N2O Formation via Reductive Disproportionation of NO by

Mar 14, 2017 - Synopsis. The mechanism of the disproportionation reaction of nitrogen monoxide (NO) to form N2O, catalyzed by 3,5-substituted tris(pyr...
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N2O Formation via Reductive Disproportionation of NO by Mononuclear Copper Complexes: A Mechanistic DFT Study Sebastian Metz* Scientific Computing Department, STFC Daresbury Laboratory, Daresbury, Warrington, U.K. S Supporting Information *

ABSTRACT: The mechanism of the copper(I)-mediated reductive disproportionation reaction of NO to form N2O was investigated for five different 3,5-substituted tris(pyrazolyl)borate copper complexes (CuTpR1,R2) by means of DFT calculations. A thorough search of the potential surface was performed, using the B3LYP functional with the def2-SVP basis set for optimization purposes and def2-TZVP single-point calculations for constructing the potential energy surface for two of these complexes. The results can be condensed into six competing reaction mechanisms, two of which were more closely investigated using full def2-TZVP optimized potential and free energies. The results consistently predict the same mechanism to have the lowest overall barrier. For all five different complexes, this is found to be in good agreement with the experimental reaction barriers. The key intermediate for the transition from the N-bound reactant to the O-bound product contains a stable (NO)3 unit with one N−Cu and one O−Cu bond, which was not included in the mechanistic considerations reported in the literature. Further analysis of the charge distribution and the spin density demonstrates the formation of a Cu(II)−(N2O2−) intermediate and the electronic influence of the different ligands.

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INTRODUCTION Nitric oxide (NO, aka nitrogen monoxide), its nitrosyl complexes, and its reactivity with various metal centers,1,2 as well as its disproportionation properties, are of great importance in many inorganic and biochemical reactions.3−5 While the conversion of three NO into N2O and NO2 has a thermodynamic driving force of ΔG° = −24.9 kcal/mol,2 it is kinetically hindered and catalysts, mostly in the form of transition-metal (TM) reaction centers (of Mn,6,7 Fe,8,9 Ru,10−12 Co,13−16 Ni,17,18 Pd,19,20 and Cu21−23) are required for this transformation. Based on the measured kinetics and isolated intermediates, potential reaction mechanisms have been postulated, but so far a mechanistic study presenting a complete mechanism with all intermediates is lacking. The current study therefore uses quantum mechanical calculations to test the postulated intermediates and their importance for the reaction mechanism, focusing on the reactivity of 3,5substituted tris(pyrazolyl)borate copper complexes (CuTpR1,R2, see also Scheme 1).22−25 For these particularly well-investigated complexes, three different potential pathways (Mechanisms A− C, see Scheme 1) have originally been postulated.22 The kinetic measurements23 show a pseudo-first-order reaction mechanism with respect to CuTpR1,R2, which excludes mechanism C as a viable option. No distinction, however, is possible between mechanisms A and B. Structural, electronic, and kinetic data (kobs2) of five different CuTpR1,R2 species has been obtained from FTIR, EPR, NMR, and UV−vis spectroscopies,23 which allows the mechanism of each individual species to be studied as well as the relative trend between different species, including steric and electronic influences. © 2017 American Chemical Society

Scheme 1. Potential Reaction Pathways for Disproportionation Reactivity of TpR1,R2Cu-NO Reacting with Two Additional NO Moleculesa

a

Mechanism A assumes the ligand arm remaining attached to the copper throughout the reaction, mechanism B involves reduced coordination number at the copper center before the reaction continues and mechanism C involves two copper centers, but could be ruled out by experiments.

For the CuTpR1,R2 systems, only the reactant structure (the N-coordinated nitrosyl complex 1, see Scheme 2) and the Received: October 21, 2016 Published: March 14, 2017 3820

DOI: 10.1021/acs.inorgchem.6b02551 Inorg. Chem. 2017, 56, 3820−3833

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Scheme 2. Stable Minimaa on the Potential Surfaces with Structures Containing One (1−3), Two (4−11), and Three NOs (12− 18, 20), a Copper-Oxide Intermediate (19), and Finally Three Different Nitrite Complexes (21−23)

a Relative energies (in kcal/mol) given for the CuTpCF3,CH3 (blue) and CuTpCH3,CH3, complexes (red). Structures 10 and 13 are not stable minima for CuTpCH3,CH3.

product (the η2-O-coordinated nitrate complex 22) are observed crystallographically.22−24 To convert the former to the latter, two additional NO molecules are needed together with three distinctive bond-forming/bond-breaking events, as shown in Figure 1: We have to (a) break one N−O bond, (b) form a new N−N bond (the one in N2O), and (c) form a new N−O bond (the one in the NO2 fragment). At the same time, the coordination of the copper center changes from Ncoordinated to O-coordinated. On top of the above-described disproportionation (three NO forming a N2O and a NO2 fragment) an electron transfer from the copper center to the

attached NO2 occurs, resulting in an oxidized Cu(II) and a reduced NO2− fragment,26 hence the definition as reductive disproportionation. The investigated group of CuTpR1,R2 complexes closely resembles the T2 center of copper-containing nitrite reductases (CuNiR, EC 1.7.99.3),27 which shows a distorted tetrahedral geometry, involving coordination from three nitrogen atoms (belonging to three histidine side chains) and one oxygen atom (belonging to a water molecule).28,29 For the CuNiR T2 center, numerous model compounds have been synthesized, containing the [Cu(I)−NO]+ unit,23,24,30,31 the [Cu(II)−(NO2−)]+ unit,23,32−45 and also a [Cu(I)−(NO2−)]0 unit.39,40,46−51 These model compounds provide valuable insights on other conformers and/or spin states of these structures. A recent review article by Merkle and Lehnert26 gives an overview of the binding and activation of NO and NO2− in CuNiRs and corresponding model complexes. While the binding of NO to the copper center in all model complexes is N-coordinated end-on,23,24,30,31 a side-on coordination of NO to the copper center has been reported for a crystal structure of CuNiR (PDB: 1SNR).29 While this finding has been questioned based on further experimental and theoretical results52 the latter show that a side-on complex is a stable minimum and that therefore other coordination patterns

Figure 1. Changes occurring during the copper-catalyzed disproportionation reaction: the copper center changes from Cu(I) to Cu(II), and its coordination changes from one coordinating nitrogen to two coordinating oxygen atoms. In addition, two new bonds are formed (one N−O bond within the NO2 unit and one N−N bond in the N2O unit), and one N−O bond is broken. 3821

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Scheme 3. Calculated Pathwaysa that Lead from the Initial, Nitrogen-Bound Form of NO (1) to One of the Three Different Nitrite Complexes (21−23)

a In total, six different mechanisms (A1−A6) were identified and are further described in the text. Mechanism A4 only exists for CuTpCF3,CH3, and for CuTpCH3,CH3, structure 10 is no stable intermediate; while that changes the reaction pathway in a specific detail, the general mechanism remains the same.

same ligand, Fe and Co both form dinitrosyl complexes,59 while Ni only forms a mononitrosyl complex.66 While no crystal structure containing an O−N−N−O unit is reported for copper, they exist for several other transition metals (all formally classified as hyponitrite, ONNO2−): A cis− O−N−N−O unit coordinating with both of its oxygen atoms (structurally analogous to 9) is dominant for electron-rich Ni18,67,68 and Pt68,69 complexes. A cis−O−N−N−O unit coordinating via both nitrogen atoms has been reported to bridge two Ru centers.11 Finally, a cis-hyponitrite complex including three Ni centers is reported to have both of the above features: both oxygen atoms coordinating to one Ni center, and the two nitrogen atoms bridging two different Ni centers.17 A trans−O−N−N−O unit coordinating to two Fe centers via the terminal oxygen atoms70,71 or to two Ru centers by one oxygen and the neighboring nitrogen. 72 No crystal structures

of the NO rather than just the N-coordinated end-on complex might play a role in the mechanism with CuTpR1,R2. For the investigated complexes, the NO2− binding to the copper center in η2-O-coordinated fashion (as in 22) is most stable.22,23 However, η1-O-coordinated (21) and η1-N-coordinated nitrite complexes (23) are also known for Cu(II) complexes from crystal structures (see ref 26 and refs therein). In its [Cu(I)−(NO2−)]0 form, the O2N−Cu(I)TpCH3,CH3 complex is in fact an η1-N-coordinated complex53 (23). All three different coordination modes therefore have to be considered as potentially viable intermediates. Crystal structures of dinitrosyl complexes as in 4 and 5 are reported for several first-row transition metals, namely, for V,54 Cr,55,56 Mn,57,58 Fe,59−61 and Co.59,62 While especially dinitrosyl iron complexes (DNIC) are very broadly investigated,63−65 this list lacks the late transition metals Ni and Cu. In that regard, it is particularly interesting to see that, for the 3822

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calculations (as before) and once with the unbound NO molecules being included in the calculations of the CuTp complexes as “spectator molecules”; representative pictures of these systems can be found in the Supporting Information. The energies and Gibbs free energies of these full systems are denoted Efull(def2-TZVP) and Gfull(def2-TZVP), respectively. For CuTpCF3,CH3 and CuTpCH3,CH3, the product-bound crystal structure23 of ONO-CuTpCF3,CH3 was used as the starting geometry and modified manually to obtain the intermediates 1−23. A broad range of scans to link these structures via transition states was performed; the extensive list of transition states (many more than reported in Scheme 3) that were located can be found in Tables S2 and S3. Some of the unsuccessful scans are mentioned in the Results Section. Additional NEB scans were performed to prove the barrierfree decay of 9 to the product. The mechanisms as summarized in Scheme 3 are defined by the six structures that can decay into the products (namely, structures 9, 13, and 15−18) and the lowest energy path from 1 to generate these intermediates; that is, the mechanisms have been defined a priori, based on all calculated structures. Based on these results, the key intermediates for the mechanism with the lowest barrier were calculated for the other complexes (namely, 1, TS1_7, 7, 15, TS15_22, and 22). For all CuTpMes,H and CuTpPh,Ph complexes, the crystal structure23 of (THF)−CuTpMes,H was used as starting geometry, and other intermediates were prepared manually from it. Similarly, the crystal structure23,25 of ON−CuTptBu,H served as the starting geometry for the intermediates of all CuTptBu,H complexes.

containing (NO)3 units are reported in the literature, indicating that these intermediates are transient and not very stable. Computationally, for the most fundamental Cu+ complexes with NO, [Cu(NO)x]+ (x = 1−5) structures and energetics have been reported.73−75 Apart from this, there are two main structures that have been investigated intensively for CuTpR1,R2 itself,25,76−78 or very similar systems,50,53,77,78 namely, the [Cu(I)−NO]+ and/or the [Cu(II)−(NO2−)]+ complex. This is due to the fact that these structures occur in the enzymatic reduction of NO2− to NO by CuNiRs, which has been the main focus in this area. Additionally, there are theoretical investigations related to the structure of the T2 center focusing on the influence of different solvent molecules,79 the NO coordination,80−84 and NO2− coordination patterns towards Cu(I) and Cu(II) at the T2 center of these enzymes.43,53,82,84−88 For the interaction of two NO molecules with a copper site, there are studies for an embedded Cu(I) in zeolites, (see refs 75 and 89−91 and refs therein) providing different coordination patterns at the copper center. But even for the extremely well investigated zeolite cases the experimentally observed disproportionation reactivity21 has not been investigated theoretically in form of a reaction mechanism. Apart from a much less exhaustive study on a model system for guanidine complexes92 that show a similar reactivity,93 no work has been published on theoretical studies dealing with the disproportionation reaction at a copper center. While the uncatalyzed disproportionation reaction of three NO to form N2O and NO2 has been addressed before,94 the current study makes a thorough and exhaustive attempt to characterize the energy potential surfaces along different routes of the coppercatalyzed disproportionation reaction. This ultimately provides the lowest-energy pathway including intermediates that are elusive to experiment.

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RESULTS AND DISCUSSION Structures and Spin States. Three different modes for NO to coordinate to the copper center were located: end-on with coordination via the nitrogen (1), side-on (2), and end-on with coordination via the oxygen (3), see Scheme 2. In agreement with the experimental findings,23,25 structure 1 is calculated to be the most stable nitrosyl complex. It is therefore chosen as the starting point for all the considered mechanisms. While crystallographic results of an end-on complex for CuNiR (PDB: 1SNR)29 do not stand undisputed,52 theoretical calculations confirmed the side-on complex 2 as a minimum on the energy potential surface.52,83 The energy difference between 1 and 2 for CuTpCF3,CH3 is calculated to be 7.0 kcal/ mol and therefore is in reasonable agreement with values reported in the literature for similar complexes.83 While 3 is 14.6 kcal/mol less stable than 1, from an energetic perspective, neither 2 nor 3 can a priori be excluded as potential intermediates. All three structures containing one NO unit (1−3) are doublet spin states in accordance with the literature for Cu(I)−NO complexes.25,83 Structures 4 and 5, which have been postulated as intermediates for the investigated mechanism,22,23 consist of two individual NO molecules coordinating to the copper center with the nitrogen side, one in cis orientation, the other in trans orientation. Attempts to find minima with either a mixed coordination (one NO coordinating with the nitrogen, one with the oxygen) or with both NOs coordinating with the oxygen were not successful. While structures 4 and 5 are relatively stable (6.1 and 9.2 kcal/mol for CuTpCF3,CH3), mechanistically they turned out to be a dead end. All attempts to make one of these two structures react with a third NO molecule caused one of the coordinated NOs to detach from the copper center and lead to either a cis- or a trans-ONNO structure (discussed below). To check regarding the coupling J of the two bound NO in these complexes, broken-symmetry calculations were performed for CuTpCH3,CH3, obtaining coupling constants of J = 1658.23 cm−1 for 4 (following the

COMPUTATIONAL METHODS

Initial structure optimizations were performed using the B3LYP hybrid functional95−100 (without RI approximation) in combination with the def2-SVP101,102 basis set as implemented in the ORCA package103 together with the COSMO methodology104 (using ε = 9.08 for CH2Cl2 as solvent). The B3LYP functional has been demonstrated to provide good results with a basis set of the same quality.87 Minimum structures were obtained from geometry optimization runs in ORCA, and transition-state structures of bond breaking/forming steps were obtained performing relaxed surface scans. In more complex cases we used the nudged elastic band method105 as implemented in the DLFIND106 geometry optimization package handled by ChemShell.107,108 For the CuTpCH3,CH3, CuTptBut,H, and CuTpCF3,CH3 complexes all stationary points were verified by numerical frequency calculations. For the CuTpMes,H and CuTpPh,Ph complexes, no frequency calculations were necessary, because the nature of the stationary points was easily identified based on the consistency of the structural key features with the aforementioned complexes. In addition, single points with a larger def2-TZVP102 basis set were performed at the optimized def2-SVP geometries. As mostly ΔE(def2-TZVP//def2SVP) will be provided in this article, they will for simplicity reasons be denoted only with ΔE, rather than with the full expression and if not stated otherwise are given relative to the energy of 1 (see Scheme 2) and free NO. The charge analysis was also performed using the def2TZVP basis set. Additional geometry optimization runs and numerical frequency calculations were performed at the def2-TZVP level of theory for CuTpCH3,CH3 and CuTpCF3,CH3. This allows the fully optimized ΔE(def2-TZVP) energies to be compared with the single-point energies ΔE(def2-TZVP//def2-SVP). These calculations were performed once with unbound NO molecules being treated in separate 3823

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Table 1. Relative Energies ΔE(def2-TZVP//def2-SVP) for the Mechanisms A1−A6 of the CuTpCF3,CH3 and CuTpCH3,CH3 Species Mechanism A1 CuTpCF3,CH3 CuTpCH3,CH3 Mechanism A2 CuTpCF3,CH3 CuTpCH3,CH3 Mechanism A3 CuTpCF3,CH3 CuTpCH3,CH3 Mechanism A4 CuTpCF3,CH3 Mechanism A5 CuTpCF3,CH3 CuTpCH3,CH3 Mechanism A6 CuTpCF3,CH3 CuTpCH3,CH3

1 0.0 0.0 1 0.0 0.0 1 0.0 0.0 1 0.0 1 0.0 0.0 1 0.0 0.0

TS1_7 11.2 9.9

TS1_2 10.4 TS1_2 10.4 8.8 TS1_2 10.4 8.8

7 10.2 4.7 TS1_8 11.7 8.8 TS1_8 11.7 8.8 2 9.2 2 9.2 7.0 2 9.2 7.0

14 7.0 0.4

8 8.7 1.6 TS2_3 16.3 TS2_3 16.3 16.8 TS2_3 16.3 16.8

TS14_15 9.6 2.0 8 8.7 1.6 16 5.7 −1.3 3 14.1 3 14.1 15.4 3 14.1 15.4

15 5.4 −0.6 16 5.7 −1.3 TS16_17 23.4 19.4 TS3_6 18.6 TS3_10 16.8

TS15_22 11.9 5.4 TS16_21 25.3 16.4 17 19.7 16.2 6 15.4 10 16.4

TS3_9

9

17.6

−1.6

Yamaguchi formalism109,110). In the trans orientation of the NOs in 5, this increases to J = 1731.32 cm−1. In both cases, the ferromagnetic coupling is therefore clearly favored. Coordination of a trans-ONNO unit to the copper center occurs via one oxygen atom (6, 15.4 kcal/mol), via one nitrogen atom (7, 10.3 kcal/mol), or via one oxygen and one nitrogen atom at the same time (8, 8.7 kcal/mol). Attempts to find minima with a trans-ONON unit were not successful. While it might be natural to expect a singlet spin state as electronic ground state due to the formation of an (NO)2 unit, comparisons between closed-shell singlet and broken-symmetry singlet and triplet spin states clearly show a triplet ground state. This is in agreement with previous calculations on similar Cu(I)-(NO)2 systems92 and can be rationalized based on the charge and spin distribution, as discussed at the end of the Results Section. In the most stable structure with a cis-ONNO unit, both oxygen atoms coordinate to the copper center (9, 4.82 kcal/ mol), analogous to the crystal structures of Ni18,67,68 and Pt68,69 complexes. Structures 10 (16.4 kcal/mol) and 11 (19.1 kcal/ mol) both coordinate via one oxygen atom. Structure 10, however, could not be located as a minimum for all ligands; with respect to the overall reaction, it is only of importance as an intermediate to generate 9. Like the trans-ONNO structures, the electronic ground state for these cis-ONNO structures is a triplet. While transition-state structures for the conversion of cis- to trans-N2O2 have been located (linking 8 and 9 as well as 6 and 11, see Supporting Information for details), they are energetically not competitive to a mechanism in which one NO unit dissociates and reassociates in the opposite orientation. The mechanisms discussed in the following therefore do not include any cis−trans conversion. With the exception of 12 (5.4 kcal/mol) with two N−N bonds formed, but no new N−O bond, all reported structures with three NO possess an Oa−Na−Nb−Ob−Nc−Oc unit, in which the Na−Nb and the Nc−Ob bonds have already formed, and only the N−O bond-breaking step is lacking to form the products (see Figure 1). Structures 12 (5.4 kcal/mol) and 14 (7.0 kcal/mol) cannot decompose into one of the products (21−23) but act only as precursor for structures 13 (17.6 kcal/ mol) and 15 (5.4 kcal/mol), respectively. This is in agreement with similar results reported for (NO)3− in water.111 While

22 −49.9 −56.3 21 −42.9 −49.5 TS17_22 25.0 18.0 12 5.4 TS3/10_9 17.8 17.6 TS3/9_11 20.2 14.3

22 −49.9 −56.3 TS12_13 20.3 9 4.8 −1.6 11 19.1 12.4

13 17.6 21 −42.9 −49.5 18 7.4 −0.9

TS13_21 26.3

21 −42.9

TS18_23 14.6 5.6

23 −46.0 −51.6

there are no reports of structures that contain Cu(NO)3 units (12−18) in the literature, comparison with higher spin states demonstrated the doublet to be the electronic ground state. In the quartet spin state, all investigated structures containing a Cu(NO)3 unit decompose into a triplet Cu(I)−(NO)2 system and a free NO. While there is no crystal structure proving the existence of a copper−oxo intermediate (19, 2.7 kcal/mol) in the literature, it has been postulated as intermediate for enzymatic reactions, see ref 112 and refs therein. A number of computational studies including high correlation calculations,113−117 dealing with the [Cu−O]+ unit, have demonstrated its triplet ground state. Results show, however, that the generation of 19 from structures with a Cu(NO)2 unit (namely, oxygen-coordinated N2O2 structures 6, 9, and 11) in this case is linked to prohibitively high barriers (see details provided in the Supporting Information). In that sense, the reaction mechanism is different from that of [Cu(I)TMPA]+, which reacts with two NO molecules to form N2O and a [TMPA-Cu(II)−O-Cu(II)TMPA]2+ dimeric complex.118 The calculations resulted in three different Cu(II)−(NO2−) species (21, 22, and 23), which can convert into each other. The discussed mechanisms therefore only present the formation of one of these three species. In agreement with the literature, structure 22 is the most stable of the three Cu(II)−(NO2−) species and has a doublet ground state, as confirmed by experimental22,23,87 and theoretical85,87 findings. Based on the above-mentioned findings, the following mechanisms for the conversion of structure 1 to one of the products can be established (see Scheme 3): Mechanism A1. The first step of mechanism A1 is the formation of an N−N bond in 7. The barrier-free formation of 14 establishes the Oa-Na-Nb-Ob-Nc-Oc bonding pattern, which binds to the copper center via a Cu−Nb coordination. Before the N−O bond is broken to release N2O, the (Oa-Na-Nb-ObNc-Oc) unit establishes an additional Cu−Ob interaction in 15 (being more stable than 14 by 1.6 kcal/mol for CuTpCF3,CH3 and by 1.0 kcal/mol for CuTpCH3,CH3) and then decays into product 22. For the CuTpCF3,CH3 species, TS15_22 is rate-limiting with a barrier of 11.9 kcal/mol, whereas for the CuTpCH3,CH3 species, a different rate-limiting step (TS1_7, 9.9 kcal/mol) is obtained, which is due to the stronger stabilization of intermediate 7. It is 3824

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molecule to form a new Nc−Oa/b bond and at the same time release N2O. For both the CuTpCF3,CH3 and the CuTpCH3,CH3 species, the transition state preceding formation of 9 (TS10_9/TS3_9) is ratelimiting for mechanism A5. The only difference is that for the CuTpCH3,CH3 species, intermediate 10 is not stable, and 3 directly converts into 9. The associated barriers are ΔE‡ = 17.8 kcal/mol for the CuTpCF3,CH3 species and ΔE‡ = 17.6 kcal/mol for CuTpCH3,CH3, see Table 1. Mechanism A6. Mechanism A6 starts as A5 with conversion of 1 to 3, the latter being 14.1 kcal/mol less stable than 1 for CuTpCF3,CH3 and 15.4 kcal/mol less stable for CuTpCH3,CH3. For the CuTpCF3,CH3 species, addition of NO forms a cis-N2O2 unit, with one O−Cu bond (in 11, 19.1 kcal/ mol). For the CuTpCH3,CH3, direct formation of 11 from 3 is not possible; formation of 11 (12.4 kcal/mol) proceeds via intermediate 9 (−1.6 kcal/mol) instead. In a barrier-free reaction, 11 can react with another NO molecule to form a new Nc−Ob bond in 18, resulting in more stable intermediates for CuTpCF3,CH3 species (7.4 kcal/mol) and the CuTp CH3,CH3 species (−0.9 kcal/mol). By increasing both the Nc−Ob and Na−Oa bonds and simultaneously decreasing the Nc−Oa distance, 23 and N2O are formed. For both the CuTpCF3,CH3 species and the CuTpCH3,CH3 species, the N−N bond formation is calculated to be ratelimiting, with a potential energy barrier of ΔE‡ = 20.2 kcal/mol for the CuTpCF3,CH3 species, and ΔE‡ = 17.6 kcal/mol for CuTpCH3,CH3, see Table 1. For mechanisms A1−A3, A1 can be identified as the main reaction route. While mechanisms A2 and A3 both proceed via intermediates with similar binding patterns as A1, their overall barriers are significantly higher than that of mechanism A1 and can be neglected in the discussion. From the mechanisms proceeding via the oxygen-bound nitrosyl complex (3), mechanism A5 has the lowest barrier and the second-lowest barrier after mechanism A1. Mechanisms A4 and A6 turned out not to be competitive and can be neglected in the discussion. This, so far, enables us to identify A1 and A5 as the major two competing reaction mechanisms, see Figure 2.

noteworthy that, for the CuTpCF3,CH3 species, TS1_7 is only 0.7 kcal/mol higher in energy than TS15_22; the difference in the rate-limiting step is therefore based on a fairly low energy difference that is within the accuracy of the used method. The energies of the stationary points along the reaction path are given in Table 1. Mechanism A2. Similar to mechanism A1, the first step of mechanism A2 is the formation of a N−N bond, resulting in structure 8, which is significantly less stable for the CuTpCF3,CH3 species (8.7 kcal/mol) than for the CuTpCH3,CH3 species (1.6 kcal/mol). The barrier-free formation of the more stable 16 (5.7 kcal/mol for the CuTpCF3,CH3 and −1.3 kcal/mol for the CuTpCH3,CH3 species) establishes the Oa-Na-N b-Ob-Nc-Oc bonding pattern, including a Cu−Ob interaction. Breaking of the Nb−Ob bond then generates 21 under release of N2O. For both the CuTpCF3,CH3 species and the CuTpCH3,CH3 species, the latter step is calculated to be rate-limiting for mechanism A2 with ΔE‡ = 25.3 kcal/mol for the CuTpCF3,CH3 species and ΔE‡ = 16.4 kcal/mol for CuTpCH3,CH3, see Table 1. Mechanism A3. Mechanism A3 starts out the same as mechanism A2. However, rather than a direct breakdown of 16 we see conversion into 17, in which there are now two Cu−O bonds present, Cu−Ob and Cu−Oc. This step, however, is highly endothermic by 15 kcal/mol for the CuTpCF3,CH3 and 17.5 kcal/mol for the CuTpCH3,CH3 species. Breakage of the Nb− Ob bond releases N2O to form 22. For the CuTpCF3,CH3 species, TS17_22 determines the reaction rate, whereas for the CuTpCH3,CH3 species, the transition state TS16_17 becomes rate-limiting. The energy difference between the decay barrier of TS16_17 and TS17_22 (23.4 vs 25.0 kcal/mol for the CuTpCF3,CH3 and 19.4 vs 18.0 kcal/mol) for the CuTpCH3,CH3 is quite small, though. See also Table 1 for the energies of all intermediates. Mechanism A4. For the CuTpCF3,CH3 species, mechanism A4 starts out with the conversion of the nitrogen-bound nitrosyl compex (1) via the side-on complex (2) to the oxygenbound nitrosyl complex (3), the latter being 14.1 kcal/mol less stable than 1. Addition of one NO molecule forms 6, in which due to its orientation, only one oxygen atom of the trans-N2O2 group can coordinate to the copper center. With addition of another NO molecule, 6 (15.4 kcal/mol) can transform barrierfree into 12 (5.4 kcal/mol), in which a second N−N bond is present. Reorientation of the NO unit forms the Oa-Na-Nb-ObNc-Oc bonding pattern, including a Cu−Ob interaction in 13, which can then decay into product 21. Based on the potential energy barrier of ΔE‡ = 26.3 kcal/mol for TS13_21, the latter step is rate-limiting, see Table 1. While intermediates 6 and 12 can be located for the CuTpCH3,CH3 species, attempts to locate 13 or the transition states TS3_6 and TS12_13 or a decay of 12 into one of the products failed. Mechanism A4 therefore does not exist for the CuTpCH3,CH3 species. Mechanism A5. Mechanism A5 starts as A4 with conversion of 1 to 3, the latter being 14.1 kcal/mol less stable than 1 for CuTpCF3,CH3 and 15.4 kcal/mol less stable for CuTpCH3,CH3. Addition of one NO forms a cis-N2O2 unit, which for CuTpCF3,CH3 first coordinates to the copper center by only one of the oxygen atoms (in 10, 16.4 kcal/mol) and then rearranges to coordinate via both oxygen atoms to the copper center (in 9, 4.8 kcal/mol). For CuTpCH3,CH3, structure 10 is not stable, and 9 (−1.6 kcal/mol) with both oxygen atoms coordinating to the copper center is formed directly from 3. The latter structure can react barrier-free with another NO

Figure 2. Reaction profile for the two most favorable mechanisms (A1 and A5) for CuTpCF3,CH3 and CuTpCH3,CH3. For clarity, the energies of the additional intermediates for mechanism A5 of CuTpCF3,CH3 (TS3_10 and 10) and all product structures (22 and 23) were omitted. 3825

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Table 2. Comparison of Potential Energies ΔE and Free Energies ΔG for the Mechanisms A1 and A5 of the CuTpCH3,CH3 and CuTpCF3,CH3 Species Mechanism A1 E(def2-SVP)a E(def2-TZVP/def2-SVP)a E(def2-TZVP)a Efull(def2-TZVP)b G(def2-SVP)a Gfull(def2-TZVP)b Mechanism A5 E(def2-SVP)a E(def2-TZVP/def2-SVP)a E(def2-TZVP)a Efull(def2-TZVP)b G(def2-SVP)a Gfull(def2-TZVP)b

1 0.0 0.0 0.0 0.0 0.0 0.0 1 0.0 0.0 0.0 0.0 0.0 0.0

TS1_7 7.3 9.9 9.7 9.8 19.2 13.3 TS1_2 8.7 8.8 8.8 9.0 8.4 10.6

Mechanism A1 E(def2-TZVP/def2-SVP)a Efull(def2-TZVP)b Gfull(def2-TZVP)b Mechanism A5 E(def2-TZVP/def2-SVP)a Efull(def2-TZVP)b Gfull(def2-TZVP)b

1 0.0 0.0 0.0 1 0.0 0.0 0.0

TS1_7 11.2 10.5 9.2 TS1_2 10.4 10.3 8.7

CuTpCH3,CH3 7 2.2 4.7 4.6 4.4 16.0 7.6 2 7.0 7.0 7.0 7.2 6.7 7.4 CuTpCF3,CH3 7 10.2 9.6 8.6 2 9.2 9.1 7.6

14 −3.9 0.4 0.2 −0.4 23.8 6.1 TS2_3 16.4 16.8 16.7 17.2 14.8 17.4

TS14_15 −2.6 2.0 2.1 1.5 24.9 8.0 3 14.6 15.4 15.2 15.6 12.8 13.7

15 −7.8 −0.6 −0.8 −1.4 21.3 6.3 TS3_9 14.8 17.6 16.8 16.7 25.6 15.9

TS15_22 −1.6 5.4 5.2 4.6 27.4 11.0 9 −5.7 −1.6 −1.8 −1.9 8.4 1.6

14 7.0 5.8 6.6 TS2_3 16.3 15.9 14.5

TS14_15 9.6 8.7 8.9 3 14.1 13.8 12.5

15 5.4 4.5 6.6 TS10/3_9 17.8 17.4 16.9

TS15_22 11.9 10.9 11.8 9 4.8 4.4 5.5

a As obtained from separate calculations of the CuTpCH3,CH3 complexes and NO molecules. bAs obtained after optimizing the structure of the CuTpCH3,CH3 complexes and the NO molecules as one structure/one calculation.

TZVP) and ΔEfull(def2-TZVP) of 0.6 kcal/mol for A1 and 0.5 kcal/mol for A5. When moving from potential energies E to Gibbs free energies G, changes in the relative energies are expected. As mentioned already in the previous section, the free-energy profile looks different when dealing with the CuTp R 1 ,R 2 complexes and unbound NO molecules in separate calculations, giving unrealistically high barriers for G(def2-SVP), see Table 2. For these calculations, mechanism A5 is calculated to be favorable with TS3_9 as the rate-limiting step. However, by including the unbound NO molecules in the same calculations as the CuTpR1,R2 complexes, the free-energy profiles based on Gfull(def2-TZVP) provide the same key features as the potential-energy profiles, with mechanism A1 (13.3 kcal/mol) being favored over A5 (17.4 kcal/mol) for CuTpCH3,CH3, see Figure 3. It should be mentioned that even the provided ΔGfull(TZVP) values are solely based on frequency calculations and should still be treated with some care. Qualitatively better free-energy barriers could be obtained from combined quantum mechanical/molecular mechanical (QM/MM) calculations,119−121 which simulate the reaction environment, that is, the solvent, in a more realistic fashion. This has been done for enzymatic reactions by first calculating a QM/MM potential surface and then sampling along the corresponding reaction paths using molecular dynamics.122−124 This approach, however, goes beyond the scope of this study and will be addressed in future work. The comparison of the potential energies with the Gibbs free energies as given in Table 2 demonstrates that we can analyze the experimental kinetics by means of the relatively inexpensive E(def2-TZVP//def2-SVP) values.

It is worth mentioning that the calculated free energies (see Supporting Information) seem to provide a different picture, favoring A5 over A1 and assigning a different rate-limiting step (TS15_22) for A1. This, however is because ΔG was obtained from separate calculations (see Computational Details) for the CuTpR1,R2 complexes and the NO molecules. The next section demonstrates that the free-energy reaction profile provides the same key features as the potential-energy profile, using the CuTpCH3,CH3 and CuTpCF3,CH3 species as examples. Potential Energy E Versus Gibbs Free Energy G. When analyzing the potential energy surface for mechanism A1, the energies change up to 7.2 kcal/mol when moving from E(def2SVP) to E(def2-TZVP//def2-SVP), see Table 2. Despite the rather large change in energy, the rate-limiting step remains the same (TS1_7). When fully reoptimizing the structures on E(def2-TZVP) level of theory, results change only marginally with respect to E(def2-TZVP//def2-SVP), with a maximum difference of 0.2 kcal/mol. For mechanism A5, the energies change much less than for A1 (only 2.8 kcal/mol) when moving from E(def2-SVP) to E(def2-TZVP//def2-SVP). However, these small changes in energy lead to different assignments of the highest barriers: TS2_3 (for E(def2-SVP), TS3_9 (for E(def2-TZVP//def2-SVP), or essentially the same barrier height for TS2_3 and TS3_9 (for E(def2-TZVP), the latter due to a change of 1.0 kcal/mol for TS3_9 when fully reoptimizing the structures at the E(def2TZVP) level of theory. As the changes at the full E(def2TZVP) level of theory are very small, it is justified to rely on the E(def2TZVP//def2-SVP) results. These results hold true as well when the unbound NO molecules are included in the calculation of the CuTpCH3,CH3 complexes, leading to a maximum change between ΔE(def23826

DOI: 10.1021/acs.inorgchem.6b02551 Inorg. Chem. 2017, 56, 3820−3833

Article

Inorganic Chemistry

providing the Löwdin125 and Mulliken126 partial charges. The comparison of the two different charge schemes reveals that, while the absolute values can differ significantly, the overall trend between them is fairly consistent, see Figure 4. The numerical values for the charges of the copper atom, each of the nitrogen and oxygen atoms, and the ligand as a whole can be found in Table S4 of the Supporting Information. While it is true that the partial charge on the copper center increases for the step from TS15_22 to 22, the final value is only marginally higher than that of some of the earlier structures. This contradicts the idea of a Cu(I)→Cu(II) conversion in the last step. Further confirmation originates from the spin density, which is shown in Figure 5: starting from the initial nitrosyl complex 1, the spin density at the copper center increases with formation of 7 and remains almost constant thereafter. In addition, it should be noted that the ligand plays an at least equally important role by donating a significant amount of charge density, again already at the early stage of the reaction (the strongest change is from 1 to 7, that is, before even the third NO molecule comes into play) with only minor changes afterwards. All this indicates a Cu(I)→Cu(II) transition from 1 to 7 and therefore a classification of the (NO)x units as (NO)2− and (NO)3− confirming suggestions that electron transfer might be one cause of the increased reaction rate in the coppercatalyzed mechanism.94 Based on these results it is worth mentioning that the reactivity of the different CuTpR1,R2 complexes depends on both electronic as well as steric effects. A common way to approach the latter would be to define the cone angle φ the CuTpR1,R2 complex offers the NO for attack.127 It turns out, however, that this provides only part of the full picture:

Figure 3. Reaction profiles (potential energies E and free energies G) for the two most favorable mechanisms (A1 and A5) of CuTpCH3,CH3. For clarity, the energies of product structures (22 and 23) were omitted.

Reaction Barriers. Based on the ΔE(def2-TZVP//def2SVP) potential energies, mechanism A1 is obtained as the favored reaction pathway compared to mechanism A5, which is visualized in Figure 2 for CuTpCF3,CH3 and CuTpCH3,CH3, but holds true also for all the other investigated CuTpR1,R2 systems, see Tables S5−S7. The resulting overall energy barriers for mechanism A1 for all ligands are listed in Table 3 and show an Table 3. Experimentally Found Rate Constant (kobs2), Arrhenius Activation Energy (ΔEA), Calculated Reaction Barriers from Mechanism A1 (ΔE‡)

CuTpCH3,CH3 CuTpMs,H CuTpPh,Ph CuTpCF3,CH3 CuTptBu,H

1 × 104 × kobs2 (sec−1)a

ΔEA (kcal/mol)b

ΔE‡ (kcal/mol)

>30 3.9(1) 1.8(1) 0.40(3)