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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Synthesis and Electronic Structure Diversity of Pyridine(diimine)iron Tetrazene Complexes Amanda C. Bowman,†,‡ Aaron M. Tondreau,†,§ Emil Lobkovsky,† Grant W. Margulieux,§ and Paul J. Chirik*,§ †

Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States Department of Chemistry and Biochemistry, Colorado College, 14 East Cache La Poudre, Colorado Springs, Colorado 80903, United States § Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States ‡

S Supporting Information *

ABSTRACT: A series of i pyridine(diimine)iron tetrazene compounds, i ( PrPDI)Fe[(NR)NN(NR)] [ PrPDI = 2,6-(ArN = CMe)2C5H3N; Ar = 2,6-iPr2C6H3] has been prepared either by the addition of 2 equiv ofi an organic azide, RN3, to the corresponding iron bis(dinitrogen) compound, (i PrPDI)Fe(N2)2 or by the addition of azide to the iron imide derivatives, ( PrPDI)FeNR. The electronic structures of these compounds were determined using a combination of metrical parameters from X-ray diffraction, solution and solid-state magnetic measurements, zero-field 57Fe Mössbauer and 1H NMR spectroscopies, and density functional theory calculations. The overall electronic structure of the iron tetrazene compounds is sensitive to the nature of the tetrazene nitrogen substituent with three distinct classes of compounds identified: (i) overall diamagnetic (S = 0) compounds arising from intermediate-spin iron(II) centers (SFe = 1) engaged in antiferromagnetic coupling with both pyridine(diimine) and tetrazene radical anions (SPDI = −1/2 and Stetrazene = −1/2; R = 2-adamantyl, cyclooctyl, benzyl); (ii) overall S = 1 compounds best described as intermediate-spin iron(III) (SFe = 3/2) derivatives engaged in antiferromagnetic coupling with a pyridine(diimine) radical anion (SPDI = −1/2; R = 3,5-Me2C6H3, 4-MeC6H4); (iii) overall S = 2 compounds best described as high-spin iron(III) centers (SFe = 5/2) engaged in antiferromagnetic coupling to a pyridine(diimine) radical anion (SPDI = −1/2; R = 1-adamantyl). For both the intermediate- and high-spin ferric cases, the tetrazene ligand adopts the closed-shell, dianionic form, [N4R2]2−. For the case where R = SiMe3, spin-crossover behavior is observed, arising from a spin-state change from intermediate- to high-spin iron(III).

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structurally characterized by Doedens.7 Since these initial reports, examples with cobalt,8 nickel,9 and iridium10 have been prepared. To date, tetrazene complexes have been isolated with nearly all first-row transition metals11−16 and also include many second- and third-row examples17,18 and main-group elements.19 Metal tetrazene complexes are most commonly synthesized by the addition of an organic azide to an appropriate metal precursor with concomitant loss of dinitrogen. This process can occur either by the addition of 2 equiv of azide to the metal precursor or by the [2 + 3] addition of 1 equiv of azide to an isolated metal imido derivative.12a,14 It is likely that formation of the tetrazene complex proceeds through the [2 + 3] addition even when the metal imido cannot be independently isolated.20−22 Metal tetrazene complexes have also been synthesized from diazonium salts.10,23 Recent studies on iron tetrazene complexes have focused on more detailed spectroscopic characterization and exploration of

INTRODUCTION Tetrazene ligands [N4R2], also referred to as tetraazadienes, have long been known in coordination chemistry, often as carbonyl mimics, but have not been widely studied principally because of the challenge associated with preparing the free proligand. Tetrazene ligands, in analogy to isoelectronic α-diimines,1 are potentially redox-active2 and can adopt neutral (A), radical anionic (B), or closed-shell dianionic (C) forms (Figure 1). To date, both the radical and dianionic forms of the ligand have dominated.3−5

Figure 1. Electronic structure variations for metal tetrazene complexes.

Special Issue: Applications of Metal Complexes with LigandCentered Radicals

The first metal tetrazene complex, (CO)3Fe[(NMe)NN(NMe)], was reported in 1967 by Dekker and Knox6 and later

Received: January 15, 2018

© XXXX American Chemical Society

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DOI: 10.1021/acs.inorgchem.8b00140 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry elucidating the electronic structure of this ligand class. Fourcoordinate iron(II) and iron(III) typically prefer tetrahedral or pseudotetrahedral geometries with either radical or dianionic tetrazene ligands.14,20,21 Jenkins and co-workers have also characterized an iron(IV) example with trigonal-prismatic geometry with a dianionic tetrazene.22 Structural characterization of these complexes also establishes tetrazene ligands in either the monoanionic or dianionic forms, regardless of the molecular geometry. Interestingly, Holland and co-workers have shown that both the radical (B) and dianionic (C) forms of the tetrazene ligand can exist within the same iron complex, depending on the oxidation state.14 One-electron reduction of the β-diketiminatoiron complex LMeFeII[(N1Ad)NN(N1Ad)]0 (where LMe = HC[C(Me)N(2,6-iPr2C 6H3 )]2 yields L MeFeII[(N1 Ad)NN(N1Ad)]−, where the tetrazene ligand has been reduced from the radical monoanionic form [N41Ad2]− to the closed-shell dianionic form [N41Ad2]2−. Although many iron tetrazene complexes are inert, interesting reactivity has been observed in some cases. Hansert and Vahrenkamp demonstrated that dinitrogen extrusion from the iron tetrazene complex (CO)3Fe[(NPh)NN(NPh)] yields the unusual azobenzene compound [Fe2(CO)6(μ-Ph2N2)].24 Other groups have also shown that dinitrogen extrusion leads to formation of the corresponding diazenido17d or diimide12 complex. Bergman and co-workers reported that (η5-Cp)2Zr[(NR)NN(NR)] (Cp = C5H5; R = tBu, Ph) complexes undergo a variety of reactions such as nitrene exchange/cycloreversion, alkyne insertion, and loss of an azide fragment to regenerate the corresponding iron imide species.17a Loss of an azide fragment has also been observed with other metal tetrazene compounds.8,17d,a More recently, Jenkins and co-workers have demonstrated the catalytic aziridination of alkenes with an iron(IV) tetrazene complex under mild conditions.22 Aryl-substituted pyridine(diimine) ligands are a privileged class of redox-active chelates with earth-abundant metals such as iron and cobalt25 and support multiply bonded ligands such as carbenes,26,27 imides,28,29 and nitrides.30,31 In many cases, unusual electronic structures are observed, suggesting a potentially rich chemistry for tetrazene derivatives. Here, we describe the preparation of a family of pyridine(diimine)iron tetrazene compounds and elucidate their electronic structures. Low-, intermediate-, and high-spin ground states are observed depending on the nitrogen substituent.

Scheme 1. Synthesis of Pyridine(diimine)iron Tetrazene Compounds

smaller organic substituents, where the corresponding imido complexes were not isolable (R = 3,5-Me2C6H3, p-tolyl, benzyl). Each of the pyridine(diimine)iron tetrazene complexes exhibits a characteristic 1H NMR spectrum, allowing i routine characterization. The benzene-d6 1H NMR spectra of ( PrPDI)Fe[(N-1-adamantyl)NN(N-1-adamantyl)] [1-N 4 ( 1 Ad) 2 ; i CCDC 1816829] and ( PrPDI)Fe[(NSiMe3)NN(NSiMe3)] [1-N4(SiMe3)2; CCDC 1816830] at 20 °C exhibit paramagnetically broadened resonances over a 350 ppm chemical shift range (Figures S1 and S2). The number of peaks observed is consistent with the overall Cs symmetry and square-pyramidal geometry. The observation of Cs symmetry indicates that the apical and basal positions of the bidentate tetrazene ligand do not interconvert on the time scale of the NMR experiment. Consistent with the NMR data, solid-state magnetic moments of 4.2(1) and 3.8(1) μB were measured at 20 °C for 1-N4(1Ad)2 and 1-N4(SiMe3)2, respectively. Although the magnetic moments are slightly lower than the expected spin-only value for four unpaired electrons (4.90 μB), they are consistent with high-spin iron compounds. The magnetic data will be discussed in more detail in a later section. The aryl-substituted pyridine(diimine)iron tetrazenes, i ( PrPDI)Fe[(N-3,5-Me2C6H3)NN(N-3,5-Me2C6H3)] [1-N4i (3,5-Me2C6H3)2; CCDC 1816831] and ( PrPDI)Fe[(N-4-MeC6H4)NN(N-4-Me-C6H4)] [1-N4(p-tolyl)2], also exhibit paramagnetically shifted 1H NMR resonances at 20 °C in benzene-d6 (Figures S3 and S4). The number of peaks observed for 1-N4(3,5-Me2C6H3)2 and 1-N4(p-tolyl)2 by 1H NMR spectroscopy is consistent with C2v symmetry, arising from interconversion of the apical and basal positions of the tetrazene ligand on the NMR time scale. Solid-state magnetic susceptibility measurements at 20 °C establish effective magnetic moments of 3.1(2) and 3.3(2) μB, respectively, for 1-N4(3,5-Me2C6H3)2 and 1-N4(p-tolyl)2, consistent with two unpaired electrons and a triplet (S = 1) ground state for both molecules. The benzene-d6 1H NMR spectrum of (iPrPDI)Fe[(Ncyclooctyl)NN(N-cyclooctyl)] [1-N4(cOct)2] at 20 °C has a much narrower chemical shift dispersion (13 ppm) and exhibits

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RESULTS AND DISCUSSION Preparation and Characterization of Pyridine(diimine)iron Tetrazene Compounds. The synthesis of pyridine(diimine)iron tetrazene complexes was first explored from the addition of organic azides to isolated iron imido compounds. This route was initially selected because the desired iron tetrazene compounds were often observed as byproducts during the synthesis of imido derivatives.29 The addition of 1 equiv of RN3 (R = 1- or 2-adamantyl, cyclooctyl, SiMe3) to a pentanei solution of the corresponding pyridine(diimine)iron imide ( PrPDI)FeNR at 23 °C produced the iron tetrazene products (Scheme 1). Attempts to prepare examples with aryl azides with 2,6-aryl substituents have been unsuccessful because no reaction with the iron imides was observed after extended reaction times (∼72 h) or heating to 80 °C. A more direct route to the desired complex was achieved by the addition of 2 equiv of the organic azide to a pentane solution of the pyridine(diimine)i iron dinitrogen complex, ( PrPDI)Fe(N2)n (n = 1, 2; Scheme 1). This method enabled the synthesis of tetrazene derivatives with B


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Inorganic Chemistry Table 1. Selected Bond Distances (Å) and Angles (deg) for Pyridine(diimine)iron Tetrazene Compounds 1-N4(1Ad)2

1-N4(SiMe3)2

1-N4(3,5-Me2C6H3)2

1-N4(Bn)2

Fe−Nim Fe−Npy Fe−Nap Fe−Nbas Nap−Nβ Nβ−Nβ′ Nbas−Nβ′ Nim−Cim Cim−Cipso Cipso−Npy

2.241(2), 2.223(2) 1.976(2) 1.981(2) 1.939(2) 1.373(3) 1.280(3) 1.350(3) 1.300(3), 1.293(3) 1.458(4), 1.466(4) 1.361(3), 1.360(3)

2.2162(12), 2.2213(12) 1.9753(12) 1.9563(12) 1.9424(13) 1.3922(17) 1.2619(19) 1.3876(18) 1.2969(19), 1.2967(19) 1.455(2), 1.461(2) 1.3588(18), 1.3627(18)

2.0758(15), 2.1637(15) 1.9374(16) 1.9701(14) 1.9242(16) 1.379(2) 1.273(2) 1.378(2) 1.324(2), 1.301(2) 1.454(3), 1.470(3) 1.361(2), 1.357(2)

1.935(2), 1.997(2) 1.863(2) 1.824(1) 1.855(2) 1.341(3) 1.324(3) 1.314(3) 1.345(4), 1.319(3) 1.421(4), 1.438(4) 1.386(4), 1.360(3)

Npy−Fe−Nbas

175.14(8)

177.68(5)

176.80(6)

176.70(10)

Figure 2. Solid-state structures of 1-N4(Bn)2, 1-N4(1Ad)2, 1-N4(SiMe3)2, and 1-N4(3,5-Me2C6H3)2 at 30% probability ellipsoids (left to right). Hydrogen atoms are omitted for clarity.

iron center, and the apical nitrogen atom of the tetrazene ligand (Npy−Fe−Nap) deviates from idealized orthogonality by ∼10−15°, likely because of the constrained bite angle of the tetrazene ligand (Nap−Fe−Nbas). The iron atom is also lifted slightly out of the idealized plane of the pyridine(diimine) chelate, resulting in deviation of the Npy−Fe−Nbas angle from 180°. This deviation is likely caused by the constrained bite angle of the tetrazene ligand or by the steric interaction of the tetrazene substituents with the 2,6-diisopropyl aryl substituents of the pyridine(diimine) ligand. For the high-spin examples 1-N4(1Ad)2 and 1-N4(SiMe3)2, elongated Fe−Npy distances of 1.976(2) and 1.9753(12) Å and Fe−Nim distances of 2.223(2)/2.241(2) Å (R = 1Ad) and 2.2162(12)/2.2213(12) Å (R = SiMe3) are notably long, consistent with population of the dx2−y2 orbitals.32 Analysis of the bond distances of the pyridine(diimine) chelate in both 1-N4(1Ad)2 and 1-N4(SiMe3)2 reveals only modest distortions compared to neutral ligand reference values.32,33 For 1-N4(1Ad)2, the Cim−Cipso bond lengths of 1.458(4) and 1.466(4) Å and the Nim−Cimine bond distances of 1.300(3) and 1.293(3) Å are most consistent with either a neutral or radical anionic form of the pyridine(diimine) ligand. Similar values, Nim−Cim bond lengths of 1.2969(19) and 1.2967(19) Å and Cim−Cipso bond lengths of 1.455(2) and 1.461(2) Å, were observed with 1-N4(SiMe3)2. The values are similar to those observed in the five-coordinate, i pyridine(diimine)iron dialkyl complex, ( PrPDI)Fe(CH2SiMe3)2,34 an S = 2 molecule best described as having a high-spin iron(III) center engaged in antiferromagnetic coupling to a monoreduced pyridine(diimine) chelate.35 1-N4(1Ad)2 exhibits rotational disorder for one of the adamantyl groups, but no such disorder is observed for 1-N4(SiMe3)2. In both compounds, the Fe−Nap/bas bond distances for the apical and basal positions are elongated [1.981(2)/1.939(2) Å

peaks with visible splitting, signaling a diamagnetic molecule (Figure S5). The related iron tetrazenes, 1-N4(2Ad)2 and 1-N4(Bn)2 (CCDC 1816828), also have resonances in the typical diamagnetic window that are sharp and exhibit visible splitting but also have broadened peaks outside the typical range (Figures S6 and S7). Solid-state magnetic susceptibility measurements confirmed the diamagnetism of these compounds. As is established in pyridine(diimine)iron chemistry, the hydrogen atoms in the plane of the chelate are shifted the most dramatically from typical diamagnetic reference values. Among these, the hydrogen atom in the para position of the pyridine ring appears to be the most sensitive, where there is a near-linear correlation of the chemical shift with the measured effective magnetic moment (Figure S8). It is likely that the anomalous shifts observed with 1-N4(2Ad)2 and 1-N4(Bn)2 arise from contributions from a lowlying triplet state that mix via spin−orbit coupling, giving rise to temperature-independent paramagnetism.32 Solid-State Structures. The solid-state structures of four representative pyridine(diimine)iron tetrazene complexes from each of the various spin states (S = 2, 1, and 0) were determined by X-ray diffraction. The coordination geometries of each along with the distortions to the chelates were of interest, with the latter being diagnostic of the redox activity.32,33 Table 1 reports selected bond distances and angles, while representations of the molecular structures are presented in Figure 2. Bond labels corresponding to the solid-state structures of the pyridine(diimine) iron tetrazene complexes are given in Figure S9. In all four structures, an idealized square-pyramidal geometry was observed with the three nitrogen atoms of the pyridine(diimine) chelate and one of the tetrazenes defining the basal plane. In each case, the sum of the angles about iron is close to 360°, indicating nearplanarity. The angle between the pyridine nitrogen atom, the C


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Inorganic Chemistry (R = 1Ad) and 1.9563(12)/1.9424(13) Å (R = SiMe3)] and are consistent with Fe−N single bonds. Within the tetrazene ligand, the internal Nβ−Nβ′ distances of 1.280(3) Å (R = 1Ad) and 1.2619(19) Å (R = SiMe3) are consistent with a double bond, while the terminal N−N bonds (Nbas−Nβ′/Nap−Nβ) of 1.350(3)/1.373(3) and 1.3876(18)/1.3922(17) Å, respectively, are between single and double bonds (Table 1). Taken together, these metrical parameters are most consistent with the dianionic form on the tetrazene ligand, [N4R2]2− (C; Figure 1). If the pyridine(diimine) is taken to be in its radical anionic form, then both 1-N4(1Ad)2 and 1-N4(SiMe3)2 are best described as highspin iron(III) complexes. The solid-state structure of S = 1 1-N4(3,5-Me2C6H3)2 (Figure 2) has markedly different features compared to 1-N4(1Ad)2 and 1-N4(SiMe3)2. The Fe−Nim bond lengths of 2.0758(15) and 2.1637(15) Å and the Fe−Npy bond length of 1.9374(16) Å are contracted, consistent with a vacant iron dx2−y2 orbital. The bond lengths of the pyridine(diimine) chelate also exhibit more pronounced distortions from the neutral ligand reference values. The elongated Nim−Cim distances of 1.324(2) and 1.301(2) Å and the contracted Cim−Cipso distances of 1.454(3) and 1.470(3) Å are consistent with a one-electronreduced pyridine(diimine). The bond distances from the iron atom to the apical and basal positions of the tetrazene ligand of 1.9701(14) and 1.9242(16) Å, respectively, are consistent with Fe−N single bonds. Within the tetrazene ligand, the internal Nβ−Nβ′ bond distance of 1.273(2) Å is consistent with an NN double bond. As with 1-N4(1Ad)2 and 1-N4(SiMe3)2, these bond distances all indicate that the tetrazene ligand for 1-N4(3,5Me2C6H3)2 is in the dianionic form, and therefore the oxidation and spin states of the iron atom are best described as intermediate-spin iron(III). The solid-state structure of diamagnetic 1-N4(Bn)2 exhibits a unique combination of metrical parameters compared to the higher-spin iron tetrazene complexes. The Fe−Npy distance, 1.863(2) Å, and the Fe−Nim distances, 1.935(2) and 1.997(2) Å, are shorter than would be expected with population of the dx2−y2 orbital, consistent with either a low- or intermediate-spin metal center.32 The distortions of the pyridine(diimine) chelate are more pronounced with elongated Nim−Cim bond distances of 1.345(4) and 1.319(3) Å and contracted Cim−Cipso bond distances of 1.421(4) and 1.438(4) Å. Both distortions signal one-electron reduction of the pyridine(diimine) chelate. There is notable asymmetry within the pyridine(diimine) bond distances in 1-N4(Bn)2 and in several different crystalline samples of the compound. The same asymmetry was also observed for 1-N4(3,5-Me2C6H3)2 and, as will be discussed in the DFT Computational Studies section, was reproduced by density functional theory (DFT) calculations. The distances between the iron and tetrazene nitrogen atoms are notably shorter for 1-N4(Bn)2 than for the other crystallographically characterized tetrazene complexes. The bond distances between the central iron atom and the apical and basal tetrazene nitrogen atoms, 1.824(1) and 1.855(2) Å, respectively, are consistent with those of short Fe−N single bonds. The most notable differences between 1-N4(Bn)2 and the other tetrazene compounds characterized are the metrical parameters within the tetrazene ligand. The bonding within the tetrazene ligand for 1-N4(Bn)2 is delocalized, with the internal Nβ−Nβ′ distance of 1.324(3) Å and the terminal N−N bond lengths of 1.341(3) and 1.314(3) Å not significantly different and all consistent with a N−N bond order of 1.5. These metrical parameters are most consistent with the radical anionic form of the tetrazene ligand

(B; Figure 1), suggesting that 1-N4(Bn) is best described as iron(II). Zero-Field 57Fe Mö ssbauer Studies. Zero-field 57Fe Mössbauer studies were conducted on the pyridine(diimine)iron tetrazene compounds to gain additional insight into their electronic structures and to provide a spectroscopic benchmark for computational studies. Spectra were recorded at 80 K for 1-N4(1Ad)2, 1-N4(Bn)2, 1-N4(cOct)2, 1-N4(3,5-Me2C6H3)2, and 1-N4(SiMe3)2, and the experimental parameters are summarized in Table 2. The isomer shifts (δ) for the five-coordinate iron Table 2. Zero-Field 57Fe Mössbauer Parameters for Pyridine(diimine)iron Tetrazene Complexes at 80 K complex 1

1-N4( Ad)2 1-N4(SiMe3)2a 1-N4(SiMe3)2b 1-N4(3,5-Me2C6H3)2 1-N4(Bn)4 1-N4(cOct)2 a

δ (mm·s−1)

|ΔEQ| (mm·s−1)

0.57 0.53 0.42 0.43 0.23 0.28

3.10 3.26 1.32 1.37 2.99 2.98

Major species at 293 K. bMajor species at 10 K.

tetrazene complexes are generally larger than those observed for four-coordinate, intermediate-spin iron(II) bis(imino)pyridine complexes.36 Increasing δ values are often correlated with increasing coordination numbers for iron compounds, especially between tetrahedral and octahedral complexes.37 The zero-field Mössbauer spectrum of 1-N4(1Ad)2 exhibits a single quadrupole doublet at 80 K with an isomer shift (δ) of 0.57 mm·s−1 and a large quadrupole splitting (|ΔEQ|) of 3.10 mm·s−1 (Figure 3). The observed isomer shift is consistent with either iron(II) or iron(III). The combination of metrical parameters determined from X-ray diffraction and the measured effective 38 magnetic moment support a high-spin iron(III) assignment. i By comparison, the high-spin iron(II) complex ( PrPDI)FeCl2 has a significantly higher isomer shift of 0.89 mm·s−1.32 The large quadrupole splitting observed for 1-N4(1Ad)2 indicates a net electric field gradient along the z axis and is consistent with the square-pyramidal geometry of the compound. Similar values for quadrupole splitting are documented for other five-coordinate pyridine(diimine)iron compounds.32 Unlike 1-N4(1Ad)2, the zero-field 57Fe Mössbauer spectrum of 1-N4(SiMe3)2 exhibits two distinct quadrupole doublets at 80 K. One doublet has parameters similar to 1-N4(1Ad)2 (δ = 0.53 mm·s−1; |ΔEQ| = 3.26 mm·s−1), consistent with an iron(II) or iron(III) center. The other doublet has a lower isomer shift (δ = 0.42 mm·s−1; |ΔEQ| = 1.32 mm·s−1), also consistent with an iron(II) or iron(III) center. Variable-temperature Mössbauer spectra (Figure 4) collected over a 10−293 K temperature range support spin-crossover behavior for 1-N 4(SiMe3)2. The Mössbauer data demonstrate that the doublet with the lower isomer shift is the major species at lower temperatures, consistent with a change from intermediate- to high-spin at the iron upon warming.29 It is also observed that the quadrupole splitting increases significantly upon warming, which is generally observed with spin transitions from low or intermediate spin to high spin.39 The spin transition is incomplete at low temperatures (Figure S10), with two quadrupole doublets observable even at 10 K. Likewise, a small amount of the intermediate-spin fraction is still observed in the spectrum at 293 K (Table S1). The zero-field Mössbauer spectrum of 1-N4(3,5-Me2C6H3)2 at 80 K (Figure 3) exhibits a single quadrupole doublet with D


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Figure 3. Zero-field 57Fe Mössbauer spectra of 1-N4(1Ad)2, 1-N4(3,5-Me2C6H3)2, 1-N4(Bn)2, and 1-N4(cOct)2 (left to right) collected at 80 K. Open circles represent experimental data.

δ = 0.43 mm·s−1 and |ΔEQ| = 1.37 mm·s−1 (Table 2). Both parameters are similar to those observed for 1-N4(SiMe3)2 at low temperatures and are also consistent with either an intermediatespin iron(II) or iron(III) center. The magnetic data and metrical parameters from X-ray diffraction suggest that the iron(III) oxidation state assignment is most appropriate. The zero-field Mö s sbauer spectra of 1-N 4 (Bn) 2 and 1-N4(cOct)2 at 80 K (Figure 3) exhibit nearly identical quadrupole doublets, δ = 0.23 and 0.28 mm·s−1, that are lower among the iron tetrazene complexes in this study. These values are consistent with either low- or intermediate-spin iron(II) or iron(III). However, the much lower δ value of 0.03 mm·s−1 for the low-spin pyridine(diimine)iron dicarbonyl complex, i ( PrPDI)Fe(CO)2,40 suggests that the isomer shift values for 1-N4(Bn)2 and 1-N4(cOct)2 are more consistent with intermediate-spin metal centers. The quadrupole splitting values are also very similar for 1-N4(Bn)2 and 1-N4(cOct)2, with |ΔEQ| = 2.99 and 2.98 mm·s−1, respectively. Given that 1-N4(Bn)2 and 1-N4(cOct)2 do not have high-spin metal centers, these large values of |ΔEQ| may indicate that these compounds have iron(II) centers, as opposed to iron(III). The combined structural, spectroscopic, and magnetic data support three distinct electronic structure classes for pyridine(diimine)iron tetrazene compounds. The first includes 1-N4(1Ad)2 and the high-temperature form of 1-N4(SiMe3)2, which are S = 2 compounds best described as high-spin iron(III) engaged in antiferromagnetic coupling with a pyridine(diimine) radical anion and a dianionic tetrazene ligand. The second class of compounds, containing 1-N4(3,5-Me2C6H3)2, 1-N4(p-tolyl)2, and the low-temperature species of 1-N4(SiMe3)2, are S = 1 with an intermediate-spin iron(III) center, a dianionic tetrazene ligand, and a monoanionic PDI ligand. Finally, the third class, containing 1-N4(Bn)2, 1-N4(cOct)2, and 1-N4(2Ad)2, are diamagnetic with an intermediate-spin iron(II) center, a monoanionic tetrazene ligand, and a monoanionic PDI ligand. The intermediate-spin iron(II) assignment is supported by both the magnetic susceptibility and Mössbauer data. The identity of the R group on the tetrazene ligand clearly influences the electronic structure of the molecule; this dependence is likely due to a combination of steric and electronic factors. Excluding R = 1-adamantyl, there is a clear distinction for the electronic structure class between alkyl and aryl substituents. The observation that alkyl substituents generally correspond to an iron(II) center while aryl substituents correspond to a iron(III) center reflects the electron-donating character of the alkyl substituents and the relatively electron-withdrawing character of the aryl substituents, resulting in a more electron-poor

(less donating) tetrazene and, hence, leading to a more oxidized metal center. The 1-adamantyl and SiMe3 substituents are significantly sterically hindered compared to the other R substituents, with a tertiary carbon and silicon, respectively. The Fe−N distance between the iron and basal nitrogen atoms is longer than that observed for R = aryl, indicating that steric hindrance may prevent a stronger overlap between the tetrazene ligand and metal center, resulting in a high-spin iron(III) complex. DFT Computational Studies. Further support for the electronic structure assignments was provided by DFT studies. Full-molecule calculations were carried out on representative examples from each class of the pyridine(diimine)iron tetrazene compounds.41 All geometry optimizations used the initial coordinates from the crystallographically determined structure, and all calculations (including Mössbauer parameters) were run using the B3LYP hybrid functional unless otherwise noted. For 1-N4(SiMe3)2, both the S = 1 and 2 species were investigated. For the triplet state, both the open-shell (UKS) and broken-symmetry42 BS(4,2) calculations spontaneously converged to a broken-symmetry BS(3,1) solution, while for the quintet state, the open-shell (UKS) calculation spontaneously converged to a broken-symmetry BS(5,1) solution. The experimentally determined bond lengths and angles are generally in good agreement with the calculated bond lengths and angles for the quintet BS(5,1) solution (Table S2). This is consistent with the temperature at which the crystallographic data were collected (173 K) because the variable-temperature Mössbauer data demonstrate that the majority of molecules should be in the high-spin configuration at that temperature. The calculated spin densities for the triplet solution, shown in the spin-density plot (Figure 5), are +2.43 on the iron center, +0.17 on the tetrazene ligand, and −0.60 on the bis(imino)pyridine ligand. This is consistent with a total of three unpaired spins on the iron center and one unpaired spin of opposite sign on the PDI ligand. Examination of the molecular orbital diagram for the triplet BS(3,1) solution demonstrates two unpaired spins and a total of five electrons in primarily metal-based orbitals. In addition, a single unpaired spin is based on a PDI π* orbital. This PDI π*-based radical is antiferromagnetically coupled to the lowest-energy metal-based spin, giving rise to the overall S = 1 configuration of 1-N4(SiMe3)2 at lower temperatures (Figure S12). The molecular orbital diagram also demonstrates a reduction of the tetrazene ligand, consistent with the dianionic form, with a pair of electrons in the tetrazene π* orbital. The spin-density plot for the quintet solution of 1-N4(SiMe3)2 exhibits spin densities of +3.93 on the iron center, +0.56 on the tetrazene ligand, and −0.49 on the PDI ligand (Figure 5). E


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The positive spin density distributed between the iron center and tetrazene ligand is consistent with five unpaired spins on the metal center, and the spin value of −0.49 on the PDI ligand indicates one unpaired spin on the PDI ligand of opposite sign. These values are similar to those of the pyridine(diimine)iron bis(alkyl) complex, (EtPDI)Fe(CH2SiMe3)2, which has been previously described as an S = 2 high-spin iron(III) complex.35 The calculated spin densities for EtPDIFe(CH2SiMe3)2 were +4.07 on the iron center and −0.46 on the PDI ligand, similar to those observed for the S = 2 state of 1-N4(SiMe3)2. Examination of the molecular orbital diagram for the BS(5,1) solution of 1-N4(SiMe3)2 indicates a total of five unpaired spins in primarily metal-based orbitals, consistent with a high-spin iron(III) center. One unpaired spin of opposite sign is based in a PDI π* orbital. Reduction of the tetrazene ligand to the dianionic form is also observed, with a pair of electrons in the tetrazene π* orbital. Antiferromagnetic coupling is observed between the lowest-energy metal-based spin and the PDI π*-based spin, giving rise to the overall S = 2 configuration observed for 1-N4(SiMe3)2 at higher temperatures (Figure S13). Consistent with the observed spin-crossover behavior, the triplet and quintet states of 1-N4(SiMe3)2 were calculated to be very close in energy, with the triplet state lower by 0.8 kcal·mol−1. Overall, the DFT calculations support the assignment of an intermediate-spin iron(III) complex with a monoreduced PDI ligand, which undergoes a spin transition to a high-spin iron(III) complex with a monoreduced PDI ligand at higher temperatures. Mössbauer parameters were also calculated for both the triplet and quintet spin states of 1-N4SiMe3 and are summarized in Table 3. The agreement between the calculated and experimental spectroscopic data validates the computational findings. The calculated isomer shift (δ) values for both the S = 1 and 2 states are in good agreement with the experimentally observed values (within ±0.1 mm·s−1), supporting the electronic structure assignments based on the BS(5,1) and BS(3,1) solutions. The calculated quadrupole splitting (ΔEQ) values are also in good agreement with the experimentally determined values, although the sign of the quadrupole splitting was not experimentally determined from applied field measurements. For the S = 1 class of pyridine(diimine)iron tetrazene compounds, 1-N4(3,5-Me2C6H3)2 was selected for computational studies. Both the open-shell (UKS) and broken-symmetry BS(4,2) calculations spontaneously converged to a broken-symmetry BS(3,1) solution, similar to that obtained for the triplet state of 1-N4(SiMe3)2. The calculated bond lengths and angles were generally in good agreement with the crystallographically determined values, particularly for the PDI ligand (Table S2). It is notable that the triplet calculation also reproduces the crystallographically observed asymmetry in the pyridine(diimine) ligand. The spin-density plot for the 1-N4(3,5-Me2C6H3)2 BS(3,1) solution exhibits spin densities of +2.43 on the iron center, +0.24 on the tetrazene ligand, and −0.67 on the PDI ligand (Figure S14), consistent with a total of three unpaired spins on the iron center, as well as one unpaired spin of opposite sign on the PDI ligand. These spin densities are similar to those observed for the triplet state of 1-N4(SiMe3)2 and are consistent with an intermediate-spin iron(III) center. Inspection of the molecular orbital diagram for 1-N4(3,5-Me2C6H3)2 also indicates an intermediate-spin iron(III) center, with three unpaired spins and a total of five electrons in metal-based orbitals (Figure S15). As expected based on the metrical parameters of the tetrazene ligand from the solid-state structure, reduction of the tetrazene ligand to the dianionic form is observed in the molecular orbital

Figure 4. Variable-temperature zero-field 57Fe Mössbauer spectra of 1-N4(SiMe3)2. Open circles represent experimental data (blue line, δ = 0.42 mm·s−1, |ΔEQ| = 1.32 mm·s−1; red line, δ = 0.53 mm·s−1, |ΔEQ| = 3.26 mm·s−1).

Figure 5. Spin-density plots for the BS(3,1) (left) and BS(5,1) (right) configurations of 1-N4(SiMe3)2. F


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Table 3. Calculated and Experimental Mössbauer Parameters for Representative Pyridine(diimine)iron Tetrazene Compounds 1-N4(SiMe3)2 S=1 δ (mm·s−1) |ΔEQ| (mm·s−1)b a

1-N4(3,5-Me2C6H3)2

1-N4(Bn)2

S=1

S = 0a

S=2

expt

calcd

expt

calcd

expt

calcd

expt

calcd

0.42 1.32

0.39 +1.68

0.55 3.40

0.46 −2.72

0.43 1.37

0.37 +1.82

0.23 2.99

0.31 −3.53

Calculated Mössbauer parameters are from the UKS open-shell S = 0 solution. bThe sign of the calculated quadrupole splitting is given.

diagram. Antiferromagnetic coupling between the lowest-energy metal-based spin and a PDI π*-based unpaired spin results in an overall S = 1 configuration. The crystallographically observed asymmetry of the PDI ligand is reflected in this PDI π*-based orbital. One possible explanation for this asymmetry is steric hindrance from the substituents on the tetrazene-based aryl groups. In order to accommodate the aryl group in the basal position, the entire tetrazene ligand is tilted 21° to the side and therefore has good overlap with the π* system on only one side of the PDI ligand, resulting in an asymmetric molecular orbital. The calculated Mössbauer parameters for 1-N4(3,5-Me2C6H3)2 of δ = 0.37 mm·s−1 and |ΔEQ| = 1.82 mm·s−1 are both in good agreement with the experimentally obtained values (Table 3). This supports the electronic structure assignment based on the BS(3,1) solution of an intermediate-spin iron(III) center antiferromagnetically coupled to a PDI radical anion. The benzyl derivative, 1-N4(Bn)2, was selected as a representative example of an S = 0 pyridine(diimine)iron tetrazene compound. Calculations were carried out for the singlet state as both restricted closed-shell (RKS) and unrestricted open-shell (UKS). The UKS calculation spontaneously converged to a broken-symmetry BS(2,2) solution. Because the 1H NMR spectra of these tetrazene complexes exhibited an unusually wide chemical shift range consistent with temperature-independent magnetism, calculations were also carried out for the unrestricted open-shell (UKS) triplet state. This calculation spontaneously converged to a broken-symmetry BS(3,1) solution with orbitals and spin densities almost identical with those of the previously discussed tetrazene compounds and will not be discussed further. The calculated bond lengths and angles for the two singlet calculations [RKS and BS(2,2)] were both in good agreement with the experimental data (Table S2). However, the RKS solution was 3.7 kcal·mol−1 higher in energy than the BS(2,2) solution, suggesting that the open-shell solution is a better description of the electronic structure of 1-N4(Bn)2. As with 1-N4(3,5-Me2C6H3)2, asymmetry in the PDI ligand was also observed for 1-N4(Bn)2, consistent with the experimental crystallographic data. The tetrazene ligand in the singlet solutions shows roughly equivalent N−N bond lengths, as was observed experimentally, consistent with the delocalized bonds of the monoanionic form. By contrast, in the BS(3,1) solution, the tetrazene ligand has one long and two short N−N bonds, consistent with the dianionic form of the ligand. The calculated spin densities for the 1-N4(Bn)2 BS(2,2) solution, as shown in the spin-density plot (Figure 6), are +1.41 on the iron center, −0.68 on the tetrazene ligand, and −0.73 on the PDI ligand. In contrast to the other pyridine(diimine)iron tetrazene complexes, the spin density of both the tetrazene and PDI ligands is opposite in sign to the metal center. Overall, the spin-density plot indicates a total of two unpaired spins on the iron center and one unpaired spin each on the PDI and tetrazene ligands. The molecular orbital diagram for 1-N4(Bn)2 also exhibits two unpaired electrons on the metal center and is

Figure 6. Spin-density plot for the BS(2,2) configuration of 1-N4(Bn)2.

consistent with an intermediate-spin iron(II) center, in contrast to the iron(III) centers observed for the other tetrazene compounds (Figure S16). The two filled orbitals are primarily ironbased, with a small amount of PDI π* character. Of the two ironbased unpaired spins, one is coupled to one tetrazene π*-based unpaired spin and one to PDI π*-based unpaired spin, consistent with the overall S = 0 configuration observed experimentally. A second PDI π*-based orbital and the primarily dx2−y2 metalbased orbital are empty. Mössbauer parameters were calculated for 1-N4(Bn)2 based on the optimized geometry obtained for both singlet solutions. The calculated δ values of 0.31 and 0.16 mm·s−1 for the BS(2,2) and RKS solutions, respectively, are both in good agreement with the experimental value of 0.23 mm·s−1 (Table 3). Likewise, the calculated ΔEQ values of −3.53 and −3.52 mm·s−1 for the BS(2,2) and RKS solutions, respectively, are also in good agreement with the experimental value of |2.99| mm·s−1. The good agreement of the experimental data to the calculated data from the RKS and BS(2,2) solutions for 1-N4(Bn)2 supports the electronic structure assignment of the compound as an overall S = 0 molecule. Because of the lower energy of the BS(2,2) solution and the broken-symmetry character of the other pyridine(diimine)iron tetrazene complexes, the BS(2,2) solution is likely the better description of the molecule. Interestingly, the triplet BS(3,1) solution was lower in energy than the BS(2,2) solution, by 6.6 kcal·mol−1. However, the experimental data, including bond lengths, magnetic susceptibility, and Mössbauer parameters (vide infra), are in much better agreement with the corresponding data calculated from the singlet solutions, supporting the electronic structure description of 1-N4(Bn)2 as an overall S = 0 complex. Therefore, the origin of the 1H NMR chemical shifts observed for the diamagnetic tetrazene compounds is likely due to mixing of the low-energy triplet state into the singlet ground state.

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CONCLUDING REMARKS A series of pyridine(diimine)iron tetrazene compounds have been synthesized and fully characterized, including demonstration of the tetrazene ligand in both the radical monoanionic and G


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(21.5 Hz, 3H, adamantyl CH2), 1.61 (16.2 Hz, 6H, adamantyl CH2), 4.19 (49.5 Hz, 6H, adamantyl CH2), 6.95 (17.0, 2H, CH(CH3)2 or aryl), 8.06 (21.2 Hz, 2H, CH(CH3)2 or aryl), 8.23 (245.7 Hz, 2H, CH(CH3)2 or aryl), 27.42 (25.2 Hz, 3H, adamantyl CH2), 27.81 (17.2 Hz, 3H, adamantyl CH2), 48.09 (36.1 Hz, 2H, m-pyridine), 264.87 (110.2 Hz, 1H, p-pyridine).

dianionic forms (Figure 7). Three distinct classes of electronic structures have been observed as a function of the nitrogen

i

Preparation of ( PrPDI)Fe[(NSiMe3)NN(NSiMe3)] [1-N4(SiMe3)2]. A 20 mL scintillation vial was charged with 0.200 g (0.337 mmol) of i Pr PDIFe(N2)2 and ∼10 mL of diethyl ether. Azidotrimethylsilane (0.077 g, 0.674 mmol) was added to ∼5 mL of diethyl ether, which was subsequently added dropwise over the course of 5 min to the stirring solution of the iron complex. During the addition, there was a vigorous evolution of dinitrogen and a color change from green to purple. The volatiles were removed, and the residue taken up in diethyl ether and passed through Celite on a glass frit. The volatiles were removed again, and the solution taken up in a minimal amount of ether, which was cooled to −35 i°C for 12 h. A dark-purple precipitate was collected and identified as ( PrPDI)Fe[(NSiMe3)NN(NSiMe3). Magnetic susceptibility (Gouy balance, 293 K): μeff = 3.8(1) μB. 1H NMR (benzene-d6): δ −102.12 (46.0 Hz, 6H, C(CH3)), −11.21 (22.5 Hz, 2H, CH(CH3)2), −2.89 (35.8 Hz, 6H, CH(CH3)2), 0.28 (22.4 Hz, 6H, CH(CH3)2), 2.18 (58.2 Hz, 6H, CH(CH3)2), 2.68 (44.2 Hz, 6H, CH(CH3)2), 5.02 (23.7 Hz, 9H, SiMe3), 11.17 (23.3 Hz, 2H), 13.05 (25.5 Hz, 2H), 16.67 (27.4 Hz, 9H, SiMe3), 34.95 (32.6 Hz, 2H, m-pyridine), 247.71 (56.5 Hz, 1H, p-pyridine). i Preparation of ( PrPDI)Fe[(N-3,5-Me2C6H3)NN(N-3,5-Me2C6H3)] [1-N4(3,5-Me2C6H3)2]. This compound was prepared in a i manner similar to that of 1-N4(1Ad)2 with 0.101 g (0.170 mmol) of ( PrPDI)Fe(N2)2 and 0.050 g (0.340 mmol) of 3,5-dimethylphenyl azide. Recrystallization from toluene yielded 0.124 g (91%) of dark-greenbrown crystals identified as 1-N4(3,5-Me2C6H3)2. Anal. Calcd for C49H61N7Fe: C, 73.21; H, 7.65; N, 12.20. Found: C, 73.01; H, 7.35; N, 11.79. Magnetic susceptibility (Gouy balance, 293 K): μeff = 3.1(2) μB. 1 H NMR (benzene-d6): δ −84.83 (379.4 Hz, 4H, o-phenyl), −80.71 (108.5 Hz, 2H, p-phenyl or p-aryl), −59.05 (95.7 Hz, 6H, C(CH3)), −24.81 (32.2 Hz, 12H, CH(CH3)2 or phenyl CH3), −8.57 (28.8 Hz, 2H, p-phenyl or p-aryl), 1.25 (88.6 Hz, 12H, CH(CH3)2 or phenyl CH3), 2.17 (54.7 Hz, 12H, CH(CH3)2 or phenyl CH3), 9.74 (890.5 Hz, 4H), 10.72 (35.9 Hz, 4H), 29.49 (76.1 Hz, 2H, m-pyridine), 199.10 (128.6 Hz, 1H, p-pyridine).

Figure 7. Electronic structure summary of pyridine(diimine)iron tetrazene compounds.

substituent: (i) an overall S = 0 molecule with an intermediatespin iron(II) metal center antiferromagnetically coupled to both a monoanionic pyridine(diimine) chelate and a monoanionic tetrazene ligand; (ii) an overall S = 1 molecule with a dianionic tetrazene ligand and an intermediate-spin iron(III) metal center antiferromagnetically coupled to a monoanionic pyridine(diimine) chelate; (iii) an overall S = 2 molecule with a dianionic tetrazene ligand and a high-spin iron(III) metal center antiferromagnetically coupled to a monoanionic pyridine(diimine) chelate. The electron-donating character of the alkyl tetrazene substituents is reflected in the observation of iron(II) metal centers for these compounds (excluding 1-adamantyl), while the electronwithdrawing character of the aryl tetrazene substituents results in iron(III) metal centers. The observation of the iron(III) oxidation state with 1-adamantyl and SiMe3 substituents is likely due to the steric bulk of the tertiary carbon and silicon near the iron, leading to a relatively poor overlap between the tetrazene ligand and metal center. The results provided herein not only demonstrate the structural and electronic structure diversity available to iron complexes bearing two potentially redox-active ligands but also provide structural and spectroscopic parameters for identifying them.

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i

Preparation of ( PrPDI)Fe[(NCH2Ph)NN(NCH2Ph)] [1-N4(Bn2)]. This compound was prepared iin a manner similar to that of 1-N4(1Ad)2 with 0.070 g (0.118 mmol) of PrPDIFe(N2)2 and 0.031 g (0.233 mmol) of benzyl azide. Recrystallization from toluene yielded 0.057 g (62%) of iridescent green crystals identified as 1-N4(Bn2). Magnetic susceptibility (Gouy balance, 293 K): μeff = 0.3(1) μB. 1H NMR (benzene-d6): δ −9.73 (s, 6H, C(CH3)), −2.24 (br s, 2H, CH(CH3)2), −0.77 (br s, 6H, CH(CH3)2), −0.05 (br s, 6H, CH(CH3)2), 1.27 (br s, 2H, CH(CH3)2), 2.01 (br s, 6H, CH(CH3)2), 2.06 (br s, 6H, CH(CH3)2), 5.35 (t, 7.6 Hz, 2H, p-aryl), 5.58 (d, 7.6 Hz, 2H, m-aryl), 5.67 (d, 7.2 Hz, 2H, o-benzyl), 6.14 (d, 6.8 Hz, 2H, o-benzyl), 6.21 (t, 7.2 Hz, 1H, p-benzyl), 6.68 (d, 7.6 Hz, 2H, m-aryl), 6.84 (m, 2H, m-benzyl), 7.29 (t, 6.8 Hz, 1H, p-benzyl), 7.37 (m, 2H, m-benzyl), 8.48 (d, 7.3 Hz, 2H, m-pyridine), 31.55 (br s, 1H, p-pyridine), 42.27 (br s, 2H, benzyl CH2), 66.85 (br s, 2H, benzyl CH2). 13 C{1H} NMR (benzene-d6): δ 18.02 (CH(CH3)2), 25.34 (CH(CH3)2), 34.30 (CH(CH3)2), 35.77 (CH(CH3)2), 36.58 (CH(CH3)2), 51.56 (CH(CH3)2), 72.03 (C(CH3)), 108.64, 112.26, 116.33 (m-aryl), 120.63 (m-aryl), 121.03 (o-benzyl), 126.45, 126.62 (o-benzyl), 127.19 (p-benzyl), 129.74 (m-benzyl), 130.21 (p-benzyl), 130.84 (m-benzyl), 132.99 (p-aryl), 204.26, 211.09, four resonances not located.

EXPERIMENTAL SECTION i

Preparation of ( PrPDI)Fe[(N-1-adamantyl)NN(N-1-adamantyl)] [1-N4(1Ad)2]. Ai 20 mL scintillation vial was charged with 0.093 g (0.157 mmol) of ( PrPDI)Fe(N2)2 and ∼15 mL of diethyl ether, resulting in a dark-green solution. A diethyl ether solution of 0.056 g (0.314 mmol) of 1-adamantyl azide was added to the vial. There was an immediate color change to purple concomitant with bubbling, followed by the rapid formation of a brown precipitate. The reaction was stirred for 15 min, and the precipitate was collected by filtration and washed with pentane. The resulting brown powder was recrystallized from toluene at −35 °C to give 0.112 g (83%) of dark-brown crystals identified as 1-N4(1Ad)2. Anal. Calcd for C53H73N7Fe: C, 73.67; H, 8.52; N, 11.35. Found: C, 73.68; H, 8.66; N, 11.02. Magnetic susceptibility (Gouy balance, 293 K): μeff = 4.2(1) μB. 1H NMR (benzene-d6): δ −141.43 (64.2 Hz, 6H, C(CH3)), −26.99 (144.7 Hz, 6H, CH(CH3)2), −12.14 (226.0 Hz, 6H, CH(CH3)2), −10.40 (18.3 Hz, 2H, CH(CH3)2 or aryl), −3.80 (23.0 Hz, 6H, CH(CH3)2), −2.27 (20.9 Hz, 3H, adamantyl CH2), −2.05 (33.9 Hz, 6H, CH(CH3)2), −1.88 (28.3 Hz, 3H, adamantyl CH2), −1.05 (28.7 Hz, 3H, adamantyl CH2), 1.50

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00140. Complete experimental details, including general considerations, and additional spectroscopic data, including NMR spectra of new compounds (PDF) H


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CCDC 1816828−1816831 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Paul J. Chirik: 0000-0001-8473-2898 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was provided by the National Science Foundation.

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REFERENCES

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