable product.16 Andrews and Cho recently studied the (13) Buckner, S. W.; McMahon, T. J.; Byrd, G. D.; Freiser, B. S. Inorg. Chem. 2007, 26, 3511–3518. (14) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1989, 28, 2769–2770. (15) Carroll, J. J.; Weisshaar, J. C.; Siegbahn, P. E. M.; Wittborn, A. M. C.; Blomberg, M. R. A. J. Phys. Chem. 1995, 99, 14388–14396. (16) Wittborn, A. M. C.; Costas, M.; Blomberg, M. R. A.; Siegbahn, P. E. M. J. Phys. Chem. 1997, 107, 4318–4328. Published on Web 07/29/2010

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de Almeida and Duarte

reaction of laser-ablated Pt atom with methane and confirmed these findings, detecting only the hydridomethyl Pt complex product in an argon matrix.17

Th þ CH4 f ThCH2 þ H2

ð1Þ

Thþ þ CH4 f ThCH2 þ þ H2

ð2Þ

Considering the reaction of the doubly charged thorium cation and methane (eq 3), no experimental investigation has been reported yet. Gibson et al. have briefly reported the reactivity of doubly charged actinide cations with hydrocarbons, although the reaction with methane has not been mentioned.18 Nevertheless, this reaction is of special interest since it opens the possibility to access the role of 5f electrons in the reactivity of thorium species. Relatively few studies of the reactivity of doubly charged atomic transition metal cations have been performed. Among d-block elements, only Ti2þ,19 Nb2þ,20 Zr2þ,21 Ta2þ,22 and Y2þ 23 cations have been investigated, with dehydrogenation of methane being the predominant pathway for Nb2þ, Zr2þ, and Ta2þ ions. In contrast, La2þ is unreactive with methane.24 Overall, gasphase experiments using the FTICR-MS technique have shown a greater reactivity for M2þ, as compared to their analogous Mþ, toward hydrocarbons, arenes, and oxidizing reactants.20-22,25,26

Th2þ þ CH4 f ThCH2 2þ þ H2

ð3Þ

In our previous studies, the first step of the methane dehydrogenation process, corresponding to an oxidative insertion, was first studied for all neutral lanthanide and thorium atoms and, later, for the early actinide ions from Acþ-Puþ.27,28 We have found that in both cases thorium shows the best kinetic and thermochemcial conditions to react with methane. In a very recent theoretical work, the reactivity of Thþ and Uþ with methane was studied at the DFT level. The authors report the mechanisms of both reactions, indicating that only thorium is able to dehydrogenate methane by an exothermic process.29 (17) Cho, H.; Andrews, L. J. Phys. Chem. A 2008, 112, 12293–12295. (18) Gibson, J. K.; Marc-alo, J.; Haire, R. G.; Santos, M.; de Matos, A. P.; Tyagi, R.; Mrorik, M. K. Eur. Phys. J. D 2007, 45, 133–138. (19) Tonkyn, R.; Weisshaar, J. C. J. Am. Chem. Soc. 1986, 108, 7128– 7130. (20) (a) Buckner, S. W.; Freiser, B. S. J. Am. Chem. Soc. 1987, 109, 1247–1298. (b) Gord, J. R.; Freiser, B. S.; Buckner, S. W. J. Chem. Phys. 1989, 91, 7530–7536. (21) Ranasinghe, Y. A.; MacMahon, T. J.; Freiser, B. S. J. Phys. Chem. 1991, 95, 7721–7726. (22) (a) Parke, L. G.; Hinton, C. S.; Armentrout, P. B. J. Phys. Chem. C 2007, 111, 17773–17787. (b) Parke, L. G.; Hinton, C. S.; Armentrout, P. B. J. Phys. Chem. A 2008, 112, 10469–10480. (23) Hill, Y. D.; Huang, Y. Q.; Ast, T.; Freiser, B. S. Rapid Commun. Mass Spectrom. 1997, 11, 148–154. (24) (a) Ranasinghe, Y. A.; MacMahon, T. J.; Freiser, B. S. J. Am. Chem. Soc. 1992, 114, 9112–9118. (b) Roth, L. M.; Freiser, B. S. Mass Spectrom. Rev. 1991, 10, 303–328. (25) Gibson, J. K.; Marc-alo, J.; Haire, R. G.; Santos, M.; de Matos, A. P. J. Phys. Chem. A 2005, 109, 2768–2781. (26) Marc-alo, J.; Leal, J. P.; de Matos, A. P.; Marshall, A. G. Organometallics 1997, 16, 4581–4588. (27) de Almeida, K. J.; Cesar, A. Organometallics 2006, 25, 3407– 3416. (28) de Almeida, K. J.; Duarte, H. A. Organometallics 2009, 28, 3203– 3211. (29) Di Santo, E.; Michelini, M. C.; Russo, N. Organometallics 2009, 28, 3716–3726.

The main focus of the present study is to assess the ability of Th, Thþ, and Th2þ to react with methane by getting a close description of the reaction mechanism of the whole dehydrogenation process. In addition, we compare the similarities and differences in the electronic and molecular factors that provide insights into the reactivity of thorium species. Another interest of this investigation is the understanding of the chemical bonds in the thorium molecular systems, in particular, the direct and/or indirect roles of 5f electrons and 5f orbitals in the actinide reactivity, which have long been a central theme of actinide chemistry.6,7,10-12,27-32 For purpose of prospecting a little further in this direction, we have performed a systematic bonding analysis considering all thorium species involved in the reactions under investigation.

II. Computational Details Fully unconstrained geometry optimization and harmonic frequency calculations were computed at the density functional theory (DFT) level. In this study, we have used the hybrid B3LYP and GGA B3PW91 exchange/correlation (XC) functionals.33,34 We have considered all possible spin states of Th (singlet, triplet, and quintet), Thþ (doublet and quartet), and Th2þ (singlet and triplet) in our calculations due to the possibility of spin crossovers involved in the reaction pathways, a feature generally referred to as two-state reactivity.35 The Stuttgart-Dresden relativistic effective core potential (RECP) in combination with its optimized double-ζ basis set (12s11p10d8f)/ [8s7p6d4f ] (DZV) was employed for describing the atomic thorium species.36,37 This relativistic small-core RECP replaces the 60 electrons in inner shells 1-4, leaving the explicit treatment of the n = 5 shell (5s, 5p, 5d, and 5f) and also the 6s, 6p, 6d, and 7s valence electrons. For the C and H atoms, the 6-311þþG(d,p) basis sets of Pople and coworkers were used.38 The present computational methodology is well established for treating actinide systems, and it has been successfully employed in previous calculations.30,31,39-41 All optimized molecular structures have been identified as minimum energy structures or first-order saddle points on the potential energy surfaces (PESs) by monitoring the numerically calculated harmonic frequencies and their respective vibrational normal modes. We have ensured that each transition-state (TS) structure obtained on the PESs shows only one imaginary frequency and that this frequency correctly connects the (30) (a) Michelini, M. C.; Russo, N.; Sicilia, E. Angew. Chem., Int. Ed. 2006, 45, 1095–1099. (b) Michelini, M. C.; Russo, N.; Sicilia, E. J. Am. Chem. Soc. 2007, 129, 4229–4239. (c) Mazzone, G.; Michelini, M. C.; Russon, N.; Sicilia, E. Inorg. Chem. 2008, 47, 2083–2088. (31) Lyon, J. T.; Andrews, L.; Malmqvist, P.-A˚.; Roos, B. O.; Yang, T.; Bursten, B. E. Inorg. Chem. 2007, 46, 4917–4925. (32) Roos, B. O.; Malmqvist, P.-A˚.; Gagliardi, L. J. Am. Chem. Soc. 2006, 105, 17000–17006. (33) (a) Becke, A. D. Phys. Rev. A 1998, 38, 3098–3100. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (c) Lee, C; Yang, W.; Parr, R. G. Phys. Rev. 1988, 37B, 785–789. (34) (a) Becke, A. D. J. Chem. Phys. 1993, 988, 5648–5652. (b) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244–13249. (35) (a) Shr€ oder, D.; Shaik, S.; Schwarz, H. Acc. Chem. Res. 2000, 33, 139–145. (b) Armentrout, P. B.; Beauchamp, J. L. Acc. Chem. Res. 1989, 22, 315–321. (36) K€ uchle, W.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1994, 100, 7535–7542. (37) (12s11p10d8f)/[8s7p6d4f] is generated by W. K€ uchle (unpublished) http://www.theochem.uni-stuttgart.de/pseudopotentials. (38) (a) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650–654. (b) Clark, T.; Chandrasekhar, J.; Scheleyer, P. V. R. J. Chem. Phys. 1983, 74, 294–301. (c) Blaudeau, J. P.; McGrath, M. P.; Curtiss, L. A.; Radom, L. J. Chem. Phys. 1997, 107, 5016–5021. (39) Yang, P.; Warnke, I.; Martin, R. L.; Hay, P. J. Organometallics 2008, 27, 1384–1392. (40) Cao, X.; Dolg, M. Coord. Chem. Rev. 2006, 250, 900–910. (41) Batista, E. R.; Martin, R. L.; Hay, P. J.; Peralta, J. H.; Scuseria, G. E. J. Chem. Phys. 2004, 121, 2144–2151.

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Table 1. Relative Energies (in kJ mol-1) and First and Second Adiabatic Ionization Energies (IE1 and IE2, in eV) for Thoriuma

III. Results and Discussion

B3LYP

B3PW91

species

DVZb

ANOc

[Rn] 6d27s2 (3) [Rn] 6d37s1 (5) [Rn] 6d27s2 (1)

0.00 81.46 56.50

0.00 36.63 57.10

DVZb

ANOc

exptld

0.00 56.76 81.29

0.00 26.54 81.12

0.00 27.61 96.78

0.00 6.78

0.00 8.54

0.00 22.23

0.00 171.04 6.07 12.09

0.00 163.46 6.10 12.08

0.00 142.74 6.3e 11.9e

Th

Thþ [Rn] 6d27s1 (4) [Rn] 6d17s2 (2)

8.16 0.00

6.40 0.00 Th2þ

1

1

[Rn] 6d 5f (3) [Rn] 7s2 (1) IE1 IE2

0.00 169.40 6.04 12.22

0.0 167.40 6.08 12.14

a Spin multiplicities are given in parentheses. b DZV is (12s11p10d8f)/ [8s7p6d4f] basis set from ref 37 c ANO is (14s13p10d8f6g)/[6s6p5d4f3g] basis set from ref 43 d Statistically averaged spin orbit energy levels taken from ref 46. e IE1 and IE2 from ref 47a and ref 47b, respectively.

stationary points by means of intrinsic reaction coordinate (IRC) calculations. The vibrational zero-point energy (VZPE) corrections and vibrational entropic contribution to the Gibbs free energies were calculated using the harmonic approximation and unscaled vibrational frequencies. The VZPE corrections were included in all of the reported relative energies. The Gibbs free energies were obtained for a temperature of 298.15 K. The bonding analysis was performed within the natural bond orbital (NBO) scheme.42 Open-shell calculations were performed by using the spin-unrestricted methods, where spin contamination was not found to be serious. The “ultrafine” grid was used for numerical integration of the exchange/correlation potential in the GAUSSIAN 2003 program44 in all calculations. For activation barriers, the single-point B3LYP and CCSD(T) calculations were also performed on the optimized B3LYP/DZV structures by using an improved (14s13p10d8f6g)/[6s6p5d4f3g] Gaussian basis set (ANO) for thorium. In addition, the effect of spin orbit (SO) interactions was evaluated at the same level of theory, using the effective valence SO operators.43 Both polarized quadruple-ζ basis set (ANO) and SO operators were especially optimized for the scalar-relativistic small-core RECP. All B3LYP single-point calculations were done with the development version of the SODFT module of NWChem.45 (42) (a) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1985, 83, 1736– 1740. (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899– 926. (43) Cao, Xiaoyan.; Dolg, M.; Stoll, H. J. Chem. Phys. 2003, 118, 487–496. (44) Frish, M. J.; et al. Gaussian 03, revision C. 02; Gausian, Inc.: Wallingford, CT, 2004. (45) Bylaska, E. J.; de Jong, W. A.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Valiev, M.; Wang, D.; Apra, E.; Windus, T. L.; Hammond, J.; Nichols, P.; Hirata, S.; Hackler, M. T.; Zhao, Y.; Fan, P.-D.; Harrison, R. J.; Dupuis, M.; Smith, D. M. A.; Nieplocha, J.; Tipparaju, V.; Krishnan, M.; Wu, Q.; Van Voorhis, T.; Auer, A. A.; Nooijen, M.; Brown, E.; Cisneros, G.; Fann, G. I.; Fruchtl, H.; Garza, J.; Hirao, K.; Kendall, R.; Nichols, J. A.; Tsemekhman, K.; Wolinski, K.; Anchell, J.; Bernholdt, D.; Borowski, P.; Clark, T.; Clerc, D.; Dachsel, H.; Deegan, M.; Dyall, K.; Elwood, D.; Glendening, E.; Gutowski, M.; Hess, A.; Jaffe, J.; Johnson, B.; Ju, J.; Kobayashi, R.; Kutteh, R.; Lin, Z.; Littlefield, R.; Long, X.; Meng, B.; Nakajima, T.; Niu, S.; Pollack, L.; Rosing, M.; Sandrone, G.; Stave, M.; Taylor, H.; Thomas, G.; van Lenthe, J.; Wong, A.; Zhang, Z. NWChem, A Computational Chemistry Package for Parallel Computers, version 5.1; Pacific Northwest National Laboratory: Richland, WA, 2007; pp 99352-0999.

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A. Atomic Calculations. In Table 1, we collected the experimental and computed first and second adiabatic ionization energies of thorium as well as its electronic excitation energies involving the ground state and low-lying excited states with, at least, two non-f valence electrons. We can see that the DFT approaches used in this study give results in reasonable agreement with the available experimental data. The B3PW91 calculations correctly predict the ordering of the electronic states of all species investigated, whereas the B3LYP approach gives rise to an incorrect stability of the electronic states of Thþ, with the quartet ground-state [Rn]6d27s1 configuration lying 6.40 kJ mol-1 higher in energy relative to the doublet [Rn]6d17s2 configuration. The calculations using the ANO basis set give lower excitation transitions closer to experimental data. In particular, these calculations correctly reproduce the energy levels of the excited electronic states of the neutral Th atom at the B3LYP level. It is worth noting that the incorrect ordering of electronic states obtained at the B3LYP level occurs for the electronic states with very close energies. In this respect, an important point to be considered in the DFT calculations using unrestricted Kohn-Sham theory is the spin contamination. We have noted that even small deviation of the expected ÆS2æ values leads to a significant effect in the ordering of the close-energy electronic states. In atomic calculations, the computed values for ÆS2æ never exceed 3.76 for quartet states, 2.05 for triplet states, and 6.03 for quintet states. However, a slightly higher value (ÆS2æ = 0.77) was found for the doublet spin state of the Thþ ion at the B3LYP level. The B3LYP orbital population results (6d1.517s1.49) for the doublet 6d17s2 state of Thþ indicate a relatively strong mixed 4F-2D character in this electronic state. At the B3PW91 level, this mixing effect becomes appreciably smoothed (6d1.867s1.24). It should be noted that the multiconfigurational character of this electronic state is indicated in Blaise and Wyart’s tables,46 where the groundstate Thþ is not identified. In calculations of molecular complexes, ÆS2æ values are always found to be lower than the above-mentioned values, and in the specific case of doublet Thþ complexes, ÆS2æ never exceed 0.76. This is likely caused by the fact that the optimized lowest-energy spinstate complexes involved in the methane dehydrogenation by Th, Thþ, and Th2þ are substantially stabilized along the reaction pathways (see next section). B. Reaction Mechanisms. The mechanism of the homologous reactions in eqs 1-3 is believed to involve the initial step of the oxidative insertion of the metal center into one C-H bond of CH4, yielding an intermediate hydridomethyl complex, HMCH3. The activation of a second C-H bond is the next step followed by the reductive elimination of H2. Two mechanisms, described in detail in Figure 1, have been indicated for the methane dehydrogenation process by the bare TM centers.21,49 In pathway A, the activation of the second C-H bond proceeds through the methylene dihydride complex, HMH(CH2), with a subsequent reductive elimination of H2 to form the molecular hydrogen complex (H2)MCH2. In contrast, in pathway B, the molecular hydrogen complex is directly obtained through a four-centered transition (46) Blaise, J., Wyart, J.-F. International Tables of Selected Constants, Energy Levels and Atomic Spectra of Actinides, Vol. 20, Tables of Constants and Numerical Data, Paris, 1992 taken from http://www.lac-psud.fr/ Database/Contents.html.

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Figure 1. Mechanisms for the methane dehydrogenation process by the bare transition metals

state. In the present study, both mechanisms were investigated for all Th, Thþ, and Th2þ species considering all possible spin states of the metal center. Our results indicate that reactions involving Thþ and Th2þ may occur via the later mechanism, whereas in the Th þ CH4 reaction, these two alternative pathways are found to be energetically competitive with each other. It is important to mention that all potential energy profiles presented in figures in this paper were obtained considering the B3PW91 results due to the better performance of this functional in computing the atomic excitation energies of all thorium species investigated. For the sake of clarity, hereafter all numeric values cited in the text were obtained at the B3PW91 level, while the B3LYP results are given in parentheses. 1. Neutral Thorium Reaction. The potential energy profiles of the Th þ CH4 reaction are shown in Figure 2. The optimized molecular structures corresponding to the lowestenergy spin states of this reaction are displayed in Figure 3. From Figure 2, we can see that the reaction of the neutral Th (3F) with methane starts without the formation of an initial molecular precursor complex. A rather weakly bound η2-like Th(CH4) complex in a 5A state was optimized to be 10.88(33.70) kJ mol -1 above the Th (3F) þ CH4 (1A1) entrance channel. We have tried to optimize an η3-precursor for Th(CH4), but this molecular species is higher in energy than the η2-structure by 22.31(25.41) kJ mol-1. Therefore, the absence of an initial molecular precursor leads the first step of dehydrogenation process to take place with a repulsive electrostatic character, with an activation barrier of 35.46(42.57) kJ mol-1. The 3TS1 has an imaginary frequency of 1059(1227) cm-1, which corresponds primarily to motion of the transferring H atom along with a rocking motion of the methyl group as it moves from pointing toward the H atom to Th. The formation of the hydridomethyl complex, HThCH3 II (3A0 ), occurs via an exothermic process of 153.00(143.25) kJ mol-1. In our previous works performed at the B3LYP level together with the CRENBEL pseudopotential and basis set, the insertion process was predicted to be exothermic by 181.05 kJ mol-1 with an activation barrier of 8.79 kJ mol-1.27 These differences indicate the dependency of the activation barrier and reaction energy on the ECP and basis set employed. It should be pointed out that the triplet intermediate complex, HThCH3, is nearly degenerate in energy with the corresponding singlet structure. In this region, an intersystem crossing occurs between the two lowest PESs, promoting a spin change in the reaction, which will reflect the changing number of covalent bonds in the neutral Th atom of the subsequent intermediate complexes. After the crossing point, the triplet PES follows a higher energy than the singlet

(47) (a) Worden, E. F., Trautmann, N., Blaise, J., Wyart, J.-F. In The Chemistry of the Actinide and Transactinide Elements,3rd ed.; Morss, L. R., Edelstein, N. M. Fuger, J., Eds.; Springer: Dordrecht, 2006. (b) Hildenbrand, D. L., Gurvich, L. V., Yungman, V. S. The Chemical Thermodynamics of Actinide Elements and Compounds. Part 13: The Gaseous Actinide Ions; IAEA: Vienna, 1985.

one, whereas the quintet PES does not participate at any point of the whole reaction. From the HThCH3 point, the system can follow a stepwise pathway involving sequential H atom transfer to form a H2ThCH2 III (1A) dihydride intermediate, Figure 3. This intermediate complex is reached via 1TS2, which lies 75.81(55.33) kJ mol-1 below the ground-state reactant energy, giving rise to an activation barrier of 75.81(55.33) kJ mol-1. This transition state has an imaginary frequency of 1037(1008) cm-1, corresponding largely to motion of the transferring hydrogen. The dihydride intermediate III is the global minimum structure on the PESs. Continuing along the singlet surface, this intermediate complex can reductively eliminate the H2 molecule, carrying the molecule across 1TS3, which lies 4.27(8.71) kJ mol-1 above the reactants’ energy, with an activation barrier of 176.69(180.58) kJ mol-1. The imaginary frequency of 1TS3 is 1370(1880) cm-1 and describes a motion in which the two hydrogen atoms come closer. The (H2)ThCH2 IV (1A) intermediate readily dissociates to produce the dehydrogenation products: ThCH2 (1A0 ) and H2. Alternatively, the HThCH3 intermediate can proceed directly to the (H2)ThCH2 intermediate via a four-center transition state, 1TS4 (path B, which is represented by a dashed line in Figure 2). This transition state has a much lower energy than 1TS3, with an activation barrier of 120.93(138.98) kJ mol-1. The imaginary frequency of 746(930) cm-1 corresponds to the expected motion that brings the two hydrogen atoms together while making the ThCH2 moiety more planar. On the basis of these findings, we can conclude that activation of the second C-H bond of methane via path A belongs to the slowest step on the singlet reaction pathway, even though the barrier height relative to 1 TS2 is found to be lower than that for 1TS4 of path B. The energy-limiting step of the reaction is the oxidative insertion of the neutral Th into the first C-H bond, where 1TS1 lies 35.46(42.57) kJ mol-1 above the ground-state reactants, whereas the lowest-energy transition and intermediate states (path B) are localized below the energy of the reactants. The overall Th (3F) þ CH4 reaction is computed to be exothermic by 65.34(72.00) kJ mol-1. 2. Thorium Ion Reactions. The lowest-energy reactions of the Thþ and Th2þ ions with CH4 evolve along a similar reaction pathway, called path B. Different from the Th (3F 6d17s2) þ CH4 case, the first step of the ion reactions is an exothermic association process to form an electrostatically bound ThnþCH4, n = 1 or 2, complex I, which is followed by the formation of an insertion intermediate HThCH3nþ complex, obtained after the system surmounts the first transition state, TS1. Then, the H-ThCH3nþ intermediate rearranges while passing through the second transition state, 1TS4, to form the last intermediate (H2)ThCH2nþ complex. It should be noted that numerous trials were needed to search for a possible alternative three-member transition state TS2 (path A) that connects HThCH22þ and H2ThCH22þ

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Figure 2. Potential energy profiles for the Th þ CH4 reaction at the B3PW91 and B3LYP (in parentheses) levels of theory, corresponding to the singlet, triplet, and quintet spin states of the thorium atom. Spin multiplicities are given in brackets.

Figure 3. Optimized molecular structures of the lowest-energy spin state Th/CH4 complexes at the B3PW91 and B3LYP (in parentheses) levels of theory. Bond lengths are in angstroms, and angles are in degrees.

intermediates, but such a transition state is found at very high energy. Similar results were obtained for TS3 and III structures of the doubly charged ion, thus showing that path A is energetically inaccessible for the Th2þ ion. The optimized profiles of the reactions of Thþ and Th2þ with methane are shown in Figures 4 and 6, while in Figures 5 and 7 we report the main geometrical parameters for all lowest spin-state species involved in these reactions, respectively. The results for the alternative mechanism, path A, for Thþ þ CH4 are shown as a dashed line in Figure 4. As shown in Figures 4 and 6, the DFT results give rise to important differences in energetics of the Th2þ þ CH4 reaction as compared to those found for Thþ þ CH4. First, Th2þ (3F 6d15f1) leads initially to the formation of a Th2þ(CH4) (3A) adduct by an exothermic process of 143.54(144.04) kJ mol-1, while the corresponding system of the monopositive cation reaction is only 44.96(42.53) kJ mol-1 below its ground-state

reactants. Distinct initial geometries were considered for the ion-dipole Thnþ(CH4) complex, and the ones reported here with a η3-like structure are the lowest-energy structures. Second, the intersystem crossing between the two lowest PESs gives an oxidative addition barrier of 63.88(52.66) kJ mol-1 for the 1 TS1 structure, more than 2 times higher than 2TS1 in the Thþ þ CH4 reaction (26.66(27.12) kJ mol-1). It is worth noting, however, that doubly charged 1TS1 lies 79.66(91.38) kJ mol-1 below the ground-state reactant energy, whereas the singly charged 2TS1 lies only 18.30(15.41) kJ mol-1 below the Thþ (4F) þ CH4 reactants. In our previous work on the oxidative insertion of the Thþ ion into one C-H bond of methane, we have obtained a smaller value of 9.25 kJ mol-1 for the 2TS1 activation barrier at the B3LYP level.28 This result, however, is a consequence of the fact that only an η2-like structure was previously taken into account for the Thþ(CH4) complex.

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Figure 4. Potential energy profiles for the Thþ þ CH4 reaction (path B) at the B3PW91 and B3LYP (in parentheses) levels of theory, corresponding to the doublet, quartet, and quintet spin states of the thorium ion. Spin multiplicities are given in brackets.

Figure 5. Geometrical parameters of the lowest-energy spin state Thþ/CH4 complexes at the B3PW91 and B3LYP (in parentheses) levels. Bond lengths are in angstroms, and angles are in degrees.

The formation of the first HThCH3nþ intermediate is 36.21(51.37) kJ mol-1 more exothermic for Th2þ than for Thþ. The HThCH32þ intermediate is 222.19(239.82) kJ mol-1 below its ground-state reactant energy, while a corresponding value of 185.98(188.45) is observed in the Thþ case. The TS4 barrier height between II (1A) and H2ThCH2þ2 III (1A) complexes is smaller (82.63(92.84) kJ mol-1) than the corresponding one for Thþ (104.60(114.94) kJ mol-1). The (H2)ThCH22þ III (1A) lies 144.25(147.26) kJ mol-1 below the reactant asymptote, whereas a less favorable process (ΔEzpe = -81.75(-77.61) kJ mol-1) is observed for the (H2)ThCH2þ (2A) complex. The loss of H2 requires an additional 49.31(36.92) kJ mol-1 to form the ground-state products, ThCH22þ (1A0 ) þ H2, while the value of 21.97(14.95) kJ mol-1 is computed to form the ThCH2þ (2A0 ) þ H2. Finally, the

reaction of Th2þ with methane is computed to be significantly exothermic, by 94.94(110.34) kJ mol-1, while a value of 59.78(62.66) kJ mol-1 is found in calculations of the Thþ þ CH4 reaction. It is worth noting that the overall reaction of the Thþ ion with methane is an exothermic reaction, consistent with the experimental data for this reaction.11,12 Another important fact is that the results of the neutral Th þ CH4 reaction indicate a similar value of the exothermicity (65.34(72.00) kJ mol-1) compared to that computed for the Thþ þ CH4 reaction, although the latter is found to be kinetically more favorable than the former one with all ionic transition states and intermediate complexes localized below the energy of their reactant asymptote. It is important to note that the whole lowest-energy optimized pathway for the Th2þ þ CH4 reaction is localized below the ground-state reactant energy, in much lower energies

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Figure 6. Potential energy profiles for the Th2þ þ CH4 reaction (path B) at the B3PW91 and B3LYP (in parentheses) levels of theory, corresponding to the singlet and triplet spin states, with spin multiplicities of the metal center given in brackets.

Figure 7. B3PW1(B3LYP) equilibrium molecular structures of the lowest-energy spin-state Th2þ complexes. Bond lengths are in angstroms, and angles are in degrees.

than those computed for Thþ. This feature indicates therefore a high gas-phase reactivity of the Th2þ in the reaction with methane. The imaginary frequencies of all transition states of the charged reactions are shown in Figures 5 and 7 and have the same qualitative motions as those described for the corresponding structures of the neutral reaction. A comparison of our results with those obtained recently by Di Santo et al.29 for the Thþ þ CH4 reaction shows a complete agreement when the B3LYP functional is considered.29 To conclude this section, the B3LYP and CCSD(T) singlepoint results for all activation barriers are collected in Table 2 so that the electronic, vibrational, and spin-orbit effects can be better recognized. Overall, the ANO basis set slightly decreases the size of the activation barriers as compared to those

computed by using the DZV basis set, and a similar effect is observed for activation barriers obtained with B3LYP and CCSD(T) methodologies. The inclusion of the spin orbit (SO) effects causes a decrease of about 5%, on average, in activation barriers, while a fairly larger effect is obtained for the vibrational zero-point energy (VZPE) correction, which amounts to an average value of 13 kJ mol-1. The evaluation of SO corrections on the reactions between the uranium species and water has already been done using the zero-order regular approximation (ZORA) at the DFT level.30 In these studies, the SO corrections were also estimated to generally decrease the barrier height by less than 10%. C. Electronic and Geometrical Properties. By comparing the products of the actinide cation reactions with those

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Table 2. DFT/B3LYP Activation Barriers (in kJ mol-1) for the Methane Dehydrogenation Process by Th, Thþ, and Th2þ CCSD(T)

B3LYP

species

ΔEANOb

ΔEDZVa

TS1e TS2 f TS3g TS4h dissociation barrieri

44.15 115.14 173.86 140.62 41.27

47.97 103.19 181.18 144.42 44.04

ΔEANOb

ΔEANO/SOc ΔEZPEd

ΔGd

Th þ CH4 44.08 104.82 183.85 146.22 42.91

39.01 97.62 180.96 147.31 51.82

26.41 32.15 86.34 84.18 179.37 179.24 133.49 136.05 41.15 45.96

35.08 136.09 100.51 124.94 51.74

14.94 16.03 119.89 121.72 96.45 98.25 110.85 114.40 55.05 58.35

Thþ þ CH4 TS1e TS2 f TS3g TS4h dissociation barrieri

40.11 149.36 113.51 109.84 61.56

43.07 141.36 97.83 119.47 65.80

41.06 142.03 105.78 121.90 61.87

Th2þ þ CH4 TS1e TS2 f TS3g TS4h dissociation barrieri

61.08

81.33

68.73

67.81

40.65

44.25

81.72 90.45

95.57 98.33

99.29 93.01

100.76 101.39

90.92 91.88

95.06 83.30

a ΔEDZV is the electronic energies using the (12s11p10d8f)/[8s7p6d4f] basis set for thorium from ref 37. b ANO results are obtained using the (14s13p10d8f6g)/[6s6p5d4f3g] basis set for thorium from ref 43. c Δ EANO/SO are the electronic energies corrected by spin-orbit effects by using the ANO basis set. d ΔEZPE, ΔG are the spin-orbit electronic energies corrected by the harmonic vibrational zero-point energies and the vibrational entropic contributions, respectively. These vibrational contributions were computed using the DZV basis set. e Energy difference between first transition state TS1 and the first complex, I. f Energy difference between transition state TS2 (path A) and the second complex, II. g Energy difference between transition state TS3 (path A) and the third complex, III. h Energy difference between transition state TS4 (path B) and the second complex, II. i Energy difference between dissociated products (ThCH2 þ H2 or ThCH2þ þ H2 or ThCH22þ þ H2) and the last intermediate complex, III.

obtained in reactions of d-transition metal cations, it was demonstrated that thorium cations should react similarly to the third-row transition metals ions with d2 or d3 ground states.18 In this discussion, therefore, we compare our results with those obtained by Parke et al. for reactions of Taþ (5d36s1) and Ta2þ (5d3) with methane.22 They have conducted an extensive theoretical investigation of the potential energy surfaces of these reactions at the B3LYP level, providing the electronic and molecular factors involved in the reactivities of these two tantalum species. Starting with the weakly bound complex, the DFT results indicate that no favorable energy structure is found for the initial Th-CH4 molecular precursor, whereas very stable η3like conformations were optimized for both Thþ-CH4 and Th2þ-CH4 systems. The main reason for these results is related to the presence of charges in the Thþ (6d27s1) and Th2þ (5f16d1) ions, which provides a long-range electrostatic interaction with the closed-shell methane, polarizing this molecule via charge-induced dipole force. The higher the charge on Th, the greater the attractive force between the thorium species and methane. On the other hand, the absence of charge in the neutral Th atom gives rise to an overall repulsive interaction toward the apolar methane, a feature that was well accounted for in our calculations at the

beginning of the Th þ CH4 profile in Figure 2. The Th2þ-CH4 bond energy is 143.54(144.04) kJ mol-1, while a smaller value of 44.96(42.53) kJ mol-1 is found for the Thþ-CH4 bond energy. The B3LYP results obtained by Parke et al. show a much tighter binding of 254.84 kJ mol-1 for Ta2þ-CH4, whereas a similar value of 54.04 kJ mol-1 is pointed out for the Taþ-CH4 bond distance. These results suggest that the presence of one electron in 5f orbitals of Th2þ (6d15f1) may provide an electrostatic repulsion toward methane, making the approximation between the metal dication and the closed-shell molecule more difficult and, thus, decreasing the Th-C energy bond. The computed Th-C bond lengths in the weakly bound complexes decrease from 2.73(2.79) A˚ in Thþ-CH4 to 2.61(2.67) A˚ in the Th2þ-CH4 complex. The Ta-C bond distance in Ta2þ-CH4 is 2.188 A˚, much shorter than that in Taþ-CH4, 2.626 A˚. In order to understand the electronic factors involved in activation of the first C-H bond of methane, it is interesting to review the ground and first low-lying excited electronic states of Th, Thþ, and Th2þ, which are given as follows: for the Th atom, [Rn]6d27s2 is the ground state, while the [Rn]6d37s1 and [Rn]6d4 low-lying states are 66.59 and 211.98 kJ mol-1 higher in energy, respectively. For the Thþ ion, the ground-state is [Rn]6d27s1 and its low-lying electronic states are [Rn]6d17s2 (49.23 kJ mol-1) and [Rn]6d3 (83.80 kJ mol-1). Finally, the ground state of Th2þ is Rn[5f16d1], with the [Rn]6d2 configuration only 0.80 kJ mol-1 higher in energy. Gas-phase investigations involving the d-block TM elements also have indicated two points of major importance to be considered.15,16,22,48 The first one is the promotion energy to an excited electronic state of metal with, at least, two unpaired electrons (dnþ1s1 or dns0), which will allow the formation of two covalent bonds in the first intermediate complex. If one of these electron configurations is not the ground state of the metal atom or ion, a promotion energy to one of these excited states will be the cost that will directly enter into the final bond strength. The second factor is that σ-bond activation at a metal center requires an electronic configuration in which there is an empty acceptor orbital on the metal ion into which the electrons of a bond to be broken are donated. In this respect, it has long been noted that if the s orbital is occupied, a repulsive interaction can result, leading to inefficient reaction by introduction of an activation barrier. This donor-acceptor feature was particularly used to explain the higher reactivity Ta2þ, compared to Taþ, in reaction with methane.22 The considerations mentioned above offer insights to rationalize the energetics observed in our calculations. First of all, comparing Th and Thþ results, the higher activation TS1 barrier computed for the Th atom may be caused by the higher electron density on the s orbital of its [Rn]6d27s2 ground state relative to that in the [Rn]6d27s1 ground state of the Thþ ion. Furthermore, the s1d2 state of Thþ, used to form two covalent bonds in complex III, does not require a promotion energy, thus favoring the thermochemical conditions of this reaction. In contrast, a substantial amount of energy is needed for the neutral Th atom to make two covalent bonds in the HThCH3 complex since its favorable electronic states are significantly higher in energy. Another (48) Westerbergm, H.; Blomberg, M. R. A. J. Phys. Chem. A 1998, 102, 7303–7307. (49) Buckner, S. W.; McMahon, T. J.; Byrdm, G. D.; Freiser, B. S. Inorg. Chem. 1989, 28, 3511–3518.

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Table 3. Natural Bond Orbital Analysis for the Lowest Spin State Thorium Complexes at the B3PW91 and B3LYP (in parentheses) Levels of Theorya natural electron configuration species

natural charge

7s

6d

5f

2.92(2.96) 1.68(1.57) 0.64(0.63) 0.79(0.77) 0.86(0.87) 1.01(0.97) 1.01(0.99) 0.71(0.70) 0.72(0.72)

0.01(0.01) 0.23(0.22) 0.16(0.16) 0.25(0.23) 0.23(0.22) 0.32(0.32) 0.32(0.29) 0.20(0.20) 0.19(0.19)

1.25(0.72) 1.08(0.99) 0.85(0.83) 0.75(0.76) 0.68(0.69) 0.79(0.77) 0.95(0.90) 0.99(0.95) 0.86(0.81)

0.48(0.72) 0.38(0.37) 0.19(0.18) 0.24(0.26) 0.21(0.22) 0.23(0.22) 0.29(0.28) 0.25(0.24) 0.25(0.24)

0.78(0.63) 0.63(0.62) 0.57(0.56) 0.65(0.66) 0.74(0.75) 0.77(0.78)

0.70(0.73) 0.41(0.40) 0.27(0.26) 0.38(0.39) 0.34(0.32) 0.34(0.32)

Th þ CH4 Reaction Th-CH4(5) TS1(3) HThCH3(3) TS2(1) H2ThCH2(1) TS3(1) TS4(2) (H2)ThCH2(1) ThCH2(1)

0.06(0.29) 0.74(0.75) 1.43(1.43) 1.91(1.91) 2.55(2.54) 2.07(2.15) 2.07(2.08) 1.23(1.23) 1.20(1.21)

0.99(1.00) 1.32(1.42) 1.75(1.75) 1.06(1.09) 0.37(0.40) 0.59(0.57) 0.59(0.57) 1.87(1.88) 1.89(1.89)

Thþ þ CH4 Reaction Thþ-CH4(2) TS1(2) HThþCH3(2) TS2(2) H2ThCH2(2) TS3(2) TS4(2) (H2)ThþCH2(2) ThþCH2(1)

0.98(0.99) 1.52(1.54) 2.20(2.19) 2.60(2.61) 2.70(2.72) 2.59(2.60) 2.09(2.08) 2.11(2.10) 2.10(2.09)

1.28(1.57) 1.04(1.12) 0.76(0.80) 0.45(0.41) 0.43(0.41) 0.42(0.42) 0.71(0.77) 0.68(0.73) 0.83(0.88)

Th2þ þ CH4 Reaction Th2þ-CH4(2) TS1(2) HTh2þCH3(2) TS4(2) (H2)Th2þCH2(2) Th2þCH2(1) a

Figure 8. Metal valence population of the s, p, and d orbitals in the Th-C bond in all minima and transition states of the thorium and methane reactions.

important result is that even though no electron density is found on the s orbital of the [Rn]5f16d1 ground state of Th2þ and also on its almost degenerate low-lying excited state ([Rn]6d2), the TS1 barrier of this reaction is computed to be the highest one among those obtained for the thorium species investigated. This result may again indicate that the presence of one electron in the 5f orbitals of the Th2þ cation should have an effect similar to, or maybe even stronger than, that observed for electrons in the s orbitals, providing an electrostatic repulsion to the closed-shell methane. This feature is in accord with our previous results obtained for methane activation by the early actinide ions (Acþ-Puþ), where a positive correlation was observed between the increasing number of 5f electrons in the early actinide ions and the increasing size of their activation barriers.28 Regarding the thermochemical

1.96(1.94) 2.80(2.81) 3.04(3.05) 2.88(2.88) 2.90(2.91) 2.93(2.93)

0.56(0.68) 0.21(0.23) 0.15(0.17) 0.12(0.14) 0.06(0.05) 0.01(0.01)

All results are taken from the metal center.

conditions, the two close-energy Rn[5f16d1] and [Rn]6d2 electron configurations of Th2þ favor the formation of two covalent bonds in the HThCH32þ complex, thus explaining the highly exothermic conditions for this reaction. Considering the geometrical properties of the TS1 complexes, a distorted η2-structure is found for HThCH3, while a distorted η3-like atomic arrangement is obtained for both Thþ and Th2þ complexes. All these complexes are a typical “early” transition structure, closer in energy to the respective initial molecular complex. A notable feature in the TS1 structure of Thþ is the presence of an agostic H-Th interaction, which additionally stabilizes this structure, favoring the kinetic conditions of this reaction. The structure II of all insertion intermediate complexes shows a similar atomic arrangement with a cis conformation with respect to Th-H and one of the C-H bonds. The main difference among the optimized geometries of the HMCH3 complexes is that the Th-C bond distance becomes significantly shorter going from Th (2.32(2.35) A˚), to Thþ (2.29(2.31) A˚), to Th2þ (2.21(2.23) A˚). A similar trend is observed for the H-M-C bond angles, which decrease from 114.1(126.2) in the neutral Th complex to 96.7(96.6) in the Th2þ structure. With respect to the activation of the second C-H bond of methane, it is important to note that the higher stability of path A, as compared to path B, depends on the capability of the metal center to form up to four chemical bonds in the dihydridomethylidenethorium complex (III), which involve one double covalent bond to the CH2 group, plus two covalent bonds to the H atoms. To accomplish this, the metal needs to use four singly occupied atomic orbitals,

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which are easily understood in terms of the four valence electron configuration. Among Th, Thþ, and Th2þ species, only the neutral thorium atom is able to form four covalent bonds in intermediate complex III. The DFT energy results for the planar H2ThCH2 and H2ThþCH2 complexes agree very well with this expectation, showing a global minimum of -172.42(-171.88) kJ mol-1 for the early complex, whereas the latter complex is found to be -85.32(-83.26) kJ mol-1 lower in energy than its ground-state reactants. It is worth noting that previous investigations have shown that metals rich in valence electrons usually proceed through path A, while TM centers that do not have enough valence electrons often follow path B.49 This feature was observed in investigation of the Taþ and Ta2þ reactions with methane, where path B was found to be the lowest energy pathway, in accord with our results for the thorium species.22 Another important geometrical property observed in thorium complexes is the formation of an agostic bonding interaction. Comparing the three last complexes of the Thþ and Th2þ reactions in Figures 5 and 7, we can see that the Th-H agostic distance decreases by about 0.1 A˚ going from TS4 to the final products. A larger decrease is observed for the Thþ-C-H agostic angle, which has a value of 91.05(92.89) in TS4 and becomes 87.65(89.51) in ThCH2þ. The value for the Th2þ-C-H agostic angle is slightly lower, 90.13(91.63), for the TS4 structure, whereas a slightly higher value of 89.68(91.34) is observed in the ThCH22þ complex. Finally, in Figure 3, we can see that no agostic interaction is observed for the last complexes of the Th þ CH4 reaction, a result likely caused by the longer bond lengths optimized in these complexes relative to those found in Thþ and Th2þ complexes. D. Bonding Properties. The natural metal charges and the metal valence population of all lowest-energy Th, Thþ, and Th2þ complexes are collected in Table 3, while Figure 8 shows the atomic contribution of the s, d, and f orbitals of thorium to the Th-C bonds of all lowest-spin complexes. As can be seen in Table 3, the natural charges on the thorium centers increase as one goes from the initial molecular complex I to H2MCH2 structure III. As a consequence, carbon becomes more negative across these systems, indicating that the ionic character of the Th-C chemical bonds increases in this direction. Interestingly to note is that the increasing of natural charge on the metal follows the increasing number of the chemical bonds around the metal center, reaching a maximum of four covalent bonds in the H2MCH2 complex. The final methylidene complexes are characterized by lower charges close to þ1, þ2, and þ3 in Th, Thþ, and Th2þ complexes, respectively. The natural electron configuration on the metal center in all complexes shows that the thorium atomic orbitals participate in the chemical bonds with a mixed sdf configuration. The NBO analysis indicates that all Th-C and Th-H chemical bonds have a predominant 6d character independently of whether Th, Thþ, or Th2þ is considered. It is important to mention that this feature has been observed previously in other thorium molecular compounds as well as for uranium molecular systems.12,31,32 Quite interesting results are observed in Figure 8. The first one is that the percentage of the s, d, and f metal orbitals in the Th-C chemical bonds varies smoothly along each reaction pathway. This indicates that the character of the chemical bonds in the thorium complexes may remain nearly unchanged along each reaction investigated. An apparently larger oscillation is observed for the percentage of the s orbital, which shows values varying


between 3% and 12% along the species investigated. Another important result from this figure is relative to the contribution of the 6d and 5f atomic orbitals to the Th-C bonds, which varies significantly across the Th, Thþ, and Th2þ complexes. While the average percentage of 5f orbitals grows from 20% in the neutral thorium complexes to 30% in the doubly charged Th2þ complexes, the average contribution of 6d orbitals decreases from 75% to 55% in these molecular systems. It is worth noting that shorter bond lengths are observed in the Th2þ complex than in the Th and Thþ molecular systems. The primary reason for this is likely the larger charge on Th2þ. However, this feature may also indicate that the participation of 5f orbitals in the chemical bonds might depend on the distance between metal and ligand. This idea has been already mentioned in an early ThH4 model study performed by Pyykk€ o and Desclaux.50 A comparison with other previous studies shows that the trends in the reactivity of d-block TM ions toward methane have been associated with the bond strength of MCH2þ. It has been observed that the reaction with methane takes place exothermically only if the bond dissociation energy between the metal center and methylene exceeds 458.79 kJ mol-1.51 We computed the bond strengths (D0) for ThCH2, ThCH2þ, and ThCH22þ complexes, and the values obtained are respectively 504.25(509.86), 506.55(503.49), and 538.36(543.34) kJ mol-1 at the B3PW91(B3LYP) levels. The B3LYP values for TaCH2þ and TaCH22þ are 464.31 and 528.02 kJ mol-1, respectively.22 The analysis of our results indicates that the participation of 5f orbitals plays an important role in the overall strengths of the Th-C and Th-H bonds, increasing their values as the percentage of 5f orbitals becomes larger. At this point, it should be noted that we have previously studied the strengths of the An-C chemical bonds for the early actinide ions from Acþ to Puþ, and we have found that lower bond strengths are observed for the actinide ions, which exhibit sdf hybridization with a predominant character of 5f orbitals (Paþ, Npþ, and Puþ).28 These results indicate, therefore, that only a proper mix of 5f orbitals with the 6d7s valence shell is able to provide the enhanced strengths of the An-H and An-C bonds. The predominant character of the 6d orbital seems to be the main factor to achieve this. From gas-phase d-block studies, it has been found that the most efficient TM ions for dehydrogenation of CH4 are Irþ and Ptþ ions.52,53 Irikura and Beauchamp52 showed that these ions react exothermically with methane to yield the corresponding carbene complexes. Perry et al.,53 by using the modified coupled pair functional method, indicated an overall exothermicity of about 34 kJ mol-1 to yield IrCH2þ and H2 products, and the bond energy for Irþ-CH2 product was estimated to be D0 = 485.58 kJ mol-1. The rate-determining step of the reaction (path A) was predicted to occur for the TS3 structure, with an activation barrier of 230 kJ mol-1, pronouncedly higher that that computed in the present calculation of Thþ. For the Ptþ þ CH4 reaction, Pavlov et al.54 computed an exothermic reaction of 3.35 kJ mol-1 at the (50) Pyykk€ o, P.; Desclaux, J. P. Chem. Phys. 1978, 34, 261–280. (51) Lias, S. G., Bartmess, J. E., Lieberman, J. F., Holmes, J. L., Levin, R. D., Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1. (52) Irikura, K. K.; Beauchamp, J. L. J. Phys. Chem. 1991, 95, 8344– 8351. (53) Perry, J. K.; Ohanessian, G.; Goddard, W. A. Organometallics 1994, 13, 1870–1877. (54) Pavlov, M; Blomberg, M. R. A.; Siegbahn, P. E. M.; Wesendrup, R.; Heinemann, C.; Schwarz, H. J. Phys. Chem. A 1997, 101, 1567–1579.

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B3LYP level, whereas the experimental value is found to be 12.14 kJ mol-1, which is based on the determined value of 470.9 kJ mol-1 for the Ptþ-CH2 bond strength.55 On the other hand, Carroll et al.15 reported an experimental and theoretical study on gas-phase reactions of the neutral ground states of Ir and Pt atoms with small alkanes. The ground-state Pt was the only neutral metal atom to react with methane at 300 K. The reactions with methane were computed to be endothermic by about 29 kJ mol- for Ptþ and 6 kJ mol-1 for Irþ. The B3LYP and PCI-80 (parametrized configuration interaction with parameter 80) calculations predicted clearly that the product of the Pt þ CH4 reaction is the long-lived intermediate H-Pt-CH3 complex. A large potential barrier (higher than 251 kJ mol-1) was found to separate H-Pt-CH3 from H2 elimination products. On the basis of all this information, the present results indicate a high reactivity of the thorium species in reaction with methane. In accord with our results this ability comes mainly from the interplay between the 5f and 6d7s valence orbitals so that stronger Th-C chemical bonds are formed along the whole reaction pathways.

IV. Conclusions DFT calculations have been performed for investigating the gas-phase methane dehydrogenation process by Th, Thþ, and Th2þ. The effects of the spin states of metal centers and the use of different XC functionals were analyzed. The ability of all thorium species to change spin along reaction pathways was found. Two mechanisms were investigated for all Th, Thþ, and Th2þ species in the reaction with methane. Our results indicate that the reactions involving Th, Thþ, and Th2þ may preferentially occur via a four-centered transition state, path B. The reactions of the neutral Th atom and Thþ ion with methane are computed to be exothermic by around 60 kJ mol-1, although the later reaction is found to be kinetically more favorable, with all transition states and intermediates below the ground-state reactant energy. (55) Heinemann, C.; Hertwig; Schwarz, H.; Koch, W.; Dyall, K. G. J. Chem. Phys. 1996, 104, 4642–4651.

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The results of the Th2þ reaction give rise to important insights to understand the reactivity of thorium species. First of all, the highest value of the oxidative insertion barrier (around 63 kJ mol-1) is found for Th2þ. This result indicates that the electron in the 5f orbital has an effect similar to, or maybe even stronger than, that observed for electrons in the s orbital, providing an electrostatic repulsion to the closedshell methane, thus increasing the value of this activation barrier. On the other hand, among thorium species, the best conditions are observed for Th2þ, with an exothermic reaction around 105 kJ mol-1 and all transition states below its the ground-state reactants. The NBO analysis shows that the atomic orbitals of thorium participate in the chemical bonds with a mixed sdf configuration and that all Th-C and Th-H chemical bonds have predominantly 6d character independently of whether Th, Thþ, or Th2þ is considered. However, it was found that the percentage of d and f atomic metal orbitals in the Th-C bonds varies significantly across the Th, Thþ, and Th2þ complexes. While the average percentage of 5f contribution grows from the neutral thorium complexes to the Th2þ complexes, the average 6d contribution decreases in this direction. The present results indicate that the participation of the 5f orbitals plays an important role in the overall strengths of the Th-C and Th-H bonds, increasing their values as the contribution of 5f orbitals becomes larger. The inclusion of spin-orbit corrections generally decreases the activation barriers by about 5%. A comparison with previous studies, including those involving d-block transition metals, led us to indicate a high reactivity for the thorium species in reaction with methane in the gas phase. This capability comes mainly from the mixing between the 5f and 6d7s valence orbitals in thorium, so that stronger Th-C and Th-H chemical bonds are formed along the whole reaction pathways.

Acknowledgment. The Brazilian agencies Conselho Nacional para o Desenvolvimento Cientı´ fico e Tecnologico (CNPq) and Fundac-~ao de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) are gratefully acknowledged for providing financial support.

Dehydrogenation of Methane by Gas-Phase Th, Th+ - American

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