Reaction of Ta3 - Clusters with Molecular Nitrogen: A Mechanism Investigation.

Because of the inertness of molecular nitrogen, its practicable activation under mild conditions is a fundamental challenge. Ta3 - is an exceptionally small cluster that reacts with N2 at room temperature, leading finally to Ta3N2 -; Ta3N2 - also could react with N2 at room temperature, leading finally to Ta3N4 -, a product of interest in its own right because of its potential as a nitrogen fixation medium. The mechanisms of the Ta3 -- and Ta3N2 --mediated activation of the N≡N triple bond have been investigated. Our extensive computations elucidate mechanisms for the ready reactions, leading to stepwise cleavage of the N≡N bond. Initial isomeric N2/Ta3 - complexes, N≡N elongation, undergo a N≡N split over generally low barriers in a highly exothermic process. The nitrogen-atom or molecular exchange reactions found in the Ta3N2 -/N2 system may be of paramount importance in both applied and fundamental studies.

Introduction

The atmospheric abundance, accessibility, and nontoxicity of N2 make it particularly desirable for us to construct N-containing compounds,[1−4] such as typical synthetic ammonia reaction.[5−9] However, the functionalization of N2 represents a major challenge for modern chemistry due to its stability. The stability could be accounted for the lack of the dipole moment, the high bond dissociation energy (941 kJ mol–1), high ionization energy (15.58 eV), the low proton and electron affinities (5.1 and −1.9 eV respectively),[6,10−12] as well as the very low lying, completely filled σ- and π-molecular orbitals and substantial energy gap between the highest occupied molecular orbital (−15.6 eV) and the lowest unoccupied molecular orbital (7.3 eV).

Vol’Pin and Shur were the first to study nitrogen fixation with transition-metal complexes.[13] Transition metals (M) could weaken or break the strong triple bond (N≡N) by donating electrons from d orbitals to empty antibonding π and σ orbitals of N2 (Scheme a). In return, electron donation from fully filled π- and σ-orbitals of N2 to vacant M orbitals could be found as well (Scheme b).[14−16] The former donation is vital in enabling N2 binding and reduction, following which metal–nitrogen formed and strengthened. However, the latter donation is relatively small. By extension, the complete splitting of the N≡N by metal clusters is essentially governed by combining the two donations.[16,17]

Scheme 1

Orbital Interactions between N2 and Transition Metal (M)

Moreover, the M–N2 binding mode strongly depends on the nature of the metal center. The different coordination modes generally show different orbital interaction modes and charge transfer and also different kinds of activation of the N≡N bond.[18,19] There are four possible coordination modes (Scheme ): (1) end-on (η1-N2, M–M–N≡N, Scheme a), N2 gets activated upon η1-coordination to the first metal center, so the electron density in the antibonding orbitals in N2 increases, rendering the coordinated molecule a better base for another metal center, (2) end-on bridging (Scheme b), μ-η1-η1-N2, generally, M–M–N≡N and M–N≡N–M are more or less linear to allow for efficient orbital overlap. (3) Side-on mode (η2-N2, Scheme c) and μ-η2-η2-N2 bridging coordination mode (Scheme d) is not as usual as the end-on one. Compared to end-on mode involving two M–N π-bonds, there is only one π-bond, while σ donation and backdonation (Scheme a,b) probably were not involved. Therefore, the end-on mode usually is energetically preferred than the side-on mode.[20] (4) Side-on-end-on (μ-η1:η2-N2) (Scheme e), exhibiting a side-on coordination of N2 to one metal center and an end-on coordination to the other.

Scheme 2

Possible Modes of N2 Coordination to Transition Metal

Metal clusters have been found to be able to react with N2.[21−30] However, most of the studied clusters can only adsorb N2, and a few of them can split the N≡N under moderate conditions such as Sc, Ti, Gd, Co, Fe, and Ta clusters.[17,31−41] Among them, it was recognized that Ta clusters give outstanding performances to split the N≡N completely since the Ta–Ta center has enough reductivity to store electrons of N2.[42,43]

As shown by the recent investigations, the extent of N≡N elongation varies with the model cluster size.[44] Larger clusters are favorable for N2 adsorption. However, it does not necessarily have higher activity towards N2 activation. Studies predicted that N2 molecule activation is accessible at ambient temperature by small Ta+ clusters (n = 2, 3, 4). The rate-limiting transition states is located at −55, −44, and −59 kJ mol–1 for Ta2+,[16] Ta3+, and Ta4+,[45] respectively, however it is located above the entrance asymptote for Ta6+.[34] Significantly, during N2 activation by Ta4+ and Ta6+, the surface Ta–Ta–Ta acted as a protagonist, and the other Ta atoms were not directly involved or played only a minor role in N2 cleavage. The Ta3 moiety is the key structural unit of Ta series clusters and surfaces in N2 cleavage. It is particularly important to study N2 activation by Ta ternary clusters. Moreover, our studies indicated that an anionic system can give better kinetic activity and thermodynamic stability of the product than cationic and neutral ones.[46,47] V and Ta-nitride,[36,48] V and Ta-carbide,[35,49−51] and Co hydride[52] anion clusters are identified to be highly reactive toward N≡N bond cleavage by combining quantum chemistry calculations and experimental studies. Motivated by the vivid and splendid studies, we present detailed mechanisms of the first and second N2 activation by anion cluster Ta3– at a molecular level, which probably would be taken as a model in the cluster and surface reactions.

Computational Details

All calculations were carried out by using the Gaussian 09 package.[53] The high quality of the triple-ζ def2-TZVP basis set was confirmed in previous, rather extensive studies.[54−56] For the Ta metal atoms, an effective core potential (ECP) is used for an approximate treatment of relativistic effects. We used the Becke-3-Lee–Yang–Parr (B3LYP) functional, which has already been successfully applied in the Ta2+/N2 and Ta2N+/N2 systems.[16,17] Furthermore, Armentrout and co-workers reported that B3LYP provides bond energies for MO+ and MO2+ (M = Ta, W), which correspond very well to experimental data.[200]

Harmonic vibrational frequencies were computed to verify the nature of the stationary points. To corroborate the correct link between the minima and the transition states (TSs), intrinsic reaction coordinate[57−60] calculations were performed. Unscaled vibrational frequencies were used to calculate the zero-point energy contributions; thermal corrections to the enthalpy (ΔH) within the ideal-gas, rigid-rotor, harmonic-oscillator approximation at a temperature of 298 K and a pressure of 1 atm have been applied.

To obtain possible low-energy structures on the landscapes of the Ta/N and TaN/N couples, the ABCluster[61] has been used to generate guess structures of TaN and TaN clusters. The def2-SVP basis set was adopted in the initial calculations, which produced more than 200 optimized structures. Subsequently, the lowest-lying isomers were re-optimized at the B3LYP/def2-TZVP level to obtain the global minimum structures of TaN and TaN.

Results and Discussion

Ta3– Mediates the N≡N Bond to Form Ta3N2–

The optimal potential energy surface (PES) and structural parameters of key species for Ta3– mediates N≡N activation at B3LYP/def2-TZVP are shown in Figure . Three possible spin states, singlet, triplet, and quintet, are invested (Figure S1). The left superscript 1/3/5 is used to represent the singlet/triplet/quintet state (e.g., 1/3/51). The ground state of Ta3– is a quintet, which is 20 and 29 kJ mol–1 lower than the triplet and singlet, respectively.

Figure 1

Simplified PES (ΔH298K in kJ mol–1) for Ta3–/N2 coupling at the B3LYP/def2-TZVP + ECP level of theory. Key structures including selected geometric parameters are also provided. Bond lengths are given in angstrom and relative energies are given with respect to the entrance asymptote. ΔG (kJ mol–1) is behind the vertical line.

The Ta3–/N2 coupling starts from either the quintet or triplet separated reactants, and it is subject to a two-state reactivity mechanistic scenario. The triplet/quintet PES crosses at the minimum energy crossing point (MECP,–60 kJ mol–1), which could turn a spin flip from the quintet to the triplet surface and lead to obtaining the intermediate 31, releasing −67 kJ mol–1 of heat. The optimized structure indicates an end-on η1-N2 coordination mode with the distances of Taa–Na = 2.05 Å and Na–Nb = 1.15 Å. Subsequently, the triplet dominates the PES, so the triplet mechanism is mainly discussed below. Tab attacks N≡N further in a side-on manner to obtain a well-known combining end-on/side-on mode 32 (μ-η1:η2-N2) releasing −118 kJ mol–1 energy. In 32, the end-on bond length between the terminal nitrogen atom (Na) and Taa is 1.96 Å, and the side interaction between Tab and Na–Nb forms Tab–Na (2.12 Å) and Tab–Nb (2.00 Å) bonds. Compared with the separation reactant, the N≡N bond is weakened, and the bond length of the N≡N bond is elongated by 0.20 Å. Meanwhile, the Taa–Tab bond is elongated from 2.47 to 2.58 Å. Note that from 31 to 32, no barrier is encountered. However, in the Ta4+/N2 system studied by Fries et al., this step requires merely an activation of 5 kJ mol–1.[45]

The N≡N bond is elongated to 1.41 Å by the interaction of Nb with the third Ta atom (Tac) through the transition state 3TS1 with an energy below the entrance asymptote of −92 kJ mol–1 generating 33 (−160 kJ mol–1; C symmetry). Nb is changed from being interacted only with Tab in 32 to being interacted with the three Ta atoms. That is, the geometric structure is transferred from a η2 to η3 coordination, and this transformation is the rate-limiting step which is called the across edge-above surface (AEAS) mechanism by Fries et al. The prediction that AEAS operates significantly more likely on small clusters is confirmed.[45] Note that the rate-limiting transition state 3TS1 in Ta3–/N2 coupling has the lowest energy among those in Ta2+, Ta4+, and Ta6+/N2 couplings.[16,34,45] Finally, N≡N is completely broken through the transition state 3TS2 with a low energy barrier of 10 kJ mol–1, generating the lowest energy intermediate 34 (−469 kJ mol–1; C symmetry). In addition, there are other reaction paths for Ta3–/N2 coupling (Figure S2), but they are disadvantageous on PES.

Ta3N2–/N2 Coupling

Ta3N2– (4 in Figure )/N2 coupling is quite complicated (Figure S3). Only the optimal PES and structural parameters of key species are shown in Figure . The ground state of Ta3N2– is triplet, which is 32 and 67 kJ mol–1 lower than singlet and quintet, respectively (Figure S1). Moreover, the triplet species along the PES have more thermodynamic stability than the other two states, and there is no crossing point on the PES. Therefore, only the triplet state is studied.

Figure 2

Simplified PES (ΔH298K in kJ mol–1) of Ta3N2–/N2 coupling at the B3LYP/def2-TZVP + ECP level of theory. Key structures including selected geometric parameters are also provided. Bond lengths are given in angstrom and relative energies are given with respect to the entrance asymptote. ΔG (kJ mol–1) is behind the vertical line.

First, N2 approaches the Ta3N2– through the end-on mode (μ-η1) to form 35 (−57 kJ mol–1). Inspecting the geometric features of 35, the Nc–Tab bond length is 2.07 Å. Compared with the separated reactant, the N≡N bond is slightly weakened and the length is elongated by 0.05 Å. Then, Nc and Nd interact further with Tac in a side-on manner to obtain end-on/side-on mode 36 (μ-η1:η2-N2), releasing −144 kJ mol–1 energy. The length of the N≡N bond in 36 is elongated by 0.16 Å than that of 35. The extension of the N≡N bond is similar to that in the Ta3–/N2 coupling. At the same time, the three Ta atoms become detached and Ta and N become intimate in 36, for instance, the Tab–Tac bond is elongated to 2.64 Å, the end-bonded Tab–Nc bond length is 1.96 Å, and the side-bonded Tab–Nc and Tab–Nd bond lengths are 2.07 and 2.00 Å, respectively. The transition state 3TS3 is located 10 kJ mol–1 above that of 35. However, in Ta3–/N2, this step is no barrier.

The N≡N bond is elongated for a third time similar to AEAS. Nd interacts with the third Ta atom (Taa) through 3TS4, which is located −88 kJ mol–1 below the entrance asymptote to generate 37 (−132 kJ mol–1; C symmetry). In 37, the N≡N bond is elongated to 1.40 Å, which is 0.10 Å longer than that of 36. Subsequently, from 37, the N≡N bond could also be a cleavage finally through one transition state (3TS17), generating 318. However, the energy barrier (−6 kJ mol–1 below the entrance) is much higher and 318 is not the lowest energy structure on the landscapes. Surprisingly, a lower energy channel was detected, and it can lead to the lowest energy structure (39, −418 kJ mol–1) on the landscapes, which is one step more than Ta3–/N2 coupling. This path can be described in detail as follows. From 37 to 38, Ta and N become more intimate; for instance, the Tab–Nc bond is shortened from 2.09 to 1.93 Å, and Tac–Nd is shortened from 2.18 to 2.07 Å. Meanwhile, the Tab–Tac bond is elongated to 2.70 Å. In this process, the N≡N bond is only slightly elongated, from 1.40 to 1.41 Å, and only needs to pass through the transition state 3TS5 with an energy of −117 kJ mol–1. However, the energy of the transition state 3TS6 (−54 kJ mol–1) through which the Nc–Nd bond is completely destroyed is much higher than that of 3TS2 (−150 kJ mol–1) in the Ta3–/N2 coupling. From the perspective of the activation energy barrier, the rate-determining transition state is 3TS6.

Incidentally, if the remaining intermediate 39 is taken as the start of the PES, Ta314N15N– + 14N15N or Ta315N2– + 14N2 would be the product. This scenario only could be presented when N is labeled; otherwise, N2 activation may be hidden without being discovered. The scenarios that N atoms or N2–ligand exchange reactions between 15N2 and Ta314N2 revealed follow the Mars–van Krevelen (MVK) mechanism.[17] The highly symmetrical structure of 39 is the key to N exchange.

Crucial Properties

Density functional theory (DFT) calculations are further employed to probe the crucial properties including the electronic structures of the key complexes in Ta3–/N2 and Ta3N2–/N2 couplings.

In Table , we present the natural bond orbital (NBO) charge and the energy of the d donating orbital of the Ta3– and Ta3N2– clusters. The detailed evolution of the electronic structure along the reaction coordinate is shown in Figure S4. The activation of N2 by a metal cluster is the reduction of N20 into 2N3–; therefore, the stronger the electron supply ability and oxidation of metal, the stronger its ability to activate N2. Compared with Ta3–, the metal oxidation state of Ta3N2– is increased, and its ability to donate electrons becomes weaker. Correspondingly, the activity of Ta3N2– is weaker than that of Ta3–. In addition, the orbital energy of πb in Ta3N2– is also reduced, which makes it more difficult for the transfer of d electrons to the π*(N–N) or σ*(N–N) orbital.

Table 1

NBO Charges and Orbital Energies (Unit: eV) of the Major π Backdonation Donor Orbital (πb) of Ta3– and Ta3N2– Clusters at the B3LYP/def2-TZVP + ECP Level

	nature charge
clusters	Ta	Ta	πb
Ta3–	–0.29	–0.42	1.25
Ta3N2–	0.06	0.22	0.90

The binding of N2 to the Ta3– or Ta3N2– cluster can occur in either the side-on (10 and 15) or end-on (5 and 10) configurations. IR spectra as a function of wavelength were calculated at the B3LYP/def2-TZVP + ECP level (Figure S5). This behavior is similar to that shown in M+–(N2) systems.[21,22] End-on binding reproduced its favorite. The end-on binding is more strongly bound by 29 and 26 kJ mol–1 than the side-on binding for the triplet state for Ta3–/N2 and Ta3N2–/N2, respectively.

In order to explore the effects of temperature and pressure on the reaction, the transition state 3TS1 of the rate-determining step in the Ta3–/N2 reaction was selected. Figure shows the change of relative Gibbs free energy (ΔG, kJ mol–1) along with temperature (K) at a pressure of 1 atm. One can see that ΔG increases linearly with the increase of temperature. However, ΔG decreases with increasing pressure at the temperature of 298 K although the change is small (Figure S6).

Figure 3

Change of relative Gibbs free energy (ΔG, kJ mol–1) for 3TS1 with temperature (K) at a pressure of 1 atm using B3LYP/def2-TZVP + ECP.

DFT Gauging

In previous studies, it was found that the structural factor plays a minor role in the single point energy (SPE) calculations, and reaction energy prediction is quite challenging for DFT methods. SPE calculations on the structures obtained at B3LYP/def2-TZVP + ECP were performed by using 13 density functionals (Table ),[62−76] and the def2-QZVPP + ECP basis set was used. Table displays the energy differences of the two spin states and the apparent barriers as computed by the 13 methods listed in Table . One can see that all these methods predict that the quintet state is the ground state of Ta3– except for M11 and most of the 13 methods could yield similar energy differences between the singlet or triplet and quintet states. Most hybrid functionals give higher results, while pure functionals give lower ones. In general, the apparent barriers increase with the increasing amount of Hartree–Fock (HF)-exchange. The highest value is twice as high as the lowest value, and some are even nearly 5 times higher. The functional with an HF-exchange percentage of about 20% such as B3LYP gives more moderate results.

Table 2

List of Density Functionals Useda

The color codes are as follows: (a) pure functionals (gray) and (b) hybrid functionals (yellow).

Table 3

Apparent Barrier ΔE (kJ mol–1) for the Transition States Obtained by Various Methods at the def2-QZVPP + ECP Level

Conclusions

Detailed mechanisms of Ta3– and Ta3N2– clusters to activate N2 have been explored with DFT. Thermodynamic analysis shows that Ta3– and Ta3N2– can adsorb N2 at room temperature and cleave N≡N, and Ta3– has higher activity than Ta2+, Ta4+, and Ta6+/N2 couplings to cleave N≡N.[16,34,45] AEAS is operated significantly on this small cluster Ta3–. From the functionals selected in this paper, for the time being, the density functional with an HF percentage of 20% might be used as a suitable choice for the study of such anion transition-metal systems. In addition, in the rational design of the catalyst, increasing the energy of the π-donor orbital may be a constructive strategy to reduce the effective cracking of N≡N.

Nitrogen atoms or N2 molecules’ exchange in the Ta3N2–/N2 scenarios are revealed following the MVK mechanism. This constitutes a rare example of complete nitrogen balance during cluster-mediated gas phase activation and is of great significance in the development of N2 fixation as well as activation catalysts.