The design of earth abundant metal catalysts for nitrous oxide-based oxidations: Part I. N₂O coordination and oxygen-transfer to metal

Abstract

Nitrous oxide (N₂O) is thermodynamically unstable, but kinetically unreactive, and thus presents a fundamental challenge for catalysis. It is also a potent greenhouse gas, yet it is underutilized as a chemical feedstock and thus provides a practical opportunity for catalysis as well. A computational design approach is employed in this first part of a two-part study to evaluate the potential of selected first row transition metal complexes to activate N₂O as an oxidant for various substrates. Density Functional Theory (DFT) calculations are employed on several ligated transition metal fragments LM, M = V(III), Fe(II), Mn(II), Cr(II), Cu(I) and second row Ru(II) with 4/5-coordinate geometries to assess their N₂O binding affinity and energetics for N–O cleavage to LMO. The effects of the ligand, coordination number, the metal, its spin state, charge, etc. are addressed. The key points from the DFT analysis and energy profiles are: (1) favorable N₂O binding (ΔG_a < 0) is correctly predicted for known N₂O complexants: (N-3Pyr)V, [Al(OR_F)₄]Cu and (NH₃)₅Ru²⁺; (2) for a range of unproven complexants, the N₂O-affinity ranges from moderate (ΔG_a −5 to +2 kcal mol⁻¹) to low (ΔG_a > +5 kcal) in the order Cr(II) > Ru(II) ≥ Fe(II) ≅ Mn(II) ≅ Cu(I); (3) M–N binding to N₂O is generally more stable than M–O binding, but is nearly isoenergetic for many high spin metal fragments; (4) N–O cleavage via monometallic complexes, LM–ON₂ (M = Fe(II), Mn(II), Cu(I)) requires moderate-to-high activation energies, (23–40 kcal mol⁻¹), but the barriers are much lower for LCr(II) and LRu(II) species (3–17 kcal mol⁻¹); (5) N–O cleavage is facilitated by pyramidal and penta-coordinating ligands; (6) from bent N₂O-bimetallics is very low: 1–5 kcal mol⁻¹; and (7) the total activation energy barriers for bimetallic-N₂O complexes, ca. 20–30 kcal mol⁻¹, are 5–8 kcal mol⁻¹ lower than for mono-metallics, providing a bimetallic advantage for N₂O scission to oxido-metals, LM=O.

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Introduction

Nitrous oxide (N₂O) is an abundant, atmospheric component with rather limited commercial use, including as a mild anesthetic (‘laughing gas’), a fuel enhancer (‘nitro’) and an aerosol propellant. These uses of nitrous oxide are dwarfed by its emissions from both natural and man-made sources. It is emitted predominantly by biological sources¹ in soil and water and secondarily from diesel vehicle exhaust² and in nylon production.³ Nitrous oxide is an important long-lived greenhouse gas, approximately 300 times more potent than carbon dioxide, contributing significantly to global warming.⁴ The atmospheric levels of N₂O have been rising, primarily due to the surging use of fertilizers to meet the food needs of a growing global population. The impacts of this imbalance between N₂O emission and utilization calls for solutions that increase its chemical utilization and/or destruction.

Nitrous oxide is thermodynamically unstable with respect to its decomposition products, N₂ and O₂ (ΔG_dec −26 kcal mol⁻¹).⁵ However, N₂O decomposition and many of its other potential chemical transformations are kinetically challenging for a lack of established low barrier energy pathways. The most important known catalyzed reactions of N₂O are its decomposition and NH₃ reduction relevant to diesel exhaust and environmental mitigation,⁶ typically conducted over solid iron- and copper-zeolite catalysts operating at temperatures >300 °C.⁷ The Solomon and Sels team have performed valuable experimental and computational analysis of the binding, activation and conversion of N₂O on these supported catalysts. The Cu-zeolites were suggested to contain structurally diverse active sites for both mono and bi-metallic binding; in particular, Cu₂O sites with O,O- or N,O-bridged bimetallic binding modes provide the lowest energy N–O scission pathways (ΔH* ca. 5 kcal mol⁻¹).⁸ For Fe-zeolite beta, a monometallic Fe(II) site has been implicated to bind N₂O in a terminal fashion (N- or O-), the latter of which transforms to Fe(IV)=O site with a higher activation enthalpy of 25 kcal mol⁻¹.⁹ For the decomposition reaction, O₂ evolution from the oxidized M–O site is likely turnover-limiting. However, the structural heterogeneity and immutability of the active sites in these solid catalysts impede rational performance improvement. In a recent study, we reported computational modeling of several potential molecular (homogeneous) catalysts for nitrous oxide decomposition and proposed the viability of low temperature catalytic N₂O-splitting by Ru(Cl)(POR).¹⁰

Reduction of nitrous oxide (to N₂ and H₂O) occurs naturally under ambient conditions in some plants, as catalyzed by the enzyme nitrous oxide reductase (N₂OR).¹¹ This biocatalyst has a novel protein-bound Cu₄S active site,¹² at which N₂O was suggested to engage in multicenter binding and activation,¹³ but the detailed pathway to dinitrogen and water remains unknown. Structural and, more recently, functional model compounds for the Cu₄S active have been developed, by the Mankad¹⁴ and Tolman¹⁵ groups. In the realm of synthetic molecular catalysts for N₂O reduction, the Millstein group has reported a Ru(II)–pincer complex that catalyzes the hydrogenation and hydrosilation of N₂O.¹⁶ The electrocatalytic reduction of N₂O by synthetic catalysts has received increasing attention, employing both solid and homogeneous transition metal-based catalysts.¹⁷ Generally, in these systems a reduced form of the metal species, e.g. Fe(I,0) and Co(I), has been implicated in the transient coordination and transformation of N₂O. In some instances, it appears that bimetallic centers can moderate kinetic barriers, as in an earlier study by Collman et al. showing the accelerated electrocatalytic reduction of N₂O by tethered bimetallic cobalt-porphyrins.¹⁸ Detailed mechanistic pathways and structure/activity relationships for these electrocatalytic systems are yet to be established.

Outside of catalytic decomposition and reduction reactions, other catalytic transformations of N₂O are rather undeveloped. A few early reports of homogeneous metal-catalyzed oxidations with N₂O have been published involving Ru(porphyrin) species, including (TTP)RuO₂-promoted benzylic hydrocarbon hydroxylation,¹⁹ benzylic alcohol oxidation²⁰ and alkene epoxidation,²¹ presumably via (POR)Ru(O_0,1)(N₂O) intermediates (Fig. 1). Newer additions to the realm of transition metal-based catalytic transformations of N₂O are C–X (aryl halide) to C–O (aryloxide) substitutions enabled by low valent Ni-complexes.²²

Fig. 1 Catalytic oxidations by N₂O with (POR)RuO₂.

The design and development of catalysts for various nitrous oxide conversions could benefit significantly from an enhanced fundamental knowledge and understanding of the interaction and reactions of N₂O with metallic and other potentially activating species. Several reports have shown that nitrous oxide can react directly with powerful nucleophiles²³ such as amide²⁴ and hydrazide salts,²⁵ organo-metals,²⁶ N-heterocyclic carbenes²⁷ and phosphines²⁸ to form N-bound adducts (Fig. 2A) or can transfer its oxygen atom to the nucleophile (Fig. 2A). Reactions of N₂O with frustrated Lewis pairs (FLP), which typically incorporate a nucleophilic and an electrophilic center, produce adducts, which can feature a distinctly bent N₂O bridge and an elongated (presumably weaker) N–O bond (Fig. 2B).²⁹

Fig. 2 Reactions between N₂O and nucleophiles (A) and FLPs (B).

All the structurally confirmed N₂O–metal complexes exhibit one of two binding modes: terminal N-binding (η¹-N) or side-on N–N binding (η²-N,N) (Fig. 3).³⁰ In the η¹-N mode, the M–N₂O unit is essentially linear and the bond lengths of the coordinated N₂O unit are rather little changed from free N₂O (vide infra), suggesting little electronic perturbation of the N₂O fragment.^31a–c In the η²-N,N mode the N₂O unit is substantially bent (ca. 130°) and the N–N bond is elongated, indicative of substantial modification of the electronic character of the N₂O unit.³² Although the number of examples is still small, the metal centers in these molecules are in low-to-middle oxidation states, i.e. have metal fragments that are relatively electron rich. It is noteworthy that although M(η¹-O-N₂) coordination has been proposed or assumed in O-transfer reactions of N₂O with low oxidation state metal-complexes, no direct experimental evidence has been reported for such species.

Fig. 3 Structurally established modes of nitrous oxide coordination.

In addition to the formation of metal–N₂O complexes, a highly reduced metal species, e.g. ligated Ti(III),³³ V(III),³⁴ U(III),³⁵ Ru(II),³⁶ can abstract the O-atom from N₂O to produce an oxido-metal, LMO, and dinitrogen (Fig. 4). The presumed metal–N₂O intermediates in these oxidations have not been identified. Such O-transfer oxidations of electron rich metal-species are analogous to those of non-metallic nucleophiles (Fig. 2a). Another class of reactions between N₂O and transition metal complexes is insertion into metal–carbon bonds, which results in O-transfer to carbon or the metal as illustrated by Hillhouse and coworkers.³⁷

Fig. 4 O-transfer oxidation of metal-based species by N₂O. (A) General equation; (B) N₂O-deoxygenation by (TMP)Ru(THF)₂.³⁶

There is a scarcity of systematic, broad scope experimental and theoretical studies of the interaction and transformations of N₂O with potential transition metal activators.^23,30 We are especially interested in evaluating the factors that affect the viability of schemes that utilize N₂O as a reagent for oxygen atom-transfer (OAT, oxidation) and nitrogenation reactions. The reports of Ru-promoted hydrocarbon oxidation by N₂O stimulated our conception of a general two-stage catalytic pathway for substrate (e.g. hydrocarbon) oxidation by earth-abundant transition metals, wherein initially N₂O transfers its O-atom to a LM-fragment to form a reactive LMO (oxido) species (releasing N₂), which, in turn, can oxidize the substrate (Fig. 5). For practical, economic reasons we are particularly interested in developing such processes with earth-abundant metal-centered catalysts. In the present study, we employ DFT calculations on several divalent metal fragments LM, M^II = Fe, Mn, Cr, Ru and Cu^I having common 4/5-coordinating ligands to assess their N₂O binding affinity, the structures and energies of the resulting metal complexes, LM(N₂O), and the energetics of N–O cleavage to LMO to reveal the effects of the ligand, coordination number, the metal, its spin state, charge, etc. (Fig. 5A). In a subsequent report, we will evaluate the potential for hydrocarbon oxidation by the derived LMO species (Fig. 5B) and gauge the overall kinetic viability of rebound oxidation energetics according to the scheme in Fig. 5. Instead of the typical, empirical, hit-or-miss and often inefficient approach to reaction discovery and catalyst development, we present here a predictive computational study of catalyst design and virtual screening, seeking the development of new catalytic reactions of nitrous oxide.

Fig. 5 Rebound pathway via oxido-metals (A + B) for catalytic oxidations with N₂O (C).

Computational methods

DFT methods, when applied to transition metal complexes, are widely recognized for their structural accuracy, reasonable prediction of many electronic properties and ligand dissociation energies, at a relatively low computational cost.³⁸ Presently, however, there are no universally proven methods that will provide accurate spin-dependent energies for odd-electron (open-shell) transition metal species.³⁹ For Fe(II,III) and, to a lesser extent, other open-shell first row transition metals, several studies have shown that the B3LYP (hybrid functional)⁴⁰ and OPBE⁴¹ functionals are usually reliable for determining ground state spin multiplicities, but methods for obtaining accurate energies of higher states are still being sought.⁴² Since many transition metal complexants (fragments) are coordinatively unsaturated, they are inherently reactive/unstable and their ground spin states are often experimentally unknown.

With the above issues in mind, quantum electronic calculations were carried out using the Gaussian 16 software suite.⁴³ Unless otherwise specified, all structure optimizations were performed using the B3LYP functional,⁴⁴ with the LANL2DZ basis set on the metal⁴⁵ and 6-31G(d) for 1^st and 2^nd row atoms and 6-311+G(d,p) for 3^rd row non-metal atoms.⁴⁶ Following B3LYP geometry optimization and frequency calculation, corrections for dispersion and solvation were applied in single point energy calculation using the D3 dispersion⁴⁷ and SMD solvation⁴⁸ methods to give the free energy (G) values in solution. For almost all species dichloromethane was the virtual solvent selected based on its intermediate dielectric and the many moderately polar (some ionic) complexes targeted here. Solvation is expected to have significant energetic effects given the differing polarities of the various ligated metal species. Some optimizations were also run using the OPBE functional, which typically gave qualitatively similar results on the energy ordering of the LM(N₂O) spin states (see SI). In a few cases tested, e.g. (N-3Pyr)M(N₂O), M = V, Fe, the G_solv values from B3LYP/D3/SMD (6-31G(d)/LANL2DZ basis sets) and M06/SMD⁴⁹ (6-311+G(d,p)/SDD basis sets; no explicit dispersion) were compared and gave similar values (±2 kcal mol⁻¹) of binding affinities (SI). Hence, for uniformity and computational economy the B3LYP/D3/SMD (6-31G(d)/LANL2DZ) method was employed across all species. Transition states were found by relaxed scans of the M–O or N–O bonds, followed by a TS Berny optimization⁵⁰ (showing one imaginary frequency along the reaction coordinate) and confirmed with IRC calculations in both the forward and reverse directions. Orbital analysis was carried out using the canonical orbitals from the B3LYP optimizations or the intrinsic bonding orbitals (IBOs).⁵¹ The energy profile graphs were created using EveRplot.⁵²

Results and discussion

Candidate complexes (complexants) for N₂O binding and O-transfer

A large set of potential N₂O-complexants/activators was selected for structural and energetic analysis with the several considerations in mind (Fig. 6). A small set of complexants, LM, was selected that are experimentally known to coordinate or react with N₂O for structural and energy-benchmarking to support the validity of the computational methods employed; these include (N-3Pyr)V (1a), [(CF₃O)₄Al]Cu (6) and (NH₃)₅Ru²⁺ (7). Since we are especially interested in identifying potential activators among the earth-abundant transition metals, we have focused on coordinatively unsaturated, reducing first row transition metals- Fe(II), Mn(II), Cr(II) and Cu(I)- with common supporting ligand types. Many of these metal centers have shown ability to coordinate or react with small unsaturated substrates (e.g. CO, ethylene, O₂, RN₃, N₂O) and the corresponding oxido-metal (LMO) species resulting from O-transfer are known, and some have demonstrated oxidizing ability.⁵³ Precious, second row LRu(II,III) species are also included for reference in this study because of their experimental precedents of N₂O complexation, activation and catalysis.^{16,19–21,31,36} The ligand and coordination geometries include: tricoordinate N,N,N-(tris)pyrazolylborate/methane (TPB, TPM), tetracoordinate planar N₄-donors-porphyrin (POR), dipyrolyl-diimine (DPDI) and N₂O₂-donor-salen; 4-coordinate pyramidal ligands, e.g. N-3Pyr and 5-coordinate N-4Py and known derivatives with monodentate CN⁻ and NH₃ ligands. Many of the first-row metal derivatives of Fe(II), Mn(II), and Cr(II) are known or expected to be mid/high-spin species in their ground states.⁵⁴ Together the diversity of metal and ligand types selected will provide a broad assessment of the effects of metal, oxidation and spin states on the energetics of N₂O coordination and O-transfer to the metal.

Fig. 6 Metal complexants evaluated for N₂O coordination and activation.

Structural comparison of computed and experimental N₂O-complexes

In order to establish the reliability of the B3LYP methodology for predicting the structures of N₂O–metal complexes, we compared the X-ray structures of the experimental [N-(Ar-Pyr)₃]V(N₂O) and copper–N₂O complexes (not shown) with the DFT-optimized structures of the ligand-truncated models (N-3Pyr)V(η¹-N₂O) (1a)^31c and [Al(OCF₃)₄]Cu(η¹-N₂O) (6) (Fig. 7).^31b For both optimized structures the same experimentally observed linear η¹-N bonding mode was found; the calculated bond lengths and angles also were in very good agreement with the X-ray metrics (<±5%). We note also that the bond lengths within the N₂O unit are virtually unchanged upon coordination for these LV and LCu complexes, cf. Fig. 7 with free N₂O:⁵⁵ N–N 1.13 Å, N–O 1.18 Å, N–N–O 180°. This suggests rather little electronic perturbation to the N₂O unit upon coordination to these metal centers. The linear metal–N₂O geometry is also predicted for the low-spin Fe(II) derivatives evaluated, e.g. for Fe(CN)₅(N₂O)³⁻ (8-N₂O, Fig. 7) and Fe(N-4Py)(N₂O)²⁺ (3-N₂O) (SI). However, the more common mid/high spin iron(II) derivatives⁵⁴ that are investigated here typically optimized to a bent M–N₂O arrangement, e.g. Fe(POR)(N₂O)^t,qn (9-N₂O) (Fig. 7) and (N-3Pyr)Fe(N̲₂O)^qn (1b-N₂O, SI). A stronger metal–N₂O interaction in the linear LM–N₂O bonding mode is suggested by the considerably shorter Fe–N bond and longer N–O bond in the N₂O-adducts of complexants 3 and 8 compared to the angular 9.

Fig. 7 B3LYP-optimized structures of η¹-N-bonded LM(N₂O)^x: (N-3Pyr)V(η¹-N₂O)^t, [(CF₃O)₄Al]Cu(η¹-N₂O)^s, (CN)₅Fe(η¹-N₂O)^(3−)s, (POR)Fe(η¹-N₂O)^qn; x = spin state, s = singlet, d = doublet, t = triplet, q = quartet, qn = quintet; atom colors: C = grey, H = white, blue = N, red = O, F = green, Al = pink, V = dark grey, Cu = bronze, Fe = turquoise.

The experimentally unknown O-bonding mode was also computationally evaluated for its geometrical and bonding features. This matter is of fundamental and practical importance because the most viable pathways for N–O cleavage likely involve LM–O̲–N₂ coordination. All the representative examples shown in Fig. 8 illustrate the favored bent arrangement of the M–O–N₂ unit (the N–N–O moiety remaining linear). As is the case with many of the N-bound complexes, the calculated metrics of the M–O̲–N₂ bound species show little O–N or N–N bond lengthening and the same linear N₂O geometry as in unbound N₂O; this indicates a small electronic perturbation to the coordinated N₂O for most, but not all, of the complexants investigated here.

Fig. 8 DFT-optimized structures of O-bonded LM(η¹-O̲N₂). (N-3Pyr)V(η¹-ON₂), [(CF₃O)₄Al]Cu(η¹-ON₂), (salen)Fe(η¹-ON₂)^qn; free N₂O: N–N 1.13 Å, O–N 1.18 Å, N–N–O 180°.

To better understand the principal M–N₂O bonding components of the η¹-bonding modes the frontier bonding orbitals of representative complexes were examined. A canonical FMO for the linear (CN)₅Fe(η¹-N₂O)³⁻ (8-N₂O) shows classical Fe–N₂O dπ–pπ* back-bonding (Fig. 9) with N–N π and O–N π* character. The optimized structure of 8-N₂O^s (Fig. 7) shows a somewhat lengthened N–O bond (1.24 Å) relative to free N₂O (1.18 Å), probably reflecting substantial Fe–ON₂ electron density transfer, and decreased N–O bond order. The analogous, lower energy FMO for O-bound (N-3Pyr)V(η¹-ON₂) (Fig. 9) has a smaller V d-orbital contribution, which could indicate lesser M–L back-bonding and shorter N–O distance (1.21 Å) relative to N-bonded 7-N₂O.

Fig. 9 HOMO-3 for Fe(CN)₅(η¹-N₂O)³⁻ (left); HOMO-7 for (N-3Pyr)V(η¹-ON₂) (right) showing metal–(N₂O) π-(back) bonding contributions.

In contrast, both N- and O-bound linkage isomers of (N-3Pyr)Cr(N₂O)⁻ (1c-N̲₂O and 1c-O̲N₂) exhibit acutely bent N–N–O fragments in both the N-bound and O-bound modes and a substantially elongated N–O bond relative to free N₂O (Fig. 10): Cr–N₂O 1.24 Å, Cr–ON₂ 1.37 Å, free N₂O 1.19 Å; and a slightly longer N–N: Cr–N₂O 1.21 Å, Cr–ON₂ 1.18 Å, free N₂O 1.13 Å. The bending of the N₂O unit may be the result of substantially greater Cr–X back-bonding relative to Fe(II). For the Cr-species the coordinated N₂O unit is essentially reduced, being electronically similar to the N₂O anion.⁵⁶ This species has a similar bent geometry with elongated N–O and N–N bonds relative to free N₂O. This view is also supported by the APT charges calculated for (N-3Pyr)Cr–O–N₂⁻: Cr +1.86, O −0.71, N(1) +0.30, N(2) −0.27 (net −0.68e⁻) vs. free N₂O: N(1) −0.31, N(2) +0.82, O −0.50. Significant electron spin density also resides in the coordinated N₂O unit: Cr 3.13, N(1) 0.14, N(2) 0.41, O 0.30 (though primarily local on Cr). The other high spin M–O–N₂ complexes show electron spin density located primarily on the metal and relatively little on the N₂O unit; e.g. in (N-3Pyr)V–O–N₂: V 2.06, N(1) −0.07, N(2) 0.08, O 0.06.

Fig. 10 Optimized structures of “abnormal” bent (N-3Pyr)Cr(N̲₂O)⁻ and (N-3Pyr)Cr(O̲N₂)⁻.

Although there are no structurally proven examples of bimetallic N₂O complexes, at least one such species has been partially characterized⁵⁷ and others have been implicated in kinetics³⁴ and computational⁸ studies of metal-promoted reactions of N₂O. Related non-metal bifunctional derivatives are represented in the frustrated Lewis pair (FLP) adducts of N₂O, R₃P-N₂O-BX₃.^29b,c Accordingly, the structures and energetic viability of forming N₂O-bridged bimetallics was assessed for a set of metal complexants, specifically Fe(POR)^qn (9), Fe(salen)^qn (12), Fe(DPDI)^t (15), Cu(TPB)^s (5), Ru(salen)(im)^s (14b) and Ru(salen)Cl^d (14a) (Fig. 11). We were able to identify and optimize two types of structures- one with a linear bridging N₂O unit, generally of lower energy, and one with a distinctly bent N₂O-unit of higher energy. For the linear bimetallic iron derivatives, e.g. (salen)Fe-N₂O-Fe(salen) (12-N₂O-12), the N–N and N–O bond lengths are little changed from free N₂O and the Fe–O (3.5 Å) and Fe–N (3.1 Å) distances are long, more typical of non-covalent encounter complexes held by dispersion/London electrostatic forces.⁵⁸ Linear (TPB)Cu-N₂O-Cu(TPB) (5-N₂O-5) shows more typical Cu–N,O bond lengths and little changed N–N and N–O distances relative to free N₂O. The linear (salen)(im)Ru-N₂O-Ru(salen)(im) species (14b-N₂O-14b) exhibits typical covalent Ru-N,O bond lengths, and somewhat longer N–O distances, suggesting appreciable Ru-O,N back-bonding. For the bent bimetallic complexes, e.g. (salen)Fe-N₂O-Fe(salen) (12-N₂O-12) one sees marked bending of the N₂O unit and lengthening of the N–N and N–O bonds: N–N 1.19 Å, N–O 1.37 Å, N–N–O 125° relative to its linear counterpart (Fig. 11). The shorter Fe–N and Fe–O distances imply a stronger M–N₂O interaction and perturbation of the N₂O electronic character. One finds similar features for the corresponding bent (DPDI)Fe derivative 15-N₂O-15. Metrics of the bent N₂O mode in these examples are indicative of considerable structural and electronic perturbation of the coordinated N₂O unit, comparable to those of the N₂O anion.⁵⁶ This suggests considerable electron transfer from iron to the N₂O-unit, i.e. reduction, in the bent bimetallics and is supported by the calculated APT charges, e.g. for bent 12-N₂O-12, Fe(+1.70)–O(−0.77) and Fe(+0.51)–N1(0.29) vs. for linear 12-N₂O-12, Fe(+0.80)–O(−0.44) and Fe(+0.80)–N1(−0.29).

Fig. 11 Top: optimized μ-linear structures of (salen)Fe-N₂O-Fe(salen)^qn, (TPB)Cu-N₂O-Cu(TPB)^s and (imid)(salen)Ru-N₂O-Ru(salen)(imid)^s. Bottom: optimized μ-bent structures of (salen)Fe-N₂O-Fe(salen)^qn and (DPDI)Fe-N₂O-Fe(DPDI)^qn.

Energetics of N₂O binding

The free energy of association ΔG_a between N₂O and the metal complexants was calculated by determining the free energy values for each species in its optimized ground spin state for the reaction, LM + N₂O → LM(N₂O). For a more accurate comparison to typical experimental solution data, corrections to the free energy in vacuo were made for dispersion (D3) and solvation (SMD). The free energy results for the set of experimentally investigated N₂O complexes, Group I, are summarized in Table 1. The dispersion correction generally lowered the ΔG_a (increases K_a), while the solvation correction typically raised ΔG_a, which tended to offset. In cases that were compared, the free energies of binding, ΔG_a, with B3LYP-D3/SMD or M06/SDD-6-311+G(d,p)/SMD were quantitatively similar, ±2 kcal.

Table 1 Computed thermodynamics of nitrous oxide association with metal complexants

LM + N2O → LM(N̲2O) ΔGa
LL′M	Ground spin state^a LM/LM (N2O)	ΔGN/O(rel)^b (kcal mol^−1)	ΔGa(vac)^c (kcal mol^−1)	ΔGa(D,CH2Cl2)^d (kcal mol^−1)
a Spin state multiplicities: S = singlet, T = triplet, Q = quartet, Qn = quintet, Sx = sextet Solvent = H2O.b N/O selectivity, ΔGN/O = GLM(O̲–N2) − GLM(N̲2O)c ΔGa(vac) = GLM(N̲2O) − GLM + GN2Od ΔGa(D,CH2Cl2) = ΔGa(vac) corrected for dispersion (D3) and solvation (SMD-CH2Cl2)e Optimization of LM(η^1-O̲N2) did not convergef SMD solvent = H2O
Group I
(N-3Pyr)V (1a)	T/T	7.0	−2.9	−1.4
(NH3)5(H2O)Ru^2+ (7)	S/S	7.7	9.0	−2.4^x
(POR)(THF)Ru (10)	S/S	10.3	−3.9	−7.3
[(CF3O)4Al]Cu (6)	S/S	25.7	−11.9	−7.0
Group II (M = Fe)
(POR)Fe (9)	Q/Q	0.3	2.1	1.8
(DPDI)Fe (15)	T,T	−0.1	3.0	1.2
(salen)Fe (12)	Qn/Qn	0.2	3.6	2.9
(salOpr)Fe (13)	Qn/Qn	0.1	6.2	6.5
(N-3Pyr)Fe^1− (1b)	Qn/Qn	—^e	4.5	4.1
(N-2Pyr-Py)Fe (2)	Qn/Qn	−0.1	−1.1	4.7
(TPM)Cl2Fe (4)	T/S	0.4	0.3	3.2
(N-4Py)Fe^2+ (3)	S/S	6.7	−6.3	−6.8
(CN)5Fe^3− (8)	T/S	—^e	0.6	3.4^f
Group III (M ≠ Fe)
(salen)(imid) Ru (14a)	S/S	4.7	−3.7	−1.5
(salen)ClRu (14b)	D/D	0.9	3.6	1.4
(POR)ClRu (10a)	D/D	0.8	6.6	10.1
(TPB)Cu (5)	S/S	5.3	−3.0	−1.5
(POR)(Py)Cr (11a)	T/T	2.3	−12.0	−14.5
(N-3Pyr)Mn^− (1d)	Sx/Sx	0.1	4.6	5.2
(N-3Pyr)Cr^− (1c)	Q/Q	−3.6	−1.7	−1.4

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Each of the Group I examples of experimentally implicated N₂O complexes shows a thermodynamically favorable (exergonic) free energy of association ΔG_a (binding affinity) in the solution phase, which qualitatively agrees with the demonstrated isolability/stability of these compounds. For the models of the isolated/X-rayed vanadium- and copper-complexes, 1a-N₂O and 5-N₂O, modest to substantial binding free energies (−1.5, −7.0 kcal mol⁻¹) are calculated when both dispersion and solvation effects (in CH₂Cl₂) were factored in; corresponding K_a values would be on the order of 10²–10¹⁰. Unfortunately, the experimental equilibrium constants for these complexes have not been measured. For the (POR)Ru(THF)/N₂O system (10a-N₂O) a very favorable binding affinity (ΔG_a −7.3 kcal mol⁻¹) is estimated. We note that a transient (undetected) N₂O adduct is presumed in the room temperature reaction between (TMP)Ru to form (TMP)RuO₂.³⁶ In the three examples of isolable N₂O complexes, the experimentally established N-bound linkage isomer was strongly favored by 7–25 kcal mol⁻¹ over the O-bound form. A recent DFT analysis of (NH₃)₅Ru(N₂O)²⁺ (7-N₂O) reported the same structures and selectivity (ΔG_O/N 6.9 kcal) in favor of the N-bound mode as here.⁵⁹ In the case of the only N₂O association equilibria experimentally studied, the (NH₃)₅Ru(H₂O)²⁺/N₂O system,^31a we calculated a value for ΔG_a of −2.4 kcal mol⁻¹ for the aqueous phase reaction LRu(H₂O) + N₂O → LRu(N̲₂O) + H₂O, corresponding to a K_a = 57. This can be compared to the experimentally determined K = 7 (ΔG ca. −1.1 kcal mol⁻¹). The quantitative discrepancy between theory and experiment may be the composite result of several factors: (1) the neglect of the counter anion in the calculation; (2) the inaccuracy of the DFT functional or the solvation model for this 2+ complexed ion, where specific H-bonding could be significant between the ligated NH₃, N₂O and the solvent H₂O; and (3) the inaccuracy of the experimental measurement. Nonetheless, semi-quantitative agreement was found between calculation and experiment for the N₂O binding affinities among these experimentally established LM–N₂O systems.

For the Group II iron-based potential N₂O-complexants (Table 1) several significant features of the binding free energy, ΔG_a, were discovered. First, with few exceptions the ΔG_a values for the 4-coordinate complexants are slightly to considerably unfavorable, in the range of +1 to 6 kcal mol⁻¹. There is some variation in ΔG_a among the planar ligated iron species, with little difference among the N₄- and N₂O₂-ligated species, FeL = POR (9), salen (12), and DPDI (15), but lower affinity for the expectedly weaker donating O₄-ligand, (salOpr)Fe (13). For the 4-coordinate pyramidal fragments, M(N-3Pyr) (1b) and N-2Pyr-Py (2), the binding free energies ΔG_a are comparable to the planar ones, which at first seems inconsistent with the experimental O-transfer reactivity of the Fe-derivative 1b (R = Ar) with N₂O reported by Chang's group.⁶⁰ This issue is addressed subsequently with the Group III results of Table 1 and the energetics of the O-transfer activation energies (Table 2). An indication that the pyramidal N-3Pyr ligand can provide for favorable N₂O binding and activation is evidenced by the proven (N-3Pyr)V(N₂O) complex (1a-N₂O)^31c and the virtual Mn- and Cr-N₂O derivatives 1d, 1c that we present later. Among the 5-coordinate iron(II) complexants (L = N-4Py, 3 and Fe(CN)₅³⁻, 8) there is some variation in the calculated ΔG_a values, but N₂O-binding appears to be somewhat more favorable with these species, ΔG_a(av) = −0.4 (vac), +1.7 (CH₂Cl₂), relative to the planar derivatives. The strongest predicted iron(II)–N₂O complexant is 5-coordinate [(N-4Py)Fe]²⁺ (3), ΔG_a < −6.3/−6.8 kcal mol⁻¹ (vac/CH₂Cl₂). As to the origin of this expected affinity, we note the differences in both charge (2+), coordination number (5) and favored spin state (singlet) vis a vis the other 4- and 5-coordinate iron(II) species, which usually have triplet- or quintet ground states.⁵⁴ Based on the set of iron(II) complexants considered here, 5-coordinate, square pyramidal, low spin complexes should bind most favorably to N₂O. Another interesting feature of the Group II data in Table 1 is the much smaller difference in binding free energy between the N- and O-bound adducts of the high spin species, ΔG_N/O ±2 kcal, when compared to the known/implicated (Group I) and low spin N₂O complexes, ΔG_N/O 6–25 kcal favoring the N-bound isomers. This smaller N/O-binding selectivity among the high spin adducts also parallels their similar and longer metal-O,-N bond lengths and bent geometries compared to the low spin linear M–N₂O adducts, e.g. in Fig. 7 and 8.

Table 2 Energetics of O-transfer via mono and bimetallic N₂O complexes^a

LM fragment^b	ΔGa LM(O̲N2)(ML) (kcal mol^−1)	(kcal mol^−1)	(kcal mol^−1)	ΔGOT (kcal mol^−1)
a B3LYP/D3/SMD-CH2Cl2, T = 298 K.b Superscripts indicate ground spin states of LM(ON2) or LM–N2O–ML and LMO respectively; spin state multiplicities: s = singlet, t = triplet, q = quartet, qn = quintet, sx = sextet.c O-bound isomer did not optimize.d Estimated energy barrier from two-dimensional M–O/N–O scans corrected for dispersion and solvation.e = free energy change from lowest energy intermediate to transition state.f
Monometallic
Fe(POR)^qn,t (9)	1.8	25.4	27.2	−24.1
Fe(DPDI)^t,t (15)	1.2	32.4	33.6	−21.0
Fe(N-4Pyr)^(2+)s,t (3)	2.0	27.2	29.2	−36.5
Fe(salen)^qn,t (12)	2.2	31.8	34.0	−19.1
Fe(N-3Pyr)^(−)qn,qn (1b)	—^c	—^c	26.0	−29.9
Fe(N-2Pyr-Py)^qn,qn (2)	4.7	23.0	27.7	−27.1
Fe(TPM)Cl2^t,t (4)	2.0	31.7	33.7	−18.4
V(N-3Pyr)^(−)t,s (1a)	5.4	13.6^d	19.0^e	−114.9
Mn(N-3Pyr)^(−)sx,q (1d)	4.7	22^d	26.7^e	−67.2
Cr(N-3Pyr)^(−)qn,t (1c)	−1.7	2.6	0.9	−67.1
Cr(POR)(Py)^t,t (11)	3.4	5.6	9.0	−62.8
Cu(TPB)^s,t (5)	4.2	33.6	37.8	−4.8
Ru(POR)(THF)^s,s (10)	3.0	16.5	19.5	−47.4
Ru(salen)(imid)^s,s (13a)	3.3	17.3	20.6	−43.6
Ru(salen)Cl^d,d (13b)	3.5	21.2	24.7	−29.5
LM–N2O–ML Bimetallic			(bimet. adv.)^f
Fe(POR)^qn,t (9)	22.0 (μ-bent)	1.7	23.7 (−3.5)	−24.1
Fe(DPDI)^qn,t (15)	20.1 (μ-bent)	2.2	22.3 (−11.3)	−21.0
Fe(salen)^qn,t (12)	3.2 (μ-linear)	22.6	25.8 (−8.2)	−19.1
	21.7 (μ-bent)	4.1	25.8 (−8.2)	−19.1
Cu(TPB)^s,t (5)	2.0 (μ-linear)	18.0	20.0 (−15.6)	−4.8
Ru(salen)(im)^s,s (14a)	−2.6 (μ-linear)	4.7	2.1 (−18.5)	−43.6
Ru(salen)Cl^d,t (14b)	11.8 (μ-bent)	−0.5	11.8 (−12.9)	−29.5

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The binding affinity data for a set of similarly ligated, non-ferrous metal complexants (Group III) are also provided in Table 1. For the (salen)Ru(imid) relative 14b in its most stable singlet state, the ΔG_a for N₂O is exergonic, −3.7 (vac) and −1.5 (CH₂Cl₂) kcal mol⁻¹, in contrast to that of its high spin, iron relative (ΔG_a =+3.6 kcal mol⁻¹). Higher oxidation state d⁵-(L)Ru(III)Cl derivatives (e.g. L = POR, salen) were found to have lower N₂O affinities, ΔG_a for 13b-N₂O +3.6 (vac), +1.4 (D, solv) kcal mol⁻¹; for 9a-N₂O +6.6 (vac) and +10.1 (CH₂Cl₂) kcal mol⁻¹. The oxidation state effect on binding affinity illustrated here is consistent with the weak σ-donor, moderate π-acceptor character of N₂O and the more electron-accepting, weaker back-bonding character of Ru(III) vs. Ru(II). The last set of Group III complexants include derivatives of non-precious Mn, Cr and Cu. The (TPB)Cu singlet species (5) is calculated to form a relatively stable N-bound adduct, ΔG_a = −3.0 (vac) and −1.5 (CH₂Cl₂) kcal mol⁻¹, making it a good prospect for reactivity studies with N₂O. We note the proven ability of (TPB)Cu derivatives to bind weakly donating/pi-accepting substrates (CO, acetylene, ethylene).⁶¹ Our calculations suggest that N₂O-binding to (TPB)Cu (5) would be less favorable energetically than for the isolated [(R_FO)₄Al]Cu-N₂O (6).^31b The (POR)(Py)Cr(N₂O) species (11-N₂O), which is predicted to be a GS triplet, is calculated to have the strongest binding affinity to N₂O among the monometallic species considered here, ΔG_a = −12.0 (vac) and −14.5 kcal mol⁻¹ in CH₂Cl₂.

An indication that N₂O binding and activation may be facilitated more generally by low valent complexes of the N-3Pyr ligand is supported initially by our computational results for the M = V(III) (1a-N₂O) and Fe(II) (1b-N₂O) models of the complexes that react with N₂O at room temperature.^31c,60 The computational picture for the (N-3Pyr)Fe⁻/N₂O interaction is complicated; the more stable quintet fragment doesn't show high affinity for N-binding, ΔG_a +4 kcal mol⁻¹, while binding to the less stable triplet is very favorable, −6.4 kcal mol⁻¹ (for the N-bound isomer). Energy scans on the quintet LFe⋯ON₂ surface revealed no distinct LFe–O–N₂ minimum or TS (more later). N- and O-bound N₂O adducts could be optimized for the corresponding (N-3Pyr)Mn/N₂O system (1d-N₂O) in the most stable high spin (sextet) state but, again, the binding equilibrium with N₂O is unfavorable. As noted earlier, (N-3Py)Cr(N₂O)^t (1c-N₂O) optimized to the unusual bent/bent coordination modes for both the N- and O-bound species (Fig. 9). Moreover, both showed mildly exergonic binding to N₂O and with little expected N/O-binding selectivity as often seen for the high spin complexants. This system provides a unique example of likely favorable N₂O-binding with little expected N/O-selectivity. Could an O-bound N₂O complex be produced selectively in this case? Our computational results, combined with experimental support from the N₂O interactions with (N-3Pyr)-V^31c and -Fe⁶⁰ suggest a special ability of low valent M(N-3Pyr) species to react with and transform N₂O (vide infra). Considering the computational results summarized with this set of ligands, the following metal-dependent binding affinity order is predicted based on ΔG_a: LCr(II) > LRu(II) > LV(III) > LFe(II) ≈ LMn(II) ≈ LCu(I). This ordering of binding affinity correlates with M–N₂O or M–ON₂ bond strength and roughly parallels the oxidation potentials and electronegativity trends among the free metal ions. Since N₂O is a weak σ-donor/strong π-acceptor, stronger binding will result with stronger pi-donating (back-bonding) and weak acceptor complexants – i.e. earlier TMs in lower oxidation states, e.g. Cr(II), V(III) > Fe(II), Mn(II), Cu(I) and second row > first row transition metal moieties, e.g. Ru(II) > Fe(II).

O-transfer to metal

To facilitate N–O scission one presumes that a potential monometallic complexant, LM, would bind to N₂O via the O-atom, producing LM(η¹-O̲N₂). From the O-bound complex, O-transfer to the metal would proceed via O–N bond-breaking (and O–M bond-making) to yield the O=ML species with N₂ dissociation. Transition states (TSs) for O–N scission for each of the selected complexants (in their ground spin states) were located by 1D or 2D ModRedundant scans along the O–N and/or O–M coordinates followed by Berny TS optimization. A set of representative TSs located by this approach is displayed in Fig. 12. Each of these species shows a bent O–N₂ unit with a considerably elongated O–N distance (1.26–1.57 Å) relative to its precursor N₂O complex (see e.g. Fig. 7) and to free N₂O. The TS structure for (N-3Pyr)Cr(O-N₂)⁻* (Fig. 12) showed shorter Cr–O (1.90 Å) and longer O–N (1.57 Å) bond lengths compared to its precursor 1c-ON₂; 1.92 Å, 1.37 Å; (Fig. 9), as expected for continuation of N–O scission en route to (N-3Pyr)CrO⁻ and N₂. The variable length of the cleaving N–O bonds in these TSs (Δ_O–N 0.30 Å) is substantial and not obviously correlated with the corresponding activation energies from the precursor LM–ON₂ complexes (vide infra). It is noteworthy that among these, two dihedral M–O⋯N–N conformations, syn and anti, are displayed.

Fig. 12 Transition state structures for monometallic LM–O⋯N₂*.

Some insight into the electronic and bonding changes that occur in transforming the O-bound intermediates to their transition states is provided by analyzing the change in atomic charges and frontier molecular orbitals (FMO). As an example, for the (salen)Fe–ON₂ to (salen)Fe–O⋯N₂* transformation, the APT (Atomic Polar Tensor)⁶² charge distribution within the Fe–O–N–N unit changes are: Fe +1.34 to +1.43, O +0.56 to −0.24, N1 +0.76 to −0.05, indicating partial iron oxidation and O- and N-reduction. Further conversion to the products, (salen)Fe=O^qn and N₂, show further redox changes: Fe +1.54 (oxidized), O −0.45 and N 0.0 (reduced). In Fig. 11 we show selected FMOs with important contributions to Fe–O–N–N bonding and their energies for the same conversion. For (salen)Fe(η¹-ON₂): SOMO-5 is weakly Fe–O π-bonding (π), O–N is π-antibonding (π*) and N–N is π, while SOMO-6 is Fe–O σ, O–N π* and N–N π. For (salen)Fe(η¹-O⋯N₂)*: SOMO−5 is Fe–O π, O–N π* and N–N π, while SOMO-8 is Fe–O σ, O–N π* and N–N π. The lower energy (stabilization) of these FMOs in the TS relative to the reactant LFe(ON₂) intermediate thus increases the Fe–O and N–N bond orders and decreases the O–N bond order. This is consistent with the electron flow suggested by the APT analysis and the bond-making/breaking represented in the simple valence bond picture of Fig. 13c. The valence electron pair model is an oversimplification, however, given the likely open shell electronic state of (12-ON₂) and most of the other iron(II) complexes.

Fig. 13 Correlated FMOs involved in Fe–O–N₂ bonding and their relative energies (Hartree) for (a) (salen)Fe(O-N₂)^qn; (b) TS (salen)Fe(η¹-O⋯N₂)*; (c) the valence bond representation of electron flow during LMO⋯N₂ scission.

The structural and energetic viability of bimetallic N₂O coordination and promotion of N–O cleavage was also evaluated. Among the several bimetallic N₂O-complexes optimized previously (Fig. 11 and Table 1), we located and optimized most of their transition state structures. Two representative examples are shown in Fig. 14. For both the salen-iron (12-N₂O-12) and the related ruthenium species (14b-N₂O-14b), one finds bent M–N₂O–M units and very long N–O distances indicative of advanced N–O bond-breaking in a very late transition state. Comparison of the iron bimetallic intermediate 12-N₂O-12 (Fig. 11) to the corresponding TS (Fig. 14) shows longer N–O distances (1.37 vs. 1.58 Å) and shorter N–N (1.19 vs. 1.15 Å) and Fe–O (1.95 vs. 1.88 Å) lengths in the TS, as expected for progress along the reaction coordinate to the products- LFe=O, LFe and N₂. Similar changes are found for the Ru-intermediate (14b-N₂O-14b) and TS (SI).

Fig. 14 Transition state structures for (salen)Fe-N₂O-Fe(salen)*^qn and (imid)(salen)Ru-N₂O-Ru(salen)(imid)*^s.

Energetics of O-transfer to mono-metallic species

Free energies for the optimized structures of intermediates and TSs for the O-transfer to LM are tabulated in Table 2 based on the pathway: LM–O–N₂ and LM–N₂O–ML to LM=O (+LM) + N₂. Key results and trends for the monometallic complexants are summarized first. For most of the mono-LFe(II) complexes the overall reaction free energy ΔG_OT is moderately to highly exergonic (−13 to −36 kcal/mole) and the affinity for O-binding is modest (ΔG_a +1–5 kcal mol⁻¹). The activation energies for O–N cleavage of LFe–O–N₂ generally are moderate to high, ranging from 23–32 kcal, with the corresponding energy span barriers, ,⁶³ (from LM + N₂O) being slightly higher, 25–34 kcal mol⁻¹. The pyramidal N-2Pyr-Py ligand confers a somewhat lower activation energy to its iron(II) complex 2-ON₂ (23 kcal mol⁻¹) and a lower energy span barrier (27.7 kcal mol⁻¹) than do the various planar ligands. The consequences of the calculated energetics for these species are that generation of potentially reactive oxido-metal intermediates, LFe(IV)=O, should be practically viable at moderate to relatively high temperatures, e.g. 100–150 °C.⁶⁴

The (N-3Pyr)M platform has two representatives, M = V and Fe, with experimentally demonstrated N₂O reactivity, the former providing an isolable (N-bound) complex^31c and the latter deoxygenating N₂O readily.⁶⁰ Therefore, we sought to analyze these and two unknown congeners computationally, M = V (d²), Cr (d⁴), Mn (d⁵) and Fe (d⁶). The (N-3Pyr)M(O-N₂) complexes have large to huge calculated exergonicities for the O-transfer reaction to produce (N-3Pyr)M=O⁻ (>−30 to −115 kcal, Table 2). B3LYP calculations predict that all but the (N-3Pyr)Fe derivatives change ground spin states (GSS) between the LM–ON₂ reactant and product LM=O: i.e. V, T/S; Cr, Q/T; Mn, Sext/Q. This set of complexes provided significant computational challenges to locate well-defined LM–O–N₂ intermediates and transition states, and complicated by these spin-state changes.⁶⁵ The (N-3Pyr)Fe⁻ complexant 1b is the exception here as both LFe(O-N₂) and LFe=O are calculated as GS quintets. However, a discreet (N-3Pyr)Fe-ON₂^qn intermediate was not found, but a true TS on the quintet surface was located displaying typical features of the transforming M–O–N₂ unit, i.e. the bent linkage and elongated O–N distance (1.46 Å, Fig. 12). A moderate activation barrier, of 26.0 kcal mol⁻¹ (from the unbound complexant + N₂O) is found, consistent with the experimentally observed facile reaction of [N-3(Mes-Pyr)]Fe⁻ with N₂O.⁶⁰ The association of N₂O and O-transfer conversion process in this case appears to be essentially concerted. While N-binding of N₂O to the triplet V-derivative (1a) is exergonic (ΔG_a −1.4 kcal), consistent with its experimental isolation,^31c O-binding is unfavorable (ΔG_a +5.4 kcal). The lowest energy pathway from the ground state triplet of (N-3Pyr)V(η¹-ON₂) (1a-ON₂) to the GS singlet of (N-3Pyr)VO (+N₂) is unclear. One dimensional and 2D scans along the V–O and O–N distances of (1a-ON₂)^t towards LVO^t increase in energy with a maximum at about 20–24 kcal and then descend toward the triplet product +N₂ without a verifiable TS (SI). A TS could be located on the singlet surface with a moderately large activation energy, , but given the extraordinary exergonicity overall to produce the singlet LVO species (>100 kcal mol⁻¹), it seems probable that as the triplet LV–O⋯N₂ maximum is approached there is spin crossover to the singlet surface as the energy plunges to the singlet product with N₂ dissociation. The O–N scission process for the hypothetical (N-3Pyr)Mn-ON₂⁻ formulated as a GS sextet, is similar to the vanadium relative, with unfavorable binding (ΔG_a +4.7 kcal). Like the LV(O-N₂) OT conversion, two-dimensional O–N and Mn–O coordinate scans from the (N-3Pyr)Mn-O-N₂⁻ sextet rose energetically through a maximum that did not optimize to a legitimate TS. The species at the spin crossover point to the quartet surface of the product, when compensated energetically with thermal/frequency, dispersion and solvent corrections, led to an approximate maximum with an estimated of a moderate 22 kcal mol⁻¹. In contrast, as noted earlier, the O-bound (N-3Pyr)Cr-ON₂ intermediate (1c-ON₂) could be optimized (Fig. 10) and showed a rare favorable binding energy for both the N- and O-bound isomers (ΔG_a −3.6, −1.7 kcal). From 1c-ON₂ a true TS was located (Fig. 12) with a remarkably small activation energy ΔG* = 2.6 kcal and a highly exergonic overall O-transfer energy (−67 kcal mol⁻¹). After mounting this negligible barrier, presumably spin crossover to the GS triplet of the product (N-3Pyr)Cr=O would occur. The Cr(II) complexant 1c is thus predicted to readily deoxygenate N₂O to generate the potentially reactive (N-3Pyr)Cr(IV)(O)⁻ species.⁶⁶ The other Cr(II) species (POR)(Py)Cr^t (11) is calculated to have modest affinity for O-bound N₂O (ΔG_a +3.4 kcal), but it too was found to have a low activation energy and energetic span barrier, 5.6 and 9.0 kcal mol⁻¹ respectively for N–O scission via an early TS (Fig. 12). This low barrier prediction is in accord with the reported ambient deoxygenation reaction between N₂O and (TMP)Cr/N₂O.⁶⁷ These Cr(II) derivatives constitute attractive systems for further experimental reactivity studies with N₂O (and with oxidizable substrates). In contrast, the late first row metal complexant Cu(TPB)^s (5) was found to have a modest O-binding affinity for N₂O (ΔG_a +4 kcal mol⁻¹), a rather large activation energy of 33.6 kcal ( 37.8 kcal), and a comparatively small exergonicity for the overall O-transfer reaction (ΔG_OT −4.6 kcal), probably because of the instability of the incipient late metal (TPB)Cu–O oxido/oxyl species.⁶⁸

Among the LRu(II,III) species evaluated we found highly exergonic reaction energies (ΔG_OT > −40 kcal mol⁻¹) for the two Ru(II) derivatives L = POR/imid (10a), salen/imid (14b) and a moderate one (ΔG_OT −29.5 kcal mol⁻¹) for the Ru(III) derivative 14a (producing a (POR)ClRu(V)O species). Although the ΔG_a values to form the LRu^II-O̲N₂ intermediates are somewhat unfavorable (ca. +3 kcal mol⁻¹; Table 2), the activation barriers of 16.5 and 17.3 kcal mol⁻¹ and a of ca. 20 kcal mol⁻¹ for N–O cleavage are 10–15 kcal mol⁻¹ lower than for the corresponding (POR, salen)Fe(II) species. This substantial barrier lowering, predicts far more facile O-transfer reactivity with N₂O for planar LRu(II) species, which is consistent with the room temperature reaction of Ru(POR)(THF) with N₂O to produce (TMP)RuO₂.³⁶ The corresponding (salen)Ru(III)Cl species 14a shows a comparable binding energy ΔG_a to the Ru(II) species, but displays a significantly higher activation energy for O-transfer, and . These barriers for LRu(III) are still about 5 kcal mol⁻¹ lower than for the analogous Fe(salen) complexant.

The activation barrier trend among the set of complexants based on the metal ion is as follows, : Cr(II) ≤ Ru(II) < Ru(III) < Fe(II). With one apparent exception, the ligand effects on the ease of O–N scission are modest: for the planar ligands: salen ≈ POR ≈ DPDI ≈ salOpr. Anionic complexes of the pyramidal (N-3Pyr)M⁻ (M = Fe, Mn, Cr) generally are calculated to facilitate N–O scission, ranging from 1–25 kcal mol⁻¹.

Energetics of O-transfer in bimetallics

We now consider the energetics of N₂O binding and N–O O-transfer to the set of selected bimetallic complexes. Note firstly that the exergonic overall O-transfer reaction energy of the mono-metallic counterparts is the same for the pathway through the bimetallic analogs (same net chemical change). With the (salen)Fe species formation of the linear bimetallic complex with N₂O was nearly thermoneutral ΔG_a = +1.1 kcal mol⁻¹, suggesting some possibility for its detection/isolation. This prediction is supported by preliminary experimental observations in our laboratory in which (salen)Fe (12)^54f was found to react with N₂O (5 atm, CH₂Cl₂, rt) as indicated by a burgundy to rust color change and formation of a rust-colored precipitate. Positive ion ESI-MS of the isolated solid showed a prominent ion cluster with a 2Fe isotope pattern centered at m/z of 689.0782, consistent with a formulation of (salen)Fe-N₂O-Fe(salen) + H⁺ (see SI). Formation of the bent N₂O-bridged bimetallic complexes with all three planar ligands (e.g. 9, 12, 15; Fig. 10) is calculated to be highly endergonic (ΔG_a +20–22 kcal mol⁻¹), so that detection or isolation of such iron complexes is therefore improbable. These high energy bent-bridged intermediates were very close structurally and energetically to the corresponding transition states for N–O scission. Thus, the for N₂O-bridged 9, 12 and 15 were remarkably small (1.7–4.1 kcal) with total activation energy spans in the moderate range of 22–27 kcal mol⁻¹. The barriers for O–M cleavage via the bimetallic complexes are seen to be uniformly lower, −3.5 to −11 kcal mol⁻¹, than those for the corresponding mono-metallic derivatives, LFe(O-N₂), an energy benefit that we term the ‘bimetallic advantage’, offering a lower energy pathway for N–O cleavage. For the late first row metal species, (TPB)Cu (5), the bimetallic energy advantage via 5-N₂O-5 is especially large, 15.6 kcal mol⁻¹ (Table 2), facilitating O–N scission, but this is accompanied by a rather small exergonicity to cleave to the copper-oxyl LCu-O (+LCu(I) + N₂). This probably reflects the instability of late TM oxido/oxyls.⁶⁸

Finally, among the selected Ru(II) and Ru(III) complexes, Ru^II(salen)(im)^s (14b) features exergonic N₂O binding to form the linear N₂O-bridged bimetallic 14b-N₂O-14b (ΔG_a −2.6 kcal), a remarkably low activation energy ΔG* of 4.7 kcal mol⁻¹ for N–O scission, and a large overall O-transfer exergonicity (−43.6 kcal mol⁻¹). These features, coupled with the very large bimetallic advantage for this system, suggest that the bimetallic N–O cleavage pathway should be especially favorable here relative to the monometallic mechanism. This possibility has been suggested by Groves³⁶ for the N₂O/Ru(TMP) reaction and by Schomaker²¹ in the (TMP)RuO₂-catalyzed N₂O-based alkene epoxidation, but without direct experimental evidence. We note that the entropic price that is paid in forming the bimetallic N₂O-complex is more than counterbalanced by a favorable enthalpic benefit in the N–O cleavage step. This could be a general effect for many metal complexants, as supported by the several examples in Table 2. Finally, we note the bent bimetallic LM–N₂O–ML TSs (above) and the bent chromium monometallic (N-3Pyr)Cr–O–N₂* species are very similar both structurally in the metal–O–N₂ metrics and energetically – with all having very low activation barriers of 5–6 kcal mol⁻¹.

Energy profiles for O-transfer pathways

In this last section we display representative reaction energy profiles for the N₂O-transfer reactions of selected complexes in Fig. 15. The reaction pathway in the graphic begins with the N₂O O-coordination by the metal complexant to either the monometallic or bimetallic complex, followed by the O–N cleavage step via a transition state (ΔG*) and conversion to the oxido-metal LMO and N₂. Included in Fig. 15 are two planar mono-Fe species, Fe(POR) (9) and Fe(salen) (12), showing relatively high activation energies for the LFe–O–N₂ cleavage step (27–36 kcal mol⁻¹), with the (POR)Fe species having a somewhat lower barrier. A comparable O–N cleavage barrier (28 kcal mol⁻¹) is seen with the Fe-derivative of the non-planar N-2Pyr-Py ligand (2). The pyramidal (TPB)Cu (5) has a high barrier (38 kcal mol⁻¹). On the other hand, the unknown Cr(N-3Pyr)⁻ species (1d) shows slightly exergonic N₂O coordination, followed by a remarkably low O–N scission barrier (ca. 1 kcal), reflecting the combined effects of an activating ligand and a strongly reducing metal center. The Cr species 1d also shows the largest overall exergonicity for O-transfer among the monometallic complexants. Also illustrated in Fig. 15 is the substantial decrease in the O–N cleavage barrier that accrues to the LFe(II) (L = salen) and LCu(I) (L = TPB) species via bridged bimetallic coordination, ΔΔG* ca. 10–15 kcal mol⁻¹. The bimetallic advantage is gained mostly from facilitating the O–N scission step.

Fig. 15 Energy profiles for the O-transfer reaction pathway of N₂O with selected ligand–metal complexants. Complete energetic data is provided in Table 2.

Conclusions

DFT calculations have been utilized on several transition metal complexants, LM, M = Fe^II, Mn^II, Cr^II, Ru^II and Cu^I, with common 4/5-coordinate ligands to assess their N₂O binding affinity and the energetics of N–O cleavage to LMO. The key take home lessons from this study are: (1) the N₂O binding affinities (ΔG_a) range from as high as −5 kcal mol⁻¹ to moderate (ΔG_a ca. 0 kcal) to low (ΔG_a > +5 kcal mol⁻¹) in the order Ru(II) ≥ Cr(II) > Fe(II), Mn(II) for a variety of 4- and 5-coordinate N,O-donor ligands; (2) N-binding of N₂O is generally more stable than O-binding (ΔΔG_a 1–10 kcal mol⁻¹), with the N,O-selectivity decreasing with increasing spin multiplicity of the complexant; (3) N₂O-binding and cleavage is modestly favored by pyramidal ligands; (4) monometallic O-bound complexes LM–ON₂ generally undergo O–N cleavage with moderate-to-high activation energies, ΔG* 23–40 kcal mol⁻¹; (5) detectable bimetallic linear μ-N₂O complexes are energetically viable; (6) the higher energy bent bimetallics feature very low activation energies for N–O cleavage, 1–5 kcal mol⁻¹; (7) the total activation span energy for bimetallics, ca. 20–30 kcal mol⁻¹, averages 5–8 kcal mol⁻¹ lower than for monometallic complexants, providing a lower energy pathway for N–O scission.

Based on this computational study we suggest that monometallic LCr(II) and pyramidal L′Fe(II) and Mn(II) (L′ = N-3Pyr, N-4Py), and (TPB)Cu are among the best prospects for forming isolable/detectable LM–N₂O complexes for first row TMs since they have near zero ΔG_a. Binding should be enhanced at low temperatures (which minimizes the TΔS term on ΔG) and with high pressures (>concentration) of N₂O. Isolation of linear N₂O-bridged bimetallic complexes are also possible for many of these complexants and with the planar LM species. We envision that the deployment of tethered binucleating ligands could further stabilize these by minimizing the entropic cost in the N₂O-association step. The computational evidence for a bimetallic energy advantage for N–O scission supports a role for multi-centered catalysis in metal-zeolite and N₂OR catalytic processes of N₂O. Experimental investigations are underway with a collaborative team at the University of Oklahoma and Toulouse University (FR) to test the efficacy of these high priority systems for reactivity with N₂O and to design next generation complexes that facilitate N–O cleavage through bimetallic activation. Finally, we will report soon on the second phase of the development of nitrous oxide based catalytic oxidations, focusing on identifying the pathways and energetics of hydrocarbon reactions with N₂O-derived oxo-metals.

This contribution provides a number of fundamental, broader insights into the potential development of catalytic reactions of nitrous oxide. Structure–reactivity relationships have been established for several activating metal–ligand complexants (LM) with favorable N₂O binding (the first step in activation/catalysis) and for N–O bond scission leading to oxidizing LM=O species. By evaluating the O–N scission via likely experimentally undetectable N₂O̲–M bonded species, we have identified LCr(II) agents that should adopt novel bent M–O̲–N₂ structures with very low barriers to N–O scission. We also documented the energetic benefits of bimetallic complexants for N₂O binding and N–O cleavage, underscoring the importance of bifunctional activation in FLP-systems, the Cu-enzyme nitrous oxide reductase (N₂OR) and Cu-zeolite diesel N₂O-abatement (heterogeneous) catalysts and (4) we document the influence of the spin states of first-row transition metal complexants on reactivity—an aspect that has only recently been addressed in a few DFT reactivity studies and is relevant to natural and synthetic metallohydroxylases. Moreover, the study advances sustainability and green chemistry by identifying prospective earth-abundant catalysts for N₂O-based oxidations, which, to date, have only been demonstrated with a precious metal (Ru). Finally, the insights into nitrous oxide reactivity—a potent greenhouse gas and underutilized chemical resource—is of significant interest to the catalysis community and may contribute to a deeper understanding of catalytic design strategies.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6dt01002d.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

K. N. is grateful for partial support of this project from the National Science Foundation (CHE 1566213 and 2535175), from an A. C. Cope Scholar Award and from the University of Oklahoma (Faculty Development Award and the OU Supercomputing Center for Education and Research). Helpful inputs and discussions with Drs I. Sharma and Y. Shao and Messrs. Chance Lander and Deacon Herndon are also gratefully acknowledged.

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