Methane Dehydrogenation by Niobium Ions: A First-Principles Study of

Article pubs.acs.org/Organometallics

Methane Dehydrogenation by Niobium Ions: A First-Principles Study of the Gas-Phase Catalytic Reactions K. J. de Almeida* Departamento de Quı ́mica, Universidade Federal de Uberlândia, Av. João Naves de Á vila, 2121, Santa Mônica, Uberlândia, CEP 38400-902, MG, Brazil

T. C. Ramalho, J. L. Neto, and R. T. Santiago Departamento de Quı ́mica, Universidade Federal de Lavras, CP 3037, Lavras, MG, Brazil

V. C. Felicíssimo Departamento de Quı ́mica, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, CEP-49100-000, São Cristóvão, SE, Brazil

H. A. Duarte Departamento de Quı ́mica, Universidade Federal de Minas Gerais, Avenida Antonio Carlos, 6627, CEP-31270-901, Belo Horizonte, Minas Gerais, Brazil ABSTRACT: The issue of reactivity differences of the ions Nb+ and Nb2+ toward methane (CH4 + Nb+ → NbCH2+ + H2 and CH4 + Nb2+ → NbCH22+ + H2) is addressed using CCSD(T)//MP2 and CCSD(T)//B3LYP calculations. A thorough description of the reaction mechanisms and analyses of the geometrical structures, chemical bonds, and molecular orbitals provide important insights into the chemistry of the niobium species. The overall results indicate highly labile kinetics and more favorable thermochemical conditions for Nb2+. The NBO, AIM, and FERMO analyses provide a better understanding of the reactivity differences in the niobium reactions.

I. INTRODUCTION

Several experimental studies have been performed on the reactivity of methane toward nearly all singly charged transition-metal (TM) ions.2−7 In particular, the products of the gas-phase Nb+ + CH4 reaction were studied by Sievers and co-workers.8 In this study it was found that methane dehydrogenation takes place at temperatures below 400 K. From computational investigations, while several Hartree−Fock (HF) and density functional theory (DFT) studies have been used to investigate the singly charged ions of the first- and third-row transition metals,9,10 a rather limited number of studies has been performed so far for the second-row TM ions, even considering singly charged ions.11 For niobium ions, Blomberg and co-workers studied, at the ab initio level, the first step of methane dehydrogenation by Nb+.10

There has been much interest in the reactivity of the gas-phase metal ions with alkanes, in particular, methane, as discussed in a review article on this topic.1 This research is stimulated by both the challenging inertness of this simplest hydrocarbon molecule and the substantial interest in the use of natural gas resources. In spite of the important progress made in this field, some questions are still open. Further efforts to understand possible factors which control the reactivity and selectivity of the alkane conversion process are still required. Gas-phase studies have proved to be of major importance, as the collected data from these studies are restricted only to the metal center in the absence of perturbing factors such as solvation, ligands, and lattice environment. Thus, these results can be used as valuable guidelines in the development of novel, stable, and selective catalysts for the direct conversion of methane to more valuable product outcomes. © 2013 American Chemical Society

Received: September 11, 2012 Published: February 5, 2013 989

dx.doi.org/10.1021/om300856c | Organometallics 2013, 32, 989−999

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II. COMPUTATIONAL DETAILS

Relatively few experimental studies of the doubly charged transition-metal cations have been hitherto performed. The scarcity of atomic metal dication reactivity studies is partially caused by the difficulty in generating doubly charged atomic cations in comparison to the singly charged ions. In the last three decades, the understanding of dications has been substantially enhanced and the mass spectrometric studies of multiply charged ions have become more active in recent years.12−17 Freiser and co-workers studied, in a broad range of electron affinities (11.1−16.2 eV), the gas-phase reactions of dipositive TM ions with alkanes. The d1 (Sc2+, Y2+, and La2+)12,13 d2 (Ti2+ and Zr2+),14,15 and d3 (Nb2+ and Ta2+)16,17 ground-state electronic configurations were considered. In these experiments, the authors were able to verify that the d1 metal ions have distinct chemical behavior relative to the d2 and d3 metal ions in terms of the formation of doubly charged products. These differences were interpreted through the occurrence of different reaction mechanisms: bond insertion for d2 and d3 metal ions and hydrogen abstraction or concerted bond activation for the d1 metal ions. In the Nb2+ reactions with methane and ethane, Freiser and co-workers have found that dehydrogenation is a prominent reaction pathway, whereas with propane and butane, charge transfer is virtually the only reaction pathway observed for this cation.16 From theoretical studies of the TM d-block dications, only Parke and co-workers investigated the methane C−H bond activation by Ta2+ ion.17 Regarding f-block ions, Marçalo et al. screened the series of the lanthanide dications (Ln2+) and found an interesting correlation between the reactivity of these dications toward hydrocarbons and the ionization energy difference IE(Ln+) − IE(CmHn).18 In this study, it was also found that none of the Ln2+ ions are able to react with methane under thermal conditions. Very recently, Di Santo et al. studied, through both experiment and theory, the gas-phase reactions of the smallest alkanes with two dipositive actinide ions, Th2+ and U2+.19 The highest reactivity of Th2+ with methane, which had been already indicated in our previous computational work,20 was in fact confirmed. In the present work, we report the mechanistic details of methane dehydrogenation by Nb+ and Nb2+ ions. The main purpose of the present computational study is to assess the ability of Nb+ and Nb2+ ions to react with methane. In addition, we compare the similarities and differences in the electronic, bonding, orbital, and molecular factors that provide some insights into the chemistry of the niobium species. A noteworthy fact is that several different theoretical studies have been carried out so far for almost all first charged TM ions of the first and third row of the periodic table, thus providing a quite good picture of their reaction mechanisms. However, very little information is available for the second row, even considering the first charged TM ions. The present work is a contribution to this field, where full unrestricted optimization and frequency calculations were performed at the second order Møller-Plesset perturbation theory (MP2) and DFT levels. The MP2 results allow estimation of the influence of the post-HF electron correlation and dispersion effects on the structural parameters of niobium complexes. In order to better evaluate the kinetic and thermodynamic aspects of the reactions under investigation, single-point CCSD(T) calculations were employed and compared to the previous results.

The reaction mechanisms for methane dehydrogenation by Nb+ and Nb2+ were investigated following the general schemes proposed for these reactions that involve the formation of a metal−ligand adduct, as the first step of the process, followed by an oxidative insertion of the metallic center into one C−H bond of the alkane molecule. The formation of this first insertion intermediate is often recognized as the key step of the process, since the ground state of the intermediate did not correspond to the ground state of the metal. The next steps are migration of one or more atoms or groups of the alkane molecule to the metal, and thus the reductive elimination of an H2 molecule is provided, since the intermediates have sufficiently high lifetimes to undergo rearrangements. In the first step, MP2 and DFT geometry optimizations and frequency calculations were run to locate all stationary points and transition states (TS) on the singlet, triplet, and quintet states of the potential energy surfaces (PESs) of the Nb+ + CH4 reaction. For the Nb2+ + CH4 reaction, these calculations were performed on the doublet and quartet state PESs. For DFT calculations, Becke’s threeparameter hybrid functional was combined with the Lee, Yang, and Parr (LYP) correlation functional, denoted as B3LYP.21,22 The LANL2DZ effective core potential23,24 was used for the metal center, while the standard 6-311++G(d,p) basis sets were employed for the other atoms.25 No symmetry restrictions have been imposed during the geometry optimizations. Vibrational analysis has been performed to determine the character (minimum or saddle point) of all stationary points. We have ensured that each transition state (TS) structure obtained on the potential energy surfaces (PESs) shows only one imaginary frequency and that this frequency correctly connects the stationary points by means of intrinsic reaction coordinate (IRC) calculations. In the second step, the lowest energy states of the niobium molecular complexes were reoptimized at the B3LYP and MP2 theory level by using a larger LANL2TZ effective core potential26 for Nb, while the polarized extended atomic basis set, named 6-311+ +G(df,pd), was employed for the remaining atoms.27 At this computational level, the relative energies of all species involved in reactions under investigation were then refined by single-point CCSD(T) calculations.28,29 The B3LYP zero-point vibrational energy (ZPVE) corrections are included in all relative energies. We have considered all singlet, triplet, and quintet spin states for Nb+ as well as doublet and quartet spin states for Nb2+ due to the possibility of spin crossovers involved in the reaction pathways, a feature generally referred to as two-state reactivity.30 Open-shell calculations were performed by using the spin unrestricted methods, where spin contamination was not found to be serious. With large LANL2TZ, the computed values for S2 of the atomic and molecular calculations never exceed 6.005 for quintet states, 3.753 for quartet states, 2.005 for triplet states, and 0.752 for doublet states. The bonding analysis was performed within the natural bond orbital (NBO) scheme with the purpose of gathering insights about the participation of the atomic metal orbitals in the chemical bonds of niobium complexes.31 The ultrafine grid was used in all DFT calculations for numerical integration of the exchange/correlation potential. All calculations were performed with the Gaussian 2009 program.32 The topological properties of electron density in the Nb−C and Nb−H chemical interactions were performed using the atoms in molecules (AIM) theory of Bader as implemented in the AIM2000 program.33 The molecular orbital (MO) figures of the frontier effective for reaction molecular orbital (FERMO) and singly occupied molecular orbital (SOMO) were prepared using the Gauss View 2.1 package 29 with a contour value of 0.020. All calculations were performed in the gas phase.

III. RESULTS AND DISCUSSION A. Initial Calculations. To assess the reliability of the present computational method, in Table 1, we collected the experimental and computed geometrical, vibrational, and energy parameters of the carbene products (NbCH2n+, n = 1, 990


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Table 1. Comparison of the Bond Lengths, Vibrational Frequencies, and Dissociation Energies of the Niobium Product Complexesa R(Nb−C) (Å)

R(H−Nb)b (Å) Nb

B3LYP MP2 CCSD(T) CCSD(T)//DFT CCSD(T)//MP2 exp.c

1.836 1.787 1.842

∠H−C−Nbb (deg)

ν(Nb−C) (cm−1)

D00 (kcal mol−1)

82.3 77.5 76.2

827.14 841.78 836.24

102.3 89.0 106.2 105.1 105.8 107 ± 10

85.3 82.0 79.2

827.94 836.24 849.20

131.3 106.8 115.9 116.2 116.7 >112

+

2.024 1.881 1.928

Nb2+ B3LYP MP2 CCSD(T) CCSD(T)//DFT CCSD(T)//MP2 exp.d

1.821 1.774 1.839

2.073 1.958 1.980

metal ionization potential IP(1) IP(2)

B3LYP

MP2

CCSD(T)

exptl

6.84 15.3

5.05 14.6

6.75 14.4

6.9e 14.3e

The first and second adiabatic ionization energies (IP(1) and IP(2), respectively) for the atomic niobium are presented in eV. bAgostic Nb−H bond lengths and H−C−Nb bond angles. cFrom ref 2. dFrom ref 16. eFrom ref 46.

a

2) of the dehydrogenation reactions of the Nb+ and Nb2+ ions with methane. The calculated data were done at the B3LYP, MP2, and CCSD(T) theory levels. No experimental data of the geometrical parameters of NbCH2n+ (n = 1, 2) can be found in the literature. However, due to the fact that, among the theoretical approaches, coupled-cluster methods such as CCSD(T) with a large atomic basis set have been considered to be the most reliable method to study the transition metal complexes, including dispersion binding,29 the CCSD(T) values are considered in the present work as the reference for the geometrical and vibrational parameters of the niobium complexes. As can be seen in Table 1, the Nb−C bond lengths calculated by using the B3LYP method are in very good agreement with CCSD(T) values, whereas MP2 underestimates the bond lengths (around 0.05 Å) independently if the Nb+ or Nb2+ complexes are considered. Another important result is that the B3LYP calculations overestimate the frequency values by 40−50 cm−1, while MP2 calculations underestimate the frequencies by 40−50 cm−1. It is worth noting that the agostic interactions are present in the metal carbene complex. As shown in Table 1, the MP2 calculations are able to accurately describe the results of the agostic Nb−H chemical bonds and H−C−Nb bond angles of niobium species, as compared to the CCSD(T) values, whereas B3LYP overestimates these geometric parameters. This feature may be an indication that agostic interactions could be related to dispersion effects in these organometallic complexes. In this case, the well-known inability of standard DFT functionals to describe the dispersion interaction could explain the better MP2 performance in predicting these geometric parameters. Regarding the bond dissociation energies of the Nb−C chemical bonds, as shown in Table 1, the calculated dissociation energy is quite sensitive to the methodology employed. Not surprisingly, the CCSD(T) results show the best agreement with experimental data. The MP2 calculations underestimate Nb−C bond strength of NbCH2+ and NbCH22+ complexes by about 15 kcal mol−1. While the B3LYP value of NbCH2+ is close to the CCSD(T) value, in the NbCH22+ complex, the

B3LYP computed bond length is very far from the experimental findings. A comparison of the CCSD(T)//DFT and CCSD(T)//B3LYP results shows rather small differences, thus indicating that B3LYP and MP2 calculations give a truly satisfactory description of the geometries of Nb+ and Nb2+ complexes. Overall, the CCSD(T)//MP2 and CCSD(T)// B3LYP energy differences can somewhat provide the energy contribution of the agostic and dispersion interactions to the niobium complexes. Finally, with respect to the atomic ionization energy results shown in Table 1, we can see that the B3LYP and CCSD(T) IP(1) results are in better agreement with the experimental value than those obtained with MP2 calculations. On the other hand, the CCSD(T) and MP2 calculations give rise to a better description of the experimental IP(2) related to the B3LYP methodology. These results confirm therefore that CCSD(T) calculations give a reliable description of the energy parameters of niobium and methane reactions in the gas phase. B. Reaction Calculations. For the sake of clarity, hereafter all numerical values in Figures 1 and 3 were obtained at the CCSD(T)//MP2 level, while CCSD(T)//B3LYP values are shown in parentheses. All geometric numerical parameters cited in the text and in Figures 2 and 4 were obtained at the MP2 level, while the B3LYP results are always given in parentheses. The relative energies in Figures 1 and 3 are given with respect to the reactant asymptote represented by the metal center ion in its ground-state electronic configuration and the free methane molecule. 1. Nb+ + CH4 Reaction. The potential energy profiles of the Nb+ + CH4 reaction are shown in Figure 1. The optimized molecular structures corresponding to the lowest energy spin states of this reaction are displayed in Figure 2. From Figure 1, we can see that the reaction of Nb+ with methane starts with the formation of an initial molecular precursor (MP) complex. The weakly bound η2-like Nb(CH4)+ complex has a 5A′ ground state, which is computed to be lower in energy than the Nb+ (5D) + CH4 reactants by 10.9 (11.4) kcal mol−1. The corresponding 3A Nb(CH4)+ complex lies 29.4 (29.8) kcal 991


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spin multiplicity of the reaction from the triplet to the singlet state. The H2NbCH2+ (1A′) complex is reached via 1TS3, which is computed to be 14.2 (14.6) kcal mol−1 higher relative to the ground-state reactant energy, giving rise to an activation barrier of 12.5 (13.2) kcal mol−1. The Nb−C distance in 1TS3 is 2.034 (2.027) Å, and the C−Nb−H bond angle is 67.3° (68.4°). This transition state has an imaginary frequency of 949i (843i) cm−1, corresponding largely to the motion of the transferring hydrogen. The dihydride intermediate H2NbCH2+ (1A′) lies 2.6 (2.9) kcal mol−1 above the reactants and has an Nb−C distance of 1.843 (1.848) Å, while the Nb−H bond length is 1.719 (1.741) Å. Continuing along the triplet surface, this intermediate complex can reductively eliminate the H 2 molecule, carrying the molecule across 1TS4, which lies 17.2 (15.9) kcal mol−1 above the ground-state reactant energy, with an activation barrier of 14.6 (13.0) kcal mol−1. The imaginary frequency of TS4 is 1591i (1091i) cm−1 and describes a motion in which the two hydrogen atoms come closer. Alternatively, the HNbCH3+ intermediate can proceed directly to the (H2)NbCH2+ 3A intermediate via a four-center transition state, 3TS2. This transition state lies 16.8 (15.9) kcal mol−1 above the reactants’ asymptote, with an activation barrier of around 15.1 (14.5) kcal mol−1. The 3TS2 structure has an Nb−C distance of 1.747 (1.780) Å and an imaginary frequency of 1262i (1172i) cm−1, which corresponds to the expected motion that brings the two hydrogen atoms together while making the NbCH2+ moiety more planar. The (H2)NbCH2+ (3A) intermediate readily dissociates to produce the dehydrogenation products: NbCH2+ (3A) and H2. The overall Nb (5D) + CH4 reaction is computed to be endothermic by 12.8 (13.1) kcal mol−1 at the CCSD(T)//MP2 and CCSD(T)//B3LYP levels, respectively. 2. Nb2+ + CH4 Reaction. The optimized profiles of the reaction of Nb2+ with methane are shown in Figure 3, while in Figure 4 we report the main geometrical parameters for all lowest spin state molecular species involved in this reaction. As shown in Figures 1 and 3, the calculations indicate important differences in the molecular structures and energetics of the Nb2+ + CH4 reaction in comparison to those found for the Nb+ + CH4 case. The Nb2+ (4D) reaction leads initially to the formation of a Nb(CH4)2+ (4A) adduct with an η3 precursor geometry, by an exothermic pathway. Distinct initial geometries were considered for the weakly bonded Nb(CH4)2+ complex, and the η3-like distorted structure with an 4A state is the lowestenergy optimized structure. The Nb2+−CH4 binding energy is 47.6 (46.6) kcal mol−1, significantly larger than that computed for the η2-like Nb+−CH4 (5A′) complex, 10.9 (11.4) kcal mol−1. Likewise, the Nb−C bond distance, 2.384 (2.372) Å, in the Nb2+−CH4 structure is shorter than that found in Nb+−CH4, 2.602 (2.623) Å. Not surprisingly, the extra charge on Nb2+ provides much tighter binding for the Nb2+−CH4 noncovalent complex. After intersystem crossing between the two lowest PESs, the Nb−C bond distance is reduced to 1.974(2.042) Å and the system passes through a transition state, 2TS1. The oxidative addition barrier is 34.3 (32.1) kcal mol−1, significantly lower than 3TS1 in the Nb+ + CH4 reaction. It is worth noting, however, that doubly charged 2TS1 lies 13.3 (14.5) kcal mol−1 below the ground-state reactant energies at both theory levels, whereas 3TS1 structures for Nb+ lie 19.2 (18.3) kcal mol−1 above the reactants’ asymptote. The 2TS1 transition state has C1 symmetry (4A) and a H−Nb−C bond angle of 48.0° (49.1°) (Figure 4). The formation of the first HNbCH32+ (2A′)

Figure 1. Potential energy profiles for the Nb+ + CH4 reaction at the CCSD(T)//MP2 and CCSD(T)//B3LYP (in parentheses) levels of theory, corresponding to the singlet, triplet, and quintet spin states of the niobium ion. Spin multiplicities are given in brackets.

mol−1 above. We have tried to optimize an η3 precursor for Nb(CH4)+, but this molecular species converges to the η2-like Nb(CH4)+ complex. This initial molecular precursor leads to the first transition state, 3TS1 (3A), with an activation barrier of 30.1 (29.7) kcal mol−1. It is important to mention that 3TS1 structures lie 19.2 (18.3) kcal mol−1 above the reactants’ asymptote. These results are of major importance, as all gasphase bimolecular reactions can only occur under thermal conditions if the entire lowest energy reaction pathway on the PESs is computed to be lower in energy than the reactant asymptote. Furthermore, it has long been known that the activation barrier involving the TS1 structure corresponds to the rate-limiting step of the methane dehydrogenation reaction by TM ions. Our results for the first step of Nb+ and CH4 are in agreement with the data reported by Blomberg et al.,10 where the computed value of 33.3 kcal mol−1 for the insertion barrier was obtained by means of the modified coupled pair functional method, with the 3TS1 structure lying 21.5 kcal mol−1 above the reactants’ asymptote. As shown in Figure 2, the Nb−C bond length of the 3TS1 structure is computed to be 1.971 (2.013) Å, while the H−Nb−C bond angle is 42.8° (42.5°). TS1 has an imaginary frequency of 1081i (987i) cm−1, which corresponds primarily to the 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 the Nb+ ion. It is worth noting that an intersystem crossing occurs between the two PESs in this region, promoting the first spin change in the reaction. After this crossing point, the quintet PES follows at higher energy with respect to the triplet PES. The formation of the hydridomethyl complex HNbCH3+ 3 ( A) occurs via an endothermic process of 1.7 (1.4) kcal mol−1 with regard to the reactants’ asymptote. HNbCH3+ has Cs symmetry (3A′) and has an H−Nb−C bond angle of 100.3° (103.3°). In the insertion intermediate, the dominating metal bonding state is the s1d3 state, which allows two covalent bonds to be formed between Nb+ and the methane hydrogen as well as methyl groups. The Nb−H bond distance is 1.702 (1.704) Å, while the Nb−C bond length is 1.981(2.063) Å. From the HNbCH3+ point, the system can follow two reaction pathways. In the first one, the HNbCH3+ intermediate can follow a stepwise pathway involving sequential H atom transfer to form a H2NbCH2+ (1A′) dihydride intermediate (Figure 2). In this pathway, another intersystem crossing occurs, changing the 992


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Figure 2. Optimized molecular structures of the lowest energy spin state Nb+/CH4 complexes at the MP2 and B3LYP (in parentheses) levels of theory. Bond lengths are given in angstroms and angles in degrees.

more energetically stable pathway, from the HNbCH32+ system to a (H2)NbCH22+ intermediate via a four-center transition state, 2TS2. This 2A transition state has C1 symmetry with an Nb−C bond distance of 1.872 (1.884) Å, indicating that the CH2 group is quite tightly bound. The Nb−C bond length is larger than that in the respective Nb+ transition state, 1.747 (1.780) Å. The activation barrier associated with the 2TS2 structure is 14.7(15.5) kcal mol−1. Alternatively, the HNbCH32+ intermediate follows a stepwise pathway involving sequential H atom transfer to form a H2NbCH22+ (2A′) dihydride intermediate. The dihydride intermediate, lying 11.2 (11.0) kcal mol−1 above the reactants, is reached via 2TS3, which lies 13.1 (13.5) kcal mol−1 above the reactants’ asymptote. The 2TS3 activation barrier is computed to be 36.1 (36.3) kcal mol−1. Continuing along the doublet

intermediate occurs by an exothermic route of 23.0 (22.8) kcal mol−1 as compared to that of HNbCH3+, which takes place by an endothermic route of only 1.7 (1.4) kcal mol−1. It is important to note that the TS1 and the first intermediate structures of the Nb2+ + CH4 reaction stabilize, however, in different molecular conformations relative to those optimized in the Nb+ + CH4 reaction. In other words, the singly and doubly charged MP, TS1, and HNbCH3 complexes assume two distinct conformations, depending whether the η3 or η2 frame is involved: trans and cis eclipsed conformers are thus stabilized with respect to the Nb−H and C−H bonds of Nb+ and Nb2+ complexes, respectively. The HNbCH32+ (2A′) intermediate has Cs symmetry (2A′) and an H−Nb−C bond angle of 109.2° (102.6°), while the Nb−C bond distance is 1.891 (1.932) Å. On the doublet surface, the system can proceed directly, by a 993


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surface, the dihydride intermediate can reductively eliminate the H2 molecule, carrying the molecule across 2TS4, which has the following activation barrier of 7.9 (8.4) kcal mol−1. 2TS4 leads to the (H2)NbCH22+ intermediate (2A), which has a geometry similar to that of NbCH22+ (2A′) with an Nb−C bond distance of 1.782 (1.824) Å, clearly indicating a double chemical bond. The Nb−H distances are 2.121 (2.143) Å in (H2)NbCCH22+, while the H−H bond distance is 0.794 (0.802) Å. This is somewhat longer than that calculated for free H2, 0.743 (0.752) Å. The NbCH22+ bond dissociation energy is 116.7 (116.2) kcal mol−1. This last pathway involving 2TS3 and 2 TS4 is significantly higher in energy than that involving the 2 TS2 structure. Overall, the formation of NbCH22+ (2A′) + H2 is exothermic by 10.9 (9.4) kcal mol−1, considering the groundstate Nb2+ (4D) + CH4 reactants. Nb2+ binds to the CH2 group to form a planar molecule with Cs symmetry and an Nb2+−H agostic distance of 1.954(2.073) Å (see Figure 4). To conclude this section, the CCSD(T) results indicate more favorable thermochemical conditions and labile kinetic pathways for the Nb2+ + CH4 reaction. These results reproduce

Figure 3. Potential energy profiles for the Nb2+ + CH4 reaction at the CCSD(T)//MP2 and CCSD(T)//B3LYP (in parentheses) levels of theory, corresponding to the doublet and quartet spin states of the niobium dication. Spin multiplicities are given in brackets.

Figure 4. Geometrical parameters of the lowest energy spin state Nb2+−CH4 complexes at the MP2 and B3LYP (in parentheses) levels. Bond lengths are given in angstroms and angles in degrees. 994


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Table 2. Natural Bond Orbital Analysis for the Lowest Spin State Niobium Complexes metal bond charactera

natural charge species

Nb

C

metal natural electron configuration

5s

5p

4d

+

Nb−CH4(5) TS1(3) HNbCH3(3) TS2(3) TS3(1) H2NbCH2(1) TS4(1) (H2)NbCH2(3) NbCH2(3)

0.936 0.972 1.460 1.167 1.276 1.520 1.268 1.552 1.510

−0.227 −0.211 −0.462 −0.263 −0.251 −0.278 −0.377 −0.273 −0.255

Nb−CH4(4) TS1(2) HNbCH3(2) TS2(2) TS3(2) H2NbCH2(2) TS4(2) (H2)NbCH2(2) NbCH2(2)

1.848 1.847 2.095 1.825 1.795 1.842 1.741 1.826 1.951

−0.340 −0.251 −0.556 −0.219 −0.173 −0.344 −0.133 −0.243 −0.225

Nb + CH4 Reaction 5s0.464d3.58 5s0.484d3.48 5s0.774d2.66 5s0.444d3.32 5s0.564d3.01 5s0.634d2.75 5s0.544d3.09 5s0.624d2.77 5s0.654d3.73 Nb2+ + CH4 Reaction 5s0.074d3.04 5s0.124d2.91 5s0.174d2.77 5s0.094d2.95 5s0.114d2.98 5s0.184d2.79 5s0.114d2.98 5s0.194d2.72 5s0.174d2.77

32.00 14.00 9.86 25.10 12.48 13.84 30.78

(0.10) (0.00) (0.07) (8.19)

3.44 4.37 6.71 3.86 2.93 2.73 3.09

4.56 11.56 9.47 0.00 (14.41) 15.95 (0.00) 24.13 (0.83) 10.42 (0.01) 8.19 (0.00)

3.96 1.61 2.99 3.15 5.38 9.78 6.25 3.09

(5.14) (6.01) (0.56) (3.51)

64.51 81.49 83.42 71.06 84.59 83.43 88.71

(94.76) (93.99) (99.37) (96.50)

(6.93) (4.58) (2.46) (5.63) (3.50)

95.52 76.83 87.54 96.84 68.67 66.09 83.33 88.71

(78.66) (95.42) (96.72) (94.36) (96.50)

a Analysis of percentage data for niobium. The results of the metal bond character in parentheses are the percentage data of the second Nb−C chemical bond.

closed-shell methane, in the beginning of the reaction channel. Therefore, if the s orbital is occupied, a repulsive interaction can arise, leading to an inefficient reaction by the introduction of an activation barrier. The computed Nb−C bond strength in the NbCH22+ final methylidene complex is computed to be 116.7 (116.2) kcal mol−1, whereas a value of 105.8 (105.1) kcal mol−1 was found for the NbCH2+ complex. It should be noted that the ionic contribution to the bonding plays a major role for the difference of the bond lengths as already demonstrated for metal−carbon bonds.36 Experimental observation of NbCH22+ from methane implies D00(Nb2+−CH2) > 112 ± 10 kcal mol−1,16 while a value of 107 ± 10 kcal mol−1 was reported for D00(Nb+−CH2).2 The thermodynamic differences between Nb+ and Nb2+ reactions with methane should therefore be a result of intrinsic bond strength differences. In order to more carefully evaluate the electronic effects responsible for the differences in the reactivity of the Nb+ and Nb2+ cations toward the methane activation process, we selected the first molecular precursor (MP) and transition state (TS1) complexes, which are involved in the ratedetermining step of the methane dehydrogenation. In particular, we are interested in the electronic, orbital, and bonding features which provide the chemical stabilities of the MP and TS structures. To investigate further in this respect, we used AIM and FERMO analyses. In the former, the widely employed theoretical strategy AIM was performed.33 This approach is mainly employed to carefully evaluate the bonding analysis of molecular species involved in the reaction under investigation. In our particular case, we performed these calculations in the rate-limiting step of the investigated reactions, which is the metal oxidative insertion into the methane C−H bond. In the latter procedure, we used the FERMO concept, for which chemical intuitions are used, together with criteria for the composition and location of the most reactive molecular orbitals (MOs). This approach aims to localize the molecular orbitals responsible for the thermody-

well the experimental data, showing that, under thermal conditions, dehydrogenation of methane is an efficient and exothermic process only for the Nb2+ ion. C. Bonding and Orbital Properties. 1. NBO Analyses. The natural Nb and C charges and the metal valence population and bond character of all lowest energy Nb+ and Nb2+ complexes are collected in Table 2. As one can see in this table, the natural charges on the niobium centers are higher in the stable intermediate and product complexes than those found in TS structures. As a consequence, carbon becomes more negative in the former case than in the latter, indicating that the ionic character of the Nb−C chemical bonds is higher in the stable molecular complexes than in the TS structures. Considering the natural electron configurations of the metal center in all investigated complexes, we can note a slight change in all structures along the Nb+ and Nb2+ reaction with methane, with a larger variation observed in the stable intermediate and product complexes. It is worth noting a particular feature observed in Table 2, in which the atomic percentage of the s and d atomic orbitals in chemical bonds of the Nb+ and Nb2+ structures is shown. These results indicate a mixed spd configuration for both niobium ions, with rather small participation of the p orbitals. On average, a s15%p4%d81% metal contribution is observed in the chemical bonds of the Nb+ complexes, whereas there is the s7%p5%d88% hybrid participation with a smaller participation of the s metal orbital observed in the chemical bonds of the Nb2+ complexes. This feature may be taken as an indication of the higher reactivity of the dication, as compared to Nb+, in the methane activation process, where gas-phase investigations involving the d-block TM elements17,34,35 have indicated that the presence of electrons in s orbitals gives rise to a higher electrostatic repulsion to the closed-shell system in comparison to that provided by electrons in d orbitals. One reason for this is, in the entrance channel of the reaction, the spherical symmetry of s orbitals provides a higher electrostatic repulsion to the apolar 995


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Table 3. AIM Parameters, Electron Density (ρ(r)), Laplacian ∇2ρ(r), Density of the the Total Energy of the Electron (H(r)), Kinetic Electron Energy Density (G(r)), and Potential Electron Energy Density (V(r)) for bcps of the Nb−C and Nb−H Chemical Bonds of the MP and TS1 Structuresa species

ρ(r) (au)

∇2ρ(r) (au)

G(r) (au)

V(r) (au)

H(r) (au)

0.03498 0.03498 0.10430

−0.036263 −0.036263 −0.172408

−0.00128 −0.00128 −0.06811

0.059457 0.101051 0.069062

−0.071524 −0.186754 −0.130103

−0.012067 −0.085703 −0.061042

+

Nb + CH4 Reaction

a

MP MP MP TS1

Nb−C Nb−H Nb−H′ Nb−C

0.034562 0.034562 0.134784

MP TS1 TS1

Nb−C Nb−C Nb−H

0.059579 0.149279 0.115070

0.134812 0.134812 0.144785 Nb2+ + CH4 Reaction 0.189563 0.061389 0.032105

Computed results were performed using the AIM program.33

namic stability as well as the kinetic lability of the MP and TS1 structures, respectively. This concept can be understood as a complement to the HOMO−LUMO argument. Furthermore, in these analyses, both HF and Kohn−Sham orbitals lead to the same conclusions about the chemical reactivity. A more detailed discussion of the FERMO concept can be found in a report by La Porta and co-workers.37 The computed results obtained by using these two approaches are discussed in detail in the next section. 2. AIM Analyses. From the AIM analysis, we have then located the bond critical points (bcps) in the Nb−C and Nb− H bonding interactions of MP and TS1: i.e., points where the charge density function (q(r)) is a minimum along the bond path and a maximum in the other two directions. The reason for this is, as has been shown in the literature, due to the fact that a fairly good linear correlation exists between the charge densities at bcps and the strengths of the linkages.38,39 The AIM parameters of the main computed bcps of the MP and TS1 structures are collected in Table 3. It is worth noting that these AIM parameters localized at bcps are powerful tools for the characterization of chemical bonds and are also used for the analysis of chemical problems involving bond-breaking and -forming reactions.33,40 In many applications, ρ(r) has been used as a measure of the strength of the bonding interaction, particularly the σ interaction; ∇2ρ(r) indicates the regions where ρ(r) is depleted or concentrated. For shared bonds, ∇2ρ(r) is negative, while positive values are observed for interactions showing closed-shell character.33 Apart from this, valuable information about chemical bonds are obtained from H(r) and its two components G(r) and V(r), and the following equation shows the relation between these parameters:

H(r) = G(r) + V (r)

⎛ ℏ2 ⎞ 2 ⎜ ⎟∇ ρ(r) = H(r) − 1/2V (r) ⎝ 8m ⎠

(2)

definition, V(r) is negative at the bcp. Consequently, from eq 2, H(r) will be negative. For closed-shell interactions, H(r) would be positive, and this occurs as ((ℏ2/8m)∇2ρ(r) > |(1/2)V(r)|. There is another possibility that ∇2ρ(r) > 0 and H(r) < 0 indicate partially ionic and partially covalent bonds. Thus, pure closed-shell interactions without covalency are characterized by H(r) > 0, whereas H(r) < 0 include two types of interactions: a closed-shell interaction with covalent character where ∇2ρ(r) > 0 and a shared-shell interaction where ∇2ρ(r) < 0. As shown in Table 3, the ρ(r) values of the Nb−C bonds in the TS1 structures vary from 0.134784 au in the Nb+ system to 0.149279 au in the Nb2+ system. A slightly lower value (0.115070 au) is found for the Nb−H bond of the Nb2+ TS1 structure. In these systems, while H(r) values in the Nb−C bonds are −0.06811 au for Nb+ and −0.085703 au for Nb2+, in the Nb−H bond of TS1 (Nb2+) the value is −0.06142 au for TS1 (Nb2+): i.e., they are all negative. In contrast, the ∇2ρ(r) values are all positive, but a higher value (0.144785 au) is observed in the Nb+ TS1, as compared to those in the Nb−C (0.061389 au) and Nb−H (0.032105 au) bonds of the Nb2+ dication. These features follow the same behavior in the Nb−H and Nb−C interactions of the MP structures independently, whether the Nb+ or Nb2+ cation is considered. As previously mentioned, the positive ∇2ρ(r) values indicate an ionic nature of the chemical bonds, whereas a negative H(r) value points out a covalent nature.42 The higher positive values of ∇2ρ(rc) and the concomitant lower ρ(r) values in the MP structures suggest, therefore, that the Nb−H interactions in the MP Nb+ structure and the Nb−C interactions in the MP Nb2+ complex exhibit a more pronounced ionic than covalent character of these chemical bonds. Surprisingly, the same behavior can be visualized in the Nb−C bond of the Nb+ TS1 structure. On the other hand, the lowest values of ∇2ρ(rc) and highest values of | H(r)| in the Nb−C and Nb−H bonds of the TS1 Nb2+ structure clearly indicate a more covalent than ionic nature of these chemical bonds. It is interesting to note that ∇2ρ(rc) > 0 values are dominated by the kinetic energy in the region of interaction between nuclei involved in the given bond. On the basis of the above discussion, the results included in Table 3 suggest that the methane C−H bond activation energy (Eact) for the TS1 structure (Figure 4) should indeed be lower for the Nb2+ dication than for the Nb+ ion. This arises mainly from the fact that Eact shows a strong dependence on ρ(r). This

(1)

H(r), G(r), V(r), ρ(r), and ∇2ρ(r) are respectively the total electron energy density, the kinetic electron energy density, the potential electron energy density, the electron density, and the Laplacian of ρ(r). Regions where the electrons are more localized are characterized by relatively higher V(r) values, whereas large G(r) values correspond to regions where the electrons move faster.38 In general, for covalent interactions, | V(r)| > G(r), and consequently, the value of H(r) is negative. For closed-shell interactions, |V(r)| < G(r), and thus H(r) is positive.38 Equation 2 shows the relation between H(r) and ∇2ρ(r), where m is the reduced mass of the system. The combined use of both H(r) and ∇2ρ(r) has been carried out as an excellent descriptor for defining the nature of chemical bonds.41 For shared-shell interactions, ∇2ρ(r) < 0, and also by 996


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chemical species with several multiplicities, the FERMO concept became an interesting choice to approach this problem, because it unifies the acid−base behavior of molecules.37 This means that, for the same chemical reaction, we can define just one FERMO. Independent of calculation methodologies (HF or DFT techniques) and molecules involved in the chemical transformation, the FERMO is the same. Thus, we can note that the idea behind the FERMO concept is to use the MO calculations with a valence bond (VB). In MO theory, the electrons in a molecule occupy delocalized molecular orbitals made up of a linear combination of atomic orbitals. However, it should be kept in mind that the VB approaches are quite useful in situations where the localized MO representation seems indispensable. In fact, it is well known that the VB methods allow the generation of new ideas on chemical bonding.43,44 Due to the charge transfer phenomenon, the electron density in molecules must be an important factor that justifies the changes observed during the whole reaction. In this line, it is quite important to investigate the charge transfer process from an orbital point of view. In this respect, new reactivity indexes, such as ΔEFERMO, can be derived, based on the charge transfer in the system, as described in eq 3.

argument has been previously indicated by Suresh and coworkers.40 In other words, a general trend is that when ρ(r) decreases, Eact decreases, since a higher value of ρ(r) indicates greater strength. This observation is counterintuitive, as a lower ρ(r) value can be associated with a weaker bond to be formed, indicating an increase in the activation barrier. Therefore, we can conclude that the highest ρ(r) (0.149279 au) value of the TS1 Nb2+ structure is associated with a more favored kinetic lability of this ion, relative to that for Nb+, toward methane activation. Another important feature is that Eact decreases with an increase in the negative character (covalent nature) of H(r). Thus, obviously there is a fundamental difference in the interpretations above. It is not the bond strength that matters but the nature of the formed bonds; the more covalent they are, the easier the methane C−H bond activation. The dependence of ∇2ρ(r) and Eact, as explained above, nicely complements the conclusion drawn from H(r) and Eact: the more ionic the nature of the Nb−C bond to be formed, the higher the activation barrier of the methane C−H bond activation by the TM ion. Thus, the formation of the HNbCH32+ intermediate is more energetically favored in comparison to the formation of HNbCH3+ due to the stronger ionic nature of the Nb+−C bond and the more covalent character of the Nb2+−C chemical bond. 3. Orbital Analyses. On the basis of the FERMO idea, we expanded the correlations to other frontier orbitals, namely HOMO-1, HOMO-2, and HOMO-3. In addition, the MO composition and shape are taken into account to identify the MOs which will actually be involved in the key point of the reaction under investigation. On the basis of the molecular orbital composition and localization, it is possible to get a deeper insight into the MOs that govern the given chemical reaction: i.e., the FERMO orbital of the reaction under investigation. In fact, the MO shape and its atomic composition are very important parameters for analyzing FERMO. The localized FERMO for the TS1 of Nb+ and Nb2+ ions can be visualized in Figure 5. In the current case, due to the number of

ΔE FERMO = |E FERMO(MP) − E FERMO(TS1)|

(3)

The reactivity index (ΔEFERMO) shows a good correlation with the Gibbs free energy values (ΔG) and can provide some insights into the reaction. ΔG values are associated with low ΔEFERMO results; i.e., there is a more effective charge transfer taking place in the investigated process. The computed ΔEFERMO values are 0.03427 au in the Nb+ case and 0.00424 au in the Nb2+ reaction. It is reasonable that FERMO, in the Nb2+ case, is more stable and quite close in energy relative to the HOMO orbital, and it shows a larger contribution of the Nb and C atoms in comparison to the case of Nb+. Our theoretical orbital results indicate that a strengthening of the Nb−C and Nb−H chemical bonds in the HNbCH32+ (2TS1) structure is due to an empty acceptor orbital LUMO on the metal ion. Our bonding and orbital findings reveal interactions between methane and Nb2+ more efficient than those concerning the Nb+ ion, thus favoring the kinetic and thermochemical conditions for the Nb2+ ion. It can be concluded that our theoretical bonding results and also those obtained by using the FERMO idea corroborate with our results of energetics, structures, and mechanisms. D. Comparison to Previous Results. Previous studies of the gas-phase ions with methane have indicated that the trends in the reactivity of the singly charged d-block TM ions toward methane are associated with the bond strength of MCH2+. 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 110 kcal mol−1 (C−H bond energy of methane). Park et al. have reported that D00(Ta+−CH2) is equal to 110.9 kcal mol−1, and the dehydrogenation of methane by Ta2+ is exothermic and gives a lower limit for the bond dissociation energy of TaCH22+ of D00(CH2−H2) = 109 kcal mol−1.17,35 Ranasinghe et al. reported a higher value of 111 kcal mol−1 from the same observation for Ta2+, using 298 K thermodynamic values.45 It is important to compare the Ta results with those of its second-row congener, Nb. The bond energy of the doubly charged ions is D00(Nb2+−CH2) > 112 kcal/mol−1,16 while a

Figure 5. MP2 FERMO of SOMO orbitals of (left) Nb+ and (right) Nb2+. Orbital energies are in atomic units. 997


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value of 107 ± 10 kcal mol−1 was reported for D00(Nb+− CH2).2 The results indicate that the bond strength of the Ta+ chemical bonds is on average only 5% greater than those of the Nb+, whereas the Nb−C bond strength of the Nb2+ system is pronouncedly higher than that in the Ta2+ dication. The ground state of Ta+ is 5F (6s15d4) and corresponds to a suitable electron configuration for forming two covalent bonds. To reach a similar electronic state, however, Nb+ must ensure a promotion energy from its 5D(d4) ground state to the 6F (s1d3) excited state of 7.6 kcal mol−1. This feature can likely explain the lower reactivity of Nb+, as compared to Ta+, with methane. Another important fact is that on the PES for interaction of Ta+ and Ta2+ with methane, a η3-like Ta(CH4) structure with C3ν symmetry is found, independent of whether Ta+ or Ta2+ is taken into account. In this structure, the methane molecule remains intact and largely unperturbed, while a weakly electrostatic interaction occurs between these ions and methane. With regard to the Nb case, only for Nb2+ cation, a η3-like Nb(CH4) adduct is optimized, whereas a distorted η2 structure is initially formed between Nb+ and methane. This feature may be taken as an indicator of a catalytic reaction for the Ta+, Ta2+, and Nb2+ ions toward the methane dehydrogenation process more favored than that for the singly charged niobium ion. These results have already been observed in our previous investigation of the Th, Th+, and Th2+ ion actinides toward methane activation.20 Finally, in previous studies, the activation of methane by the atomic metal ions has been explained using the arguments of a simple donor−acceptor model, leading to an oxidative addition mechanism.17,35 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 tandem, metal electrons in orbitals having s-like symmetry back-donate into the antibonding orbital of the chemical bond to be broken. If the acceptor orbital is occupied, a repulsive interaction can result, leading to an inefficient reaction either by introduction of a high activation barrier to the reaction or by more direct abstraction pathways. For Ta2+, both the 4F and the 2P states have an unoccupied 6s acceptor orbital. The same feature is observed for the ground electronic and low-lying states of Nb2+, thus indicating similar catalytic facilities for both Ta2+ and Nb2+ dications.

Specifically, the minimum energy pathway for Nb+ can be described as 5Nb+ +CH4 → 5NbCH4+ → 3HNbCH3+ → 1 H2NbCH2+ → 3(H2)NbCH2+ → 3NbCH2+ + H2. The calculations indicate an endothermic dehydrogenation process for Nb+ with activation barriers localized below the reactants’ asymptote. (ii) For the Nb2+ + CH4 reaction, the minimum energy pathway was computed as follows: 4Nb2+ +CH4 → 4NbCH42+ → 2HNbCH32+ → 2(H2)NbCH22+ → 2NbCH22+ + H2. The methodology employed in this work reproduces the experimental data well, thus showing that the dehydrogenation of methane is an efficient, exothermic pathway only for the Nb2+ dication. (iii) Some factors based on the geometrical structures as well as the NBO, AIM, and orbital analyses can be pointed out to determine the differences in the catalytic efficiency of the niobium species. First, the optimized structures of the MP and TS1 complexes involving the Nb2+ ion are computed to be η3like conformations, whereas slightly distorted η2 structures are between Nb+ and methane. These features agree with previous theoretical results of the Ta and Th ions,17,20,35 which show a η3-like conformation for the most efficient initial and intermediate complexes. Second, the NBO results indicate a mixed spd configuration for both niobium ions, with a rather small participation of the p orbitals. On average, a s15%p4%d81% metal contribution is observed in the chemical bonds of the Nb+ complexes, whereas higher d participation and rather smaller s contributions are found in the chemical bonds of the Nb2+ complexes (s7%p5%d88%). With regard to the FERMO approach, we can conclude that there is a more stable FERMO in the case of Nb2+ than in the case of Nb+. Furthermore, the FERMO of the Nb2+ TS1 conformation is quite close in energy relative to the SOMO orbital, and it shows a greater contribution of the Nb and C atoms as compared to that in the Nb+ TS1 structure. Finally, the AIM results give important insights into the chemical bonds of the niobium complexes involved in the oxidative insertion step, providing some relationships between AIM parameters and TS1 barriers of the reactions under investigation.

IV. CONCLUSIONS Extensive CCSD(T)//MP2 and CCSD(T)//B3LYP calculations were performed to investigate the energetics and mechanism of the methane dehydrogenation process by specific Nb+ and Nb2+ cations. The obtained results contribute to a better understanding of the different elementary steps involved in the reactions under investigation. The effects of the metal spin states and the use of different theoretical approaches were analyzed. Two mechanisms were investigated for all niobium ions in the methane dehydrogenation process. The bonding and orbital analyses were done on the basis of NBO, AIM, and FERMO calculations. The following conclusions can be drawn from the present results. (i) For the Nb+ + CH4 reaction, the minimum energy reaction path is found not to be one of three PESs of a certain spin state. Instead, the minimum energy reaction pathway requires three crossings of the adiabatic surfaces with, consequently, different spin electron states in each reaction step. This result is different from that of the Nb2+ + CH4 reaction, in which just one spin state change is observed.

The authors declare no competing financial interest.

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AUTHOR INFORMATION

Notes

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ACKNOWLEDGMENTS The financial support of the Brazilian agency Coordenaçaõ de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES) is gratefully acknowledged. This work has also been funded by the National Institute of Science and Technology for Mineral Resources, Water and Biodiversity-ACQUA-INCT (http:// www.acqua-inct.org), and it is a collaboration research project of members of Rede Mineira de Quı ́mica (RQ-MG) supported by the FAPEMIG.

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