Electronic Structure of Three-Coordinate Fe^II and Co^II β-Diketiminate Complexes

Abstract

The β-diketiminate supporting group, [ArNCRCHCRNAr]⁻, stabilizes low coordination number complexes. Four such complexes, where R = tert-butyl, Ar = 2,6-diisopropylphenyl, are studied: (nacnac^tBu)ML, where M = Fe^II, Co^II and L = Cl, CH₃. These are denoted FeCl, FeCH₃, CoCl, and CoCH₃ and have been previously reported and structurally characterized. The two Fe^II complexes (S = 2) have also been previously characterized by Mössbauer spectroscopy, but only indirect assessment of the ligand-field splitting and zero-field splitting (zfs) parameters was available. Here, EPR spectroscopy is used, both conventional field-domain for the Co^II complexes (with S = 3/2) and frequency-domain, far-infrared magnetic resonance spectroscopy (FIRMS) for all four complexes. The Co^II complexes were also studied by magnetometry. These studies allow accurate determination of the zfs parameters. The two Fe^II complexes are similar with nearly axial zfs and large magnitude zfs given by D = −37 ± 1 cm⁻¹ for both. The two Co^II complexes likewise exhibit large and nearly axial zfs, but surprisingly CoCl has positive D = +55 cm⁻¹ while CoCH₃ has negative D = −49 cm⁻¹. Theoretical methods were used to probe the electronic structures of the four complexes, which explain the experimental spectra and the zfs parameters.

Graphical Abstract

Introduction

First row transition metal (3d) complexes with low-coordination numbers, defined here as two- or three-coordinate, have generated considerable interest in the inorganic chemistry community.^1–13 In particular, the area of single molecule magnets (SMMs)^14–17 has been greatly advanced by investigations of low-coordinate 3d ion complexes.^18–39 The properties of SMMs depend crucially on the details of the ligand-field splitting of the orbitals and the zero-field splitting (zfs) of the magnetic sublevels,^40–42 adding strong motivation to quantitatively determine these parameters.

One N-donor ligand that has been particularly effective at stabilizing three-coordinate complexes is the β-diketiminate ion,^43–46 often denoted nacnac, due to its formal derivation from β-diketonate, or acac.⁴⁷ An advantage of nacnac over acac is the ability to incorporate steric bulk on the imine/iminate substituents,⁴⁵ to prevent formation of four- and six-coordinate transition metal complexes that are common with β-diketonates,⁴⁸ e.g., (acac)₂M, M = Cu, Pd; (acac)₃M, M = Ti, V, Cr, Mn, Fe, Co, etc.; the CSD (version 5.43, update 4) yields 355 structures of 4-coordinate bis(acac) complexes (of which 245 are M = Cu) and 378 structures of 6-coordinate tris(acac) complexes. In contrast, there are only two structurally characterized complexes of (nacnac^R,R′)₃M; with M = Cr^III (CSD: IJEVUP, IJEWAW)⁴⁹ and with Y^III (CSD: XINMAJ).⁵⁰ In the former, the N-substituents are benzyl (nacnac^Bn,Me) and in the latter phenyl (nacnac^Ph,Me). Four-coordinate bis(nacnac) complexes are relatively plentiful, with 108 structures, although this includes tetraazamacrocylic complexes such as these of Ni^II.⁵¹ There are 48 structures of (nacac^R,Me)₂M transition metal complexes with two bidentate ligands. With bulky N-substituents, most commonly 2,6-diisopropylphenyl (DiPP) groups, the three-coordinate complexes of general formula (nacnac^R,R′)MX are often isolable, with the CSD yielding 401 structures wherein M = Fe, Co, Ni, Cu, Zn (primarily), and X = C, N, P, O, S, halide, etc. Specifically with the DiPP substituent, there are 255 structures of (nacnac^DiPP,R′)MX. Thus, this is a useful scaffold for constructing systematic series of three-coordinate complexes.

Our focus here is on two 3d ions of great importance in inorganic chemistry in general, and in the area of SMMs in particular, namely Fe^II and Co^II. These ions feature rich d-orbital manifolds when they have high-spin d⁶ and d⁷ electronic configurations, respectively. Cobalt(II) complexes are among the most extensively studied in connection with SMM behavior, as has been very recently reviewed,⁵² but SMM examples of Fe^II, particularly in low-coordination number, are also plentiful such as in these recent examples.^{31, 33, 34, 36} For the detailed study here, we utilize two ligands in the third coordination position, X = Cl and CH₃. These represent respectively a moderate σ- and π-donor and a strong σ-donor. Both have cylindrical symmetry (i.e., when z is chosen as the M-X σ-bond vector, the x and y directions are equivalent). These four complexes, which have been previously reported by some of us,^{4, 53, 54} are testbeds for investigating the electronic structure of 3-coordinate complexes of high-spin 3d ions. In these complexes, an extremely bulky β-diketiminate ligand is used, 2,2,6,6-tetramethyl-3,5-bis(2,6-diisopropylphenylimido)heptane anion, nacnac^DiPP,tBu, which we will abbreviate as nacnac^tBu. For further simplicity, the four (nacnac^DiPP,tBu)MX (M= Fe, Co; X = Cl, CH₃) complexes will be referred to respectively as FeCl, FeCH₃, CoCl, and CoCH₃ and collectively as MX and pairwise by metal as FeX or CoX and by ligand as MCl or MCH₃.

Using applied-field Mössbauer effect spectroscopy, certain aspects of the electronic structure of the FeX complexes have been investigated previously;⁴ however, the computational tools available at that time were insufficient for a deeper study by quantum chemical theory. Mössbauer gives an indirect assessment of the ligand-field transitions of the iron complexes, and is of course inapplicable to the cobalt complexes. Here, we use a more direct measurement of ligand-field parameters, far-infrared magnetic resonance spectroscopy (FIRMS)^{55, 56}. FIRMS directly yields the zfs of high-spin systems, which is key towards understanding their electronic structure. The results obtained herein give insights that may be applicable to other high-spin ions and to other complexes of the versatile and popular β-diketiminate ligand platform.

Experimental Section

Synthesis.

The complexes FeCl, FeCH₃, CoCl, and CoCH₃ were prepared as previously reported.^{4, 54, 57} All sample handling was done under an inert atmosphere.

Electronic absorption spectroscopy.

Electronic absorption spectra of all complexes were recorded in toluene solution on a Cary 60 spectrophotometer.

Caution! Care should be taken in the presence of high magnetic fields and in the use of cryogenic fluids.

X- and Q-Band EPR/ENDOR spectroscopy.

X-band (~9.5 GHz) spectra of CoCl and CoCH₃ in toluene frozen solution and as pure powders were recorded on a modified Bruker E109 spectrometer equipped with an Oxford cryostat. Q-band (35 GHz) EPR and ENDOR spectra only of frozen solution samples were recorded at 2 K on CW⁵⁸ and pulsed⁵⁹ spectrometers previously described, the latter using the Davies pulse sequence⁶⁰ for ¹⁴N ENDOR. CW EPR spectra under these conditions are in rapid passage and thus exhibit an absorption lineshape.^{61, 62} EPR simulations used the program QPOW^{63, 64} and ENDOR simulations used the locally written program DDPOWHE.

Magnetometry.

Magnetic measurements for CoX were performed using a Quantum Design MPMS 3 magnetometer. All samples were prepared under a N₂ atmosphere in polyethylene capsules and were solid powders restrained with eicosane in a gelatin capsule. Ferromagnetic impurities were ruled out by inspection of the 100 K magnetization data that showed no curvature in the field range of 0 – 7 T. DC magnetic susceptibility measurements were collected in the temperature range of 2 – 300 K under an applied magnetic field of 0.1 T. Variable-temperature, variable-field (VTVH) magnetization measurements were collected in the temperature range of 2–10 K under applied magnetic fields of 1 – 7 T, in 1 T increments. DC magnetic susceptibility measurements were corrected for diamagnetism, estimated using Pascals constants.⁶⁵ Magnetic susceptibility and VTVH magnetization data were simulated using the program MagProp in DAVE 2.0.⁶⁶

FIRMS.

FIRMS experiments were performed at NHMFL using a Bruker Vertex 80v FT-IR spectrometer coupled with a 17 T vertical-bore superconducting magnet in a Voigt configuration (light propagation perpendicular to the external magnetic field). The experimental setup employs broadband terahertz radiation emitted by an Hg arc lamp. The radiation transmitted through the sample is detected by a composite silicon bolometer (Infrared Laboratories) mounted at the end of the quasi-optical transmission line. Both the sample and bolometer are cooled by low-pressure helium gas to a temperature of 5.5 K. To obtain air-free measurements, the samples were loaded in the sample holder in an argon-filled glovebox. The microcrystalline powder (~3 – 5 mg) was bonded by n-eicosane and sandwiched between two n-eicosane layers for protection from oxygen and moisture. Sample loading in the FIRMS spectrometer was performed under a flow of N₂. After collection, the samples were exposed to ambient conditions for two days, after which the measurements were recollected to ensure the originally observed absorption peaks were not attributable to sample degradation from contact with oxygen or moisture (Figures S8 and S9). The intensity spectra of each sample were measured in the spectral region between 14 and 730 cm⁻¹ (0.42 − 22 THz) with a resolution of 0.3 cm⁻¹ (9 GHz). To discern the magnetic absorptions, the spectra were normalized by dividing with the reference spectrum, which is the average spectrum for all magnetic fields. Such normalized transmittance spectra are sensitive only to intensity changes induced by the magnetic field and therefore are not obscured by nonmagnetic vibrational absorption features. The data analysis was implemented using an in-house written MATLAB code and the EPR simulation software package EasySpin,^{67, 68} which uses a standard spin Hamiltonian for S = 2 (FeX) and S = 3/2 (CoX).⁶⁹

Ligand Field Theory (LFT) Calculations.

Calculations employed the locally written programs DDN and DDNFIT and the Ligfield software by Bendix (Copenhagen U., Denmark).⁷⁰ These programs employ all 210 microstates for d⁶ (FeCl, FeCH₃), and all 120 microstates for d⁷ (CoCl, CoCH₃) with the angular overlap model (AOM)^71–73 to describe σ- and π-bonding using respectively the parameters ε_σ and ε_π (which can be anisotropic: ε_π−s and ε_π−c).

Quantum Chemical Theory (QCT) Calculations.

All calculations were performed using the Orca 4.2 program package.⁷⁴ Density Functional Theory (DFT) was used to calculate the ⁵⁷Fe quadrupole splitting (ΔE_Q) and isomer shift (δ) for FeX, and the ⁵⁷Fe and ⁵⁹Co A-tensors and for CoX the ¹⁴N A- and P-tensors. Calculations were performed using the atomic coordinates from the reported X-ray structures using the B3LYP/ CP(PPP) (Fe, Co), def2-TZVP (N, Cl, coordinated C), def2-SVP (C/H) functional/basis set combination.^75–78 The calculated electron density at the Fe nuclei were converted into ⁵⁷Fe Mössbauer isomer shift values using the calibration reported by Römelt et. al. ⁷⁹ For these calculations the spin-orbit coupling operator was computed using the mean-field approximation (SOMF). Time Dependent DFT (TD-DFT) calculations were performed with the same functional/basis set described above except for Fe/Co which were changed to def2-tzvp. The TD-DFT calculations included 250 roots and the computed UV-visible absorption spectrum is reported in the SI.

The state averaged-CASSCF (SA-CASSCF) calculations used the minimum active space of six (FeX) or seven (CoX) electrons in the five 3d orbitals and, for FeX, included all five quintet and all 45 triplet states while the CoX compounds considered all 10 quartet and all 40 doublet states.

The resolution of the identity approximation and auxiliary basis sets generated using the ‘autoaux’ command were used in all CASSCF calculations.⁸⁰ Scalar relativistic effects were accounted for by the second-order Douglas-Kroll-Hess (DKH) procedure and appropriate basis sets dkh-def2-TZVP (Fe, N, Cl, coordinated C) and dkh- def2-SVP (C/H).⁸¹ The converged wavefunctions were then subjected to N-electron valence perturbation theory to second order (NEVPT2) to account for dynamic correlation.⁸² Example ORCA input files are shown in the Supporting Information.

Results and Discussion

Structures.

The crystal structures of all four complexes have been reported previously: FeCl,⁵³ (CSD: REWZUO), FeCH₃,⁴ (CSD: XOXHUN), and CoCl (CSD: XUNTAB) and CoCH₃ (CSD: XUNTEF).⁵⁴ All four complexes have a crystallographic two-fold symmetry axis coincident with the X-M vector so that the two ∠N-M-X (X = Cl, C) are equal and the molecules have roughly C_2v point group symmetry. This C₂ axis would normally be defined as the z axis, but given that these complexes are derived from trigonal planar geometry, we define the z axis as the pseudo three-fold axis (i.e., normal to the molecular plane) and the actual C₂ axis is defined as x. This assignment, which was used also by Andres et al. for the Fe^II complexes,⁴ leads to a slight redefinition of the d orbital representations in C_2v symmetry as described elsewhere and is shown in Table S7.⁸³ Andres et al. also presented a d orbital energy scheme for both the “parent” trigonal planar (i.e., a hypothetical MX₃ complex with D_3h (or C_3h) symmetry⁸⁴) and the actual structure. As such a diagram is extremely useful for both the Fe^II and Co^II complexes under study here, we reproduce it with slight modifications. Note that if there were only σ-bonding, then the degenerate $d_{xz},d_{yz}$ orbitals would be lowest in energy; however, π-donation from the N donors (and from Cl in MCl) raises $d_{xz},d_{yz}$ above $d_{z^2}$; the σ-antibonding degenerate $d_{xy},d_{x^2-y^2}$ orbitals are always highest in energy. Quantitative diagrams are given in Figures 10 and 11 for FeX and CoX, respectively. The hypothetical trigonal Co^II complex is Jahn-Teller effect (JTE) active (⁴E″ ground state), so it would distort as in actual trigonal complexes, such as Mo^III.⁸⁵ However, there is not threefold symmetry in the present Fe^II and Co^II complexes, because the bidentate β-diketiminate ligand constrains ∠N-M-N to roughly 95°. As a result, none of the (nacnac)MX complexes have an orbitally degenerate JTE active ground state; the ground state for FeX (X = Cl, CH₃) is ⁵A₁ and for CoX is ⁴A₂.

Figure 10.

The left-hand side shows a qualitative orbital energy level diagram for FeX with the dominate, non-Aufbau, ground state configuration shown. The inset shows the axis definition which has been chosen to be consistent with previous studies of these compounds (see also Figure 1). The transitions and associated excited states are colored to indicate the orbital angular momentum operator responsible for their interaction with the ground state (red, ${\hat{L}}_z$; blue, ${\hat{L}}_y$; green, ${\hat{L}}_x$). The diagram on the right shows the relative energies of the low-lying excited states, color coded as on the left.

Figure 11.

The left-hand side shows a qualitative orbital energy level diagram for CoX with the dominate ground state configuration shown. The inset defines the choice of axis which has been chosen to be consistent with previous studies of the Fe analogues of these compounds (see also Figure 1). The transitions and associated excited states are colored to indicate the orbital angular momentum operator responsible for their interaction with the ground state (red, ${\hat{L}}_z$; blue, ${\hat{L}}_y$; green, ${\hat{L}}_x$). The diagram on the right shows the energies of the low-lying excited states for CoCl and CoCH₃, color coded as on the left, and the reorganization of these states that is responsible for the change in the sign of D between CoCl and CoCH₃.

Conventional (field-domain) EPR spectroscopy.

X-band EPR spectra using parallel mode detection^86–90 were reported by Andres et al. for powder FeCl and FeCH₃.⁴ The two Fe^II complexes each exhibited an X-band (9.27 GHz) signal at low field (maxima at 35.6 mT and 59.4 mT for FeCl and FeCH₃, respectively; see Figure 8 in Andres et al.⁴). This high g′ value (~18.6 and ~11.2, respectively) signal arises from a transition within the m_S = ±2 doublet,^{86, 88, 91} which is the spin ground state (i.e., D < 0) as indicated by its temperature dependence. The energy levels for both S = 3/2 and S = 2 systems are shown in Figure 2.

Figure 2.

Energy levels for spin sublevel states in quartet (left) and quintet (right) systems with D < 0. For illustrative purposes, the rhombicity is small (|E/D| = 0.1 for both). An EPR transition within the small splitting (~0.03|D|) between the m_S = ±2 levels is observed at X-band for FeCl and FeCH₃.⁴ The transitions indicated by arrows can be observed by FIRMS (both transitions to the m_S = ±1 levels for S = 2 are readily observable while that to the m_S = 0 level is less likely and is thus shown as a dotted line).

The X-band spectrum of CoCl in toluene solution is shown in Figure 3; the Supporting Information shows the X-band spectrum of powder CoCl (Figure S3) as well as the corresponding Q-band spectra (CW and pulsed; Figure S4). The Q-band toluene frozen solution spectrum is essentially the same as at X-band except for the loss of hyperfine resolution due to g-strain,⁹² but with slightly better determination of g values. The X-band spectra for the solid and frozen solution are essentially the same, except for the inevitable loss of resolution in the magnetically non-dilute powder, which indicates that the solid state (XRD) structure is maintained in toluene solution. Qualitatively, the conventional EPR spectra of CoCl are characteristic of an S = 3/2 system with zfs (2D*, D* = (D² + 3E²)^1/2) that is large in energy relative to the microwave quantum (~1.17 cm⁻¹ at Q-band) and with D > 0, i.e., m_S = ±1/2 ground state.^{91, 93, 94} The simulations thus employ an effective spin, S′ = 1/2, with effective g′ values, as opposed to the real S = 3/2. Use of perturbation theory formulas^{91, 95} allows an estimate as to the real g values along with the zfs rhombicity, |E/D|. These formulas give |E/D| = 0.065 and g_x = 2.580, g_y = 2.585, g_z = 2.000 (g_iso = 2.39), which parameter set affords g′ = [4.644, 5.655, 1.975], coinciding with the experimental g′ = [4.62 – 4.70, 5.64 – 5.68, 1.96 – 1.97] (here ordered as g′_x, g′_y, g′_z, rather than as g′_max, g′_mid, g′_min, as in the simulation) with the range due to the use of two frequencies and different sample preparations. The real g tensor is thus essentially axial with g_⊥ > 2, g_∥ ≈ 2, and 2 < g_iso < 2.5, which is typical for d⁷ systems.

Figure 3.

Experimental X-band EPR spectra of CoCl as a toluene solution (black trace) recorded at 10 K (9.364 GHz). Simulation of the solution spectrum (red trace) uses: S′ = 1/2, g′ = [5.64, 4.60, 1.97] (defined simply by g′_max, g′_mid, g′_min), A′(⁵⁹Co) = [700, 400, 210] MHz (A′ collinear with g′), W (half-width at half-maximum (hwhm), Gaussian) = 320, 280, 60 MHz. The inset shows an expansion of the g′_∥ region for the solution with the same simulation parameters.

The ⁵⁹Co hyperfine coupling is very well resolved at g′_∥ with an average splitting of 8.4 mT. The ⁵⁹Co hyperfine coupling tensor determined by simulation is also an effective one, A′(⁵⁹Co), i.e., defined in terms of coupling to S′ = 1/2, rather than to S = 3/2.⁹⁶ It can be converted to a real (i.e., intrinsic) A(⁵⁹Co) by multiplying each component by g_i /g′_i,⁹⁷ so that A(⁵⁹Co) ≈ [220, 320, 210] MHz (here ordered as A_x, A_y, A_z, as with g), which gives A_iso ≈ 250 MHz. EPR spectra of high-spin Co^II typically exhibit broad linewidths so that ⁵⁹Co hyperfine coupling is unresolved.⁹⁸ This is presumably a function of g- and A-strain (i.e., a distribution in these parameters due to structural heterogeneity) as well as superimposed ligand hyperfine coupling (typically from ¹⁴N, but also ³¹P⁹⁸). One example where A(⁵⁹Co) was well resolved is a five-coordinate complex with only O-donors (I = 0 ligands), pentakis(2-picoline N-oxide)cobalt(II) perchlorate, prepared as a doped powder (< 0.1 mol%) in the isomorphous Zn^II host.⁹⁸ This system exhibits g′ = [5.96, 3.56, 1.91] – thus similar values to CoCl, and hyperfine structure was resolved in both the g_max and g_min (g_z, g_∥) regions corresponding to an average A(⁵⁹Co) = 243 MHz, essentially the same A_iso value as seen here. An EPR study by Tierney and co-workers of dihydrido[diphenyl]bis([3,4,5-methyl]-1-pyrazolyl)borate ([Ph₂]Bp^nMe) complexes of Co^II presented species with both m_S = ±1/2 and m_S = ±3/2 signals with resolved A(⁵⁹Co) on certain features,⁹⁹ despite the ¹⁴N-donor ligands. For example, (Ph₂Bp)₂Co had g′ = [5.50, 4.59, 2.00] – very close to CoCl, while Bp₂Co had g′ = [4.73, 4.67, 2.03] – far more axially symmetric than CoCl, but with A(⁵⁹Co)_z = 298 MHz,⁹⁹ still similar to that for CoCl.¹⁰⁰ The hyperfine coupling for CoCl is also near those measured for low-spin Co^II macrocyclic complexes with N4 coordination.¹⁰¹ Quantitative analysis of the spin Hamiltonian parameters for CoCl is given below in the computational section.

The situation with CoCH₃ is quite different. In this case, conventional EPR spectra were very difficult to obtain due to the extreme air sensitivity of the complex, which required the use of sealed tubes, precluding Q-band measurements. Nevertheless, it was clear that CoCH₃ exhibited spectra characteristic of an S = 3/2 system with D < 0 (i.e., m_S = ±3/2 ground state). Such X-band spectra are distinctive in that they exhibit a very large g′_∥ (i.e., at very low field, usually with resolved ⁵⁹Co hyperfine coupling) and a very small g′_⊥ (i.e., at very high field – by X-band standards). An example of such an EPR spectrum was reported for the three-coordinate Co^II NHC complex [Co(CH₂SiMe₃)₂(IPr)] (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene), which gave g′ = [8.85, 1.89, 1.10] with well-resolved ⁵⁹Co hyperfine coupling at low field (splitting of 17.7 mT; the spectrum was not simulated).¹⁰² Figure 4 presents the low field region of the X-band EPR spectrum of CoCH₃. In contrast to the NHC complex,¹⁰² no features attributable to g′_⊥ (g′_mid or g′_min) were definitively observed (see Figure S5). These g′ value turning points may lie beyond the maximum field of the X-band spectrometer (~600 mT, g′ ≈ 1.1). Nevertheless, both g′_z and A′_z (A′_max) are reasonably well determined and give values close to those reported for the NHC complex (17.7 mT¹⁰² versus an average splitting of 16.5 mT in CoCH₃). If we assume g_z = 2.85, based on the magnetometry (see below), then the real hyperfine coupling, A_z ≈ (1850 MHz)(2.85/8.5) = 620 MHz, as opposed to 435 MHz using g_z = 2.0. The real value for the NHC complex is likely similar. For further comparison, four-coordinate, homoleptic Co^II complexes, [Co(OAsMePh₂)₄](ClO₄)₂ ⁹⁸ and [Co(NH₂CSNH₂)₄](NO₃)₂,¹⁰³ studied as powders doped into their corresponding Zn^II hosts exhibited X-band spectra similar to that seen for CoCH₃, with neither clearly providing g′_mid or g′_min values. The arsine oxide complex yielded g′_z ≈ 8.1 and A′_z = 1586 MHz;⁹⁸ the thiourea complex was not analyzed quantitatively, but the resolved splitting appears to be ~20 mT,¹⁰³ and thus consistent with the other cases. The key qualitative finding from conventional EPR of CoX is that the sign of D is opposite between CoCl (D > 0) and CoCH₃ (D < 0), which is quantitatively analyzed in the computational section below.

Figure 4.

Experimental X-band EPR spectrum of CoCH₃ in frozen toluene solution (black trace) recorded at 10 K (9.3616 GHz). Simulation (red trace) uses: S′ = 1/2, g′ = [8.50, 1.2, 1.0] (defined simply by g′_max, g′_mid, g′_min; the last two g′ values are essentially arbitrary), A′(⁵⁹Co) = [1950, 400, 400] MHz (A′ collinear with g′), W (half-width at half-maximum, Gaussian) = 400, 500, 500 MHz. It is not possible to match exactly the experimental lineshape, but the hyperfine splitting pattern is reproduced by the simulation. As with g′, the last two A′ components and linewidths are arbitrary as there is no reliable experimental data for their determination (see also Figure S5).

ENDOR Spectroscopy.

As described above, due to their previous investigation by conventional EPR,⁴ no such experiments were undertaken here on FeX. As also indicated above, conventional X-band EPR spectroscopy in frozen solution was fruitful for CoX, although Q-band EPR was not feasible for CoCH₃. CoCl, in contrast, could be studied by Q-band EPR (Figure S4) and thus by ENDOR spectroscopy at this frequency as well. Signals due to ¹H in CoCl are seen using CW 35 GHz ENDOR as shown in Figure S6 and discussed in Supporting Information. More important are the ¹⁴N signals from the nacnac ligand. Pulsed (Davies) ENDOR spectra for CoCl recorded across its EPR envelope are shown in Figure 5. These spectra could be analyzed quantitatively by ENDOR simulation using S′ = 1/2 and g’ as above, now also with A′(¹⁴N) and P(¹⁴N) (the nqc is a purely nuclear interaction, involving no electronic spin terms, so that it is determined regardless of whether S or S′ is used). The simulations assume that the two nacnac ¹⁴N are equivalent, which is true in the solid-state crystal structure. That the X-band EPR spectra in a powder and in solution are the same (see Figure S3) suggests that the two ¹⁴N are equivalent in solution as well. Such an assumption may be an oversimplification given that ¹⁴N ENDOR can, in ideal cases (e.g., single crystal studies of hemes / porphyrins that included ¹⁵N-enrichment^{104, 105}) reveal slight magnetic differences among structurally equivalent ligands. The situation with CoCl is far from this ideal not only in lacking ¹⁵N-enrichment and single-crystals, but also having severe disadvantages with respect to the desirable, yet common, situation of S = 1/2 with hfc small relative to EPR linewidth: the high-spin state of CoCl so that the g/g′ factor operates but is not accounted for, and the ⁵⁹Co hfc, which complicates the orientation selection ability of ENDOR^{106, 107} by making a given g′ (i.e., the field at which ENDOR is recorded) shifted/split by the ⁵⁹Co hfc making the EPR linewidth used for simulation less meaningful. Nevertheless, a reasonable reproduction of the ¹⁴N ENDOR pattern is achieved as shown in Figure 5. The fit parameters are: A′(¹⁴N) = [11.8, 21.4, 7.3] MHz, P(¹⁴N) = [+1.26, −0.80, −0.46] MHz. The A′(¹⁴N) can be converted to A(¹⁴N) ≈ [11.8(2.580/5.68), 21.4(2.585/4.70), 7.3] MHz = [5.4, 11.8, 7.1] MHz, so A(¹⁴N)_iso ≈ 8.2 MHz. Despite the widespread use of the nacac ligand platform, this represents, to our knowledge, the first determination of ¹⁴N hfc for the β-ketiminate donors. For comparison, such data for more “ENDOR-friendly” S = 1/2 systems such as (nacnac)CuCl¹⁰⁸ and (nacnac)NiL, L = CO, thf,¹⁰⁹ would be useful; especially the Ni^I complexes that are absent any non-¹H hfc except from ¹⁴N. The closest comparison that can be made to the present A(¹⁴N)_iso value is the result of Tierney and co-workers¹¹⁰ who found for Tp₂Co that A(pyrazolyl-2-¹⁴N)_iso = 11.8 MHz. The electronic structure of 6-coordinate Co(II) is much more complicated than that for CoX due to unquenched orbital angular momentum,^110–113 but this A(¹⁴N)_iso value is in the range of that observed here. Also relevant is the work of Walsby et al. on a Co^II-substituted Zn^II protein, Finger 3 of Transcription Factor IIIA, ⁹⁷ which has a Cys₂His₂ coordination site. They found A(¹⁴N) = 7.2 MHz, close to what is seen here, and they point out that this value is close to that seen for histidine imidazole N coordinated to Cu^II, when the appropriate scaling factor of 2S = 3 is used:⁹⁷ A_S=1/2 = A_S=3/2(3) = 24 MHz in our case.

Figure 5.

Pulsed 35 GHz ¹⁴N ENDOR spectra of CoCl in toluene frozen solution (black traces) with simulations (red traces). Experimental parameters: temperature, 2 K; microwave frequency, 34.846 GHz; Davies sequence with t_π = 80 ns, τ = 600 ns, t_rf = 15 μs with random hopping of rf, repetition rate, 20 ms; typically 10 scans. Simulation parameters: S′ = 1/2, A′(¹⁴N) = [12.2, 20.6, 7.1] MHz, P(¹⁴N) = [+1.26, −0.80, −0.46] MHz, W_NMR = 0.5 MHz, W_EPR = 800 MHz (both Gaussian, hwhm). The broad, isotropic EPR linewidth is an attempt to model the ⁵⁹Co hfc. The A′(¹⁴N) and P(¹⁴N) tensors are each rotated by Euler angle α = 130° with respect to the g′ tensor so that the (A′,P)_z (out-of-plane) direction remains along g′_z, but (A′,P)_x,y (in-plane) is along the N-Co bond (see Figure 1).

To contextualize the observed ¹⁴N nqc, we turn to the metalloporphyrin literature, namely single-crystal ENDOR studies by Brown and Hoffman on Cu^II(TPP) (TPP = 1,5,10,15-tetraphenylporphyrin)¹¹⁴ and by Scholes et al. on aquometmyoglobin (Fe^III(PPIX), S = 5/2).¹⁰⁴ For Cu(TPP) (doped into a Zn(TPP)(H₂O) host), P(¹⁴N) = [−0.619, +0.926, (−0.307)] MHz^{114, 115} For myoglobin, the average of the four heme nitrogen donors gave P(¹⁴N) = [−0.77, +1.04, −0.27] MHz. These values for porphyrin pyrrole N donors are not only close to each other, despite the coordinated metal ions’ size, charge, and spin state, but in the same range as that observed here for β-diketiminate N donors. Note that, unlike in these single-crystal studies, we have less certainty as to the relative orientations of the g, A, or P tensors with respect to each other or to the molecular frame of reference, although we make assumptions based on the coordinate system in Figure 1.

Figure 1.

Qualitative d orbital energy diagram for (nacnac)MX complexes. The left diagram is for an idealized trigonal planar geometry (i.e., θ = 120°) with labels for D_3h symmetry (thus ignoring the difference between N and X ligands). In the case of only σ-bonding, the $d_{xz},d_{yz}$ orbitals would be lowest in energy; out-of-plane π-bonding (donation) by the N and X ligands raises them above $d_{z^2}$ in energy. The right diagram is for the idealized real geometry: planar but no longer trigonal (i.e., θ ≈ 130°). The labels are for C_2v symmetry, but with the z axis of the Cartesian coordinate frame out of plane and the x axis along the C₂ axis to correspond to the D_3h definition. This leads to $d_{yz}$ having a₂ representation and $d_{xy}$ having b₂ representation, the reverse of the standard C_2v definition. Orbital occupancy is shown with black arrows for Fe^II (d⁶, S = 2) and the magenta arrow additionally for Co^II (d⁷, S = 3/2). Adapted with permission from Figure 10 in Andres et al., J. Am. Chem. Soc. 2002, 124, 3012 – 3025. Copyright 2002 American Chemical Society.

Magnetometry.

In contrast to conventional EPR spectroscopy, magnetometry (here DC susceptibility and VTVH-magnetization) can in principle directly provide the magnitude of D. We collected the dc magnetic susceptibility data for both CoCl and CoCH₃, which are presented in the insets of Figure 6. For CoCl, the 300 K χ_MT value of 3.0 cm³K/mol supports a g_iso value of 2.52 and is consistent with the anisotropic g-values extracted from EPR spectroscopy (EPR analysis supports a g_iso value of 2.39). Similarly, CoCH₃ displays a 300 χ_MT value of 2.62 cm³K/mol, consistent with g_iso = 2.36. For both CoCl and CoCH₃, their χ_MT values begin to decrease below 150 K, ultimately reaching values of 1.97 cm³K/mol (CoCl) and 2.06 cm³K/mol (CoCH₃) at 2 K. An initial estimation of their axial zero-field splitting parameters (D) was determined by fitting their dc susceptibility data (Table 1). For CoCl, this fitting yielded D = +59(3) cm⁻¹ and g_⊥ and g_∥ values of 2.65 and 2.16, respectively. For CoCH₃, this fitting yielded D = −91(5) cm⁻¹ and g_⊥ and g_∥ values of 2.02 and 2.88, respectively. To gain a better estimate of the spin Hamiltonian parameters, we collected and fit the variable temperature, variable field (VTVH) magnetization data for CoCl and CoCH₃ (Figure 6). Our best simulations afforded D = +55(2) cm⁻¹, and g_⊥ and g_∥ values of 2.62 and 2.08, respectively, for CoCl, and D = −91(5) cm⁻¹, and g_⊥ and g_∥ values of 2.17 and 2.85, respectively, for CoCH₃. These bulk magnetization data qualitatively agree with the analysis of the EPR spectra for CoCl and CoCH₃, whose spectra were consistent with CoCl possessing a large and positive D value, while CoCH₃ possesses a large and negative value of D. More quantitatively, use of these g values from magnetization in the perturbation theory equations^{91, 95} gives for CoCH₃ a viable range from g′_x = g′_y = 0, g′_z = 8.55 for E/D = 0 to g′_x = 0.50, g′_y = 0.54, g′_z = 8.50 for E/D = 0.08. This result suggests the futility of observing g′_⊥ for CoCH₃ by conventional EPR.

Figure 6.

Variable temperature, variable field (VTVH) magnetization data of CoCl (left) and CoCH₃ (right) each collected in the temperature range of 2 – 10 K and field range 1 – 7 T. The 0.1 T dc susceptibility for both compounds are presented in the insets. The black traces are best fits to each of the VTVH magnetization and dc susceptibility data (see Table 1 for fit parameters).

Table 1.

Spin Hamiltonian parameters for MX complexes with CASSCF/NEVPT2 + SOC calculated parameters.

Complex, technique	D (cm−1), E (cm−1), |E/D|	[gx, gy, gz], giso	g′x, g′y, g′z e
FeCl
FIRMS	−38.05 ± 0.1, −2.05 ± 0.1, 0.054	[2.2, 2.2, 2.5], 2.3	---
Conventional EPR a	---	---	---, ---, 10.9
Calculated	–51.5, −2.1, 0.04	[1.90, 2.01, 2.90], 2.27
FeCH3
FIRMS	−36.92 ± 0.5, −1.22 ± 0.5, 0.033	[2.2, 2.2, 2.5], 2.3	---
Conventional EPR a	---	---	---, ---, 11.4
Calculated	–50.1, −2.0, 0.04	[1.91, 2.03, 2.89], 2.28
CoCl
FIRMS b	55.2 ± 0.2, 0, 0	2.5	---
Magnetometry c	+55 ± 2, 0, 0	[2.62, 2.62, 2.08], 2.44	5.24, 5.24, 2.08
Conventional EPR d	> 0, ---, 0.065	---	4.66(4), 5.66(2), 1.965(5)
Calculated e	+65.5, 4.6, 0.07	[2.79, 2.85, 1.95], 2.53	4.98, 6.27, 1.92
CoCH3
FIRMS b	−49.4 ± 0.2, 0	2.5	---
Magnetometry c	−91 ± 5, 0, 0	[2.17, 2.17, 2.85], 2.40	0, 0, 8.55
Conventional EPR d	< 0, ---, ---	---	---, ---, 8.50
Calculated e	–122.4, −4.9, 0.04	[1.05, 2.09, 3.59], 2.24	0.13, 0.24, 10.75

^aTaken from Andres et al.⁴ using X-band EPR with parallel mode detection.

^bOnly the D* parameter and g′_∥ can be evaluated from our experimental FIRMS data. For CoCl, the most favorable assignment for D is given, but the range 55 cm⁻¹ ≤ |D| ≤ 59 cm⁻¹ covers both possible assignments. In contrast, FIRMS for CoCH₃ is especially complicated by spin-phonon interactions. The most favorable assignment for D is given, but the range ~50 cm⁻¹ ≤ |D| ≤ ~85 cm⁻¹ encompasses all possible assignments. The positive sign of D for CoCl and negative sign for CoCH₃ is inferred from their X-band EPR spectra, and is corroborated by magnetometry and calculations.

^cThe values given are those from fits of VTVH magnetization data. Fits of DC susceptibility measurements gave for CoCl, D = +59(3) cm⁻¹, g = 2.65, g_∥ = 2.16 (g_iso = 2.49); for CoCH₃, D = −91(5) cm⁻¹, g = 2.02, g_∥ = 2.88 (g_iso = 2.31). Perturbation theory equations^{91, 95} give g′_x,y,z values (S′ = 1/2) derived from g_x,y,z values obtained from fits of magnetometry using S = 3/2. Using the parameters from DC susceptibility the results are g′ = [5.30, 5.30, 2.16] for CoCl and g′_z = 8.64 for CoCH₃.

^dX-band EPR provides |E/D| = 0.065 for CoCl from the splitting of the g′ feature (see text) using the perturbation theory equations. The range of g′ values comprises both X- and Q-band EPR measurements as well as different sample preparations. This determination is impossible for CoCH₃ as only the g′_∥ feature is observed.

^eThe g′ value ordering is taken here to match experiment using the conventional assignments in EPR and magnetometry where g_∥ ≡ g_z and g ≡ g_x,y.

Far-infrared magnetic spectroscopy (FIRMS).

FIRMS allows direct evaluation of the zfs in an S = 2 system such as found for FeCl and FeCH₃ which includes determination of the zfs rhombicity.⁹⁴ Measurement of FeX powder samples with no applied field gives spectra with two absorption peaks, which are observed at 108.3 and 120.6 cm⁻¹ for FeCl and at 107.2 and 114.5 cm⁻¹ for FeCH₃. Note that other signals are observed for which the frequency is independent of the magnetic field, and thus these are attributed to vibrational bands (phonons). The spectra are presented in Figure 7 (top), with additional spectra in Supporting Information (Figures S7 – S10). In an S = 2 system with D < 0 and E ≠ 0 (assumed E < 0, to correspond to the sign of D), these transition energies correspond to ~3|D − E| and ~3|D + E|, respectively (see Figure 2). The spin Hamiltonian parameters for the four studied complexes are given in Table 1.

Figure 7.

FIRMS color maps for FeCl (top, left), FeCH₃ (top, right), CoCl (bottom, left), and CoCH₃ (bottom, right) each collected at 5.5 K. The magnitude of the field-induced variation in the transmission spectrum is depicted in a color scale (see inset in left panels), which is same within each FeX and CoX pair of compounds. The part of the spectrum with large experimental error (>3%) is indicated in white. For FeX, the dashed lines indicate spectral positions of the magnetic resonance with the external magnetic field aligned along the zfs (D) tensor x (red lines), y (blue), and z (black) principal axes; for CoX, only axial fits were used so magenta lines indicate the field aligned along the x,y (perpendicular, ⊥) direction, with black lines again for the field aligned with z (parallel, ∥). These lines were generated visually and not by any automated fitting routine. Due to spin-phonon coupling, the non-magnetic transitions (phonons) show up as vertical lines and are often quite intense (dark blue). More traditional in appearance single-beam transmission far-IR spectra are presented in Figures S7 and S8, which respectively show the effects of applied field and of air exposure. Figure S9 presents color maps for each complex on a wider energy range (80 – 220 cm⁻¹) and also shows the effects of air exposure. Figure S10 shows an attempt to identify the |S, m_S〉 = |2, ±2〉 → |0〉 transition (Δm_S = 2; see Figure 2) in FeCH₃.

In the case of an S = 3/2 spin system, such as CoCl and CoCH₃, information on the rhombicity of the zfs (D) tensor cannot be obtained, only the zero-field energy gap between the m_S = ±1/2 and ±3/2 Kramers doublets (see Figure 3), here denoted 2D* (alternatively as Δ). These spectra are presented in Figure 8 (bottom), with additional spectra in Figures S7 – S9. Although large field-induced changes in the transmission are observed for both these compounds (see Figure S7), 2D* values are challenging to extract because all the spectra are affected by strong spin-phonon coupling effects.¹¹⁶ As a result, the ground state in these complexes is vibronic (crystal field plus phonon (vibrational mode)), therefore resulting in a hybridization of the crystal field levels leading to a complex FIRMS pattern compared to what would be expected using a simple S = 3/2 spin Hamiltonian model, namely a single absorption at 2D* (Figure 2), which would split in applied field due to the Zeeman effect. Nevertheless, the complex FIRMS pattern in Figure 7 can be interpreted by inspection of absorption peaks in the FIR transmission spectra (e.g., Figures S7 and S8) as well as the fields/frequencies where the more pronounced phonon peaks (i.e., dark vertical lines) exhibit crossing behavior, namely a drop in intensity due to a spin-phonon interaction at that point. An example is seen at ~106 cm⁻¹ and ~4 T for CoCl. From this analysis we suggest the inter-doublet energy gap (see Figure 2) to be 2D* = 110.4 cm⁻¹ for CoCl, which agrees well with the value from magnetometry (2D* = 114(4) cm⁻¹; see Table 1). CoCl exhibits an additional, nearby feature at 117.2 cm⁻¹ that might also be due to magnetic resonance absorption, which also agrees with magnetometry and calculations (see below). The situation for CoCH₃ is more ambiguous. There are zero-field absorptions at 98.8 cm⁻¹, 112 cm⁻¹, 137 cm⁻¹, and 169.3 cm⁻¹ (see Figures S8 and S9 for the higher energy region). Among these, we favor assignment of the band at 98.8 cm⁻¹ to 2D*, as given in Table 1, but none of the others can be totally ruled out. Thus, FIRMS suggests that for CoCH₃, −85 cm⁻¹ ≤ D ≤ −50 cm⁻¹, with the negative sign based on magnetometry and conventional EPR.

Figure 8.

Electronic absorption spectra (main figure, Vis-NIR region; inset UV-Vis region) on a wavenumber (energy) scale of FeX (left panel) and CoX (right panel) recorded at room temperature in toluene solution. Complete UV data are unavailable for FeCl.

Electronic absorption spectra.

The electronic absorption spectra of FeX and CoX recorded at room temperature in toluene solution are shown in Figure 8 on an energy (wavenumbers, cm⁻¹) scale. These spectra are shown on a wavelength scale in Figures S1 and S2 respectively for FeX and CoX. A simple ligand field theory (LFT) discussion of these spectra is given below followed by a definitive explanation using quantum chemical theory (QCT), specifically time-dependent density functional theory (TD-DFT).

Ligand field theory (LFT): optical spectra and zfs.

A quantitative analysis of the electronic structure of the MX series is provided using QCT in the following section, but we first discuss classical LFT because it is still instructive. We begin with an idealized trigonal planar geometry as shown in Figure 1 (left panel), Even in this relatively high D_3h symmetry the number of states is very large as shown in Table S1 (Supporting Information). To explain qualitatively the electronic absorption spectra of the complexes we employ only spin-allowed d-d transitions as their possible origin. Considering first the FeX complexes (Figures 8 (left) and S1), there are visible absorption bands at 559 nm (17 890 cm⁻¹; ε = 1700 mol⁻¹ L cm⁻¹) for FeCl and at 517 nm (19 340 cm⁻¹; ε = 590 mol⁻¹ L cm⁻¹) for FeCH₃. In D_3h symmetry, with only σ-bonding and ignoring the JTE, the ground state is ⁵E″, with the β electron of d⁶ in $d_{xz},d_{yz}$) with the first excited state being ⁵A₁′ (β electron in $d_{z^2}$) and then ⁵E′ (β electron in $d_{xy},d_{x^2-y^2}$) followed by the numerous triplet and singlet excited states. The transition ⁵E″ → ⁵E′ is dipole allowed with z polarization (⁵E″ → ⁵A₁′ is forbidden; ⁵A₁′ → ⁵E′ is dipole allowed with $xy$ polarization) so this could be the origin of the visible band. However, this assignment would require unreasonably large bonding parameters (ε_σ = 15 902 and 19 191 cm⁻¹ for FeCl and FeCH₃, respectively) so that a simple σ-only bonding model disfavors a d-d assignment for the visible band in FeX. Another option is to include π-bonding, which could be either donating or accepting. This is a serious complication in the real FeX complexes as the methyl ligand would have no π-bonding, the chlorido ligand would be cylindrical (ε_π−s = ε_π−c), and π-bonding involving the nacnac with its sp² nitrogen ligands would likely be only out-of-plane (ε_π−s = 0, ε_π−c ≠ 0). To maintain D_3h symmetry in the present model, we use the same π-bonding for all three ligands. In plane π-bonding could be included to lower ε_σ (e.g., ε_π−s = 0.2ε_σ gives ε_σ = 13 572 cm⁻¹ for FeCH₃), but its value is still too large. Out-of-plane π-bonding could instead be included, which has the advantage that with sufficient π-donation, the ground state becomes ⁵A₁′, as in Figure 1 (left). The problem is that this effect brings the ⁵E′ excited state lower in energy – further from the observed band energy making fitting even less viable. Given the total failure of the trigonally symmetric D_3h model, it is not worthwhile to modify it to closer to the real, C_2v symmetry. We conclude that the visible band in FeX is likely a charge transfer (CT) band (whether metal-to-ligand (MLCT) or ligand-to-metal (LMCT) is uncertain), which is supported by its relatively high molar absorption coefficient.

In the CoX complexes (see Figures 8 (right) and S2) there are visible bands at 514 and 540 nm (19 455 and 18 520 cm⁻¹; both ε ≈ 150 mol⁻¹ L cm⁻¹) and at 635 nm (15 750 cm⁻¹; sh) and 687 nm (14 555 cm⁻¹; ε = 130 mol⁻¹ L cm⁻¹) for CoCl and at 565 nm (17 700 cm⁻¹; ε = 130 mol⁻¹ L cm⁻¹) and at 640 nm (15 625 cm⁻¹; shoulder (sh)) and 725 nm (13 790 cm⁻¹; ε = 160 mol⁻¹ L cm⁻¹) for CoCH₃. These lower molar absorption coefficients support the assignment of these bands as being d-d transitions. In contrast to FeX, the quartet electronic states of CoX are more complicated. The free-ion ⁴F splits into ⁴A₂′, ⁴E″, ⁴A₁″ and ⁴A₂″ (degenerate in D_3h), and ⁴E′, with the states derived from ⁴P, ⁴A₂′ and ⁴E″, higher in energy. Table S2 (Supporting Information) illustrates the states for idealized CoX considering only σ-bonding (ε_σ = 7000 cm⁻¹) and with Racah parameters at 70% of their free-ion values.¹¹⁷ Using this very simplified, idealized model, one can more quantitatively rationalize the observed electronic transitions for both CoCl and CoCH₃ as being viable as d-d transitions, in contrast to the situation for FeX. This is done using three possible sets of assignments: a) the lower energy visible band corresponds to ⁴A₂′ → ⁴A₁″,⁴A₂″ and the higher energy band to ⁴A₂′ → ⁴E′ (both allowed); b) the lower to ⁴A₂′ → ⁴E′ and the higher to ⁴A₂′ → ⁴E″(P) (forbidden in D_3h, but allowed in the lower real symmetry); and c) the lower to ⁴A₂′ → ⁴A₁″,⁴A₂″ and the higher to ⁴A₂′ → ⁴E″(P). The transitions ⁴A₂′ → ⁴E″(F) and ⁴A₂′ → ⁴A₂′(P) would be respectively too low and too high in energy to be observed (see Table S2) as well as being dipole forbidden in D_3h. Fits were made using these three models with variable ε_σ and with the Racah B parameter either fixed at 70% or variable (Racah C in this model is large since doublet states were ignored). As expected, fits with fixed B were not very successful, yet model (b) agreed reasonably well with experimental data. Allowing B to vary led to perfect fits for both models (a) and (b); however, the fit values for model (a) were less realistic in that values for B were low and for ε_σ very high. In contrast, model (b) gave perfect fits with reasonable values for both parameters. The results are given in Table S3 (Supporting Information). LFT thus provides an idea as to the origin of the electronic transitions observed for the MX and in particular CoX complexes.

The next step is to use the idealized C_2v geometry with the above bonding parameters as a guideline and explore the ability of LFT to model the zfs. Use of the actual ∠X-Co-N = 130.6 ± 0.3^o and ε_σ(X) ≠ ε_σ(N) (ε_π(X,N) = 0) successfully fits the absorption bands (Table S4) with the B value and bonding parameters still reasonable. For both CoCl and CoCH₃, ε_σ(X) > ε_σ(N). This is expected for the methyl anion, and in the case of chloride, this parameter also includes π-donation that is not specifically accounted for so as to avoid overparameterization. We acknowledge that π-bonding involving the chloride is key in that it removes the degeneracy of the and $d_{yz}$ orbitals, as discussed in the QCT section, but we cannot quantify it here based on the available data. The results of these fits can then be used with inclusion of SOC to attempt to reproduce the spin Hamiltonian parameters. In this case, the Racah C parameter and the SOC constant ζ are both chosen to have the same reduction from their free-ion values as the fits obtained for B; though this is an oversimplification, it is useful for illustration. For CoCl, this model gives g′ = [5.73, 2.84, 1.76] and 2D* = 41 cm⁻¹, ignoring the small rhombicity gives D ≈ 20 cm⁻¹ – lower than the FIRMS value (Table 1), but this could be increased by an larger ζ value.¹¹⁸ The sign is positive based on the spin magnitudes (lowest doublet is 〈S_z²〉 = ±0.44; the higher doublet has 〈S_z²〉 = ±1.43). For CoCH₃, use of ζ = 425 cm⁻¹ gives g′ = [7.02, 1.76, 1.27] and 2D* = 74 cm⁻¹. Surprisingly, although the g′ tensor is not unreasonable, giving one large and two small components, the spin magnitudes (lowest doublet 〈S_z²〉 = ±0.32; higher doublet 〈S_z²〉 = ±1.31) do not support a negative D value.

Quantum chemical theory (QCT): Time-dependent DFT (TD-DFT).

The above LFT section discusses the electronic absorption spectra of the MX series. For the FeX complexes, it was proposed that the observed bands were due to transitions that involved the ligands, rather than d-d transitions that could be modelled using LFT. As shown in Figures S11 and S12, this is indeed the case. Figure S11 presents the calculated spectra for the entire MX series so that it is readily apparent that the CoX complexes exhibit d-d transitions in the visible-NIR region, while the FeX complexes lack these. In particular, the energy of the visible band at 559 nm (17 900 cm⁻¹) in FeCl (Figure 8) likely corresponds to the lowest energy LMCT transition calculated by TD-DFT (Figure S11) at 20 418 cm⁻¹ (Figure S12). For FeCH₃, no such distinct band is calculated, but the LMCT shoulders extend into the region where the band at 517 nm (19 340 cm⁻¹; Figure 8) is observed. For the CoX complexes, the visible bands were assigned to d-d transitions and analyzed approximately using LFT, which description is confirmed by TD-DFT. The longer wavelength, more intense, visible bands at 687 nm (14 555 cm⁻¹) and 725 nm (13 790 cm⁻¹) for CoCl and CoCH₃, respectively, are d-d in character, with the electron density changes (see Figure S12) entirely on the Co^II center. Their energies are matched by calculated bands (Figure S11) at 15 707 cm⁻¹ and 13 426 cm⁻¹ respectively for CoCl and CoCH₃. Additionally, the shorter wavelength, less intense, pair of visible bands for CoCl at 514 nm (19 455 cm⁻¹) and 540 nm (18 520 cm⁻¹) are matched by a calculated band at 19 421 cm⁻¹ (see Figure S11, which gives further discussion on this point).

Quantum chemical theory (QCT): ab initio calculated g-values and zfs.

Complete active space self-consistent field (CASSCF) calculations were performed on the series of complexes using the atomic coordinates derived from previously reported x-ray structures. The results of these ab initio calculations were mapped onto a ligand field Hamiltonian using the ab initio ligand field theory (AILFT) procedure.¹¹⁹ The AILFT orbital level diagram is presented in Figure 9 and the relevant parameters (3d single electron orbital energies, Racah and ζ values) are listed in Table 2. The Racah parameters determined by AILFT are greater than their free-ion values (by ~15 – 20% in B and 2 – 6% in C),¹¹⁷ so they should not be used in absolute sense, but are useful in comparison among the MX series in terms of showing that each pair of complexes with the same metal ion has essentially the same parameters despite the difference between X = Cl and CH₃. The SOC constants so determined are ~93% of the free-ion values across all four complexes.

Figure 9.

AILFT d-orbital energy level diagram derived from CASSCF calculations for FeCl, FeCH₃, CoCl, and CoCH₃. This quantitative ordering is the same as that shown qualitatively in Figure 1, except therein the splitting between $d_{yz}$ and $d_{z^2}$ orbitals is increased for illustrative purposes with $d_{z^2}$ lowest as in Andres et al. ⁴ This apparent discrepancy is the consequence of non-Aufbau occupation as described in the text.

Table 2.

CASSCF + SOC derived AILFT parameters (in cm⁻¹) for MX series.

Compound	3d Orbital Energies $\left(d_{yz},d_{z^2},d_{xz},d_{x^2-y^2},d_{xy}\right)$	ζ a	B, C, (C/B) b
FeCl	0, 96, 2391, 4512, 11556	395.6	1087, 4125, (3.80)
FeCH3	0, 87, 2376, 5288, 10862	393.4	1077, 4123, (3.83)
CoCl	0, 58, 1935, 4138, 11049	504.4	1146, 4336, (3.78)
CoCH3	0, 97, 1875, 5128, 10248	502.2	1138, 4336, (3.81)

^aThese can be compared to the free-ion values: 427 (Fe^II) and 533 (Co^II).¹²⁰

^bThese can be compared to the free-ion values: 897.1 (B), 3877.1 (C), 4.32 (C/B) (Fe^II) and 988.6 (B), 4214.3 (C), 4.26 (C/B) (Co^II).¹¹⁷

The AILFT analysis suggests that in both FeCl and FeCH₃ the $d_{yz}$ orbital is lowest in energy. However, the lowest state is shown to have a dominant configuration (~90%) where the $z^2$ orbital is doubly occupied (Figures 9 and 10 (left)). This non-Aufbau ground state indicates that there is a strong competition between electron repulsion and the ligand field, where the energy of the ground state is minimized when the lowest one-electron AILFT orbital remains singly occupied and the second lowest orbital is doubly occupied such that the lowest energy configuration is $\left[d_{yz}^1{d}_{z^2}^2{d}_{xz}^1{d}_{x^2-y^2}^1{d}_{xy}^1\right]$. This is the same orbital occupancy proposed previously by Andres et al.,⁴ but their analysis did not reveal the non-Aufbau occupation pattern so that their Aufbau occupancy, as shown in Figure 1, is $\left[d_{z^2}^2{d}_{yz}^1{d}_{xz}^1{d}_{x^2-y^2}^1{d}_{xy}^1\right]$.

After the inclusion of spin orbit coupling, the calculations for both FeCl and FeCH₃ predict negative axial values of the zero-field parameter, D, and with |E/D| = 0.04 for both compounds. This is consistent with their X-band EPR spectra, namely that these showed low field (high g′) transitions.⁴ For FeCl the ground state quasi-doublet is calculated to be separated by ~0.27 cm⁻¹ (i.e., in the X-band EPR energy range) with the first excited states at 138 and 151 cm⁻¹. The calculations on FeCH₃ predict a nearly identical separation of the ground quasi-doublet (0.26 cm⁻¹) and first excited quasi-doublet at 135 and 148 cm⁻¹. These values are all reasonably close to the experimental values and reproduce the slightly larger energy transitions in the FIRMS results of FeCl compared to the FeCH₃. The origin of this large zfs is understood by examining the low-lying excited states and their interaction with the ground state via spin-orbit coupling (Figure 10). By far the largest contribution to zfs is the coupling between the nearly degenerate orbital pair ($d_{yz}$ and $d_{z^2}$). This is consistent with the explanation previously given by Andres et al.⁴

As seen in Figure 9, the AILFT orbital level diagram predicts the same qualitative ordering of the d-orbitals in CoCl and CoCH₃ as their Fe analogues. Interestingly, in both CoX complexes the CASSCF-AILFT derived ground state contains two major configurations $\left[d_{z^2}^2{d}_{yz}^1{d}_{xz}^1{d}_{x^2-y^2}^1{d}_{xy}^1\right]$ (55% in CoCl, 45% CoCH₃) and $\left[d_{z^2}^2{d}_{yz}^1{d}_{xz}^1{d}_{x^2-y^2}^1{d}_{xy}^1\right]$ (42% in both CoCl and CoCH₃). The experimentally determined and CASSCF/NEVPT2 calculated (in parenthesis) g′-values of CoCl are g_x′ = 5.64 (6.12), g_y′ = 4.62 (4.94), and g_z′ = 1.97 (1.92). These values are consistent with a positive value of D, where the calculated value of D = +65.5 cm⁻¹ (|E/D| = 0.07 – in good agreement with the experimental value from X-band EPR of CoCl) corresponding to a zero-field gap of 2D* = 132 cm⁻¹, a slight overestimation of the experimental value. As discussed above, the X-band EPR spectrum of CoCH₃ shows only a single observable g′-value, g_z′_(max) = 8.50, which suggests this compound displays a negative D. The CASSCF/NEVPT2 calculations result in g_z′ = 9.94, D = −122.5 cm⁻¹, |E/D|= 0.04 that corresponds to a zero-field gap of 245 cm⁻¹. The difference in the sign of D between CoCl and CoCH₃ can be rationalized by examining how the excited states couple through the spin-orbit interaction into the ground state. This is shown in Figure 11 (right), which reveals that there is a substantial reordering of the excited state energies between the two compounds. This energetic reordering is responsible for the change in the sign of D and can be explained qualitatively by the difference between the methyl and chlorido ligands. The increase in energy of both the ⁴B₁ and, more importantly, ⁴A₂ excited states upon going from CoCH₃ to CoCl (Figure 11, right; also Figure 9) arises from the increase in energy of the b₁ ($d_{xz}$) and a₂ ($d_{xy}$) orbitals as result of adding π-donation from Cl⁻ (along x) that is absent in the σ-only donor CH₃⁻. There is a counteracting decrease in energy of the ⁴A₁ excited state upon going from CoCH₃ to CoCl caused by the a₁ ($d_{x^2-y^2}$) orbital decreasing in energy as the stronger σ-donor methyl is replaced by chloride. But this reordering has a lesser effect on the zfs as ⁴A₁ is more weakly coupled to the ⁴B₂ ground state than either ⁴B₁ and ⁴A₂ are. Additionally, Table S6 lists the major SOC contributions from excited states to the zfs of CoX.

The AILFT values for ζ, B, and C can be input into the LFT software (DDN program) along with the single electron d orbital energies (Table 2) to yield spin Hamiltonian parameters for modelling MX as a pure dⁿ system. For the FeX complexes, this demonstrates that there is a single g′ that is large, consistent with experiment. Use of an applied field of 50 mT (corresponding roughly to the experimental X-band resonant field) gives g′ ≈ 11.3(1) for both FeCl and FeCH₃, in good agreement with the observed values (10.9 for FeCl and 11.4 for FeCH₃).⁴ Moreover, the direction is correct in that this is g′ along x – the Fe-X bond. The splitting of the ground state quintet gives −50 cm⁻¹ > D > −70 cm⁻¹ for both FeX complexes, the negative sign and large magnitude as seen experimentally. In the case of CoCl, this procedure gives a splitting 2D* ≈ 170 cm⁻¹. Ignoring the rhombic splitting, which cannot be extracted from this calculation and is in any case small, gives D ≈ +85 cm⁻¹, ~50% off from experiment (Table 1). The sign can be readily determined since the lower doublet has spin magnitude ±0.31 and is thus m_S = ±1/2, while the higher doublet has spin magnitude ±1.19 and is m_S = ±3/2. These values were calculated using an applied field B₀ = 300 mT – a typical X-band resonant field. This calculation also yielded g′ = [2.38, 8.55, 1.32] (given as g_x, g_y, g_z, rather than the observed g_max, g_mid, g_min). This g′ is quite different from that observed for CoCl, and requires a rather peculiar set of intrinsic parameters: E/D = 1/3 with g = [2.38, 3.13, 1.80]. For CoCH₃, the spin magnitudes are more ambiguous (lower doublet ±0.06; higher doublet ±0.44), but the higher spin doublet clearly corresponds to m_S = ±1/2, hence the negative sign given here for D. The calculated 2D* ≈ 278 cm⁻¹, so D ≈ −139 cm⁻¹, larger magnitude that what is found experimentally, and g′ = [0.36, 10.08, 0.24] (again as g_x, g_y, g_z, rather than the observed g_max, g_mid, g_min), which is consistent with the limited experimental information. Overall, AILFT reproduces well the low-field X-band EPR resonances observed for both FeX and CoCH₃, although not the “conventional” EPR signature of CoCl, with the g anisotropy and zfs of both CoX complexes being overstated.

QCT Calculated Mössbauer Parameters and ⁵⁷Fe, ⁵⁹Co, and ¹⁴N Hyperfine Couplings.

Thanks to the use of variable applied magnetic fields, along with the standard Mössbauer parameters, namely isomer shift, δ, and quadrupole splitting ΔE_Q, the study by Andres et al. reported an internal magnetic field, B_int, along the x axis (i.e., C₂ axis, see Figure 1) that was quite large, +62 T for FeCl and +82 T for FeCH₃.⁴ Subsequently, in a study of N₂-binding involving related Fe^II and Fe^I β-diketiminate complexes,¹²¹ DFT calculations were performed on FeCl and FeCH₃ as well as on the novel complexes in that work. The relevant results are summarized in Table S5. This was a pioneering study given the state of DFT calculations at that time and Stoian et al. were able to reproduce the δ and ΔE_Q values reasonably well, even given the near orbital degeneracy of the FeX system. Indeed, we obtain essentially the same results for these parameters, despite using more highly developed software and having the benefit of extensive computational benchmarking of ⁵⁷Fe Mössbauer data.^{79, 122} We note that although ab initio (CASSCF) methods are suitable for the purely electronic parameters (i.e., zfs as well as orbital energies), the use of DFT for nuclear-electronic parameters (i.e., hyperfine coupling) we believe is still the optimal approach.^123–126 The calculated quadrupole splitting is reasonably close to experiment (see Table S5) although the calculated asymmetry parameter (η = V_mid − V_min)/V_max) is not, being too high for FeCl and too low for FeCH₃. In D_3h (or C_3h) symmetry as in the idealized complex in Figure 1 (left), η = 0, so the results here demonstrate the difficulty in quantifying the in-plane bonding (electron distribution) in FeX albeit not the out-of-plane behavior. The situation with respect to hyperfine coupling is more complicated as this depends on the difference between α and β spin densities at the nucleus as opposed to their sum, which determines the isomer shift. As noted above, the complete A(⁵⁷Fe) tensor was not determined for FeX, only the component along the Fe-X bond. We find here that the largest magnitude calculated component is quite far off from experiment (see Table S5) indicating the challenge of such calculations even with current computational power. Lacking the extreme orbital near-degeneracy of the FeX complexes, the CoX complexes present a potentially more fruitful area for hyperfine coupling calculations. In principle, the quadrupole coupling (i.e., yielding the electric field gradient, V_ii) of ⁵⁹Co could also be determined from EPR/ENDOR, as is possible for (excited state) ⁵⁷Fe from Mössbauer, but this was not possible and rarely is, although it has been determined for ⁵¹V in vanadyl complexes.¹²⁷ We also observe only one component of the hyperfine coupling in CoCH₃. The calculated A(⁵⁹Co) for CoCl appears to underestimate the overall coupling as well as being much more anisotropic than observed. We have no explanation for this discrepancy other than the difficulty in quantifying the small difference between α and β spin populations, which affected the FeX calculations as well. Despite this, the calculated A(¹⁴N) for the nacnac ligands in CoCl agrees reasonably well with experiment (Table S5), with A_iso(¹⁴N) differing by only ~1 MHz (~15 – 20%). The calculation also supports the two ¹⁴N being essentially magnetically equivalent. The calculated ¹⁴N quadrupole coupling for CoCl also matches experiment with each component agreeing within ~0.1 MHz (Table S5).

Conclusions

The β-diketiminate (nacnac) ligand is widely used in coordination chemistry and can support complexes with low coordination numbers. The electronic structure of four pairwise related nacnac-supported three-coordinate complexes, two each of Fe^II and Co^II and two each with chlorido and methyl ancillary ligands, is examined in detail here. The two iron(II) complexes had been previously studied by applied-field Mössbauer spectroscopy,⁴ but QCT calculations of the type performed here were impossible 20 years ago. The zfs in these Fe^II complexes was inferred earlier only from the Mössbauer measurements. Here we directly observe their zfs thanks to the use of far-infrared magnetic spectroscopy (FIRMS). These measurements definitively show the large magnitude negative zfs in both FeCl and FeCH₃ (respectively, D = −38 and −37 cm⁻¹), with very low rhombicity (|E/D| = 0.05 and 0.03, respectively). It is notable that despite the differences between a methyl and chlorido ligand, the zfs is essentially the same in the two FeX complexes. This finding has implications for the design of SMMs in that the overall geometry rather than the identities of the coordinating ligands may be the key factor, at least in S = 2 systems. In the case of the two cobalt(II) complexes, no theoretical analysis of electronic structure or advanced spectroscopic measurements had been previously performed. In these Kramers (half-integer spin) ions, conventional EPR and ENDOR spectroscopy provided information on metal (via ⁵⁹Co hyperfine coupling from EPR) and ligand (via ¹⁴N hyperfine coupling from ENDOR) spin delocalization. The results for both metal and ligand are consistent with those for related Co^II complexes, and the present study provided the first measurement of a ¹⁴N hyperfine coupling for a β-diketiminate complex. The CoX complexes exhibit large magnitude zfs (respectively, D = +55 and −49 cm⁻¹), but with a sign change from positive in CoCl to negative in CoCH₃ that comes from a rearrangement of excited-state energies due to the donor properties of Cl⁻ versus CH₃⁻. Thus, the nature of the third donor may be crucial in determining the details of electronic structure in S = 3/2 systems. Calculation of spectroscopic parameters obtained from Mössbauer and EPR spectroscopy in its various forms still represents a challenge even using ab initio methods – at least for the low-coordinate MX systems studied here. We hope that theoreticians will take up this challenge so that a better understanding of the origin of the parameters can be obtained, which will assist in the design of such complexes with desired magnetic properties.

Synopsis.

High-spin (S > 1/2), low coordination number complexes are of interest as single molecule magnets (SMMs). The β-ketiminate (nacnac) ligand can support such complexes, here of general formula (nacnac)MX, where M = Fe^II (S = 2) and Co^II (S = 3/2), and X = Cl⁻ and CH₃⁻. Advanced paramagnetic resonance spectroscopy reveals the zero-field splitting (zfs) in these complexes and theory explains the origin of zfs and the complexes’ overall electronic structure.