Experimental Spin Density Distribution

NITROGEN FIXATION VIA A TERMINAL IRON(IV) NITRIDE

5.2 Results and Discussion

5.2.5.1 Experimental Spin Density Distribution

140 the first two excited singlet states, ¹Γ_0,1and¹Γ_0,2. The next two states,¹Γ_0,3and¹Γ_0,4, are of more mixed character, containing contributions from one-electron excitations from the 3d_xy, 3d_x2−y², and (3d_z2 + 2p_z) orbitals into both the (3d_xz−πN) and (3d_yz−π*NN) orbitals, although the latter is the dominant acceptor orbital.

These calculations validate the schematic MO description of the ³Γ_0,0 excited state proposed in Figure 5.8, A, and reveal the open-shell character of the singlet ground state,

1Γ_0,0. While the electronic structure of the ground state is clearly multiconfigurational, the dominant antiferromagnetic terms involve the 3d_yz/π*NN and 3d_z2/B 2p_z interactions, leading to a succinct description of the ¹Γ_0,0 state as an intermediate-spin, S = 1 Fe(II) center coupled antiferromagnetically toS =1/2 [NNMe₂]^•−andS =1/2 [R₃B]^•−ligands.

5.2.5 Electronic Structures of [(P₃^B)Fe(NNMe₂)]^+/− from Pulsed EPR Studies

determined independently via Q-band ENDOR and HYSCORE spectroscopy (Figure 5.11 and Appendix D). The HFC tensors of the remaining two, more strongly-coupled,³¹P atoms were determined through simultaneous fitting of X-band CW and ENDOR data. As can be seen from the¹⁴N–¹⁵N difference spectrum shown in Figure 5.10, C, the final simulation is of high quality.

Table 5.4: Collectedg-tensors from Experiment and Theory

Complex g₁ g₂ g₃ g_iso ∆g^a

[(P₃^B)Fe(NNMe₂)]⁻

Expt. 2.006 2.041 2.068 2.038 0.062 10% HF 2.033 2.043 2.056 2.044 0.023 CASCI^b 2.001 2.038 2.056 2.032 0.055 (P₃^Si)Fe(NNH₂) 2.004 2.027 2.070 2.034 0.066 (P₃^Si)Fe(NNMe₂) 2.000 2.030 2.080 2.037 0.080 [(P₃^B)Fe(NNMe₂)]⁺

Expt. 2.005 2.089 2.192 2.095 0.187 10% HF 2.009 2.055 2.078 2.047 0.069 CASCI^c 2.004 2.115 2.248 2.122 0.244 [(P₃^B)Fe(NNH₂)]⁺ 2.006 2.091 2.222 2.106 0.216 [(P₃^B)Fe(NAd)]⁺ 1.970 2.058 2.419 2.149 0.449

a∆g =g₃−g₁.

bPerformed on top of a SA-CASSCF(11,10) reference averaged over the first 10 doublet states.

cPerformed on top of a SA-CASSCF(9,10) reference averaged over the first 10 doublet states.

As compiled in Table 5.6, the HFC tensors of Nα/Nβ are both dominated by their anisotropic parts (t). While Nβ is well-simulated by an axial anisotropic HFC tensor, consistent withπ-symmetry spin density on this center, Nαrequires an extremely rhombic tensor (δHFC(Nα)= 0.7). This accords well with the theoretical description of Nαin the³Γ_0,0 state of (P₃^B)Fe(NNMe₂) (vide supra), a result that can be rationalized by examination of the qualitative MO diagram shown in Figure 5.8, A. One-electron reduction of the³Γ_0,0state would occupy the 3d_x2−y²orbital, which has little overlap with the “NNMe₂” ligand orbitals and would thus correspond to a primarily metal-centered reduction. In this framework, the electronic structure of [(P₃^B)Fe(NNMe₂)]⁻ would be best described as an S = 3/2 Fe(I)

142

310 320 330 340 350

B (mT)

d² "/dB² A

B

C

290 300 310 320 330 340 350 B (mT)

d "/dB

d² "/dB²

D

E

F

Figure 5.10: (A) CW X-band EPR spectrum of [(P₃^B)Fe(¹⁴N¹⁴NMe₂)]⁻; data are plotted in black with a simuation in blue. (B) CW X-band EPR spectrum of [(P₃^B)Fe(¹⁵N¹⁵NMe₂)]⁻; data are plotted in black with a simulation in red. (C) Difference spectrum for the data shown in (A) and (B); data are plotted in black with a simulation in pink. (D) CW X-band EPR spectrum of [(P₃^B)Fe(NNH₂)]⁺. (E) CW X-band EPR spectrum of [(P₃^B)Fe(NNMe₂)]⁺; data are plotted in black with a simulation in blue. (F) Second-derivative spectra of those presented in (E). All data were collected at 77 K.

center coupled antiferromagnetically toS =1/2 [NNMe₂]^•−andS =1/2 [R₃B]^•−ligands.

This description is consistent with the relatively large isotropic ¹¹B HFC constant (15.3 MHz), which can be compared to those of planar [Ph₃B]^•− (a_iso(¹¹B) = 22 MHz) and the pyramidalized B atom of (P₃^B)Cu (a_iso(¹¹B) = 64 MHz),^78,79 the latter of which has been characterized as containing a one-electron Cu–Bσbond.

To evaluate this electronic structure in more detail, we synthesized [(P₃^B)Fe(NN- (¹³CH₃)₂)]⁻, incorporating a ¹³C spin-probe distal to the Fe center (> 3.8 Å). Q-band ENDOR spectroscopy resolves a single ¹³C HFC tensor for this isotopologue (Table 5.5).

As with the VT¹H NMR data of presented in Section 5.2.4.1, the large isotropic¹³C HFC of 19.6 MHz demonstrates that the “NNMe₂” ligand harbors significant spin density. The magnitude of this HFC constant is on par with that expected for a sp³-hybridized carbon atom bonded directly to aπ-radical center. For example, aiso(¹³C) = 38 MHz for the sp³ carbon of the ethyl radical.⁸⁰While the¹³C HFC constants of knownN,N-dimethylhydrazyl

A B

Figure 5.11: Selected HYSCORE spectra of (A) [(P₃^B)Fe(¹⁴N¹⁴NMe₂)]⁻ and (B) [(P₃^B)Fe(¹⁵N¹⁵NMe₂)]⁻, exhibiting HFC to two distinct N atoms. The top panels show the experimental spectrum, with intensities indicated by the color map. The bottom pan- els reproduce the experimental spectra in grey, and overlay simulations from a relatively strongly coupled N atom (red, assigned as N_α), and a relatively weakly coupled N atom (blue, assigned as N_β). Spectra were collected at 15 K at 1214 mT (g= 2.001).

radicals have not been determined, we can compare this toaiso(¹³C)= 37 MHz calculated by DFT methods for [NNMe₂]^•− in its equilibrium geometry andaiso(¹³C) =−22 MHz in a planar geometry resembling that observed crystallographically for the “NNMe₂” ligand of [(P₃^B)Fe(NNMe₂)]⁻.

Theg-tensor of the ground state doublet of [(P₃^B)Fe(NNMe₂)]⁺(²Γ_+,0) is significantly more anisotropic than that of its two-electron reduced congener, indicating of the presence of low-lying excited doublet states (vide infra), at least relative to the excited-state chem- istry of [(P₃^B)Fe(NNMe₂)]⁻. The overall rhombicity and anisotropy of the g-tensor of [(P₃^B)Fe(NNMe₂)]⁺ closely matches that of the protonated complex [(P₃^B)Fe(NNH₂)]⁺,¹⁶ validating the use of the former as a spectroscopic model (Figure 5.10, D and E). This is in contrast to theg-tensor of the isoelectronic imido species, [(P₃^B)Fe(NAd)]⁺, previously suggested to model [(P₃^B)Fe(NNH₂)]⁺,¹⁶ which is significantly more anisotropic (Table 5.4).

144 As above, we have determined the complete set of heteronuclear HFC tensors for [(P₃^B)Fe(NNMe₂)]⁺ using a combination of X-band CW and Q-band ENDOR/HYSCORE experiments on¹⁴N,¹⁵N, and¹³C isotopologues. An examination of Table 5.5 shows that the magnitude of the isotropic couplings almost uniformly decrease upon two-electron oxidation of [(P₃^B)Fe(NNMe₂)]⁻ to form [(P₃^B)Fe(NNMe₂)]⁺. The only exceptions are a single³¹P nucleus, which remains essentially unchanged, and Nβ, which has an increased isotropic component. However, both N atoms have notably decreased anisotropic hyperfine couplings in the oxidized complex (Table 5.6), indicating a uniform reduction in theπ-symmetry spin density on these nuclei, although we note that Nαretains its rhombicity.

This trend can be simply rationalized in terms of an exchange-coupling model of the bonding in [(P₃^B)Fe(NNMe₂)]^+/− in which oxidation produces stronger antiferromagnetic coupling between the Fe and its ligands, thereby reducing the overall degree of spin de- localization and core spin polarization. In an unrestrictedansatz, this occurs because the overlap between theαandβspin manifolds increases with greater coupling; in a CIansatz, it is because the weight of configurations with antibonding character decreases. In either framework, there are, in a sense, fewer “effectively unpaired” spins.^v Such an interpretation would be in agreement with the results of Section 5.2.4.2, where the transition from the

1Γ_0,0to the³Γ_0,0state of (P₃^B)Fe(NNMe₂) populates the repulsive 3d_xz orbital and weakens the Fe–NNMe₂(and Fe–B) coupling. Conversely, oxidation of [(P₃^B)Fe(NNMe₂)]⁻should depopulate this orbital and strengthen the spin-coupling interactions in [(P₃^B)Fe(NNMe₂)]⁺.

5.2.5.2 Computational Description of²Γ_±,0

To validate this interpretation of the electronic structures of [(P₃^B)Fe(NNMe₂)]^+/−, we turn to quantum-chemical calculations. As with the³Γ_0,0state of (P₃^B)Fe(NNMe₂), calculations of the ground states of [(P₃^B)Fe(NNMe₂)]^+/−produce solutions with BS character regardless

vThis is not to say that there is “more” than one unpaired electron in the weakly-coupled state, but rather that the distribution of the (real) spin density becomes less diffuse in the more strongly-coupled state.⁷⁵

145 Table 5.5: Collected HFC Constants of [(P₃ )Fe(NNMe₂)] from Experiment and Theory

a_iso(MHz)^b n Nucleus A₁(MHz)^a A₂(MHz)^a A₃(MHz)^a

Expt. 0% HF 10% HF 25% HF

− ¹⁴Nα −3.9 −29.2 11.8 −7.1 11.6 5.2 −5.2

− ¹⁴N_β 1.6 −5.7 1.6 −0.9 2.8 −1.2 −5.2

− N-Me¹³C 20.0 20.9 18.0 19.6 21.8/24.2 21.8/23.7 24.0/24.7

− ³¹Pα 134.6 124.6 116.6 125.3^c 159.5 133.1 86.4

− ³¹P_β 82.9 82.6 79.3 81.6^d −34.3 −53.9 −104.1

− ³¹Pγ 28.1 30.0 27.6 28.6^e 48.0 28.6 −2.6

− ¹¹B 15.9 15.2 14.7 15.3 −14.3 −32.7 −79.4

− ⁵⁷Fe 18.1 15.3 53.9 29.1 −14.2 −20.7 −31.9

+ ¹⁴N_α −10.7 −5.7 −0.1 −5.7 1.1 −0.5 −0.9

+ ¹⁴Nβ −1.5 −7.3 −1.5 −3.4 −3.8 −5.6 −10.0 + N-Me¹³Cα 9.7 8.5 11.0 9.7 13.0 12.6 14.8

+ N-Me¹³C_β 8.4 6.7 8.8 8.0 11.3 10.7 11.8

+ ³¹Pα 48.5 73.0 51.7 57.7^e −71.5 −92.4 −120.0

+ ³¹Pβ 55.2 49.0 36.5 46.9^f −65.9 −89.0 −130.4 + ³¹P_γ 40.0 30.0 36.5 35.5^g −50.2 −72.9 −112.9

+ ¹¹B 10.3 9.6 7.6 9.2 −7.3 −11.1 −22.1

+ ⁵⁷Fe 24.0 9.0 0.1 11.0 13.5 7.4 −4.3

aThe orientation of the HFC tensor isg₁=g_min,g₂=g_mid,g₃=g_max.

bThe absolute signs ofa_isohave not been determined experimentally.

cPαis taken to be P1.

dP_βis taken to be P2.

ePγis taken to be P3.

fPαis taken to be P3.

gP_βis taken to be P1.

hPγis taken to be P2

146 Table 5.6: Collected Anisotropic HFC Constants of [(P₃^B)Fe(NNMe₂)]ⁿfrom Experiment and Theory

t(MHz)^a δ_HFC

n Nucleus T₁(MHz) T₂(MHz) T₃(MHz)

Expt. 10% HF CASCI^b Expt. 10% HF CASCI^b

− ¹⁴N_α 3.3 −22.1 18.9 −11.1 −16.1 −8.0 0.7 0.6 0.6

− ¹⁴Nβ 2.4 −4.8 2.4 −2.4 −7.9 −1.8 ~0 0.1 0.2 + ¹⁴Nα −5.0 ~0 5.0 −2.5 −5.5 −1.4 ~1 0.5 0.5

+ ¹⁴Nβ 1.9 −3.8 1.9 −1.9 −5 −0.6 ~0 0.1 0.6

aThe absolute signs ofthave not been determined experimentally, but are assigned as negative to be consistent with DFT and CASCI calculations.

bUsing a SA-CASSCF(11,10) reference forn=−, and a SA-CASSCF(9,10) reference forn= +. In both cases the first 10 doublet states were included.

of the degree of HF exchange included in the exchange-correlation functional. This character is, however, systematically larger with increased HF character.

As seen in Table 5.5, at 10% HF, the prediction of the isotropic parts of the metal and ligand HFC tensors is in good agreement for [(P₃^B)Fe(NNMe₂)]⁻, with the exception of a_iso(¹¹B), which is overestimated. This is likely due to contamination of the BS spin density by determinants of higher multiplicity (for ²Γ_−,0^BS, hSˆ²i = 1.02), and suggests an empirical spin projection factor of roughly 2. The same effects can be seen for the anisotropic HFC tensors of N_α/N_β(Table 5.6), where the 10% HF calculation reproduces the experimental δ_HFC, but overestimates t by the same factor of ~2, on average. The zeroth order wave- function from CASSCF is a proper eigenfunction of spin, so to estimate the effects of spin contamination, we have also calculated the anisotropic N HFC tensors using a CASCI cal- culation on top of a CASSCF(11,10) reference, utilizing the same active space composition as before. Including the lowest 10 doublet roots in this calculation, we obtain anisotropic tensors that are in excellent agreement with experiment (Table 5.6). Given that we have neglected dynamic correlation in these calculations, our results indicate that static correla- tion effects (i.e., antiferromagnetic interactions) dominate the valence electronic structure of [(P₃^B)Fe(NNMe₂)]⁻.

For [(P₃^B)Fe(NNMe₂)]⁺, the DFT calculations give poorer agreement with experiment at each level of HF inclusion (Table 5.5). This is particularly true of aiso(³¹P), which are consistently overestimated, andaiso(¹⁴N_α), which is underestimated. However, at 10% HF, the DFT method appears to give a good description of the isotropic ⁵⁷Fe, ¹³C, and ¹¹B couplings. Examining the anisotropic parts of N_α/N_β, we again see that the magnitudes are overestimated at 10% HF, but that the symmetries are in good agreement with experiment.

As before, the agreement in t is improved from a CASCI calculation on top of a 10 root CASSCF(9,10) reference. It is noteworthy that the CASCI calculation produces an anisotropic HFC tensor for Nβ that is too rhombic, suggesting that neglecting dynamic

148 correlation in this redox state is a poorer approximation.

Collectively, these calculations give a consistent, qualitative interpretation of the²Γ_±,0 states. In ²Γ_−,0, the population of the 3d_xz orbital weakens the metal-ligand coupling interactions (cf. Figure 5.8 A), producing net negative spin densities at B and N_β, and a rhombic spin density about Nα. The same phenomenon was calculated above for the³Γ_0,0 state (Figure 5.8, B), and is confirmed experimentally for²Γ_−,0(Table 5.6). Upon oxidation, stronger antiferromagnetic couplings partially quench the ligand-centered spins, producing an electronic structure that is more approximately a “simple” metalloradical. These effects are visualized in Figure 5.12, where it can be seen that, as expected, the DFT calculations tend to exaggerate the magnitude of the ligand-centered spin densities.⁷⁷

This interpretation is made quantitative by a calculation of the polyradical character of ground-state specific CASSCF wavefunctions for the ²Γ_±,0 states. As seen in Table 5.7, the ²Γ_−,0 state has a similar degree of polyradical character as the ³Γ_0,0 state, and a number of effectively unpaired electrons significantly in excess of 1. Thus, as posited above, [(P₃^B)Fe(NNMe₂)]⁻is best viewed as anS =3/2, Fe(I) center antiferromagnetically coupled toS = 1/2 [NNMe₂]^•−and [R₃B]^•− ligands. The polyradical character decreases by 50% upon two-electron oxidation to ²Γ_+,0, indicating much stronger antiferromagnetic coupling in the ground state of [(P₃^B)Fe(NNMe₂)]⁺. The enhanced coupling is reflected by the reduced multireference character of the²Γ_+,0state (the least of the redox series, about 85% single-determinantal), although the symmetry of the antiferromagnetic interactions persists, and ND/NU remain larger than that expected for an orbitally-pure S = 1/2 state.

This leads to a description of [(P₃^B)Fe(NNMe₂)]⁺ in its ground state as an intermediate- spin,S =3/2 Fe(III) ion strongly antiferromagnetically coupled to [NNMe₂]^•−and [R₃B]^•−

ligands.

We have also examined theg-tensors of²Γ_±,0theoretically. As shown in Table 5.4, even for the relatively isotropic tensor of²Γ_−,0, DFT methods fail to capture the correct levels

4Γ_+,0

2Γ_−,0

10% HF CASSCF

2Γ_+,0

Figure 5.12: Spin density isosurfaces (isovalue = 0.005 a.u.) for the²Γ_±,0and⁴Γ_+,0states from BS DFT and CASSCF calculations. α density is shown in red, while β density is shown in green. For²Γ_±,0, the DFT spin densities were calculated using the basis sets used for the prediction of EPR properties, while that of the⁴Γ_+,0 state used the “valence” basis set described in the Experimental Section.

ofg-anisotropy, an effect that has been attributed to the tendency of DFT to overestimate metal-ligand covalency.⁸¹ An explicit treatment of the manifold of doublet excited states using CASCI producesg-tensors in much better agreement with experiment, even neglecting dynamic correlation. For ²Γ_−,0, NEVPT2 predicts the lowest-lying doublet excited state,

2Γ_−,1, to be ca. 11,000 cm⁻¹ above ²Γ_−,0, which explains the low g-anisotropy. On the other hand,²Γ_+,1is predicted to be only ca. 7,000 cm⁻¹above²Γ_+,0, and this state is almost completely responsible for the shift ofg₃above the free-electron value.

150 Table 5.7: NOON-based Chemical Bonding Indices for [(P3B)Fe(NNMe2)]^+/−from CASSCF calculations

2Γ_−,0 ²Γ_+,0

NOs n₊ n− Y^a ND NU n₊ n− Y^a ND NU

3d_z2 ±B 2p_z 1.85 0.15 0.15 0.56 0.30 1.90 0.10 0.10 0.39 0.20 3d_yz± π*_NN 1.75 0.25 0.25 0.87 0.50 1.91 0.09 0.09 0.35 0.18

CAS – – – 3.14 2.16 – – – 2.20 1.61

4Γ_+,0^b

3d_z² ±B 2pz 1.80 0.20 0.20 0.73 0.40

3d_yz± π*_NN 1.86 0.14 0.14 0.53 0.29

CAS – – – 4.33 3.71

aY =1− ⁿ⁺⁻ⁿ₂ ⁻. Note that for a spatially-matched bond/antibond pair,Y = n−.

bComputed in the quartet geometry.