Cooperativity Between Low-Valent Iron and Potassium Promoters in Dinitrogen Fixation
A DFT study was performed to understand the role of cooperativity between iron-\xce\xb2-diketiminate fragments and potassium promoters in N2 activation. Sequential addition of iron fragments to N2 reveals that a minimum of three iron centers interact with N2 in order to break the triple bond. The potassium promoter stabilizes the N3\xe2\x88\x92 ligand formed upon N2 scission, thus making the activated iron-nitride complex more energetically accessible. Reduction of the complex and stabilization of N3\xe2\x88\x92 by K+ have similar impact on the energetics in the gas phase. However, upon inclusion of continuum THF solvent effects, coordination of K+ has a reduced influence upon the overall energetics of dinitrogen fixation; thus, reduction of the trimetallic Fe complex becomes more impactful than coordination of K+ vis-\xc3\xa0-vis N2 activation upon the inclusion of solvent effects.
Introduction<!>Computational Details<!>Results and Discussion<!>Conclusions
<p>Conversion of dinitrogen (N2) into useful materials is desired for uses such as the production of ammonia (NH3), one of the most important chemicals used in synthetic fertilizers.1 However, N2 is difficult to activate due to the inherent strength of the N≡N triple bond (~235 kcal/mol). The dominant industrial method for the reductive cleavage of N2 and formation of NH3 is the catalytic reduction of N2 with dihydrogen (H2) via the Haber-Bosch process. Due to its low cost, iron is commonly used to catalyze the Haber-Bosch process.2 Potassium promoters improve the catalytic activity of iron surfaces, partially due to an increase in the rate constant for N2 dissociation on the iron surface.3 In synthetic compounds, cooperative binding of N2 by iron and alkali metal ions has been shown to weaken the N-N bond more than iron alone, and this trend has been extended to chromium,4 cobalt5,6 and nickel.7 However, these systems do not cleave the N-N bond. Further progress in cooperative N2 activation requires better understanding of two key factors: (1) the reductive cleavage of the N2 bond, and (2) the role of promoters such as potassium.</p><p>Recently, Holland and coworkers reported a soluble iron-β-diketiminate (≡ [Fe]) system that can cleave N2 to give a bis(nitride) intermediate (Figure 1).11 Relatively few Fe-nitride complexes have been reported in the literature that involve more than two iron centers interacting with nitride atoms, and no others are derived from N2.12,13 The complex in Figure 1 arises from cleavage of N2, and has three [Fe] fragments interacting directly with nitrides and a fourth [Fe] interacting indirectly through a series of chlorine and potassium interactions. Though this system is not catalytic, the chemistry depicted in Figure 1 is a potential stepping stone to a better understanding of catalysts for solution phase N2 fixation.</p><p>In this study, DFT calculations are employed to understand the role of cooperativity between multiple iron-β-diketiminate fragments. For example, how many iron atoms are needed to cleave the N2 bond in the reduction step, and what intermediates are potentially involved? Theoretical calculations have greatly aided in understanding N-N bond cleavage.8–10 The research reported here indicates that interaction of N2 with more metal centers increases the N-N activation, and thus N2 fixation benefits from cooperation between metals. The present calculations also yield insight into the effects of potassium promoters in N2 fixation.14</p><!><p>Density Functional Theory (DFT) was used to facilitate comparison between the various ground states of the [Fe]3N2 and [Fe]3(N)2 species. The Gaussian 09 software package15 was used for geometry optimizations and frequency calculations. The B3LYP/6–31+G(d) calculated geometries and properties of [Fe]N2 and [Fe]2N2 species are similar to those previously reported from MCSCF computations.17–19 Additional continuum solvent corrections are computed in THF using the SMD formulation and are compared to the gas phase energetics.20 Since computations on the monometallic and bimetallic Fe-β-diketiminate species have been reported previously,17–19 the present contribution focuses on trimetallic species, the interactions of K+ on important intermediates in an array of binding modes, and the role of reduction.</p><p>Various isomers of the [Fe]n-N2 complexes were calculated in all plausible spin states. Free energies are quoted relative to separated starting materials: (iron-β-diketiminate)n + N2 (n = number of [Fe] fragments involved in the reaction). Bond lengths are given in Å. Initial attempts to model the tetra-iron complex in Figure 1 molecule with ONIOM techniques revealed that the substituents need to be modeled with full QM techniques to due to the importance of K+/π-arene interactions. The ligands were thus truncated to C3N2H5− for computational expediency; in previous reports, we have found that this truncation gives iron-dinitrogen complexes with metrical and spectroscopic parameters that agree well with experiment and faithfully represents the core electronic properties of larger β-diketiminate supporting ligands.6,17–19 The studies here are limited to a single potassium ion and three iron atoms because the fourth iron atom in the complex reported by Holland et al.11 interacts indirectly with the Fe3N2 core via K+/π-arene interactions.</p><!><p>This paper explores the effect of sequentially adding Fe-β-diketiminate fragments to free N2 in various binding modes. The experimental route to the complex in Figure 1 starts from potassium reduction of an iron(II)-β-iketiminate starting material to give a presumed iron(I) species that were modeled here as the unsaturated fragment iron-β-diketiminate. Previous work revealed that three-coordinate iron(I) gives strong backbonding into the π* orbitals of N2, and binding of a second fragment enhances N2 bond lengthening.17,19 A single [Fe] binds N2 in an end-on (E) fashion in a quartet spin state, ΔGrel(4E-FeN2) = −13 kcal/mol. The lowest energy bimetallic N2 complex is end-on/end-on (EE) in a septet state, as seen experimentally for closely related compounds,19 with ΔGrel(7EE-Fe2N2) = −40 kcal/mol. Binding of the second fragment is thus cooperative (defined here as the extra stabilization in a bimetallic complex beyond that expected from two monometallic interactions) by 40 – (2 × 13) = 14 kcal/mol. The ligation of a second E-Fe increases the N2 bond length by 5%, from 1.127 to 1.187 Å.</p><p>The key advance here is to explore the interaction of more than two iron(I) fragments with N2, and so potential binding modes were explored for a third [Fe] fragment interacting with N2. Three isomers of trimetallic complexes were compared: end-on/end-on/side-on (abbreviated EES-Fe3N2), end-on/side-on/side-on (abbreviated ESS-Fe3N2), and all-side-on (abbreviated SSS-Fe3N2). Note that [S-Fe] indicates a side-on interaction of iron with N2, which to our knowledge has never been observed experimentally in an iron complex; thus this study gives insight into the expected geometry of such an interaction. Various conformers within each family were explored; the lowest energy geometries are given in the figures.</p><p>The lowest energy neutral trimetallic isomer, Figure 2 (left), is calculated to be 10EES-Fe3N2, ΔGrel = −62 kcal/mol, with an N-N bond length of 1.234 Å. A 10ESS-Fe3N2 linkage isomer, Figure 2 (right), dNN = 1.284 Å, is only 6 kcal/mol higher than the calculated lowest energy isomer. SSS-Fe3N2 isomers were calculated to be ther-modynamically unfavorable (by ≥ 12 kcal/mol) with respect to those in Figure 2, and are thus not discussed further. Binding of the third [Fe] fragment to 7EE-Fe2N2 to give EES-Fe3N2 is found to release 22 kcal/mol, which is 5 kcal/mol less exergonic than binding of a second [Fe] fragment to 4E-FeN2. Importantly, both EES and ESS isomers are energetically accessible, and each lengthens the N-N bond significantly more than two iron fragments in 7E-Fe2N2.</p><p>Interestingly, 6ESS-Fe2(N)2, an isomer with a cleaved N-N bond where (N)2 denotes a bis(nitride) complex, was also located (Figure 3). This complex has a N…N distance of 2.598 Å and a relative ΔGrel of −40 kcal/mol. One of the two nitrides in this species is attached to only two iron atoms. This nitride nitrogen forms an apparent double bond to one of the iron atoms with dFeN = 1.654 Å, a relatively strained interaction that may explain why it is 16 kcal/mol less stable than 10ESS-Fe3N2 (Figure 4).</p><p>Transformation from EES-Fe3N2 to ESS-Fe3(N)2 was explored by scanning the potential energy surfaces of low energy sextet, octet, and decet spin state pathways, Figure 3. The scans reveal low (< 5 kcal/mol) barriers for the transformation on each of the three potential-energy surfaces; see Supporting Information. Thus, calculations imply that isomerization could be kinetically rapid as a part of the reaction leading to N2 cleavage, but that the N-N cleavage is somewhat thermodynamically unfavorable for the neutral cluster.</p><p>Inspection of Figure 1 indicates several K+ directly interacting with the π-system of the aryl substituents and the nitrides.8 Several potential roles of the potassium in the N-N cleavage can be envisioned: K+ may enforce geometrical constraints, stabilize the nitride (N3−), and/or increase the π-backbonding capacity of the Fe centers as proposed for the heterogeneous catalyst.1 To assess the impact of K+ on N2 fixation, a K+ ion was placed in several locations in proximity to the N2 moiety for the low energy dinitrogen and dinitride structures (i.e., 10EES-Fe3N2 with an intact N2 and 6ESS-Fe (N) 6ESS-Fe3(N)2 with a broken N2 bond), respectively. Addition of K+ to 10EES-Fe3N2 always rearranges upon DFT geometry optimization to the structure in Figure 5 (left). Binding of K+ to 10EES-Fe3N2 is exergonic by 19 kcal/mol and the calculated lowest energy multiplicity of EES-Fe3N2K remains a decet. The NN bond is elongated from 1.234 to 1.268 Å (3%) upon K+ addition. Addition of K+ to 6ESS-Fe3(N)2 yielded the geometry in Figure 4 (right) with the sextet remaining the lowest energy spin state. Addition of K+ to 6ESS-Fe3(N)2 is 11 kcal/mol more exergonic than K+ addition to 10EES-Fe3N2. Thus, potassium ion addition stabilizes the bis(nitride) product more than the bridged N2 complex in the gas phase. However, the nitride complex continues to have one unusually short Fe-N bond.</p><p>Addition of K+ to 6ESS-Fe3(N)2 makes the resulting bis(nitride), Figure 4, more energetically accessible relative to the dinitrogen isomers, with a free energy for 6ESS-Fe3(N)2K+ → 10EES-Fe3N2K+ of only 12 kcal/mol, roughly half the comparable isomerization free energy in the absence of K+. Analysis of calculated atomic charges (see Supporting Information) suggests that greater stabilization of the N3- ligand by K+ coordination is responsible for the diminution of the endergonicity in the nitrogen scission reaction.</p><p>Finally, an electron was added to the 10EES-Fe3N2 complex to mimic reduction by the fourth Fe(I) fragment in the experimental reaction. This yielded [9EES-Fe3N2]− as the lowest energy state, and resulted in only slight geometric distortion (RMSD = 0.22 Å). The largest perturbation was elongation of one Fe–N bond from 1.976 to 2.089 Å for the [S-Fe] fragment, which coincided with an increase of atomic charge on the nitrogen involved in the bond, from −0.19 to −0.58. The added electron occupies a non-bonding, Fe-based orbital, Figure 6, consistent with the minor change in geometry upon reduction. Thus, addition of a single electron to the tri-iron structure has a minor impact on the degree of N2 activation by trimetallic EES-Fe3N2.</p><p>On the other hand, addition of an electron to 6ESS-Fe3(N)2 gave a significant effect. Reduction yielded [5ESS-Fe3(N)2]− as the lowest energy state. The distance between the nitride ligands is shortened from 2.598 to 2.587 Å. The added electron was found to occupy a bonding Fe-nitride orbital, Figure 7. A K+ ion was added to the reduced complexes [9EES-Fe3N2]− and [5 ESS-Fe3(N)2]− changing the overall charge on the cluster model to neutral; the resulting complexes were found to possess the same ground spin states as their anionic precursors, Figure 8.</p><p>The addition of K+ to the reduced species makes the [5ESS-Fe3(N)2K] cluster 3 kcal/mol more stable than [9EES-Fe3N2K], Figure 8. It also gives a structure in which the Fe-N bonds are closer to the experimental crystal structure where the Fe-N bonds proximal to coordinated K+ are shorter than the corresponding distal Fe-N bond lengths. Therefore, addition of three iron(I) fragments, a K+ ion, and an electron makes N-N cleavage favorable, presumably because of the stronger interaction of the potassium cation with the anionic nitride core.</p><p>While gas-phase simulations may more appropriately model an industrial nitrogen fixation catalyst, inclusion of solvent effects is more pertinent to attempts to create a homogeneous version. Continuum solvation corrections in THF were thus computed and compared to the gas phase energetics to assess the impact of solvation on the reactions of interest. The THF thermodynamics, Figure 9 (right, blue border), are calculated to be similar to the gas phase models with one interesting difference. The thermodynamics of 10EES-Fe3N2 → 6ESS-Fe3(N)2 is little changed by inclusion of solvent effects, ΔGgas = +22.0 kcal/mol, ΔGTHF = +21.5 kcal/mol, Figure 9. Similarly, there is a mild solvent influence calculated for the K+ and K-ligated reactions, e.g., 10[EES-Fe3N2K]+ → 6[ESS-Fe3(N)2K]+, ΔGgas = +11.3 kcal/mol, ΔGTHF = +14.9 kcal/mol, Figure 9. However, reduction upon the nitride to bis(nitride) transformation is significantly modulated by solvent, going from endergonic, ΔGgas = +8.4 kcal/mol, to mildly exergonic, ΔGTHF = −0.5 kcal/mol for 9[EES-Fe3N2]− → 5[ESS-Fe3(N)]−, Figure 9. Comparing the relative ΔG's in gas (ΔΔGgas) and solvent (ΔΔGTHF) indicates that K+ becomes less impactful (ΔΔGgas(K+) = 10.7 kcal/mol, ΔΔGTHF(K+) = 6.6 kcal/mol) than reduction of the system (ΔΔGgas(e−) = 13.6 kcal/mol, ΔΔGTHF(e−) = 22.0 kcal/mol) upon the inclusion of continuum THF solvent effects.</p><!><p>The present DFT simulations of the sequential addition of Fe-β-diketiminate fragments to dinitrogen are important because they show a reasonable series of metal binding and reduction events that cleave N2 to give a Fe3(N)2K core like that in a recent experimental report.7 In addition to this mechanistic insight, it reveals that three reduced iron centers acting in a cooperative fashion make N2 cleavage thermodynamically feasible. As summarized in Figure 9, the K+ promoter stabilizes the nitride ligand of the "fixed" tri-iron-bis(nitride) isomers by about 10 kcal/mol relative to the N2 isomers, and N-N cleavage is only favorable when an added electron and potassium are present. However, including a polar continuum solvent reduces the impact of the K+ on stabilizing the reduced tri-iron-bis(nitride). The results demonstrate that the cleavage of N-N bonds by a reduced iron fragment is greatly influenced by potassium, and also illustrate the impact of cooperative Fe binding upon N2 activation, indicating that at least three iron fragments are needed to cleave N2.</p>