Supporting Information - PNAS · 2012-08-16 · Supporting Information Srnec et al....

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Supporting Information Srnec et al. 10.1073/pnas.1212693109 SI Text SI Analysis. Fano analysis. According to Fanos theory (13), the absorption (abs) line shape αðνÞ can be fit to the four-parameter equation: αðνÞ α B ðνÞ RðνÞ¼ 1 þ p q 2 þ 2qðv v 0 Þ γ 1 1 þ v v 0 γ 2 ; [S1] where α 0 α N ðν 0 Þ ¼ hψ B j ~ μjΨ GS i 2 hΨ B j ~ μjΨ GS i 2 p; [S2] q ¼ hΨ S 0 j ~ μjΨ GS i πhΨ S jH i jψ B ihψ B j ~ μjΨ GS i ; [S3] γ ¼ πjhψ B jH i jΨ S ij 2 ; [S4] and α B ðνÞ is the absorption profile of a broad vibronic band (background); α 0 is the absorption at the center of the interfer- ence; Ψ GS is the ground state; Ψ B and Ψ S are broad (allowed) and sharp (forbidden) excited states, respectively; Ψ S 0 is the sharp state modified by the interaction Hamiltonian H i [in this case spin-orbit coupling (SOC)]; ψ B is a fraction of Ψ B connected to Ψ S ; and ~ μ is the electric-dipole transition operator. The three parameters p, q, and γ determine the height, shape, and width, respectively, of the Fano feature. Both ðε observed ε background Þ abs and ðΔε observed Δε background Þ MCD (MCD; magnetic circular dichroism) profiles were fit using Eq. S1, resulting in the parameters p ¼ 0.11, q ¼ 0.15, and γ ¼ 160 cm 1 for the dip in the abs spectrum (Fig. S5B), and p ¼ 0.02, q ¼ 5.0, and γ ¼ 150 cm 1 for the sharp peak in MCD (Fig. S5C). The measure of spin-orbit coupling between the broad spin-allowed ( 5 E) and the sharp spin-forbidden state, γ, remains unchanged in both abs and MCD. Similarly, the parameter p,a quantity reflecting the fraction of 5 E interacting with the spin- forbidden state, is of the same order in both fits. Importantly, the parameter q (related to the ratio of the transition-dipole matrix elements for the spin-orbitperturbed sharp and broad states) is larger in MCD than in abs (i.e., the dip in abs becomes a peak in MCD). This difference between q abs and q MCD , as well as the quantity γ, is evaluated below in terms of spin-orbit coupling of specific spin-forbidden states with the 5 Eðxz; yzÞ state. Correlating the MCD data to the complete active space sec- ond-order perturbation theory/spin-orbit complete active space state interaction (CASPT2/SOCASSI) computational analysis in Interactions of the 5 E state with spin-forbidden 3 E and 3 A 1 states of the main text: (i) The 3 A 1 state mixes weakly via SOC with the left circularly polarized (LCP) component of the 5 E state, bor- rowing its positive MCD intensity; (ii) the 3 A 1 state is approxi- mately 1; 050 cm 1 higher in energy than the LCP component (Fig. 4B), matching the relative position of the sharp peak (labeled 4in Fig. 3B) with respect to the maximum of the LCP progression; (iii) the calculated out-of-state SOC matrix element (160 cm 1 ) has to be scaled down by the overlap (in MCD) of the sharp Fano peak with the positive component of broad allowed band (approximately 7%, from the FranckCondon analysis in Fig. 3B), giving a value of 11 cm 1 (this is consistent with the value of 7 cm 1 derived from the Fano analysis of the abs spec- trum in Fig. 3B using Eq. S4); and (iv) the fact that the value of q is very low (0.15) in abs but 5.0 in MCD (i.e., a peak in MCD but a dip in abs) can be ascribed to the relative contribution of the Fano-active sublevel of the 5 A 1 ground state to the spectral intensity in the region around the Fano feature. For abs, the M s ¼ 1 sublevel contributes to the spin-forbidden Fano transition, and all sublevels (M s ¼ 0, 1, 2) contribute to the spin-allowed absorption intensity. In contrast, for MCD only the M s ¼ 1 sublevel contributes to both the spin-forbidden Fano transition intensity and the spin-allowed LCP MCD transition intensity; that is, none of the other sublevels contributes to MCD intensity. Thus, the fraction of sublevels contributing to the MCD Fano peak is large compared to abs, and q MCD >q abs . Further details of MCD 5 E pseudo-A term analysis. The energy split- ting between the LCP (positive) and LCP (negative) MCD-active M s sublevels, 2λ, can be estimated for the 5 E state for ζ 3d ðFe IV Þ¼ 515 cm 1 (4) to be þ258 cm 1 . The experimental value observed for the energy splitting of the pseudo-A term MCD intensity distribution (Fig. 1B) is þ200300 cm 1 , from a fit of the pseudo-A term with two overlapping bands. In contrast to this ligand-field (LF) estimate, the CASPT2/ SOCASSI value for the 5 Eðxz; yzÞ in-state j1; 1i and j 1; 1i energy-splitting 2λ is only þ98 cm 1 (Interactions of the 5 E state with spin-forbidden 3 E and 3 A 1 states and Fig. 4B). This indicates a reduction in λ for 1 caused by strong covalent FeO bonding, which quenches the SOC (a relativistic nephelauxetic effect) (5). However, the CASPT2/SOCASSI-predicted pseudo-A term splitting does increase from þ98 cm 1 to þ240 cm 1 after in- clusion of additional, out-of-state spin-orbit interactions, as developed in Interactions of the 5 E state with spin-forbidden 3 E and 3 A 1 states in the main text. This is consistent with the experi- mentally observed j1; 1i to j 1; 1i energy splitting of þ200300 cm 1 . SI Materials and Methods. Manipulation of all compounds was, as far as possible, conducted under an inert atmosphere using stan- dard Schlenk-line techniques and a nitrogen-filled glovebox. Di- chloromethane was dried by prolonged reflux under a nitrogen atmosphere and over calcium hydride, and freshly distilled prior to use. Butyronitrile was treated in a similar manner, but only after it had first been washed several times with concentrated hydrochloric acid to remove isonitrile impurities, and then dea- cidified and partially dried by stirring over anhydrous sodium car- bonate. ½Fe II ðd 36 -TMG 3 trenÞðCH 3 CNÞðOTf Þ 2 and the oxidant 2-(tert-butylsulfonyl)iodosylbenzene [2-ð t BuSO 2 ÞC 6 H 4 IO] were prepared according to published procedures (6, 7). Solutions of 1 (ca. 0.5, 5, and 10 mM) suitable for MCD spectroscopy were prepared, at 40 °C, by addition of 2-ð t BuSO 2 ÞC 6 H 4 IO (1.6, 1.5, and 1.2 equivalents, respectively) dissolved in dichloromethane (4, 13, and 20%, respectively, of the final volume) to butyronitrile solutions of ½Fe II ðd 36 - TMG 3 trenÞðCH 3 CNÞðOTf Þ 2 . Solutions of oxidant up to a concentration of 60 mM were routinely used. Yields of 1 were quantified using UV-vis spectroscopy, and found to be near quan- titative in the case of the 0.5- and 5-mM solutions and >85% in the 10-mM solutions. UV-visible absorption data were recorded on an HP8453A diode-array spectrometer equipped with a Unisoku cryostat and a Varian Cary 500 Scan spectrophotometer equipped with a Janis STVP-100 cryostat. Srnec et al. www.pnas.org/cgi/doi/10.1073/pnas.1212693109 1 of 8

Transcript of Supporting Information - PNAS · 2012-08-16 · Supporting Information Srnec et al....

Page 1: Supporting Information - PNAS · 2012-08-16 · Supporting Information Srnec et al. 10.1073/pnas.1212693109 SI Text SI Analysis. Fano analysis.According to Fano’stheory(1–3),

Supporting InformationSrnec et al. 10.1073/pnas.1212693109SI TextSI Analysis. Fano analysis. According to Fano’s theory (1–3), theabsorption (abs) line shape αðνÞ can be fit to the four-parameterequation:

αðνÞαBðνÞ

≡ RðνÞ ¼ 1þ p�q2 þ 2qðv − v0Þ

γ− 1

�∕�1þ

�v − v0γ

�2�;

[S1]

where

α0

αNðν0Þ¼ hψBj ~μjΨGSi2

hΨBj ~μjΨGSi2≡ p; [S2]

q ¼ hΨS 0 j ~μjΨGSiπhΨSjHijψBihψBj ~μjΨGSi

; [S3]

γ ¼ πjhψBjHijΨSij2; [S4]

and αBðνÞ is the absorption profile of a broad vibronic band(background); α0 is the absorption at the center of the interfer-ence;ΨGS is the ground state;ΨB andΨS are broad (allowed) andsharp (forbidden) excited states, respectively; ΨS 0 is the sharpstate modified by the interaction Hamiltonian Hi [in this casespin-orbit coupling (SOC)]; ψB is a fraction of ΨB connectedto ΨS; and ~μ is the electric-dipole transition operator. The threeparameters p, q, and γ determine the height, shape, and width,respectively, of the Fano feature.

Both ðεobserved∕εbackgroundÞabs and ðΔεobserved∕ΔεbackgroundÞMCD(MCD; magnetic circular dichroism) profiles were fit usingEq. S1, resulting in the parameters p ¼ 0.11, q ¼ 0.15, and γ ¼160 cm−1 for the dip in the abs spectrum (Fig. S5B), andp ¼ 0.02, q ¼ 5.0, and γ ¼ 150 cm−1 for the sharp peak in MCD(Fig. S5C). The measure of spin-orbit coupling between the broadspin-allowed (5E) and the sharp spin-forbidden state, γ, remainsunchanged in both abs and MCD. Similarly, the parameter p, aquantity reflecting the fraction of 5E interacting with the spin-forbidden state, is of the same order in both fits. Importantly, theparameter q (related to the ratio of the transition-dipole matrixelements for the spin-orbit–perturbed sharp and broad states) islarger in MCD than in abs (i.e., the dip in abs becomes a peak inMCD). This difference between qabs and qMCD, as well as thequantity γ, is evaluated below in terms of spin-orbit couplingof specific spin-forbidden states with the 5Eðxz; yzÞ state.

Correlating the MCD data to the complete active space sec-ond-order perturbation theory/spin-orbit complete active spacestate interaction (CASPT2/SO–CASSI) computational analysisin Interactions of the 5E state with spin-forbidden 3E and 3A1 statesof the main text: (i) The 3A1 state mixes weakly via SOC with theleft circularly polarized (LCP) component of the 5E state, bor-rowing its positive MCD intensity; (ii) the 3A1 state is approxi-mately 1;050 cm−1 higher in energy than the LCP component(Fig. 4B), matching the relative position of the sharp peak(labeled “4” in Fig. 3B) with respect to the maximum of the LCPprogression; (iii) the calculated out-of-state SOC matrix element(160 cm−1) has to be scaled down by the overlap (in MCD) of thesharp Fano peak with the positive component of broad allowedband (approximately 7%, from the Franck–Condon analysis inFig. 3B), giving a value of 11 cm−1 (this is consistent with the

value of 7 cm−1 derived from the Fano analysis of the abs spec-trum in Fig. 3B using Eq. S4); and (iv) the fact that the value ofq is very low (0.15) in abs but 5.0 in MCD (i.e., a peak inMCD buta dip in abs) can be ascribed to the relative contribution ofthe Fano-active sublevel of the 5A1 ground state to the spectralintensity in the region around the Fano feature. For abs, theMs ¼−1 sublevel contributes to the spin-forbidden Fano transition,and all sublevels (Ms ¼ 0,�1,�2) contribute to the spin-allowedabsorption intensity. In contrast, for MCD only the Ms ¼ −1sublevel contributes to both the spin-forbidden Fano transitionintensity and the spin-allowed LCP MCD transition intensity;that is, none of the other sublevels contributes to MCD intensity.Thus, the fraction of sublevels contributing to the MCD Fanopeak is large compared to abs, and qMCD > qabs.

Further details of MCD 5E pseudo-A term analysis. The energy split-ting between the LCP (positive) and LCP (negative) MCD-activeMs sublevels, 2λ, can be estimated for the 5E state forζ3dðFeIVÞ ¼ 515 cm−1 (4) to be þ258 cm−1. The experimentalvalue observed for the energy splitting of the pseudo-A termMCD intensity distribution (Fig. 1B) is þ200–300 cm−1, froma fit of the pseudo-A term with two overlapping bands.

In contrast to this ligand-field (LF) estimate, the CASPT2/SO–CASSI value for the 5Eðxz; yzÞ in-state j1; −1i and j − 1; −1ienergy-splitting 2λ is only þ98 cm−1 (Interactions of the 5E statewith spin-forbidden 3E and 3A1 states and Fig. 4B). This indicatesa reduction in λ for 1 caused by strong covalent Fe═O bonding,which quenches the SOC (a relativistic nephelauxetic effect) (5).However, the CASPT2/SO–CASSI-predicted pseudo-A termsplitting does increase from þ98 cm−1 to þ240 cm−1 after in-clusion of additional, out-of-state spin-orbit interactions, asdeveloped in Interactions of the 5E state with spin-forbidden 3Eand 3A1 states in the main text. This is consistent with the experi-mentally observed j1; −1i to j − 1; −1i energy splitting ofþ200–300 cm−1.

SI Materials and Methods. Manipulation of all compounds was, asfar as possible, conducted under an inert atmosphere using stan-dard Schlenk-line techniques and a nitrogen-filled glovebox. Di-chloromethane was dried by prolonged reflux under a nitrogenatmosphere and over calcium hydride, and freshly distilled priorto use. Butyronitrile was treated in a similar manner, but onlyafter it had first been washed several times with concentratedhydrochloric acid to remove isonitrile impurities, and then dea-cidified and partially dried by stirring over anhydrous sodium car-bonate. ½FeIIðd36-TMG3trenÞðCH3CNÞ�ðOTfÞ2 and the oxidant2-(tert-butylsulfonyl)iodosylbenzene [2-ð tBuSO2ÞC6H4IO] wereprepared according to published procedures (6, 7).

Solutions of 1 (ca. 0.5, 5, and 10 mM) suitable for MCDspectroscopy were prepared, at −40 °C, by addition of2-ð tBuSO2ÞC6H4IO (1.6, 1.5, and 1.2 equivalents, respectively)dissolved in dichloromethane (4, 13, and 20%, respectively, ofthe final volume) to butyronitrile solutions of ½FeIIðd36-TMG3trenÞðCH3CNÞ�ðOTfÞ2. Solutions of oxidant up to aconcentration of 60 mM were routinely used. Yields of 1 werequantified using UV-vis spectroscopy, and found to be near quan-titative in the case of the 0.5- and 5-mM solutions and >85% inthe 10-mM solutions.

UV-visible absorption data were recorded on an HP8453Adiode-array spectrometer equipped with a Unisoku cryostat anda Varian Cary 500 Scan spectrophotometer equipped with a JanisSTVP-100 cryostat.

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MCD spectra were collected on two different instruments: (i) aJasco J-730 spectropolarimeter, InSb detector (Teledyne JudsonTechnologies) and Oxford Instruments SM-4000-7T supercon-ducting magnet for the near-infrared (NIR) region; and (ii) aJasco J-810 spectropolarimeter, S1 or S20 detector photomulti-plier tubes (Hamamatsu), and Oxford Instruments SM-4000-7Tsuperconducting magnet for the UV-visible region. Data werecollected with an applied field of 7T at a series of temperaturesfrom 2–80 K, and baseline corrected by subtracting the 0Tsignals.

Spin-unrestricted density functional theory (DFT) calculationswere performed with the Gaussian 03 program (8) except wherespecified. Geometry optimization of 1 was carried out with theBP86 functional and the triple-ζ Pople basis set 6-311G*. TheS ¼ 2 geometry-optimized structure was used for time-depen-dent DFT (TD-DFT) calculations (BP86/6-311G*) in Gaussian09 (9), applying long-range exchange correction to the functionalfor more accurate prediction of charge-transfer excitations (10).Geometries for reaction coordinate energy profiles were opti-mized with B3LYP/LanL2DZ for consistency of comparison witha previous study (11) on 1. All frequency calculations to obtainΔH and ΔG values were performed at T ¼ 273 K to correspondwith the experimental kinetics, and single-point energies werecalculated with B3LYP/6-311++G** and solvated using thepolarized continuum model (PCM) with acetonitrile as the sol-vent (12–15). Molecular orbital (MO) compositions were parsedfrom the output files with QMForge (16) and visualized withLumo (17).

Complete active space self-consistent field (CASSCF) (18),state-averaged CASSCF (SA-CASSCF), CASPT2 (19), and mul-tistate CASPT2 (MS-CASPT2) calculations were carried outusing the MOLCAS 7.4 program (20). For all atoms, the Atomic

Natural Orbital Relativistic with Core Correlation basis set(ANO-RCC) [contracted to (7s6p5d2f1g) for Fe; (4s3p1d) forligating N, O atoms; (3s2p) for nonligating C, N atoms; and (2s)for H] was used (20, 21). The second-order Douglas–Kroll–Hess(DKH2) one-electron spinless Hamiltonian was applied for allcalculations in order to allow for scalar (one-component) relati-vistic effects (22, 23). States calculated in this way are referred toas “nonrelativistic.”

The computational procedure consisted of three steps: (i)geometry optimization using DFT (vide supra), (ii) calculationof single-point energies on a truncated version of 1 (replacingthe methyl groups with H-atoms) using the CASSCF method withan active space of 16 electrons in 11 orbitals (five 3d orbitals onFe, three 2p orbitals on O, and three N-based bonding orbitalswith mixed σ∕π character; Fig. S6B), followed by (iii) calculationof SOC among all states obtained in the second step using theSO–CASSI method and solving the generalized eigenvalue pro-blem of first-order quasidegenerate perturbation theory [takingthe atomic mean-field integral (AMFI) spin-orbit (two-compo-nent) Hamiltonian (24, 25) as the perturbation] to obtain theSOC-corrected quasirelativistic energies. To improve the accu-racy of the calculations, CASPT2 energies were used on the maindiagonal of the two-component Hamiltonian matrix. In all of theCASSCF calculations, a level shift of 1.5 a.u. was used in orderto improve convergence. In the CASPT2 calculations, the lowest26 orbitals were frozen, and an imaginary level shift of 0.2 a.u.was used to eliminate intruder states (26, 27). To expedite thesecalculations, the Cholesky decomposition of two-electron inte-grals with default parameters in the MOLCAS 7.4 program wasused (28). All CASPT2 potential energy surfaces presented in thisstudy were calculated along the Fe─O stretching mode as deter-mined by DFT (BP86/6-311G*).

1. Fano U (1961) Effects of configuration interaction on intensities and phase shifts. PhysRev 124:1866–1878.

2. Sturge M, Guggenheim H, Pryce M (1970) Antiresonance in the optical spectra oftransition-metal ions in crystals. Phys Rev B 2:2459–2471.

3. Lempicki A, Andrews L, Nettel SJ, McCollum BC, Solomon EI (1980) Spectroscopy ofCr3þ in glasses: Fano antiresonances and vibronic “lamb shift”. Phys Rev Lett44:1234–1237.

4. Cole GM, Jr, Garrett BB (1970) Atomic and molecular spin-orbit coupling constants for3d transition metal ions. Inorg Chem 9:1898–1902.

5. Neese F, Solomon EI (1998) Calculation of zero-field splittings, g-values, and the rela-tivistic nephelauxetic effect in transition metal complexes. Application to high-spinferric complexes. Inorg Chem 37:6568–6582.

6. England J, et al. (2009) A synthetic high-spin oxoiron(IV) complex: Generation, spectro-scopic characterization, and reactivity. Angew Chem Int Ed Engl 48:3622–3626.

7. England J, et al. (2010) The crystal structure of a high-spin oxoiron(IV) complex andcharacterization of its self-decay pathway. J Am Chem Soc 132:8635–8644.

8. Frisch, MJ, et al. (2007) Gaussian 03 (Gaussian, Pittsburgh), Revision E.01.9. Frisch, MJ, et al. (2009) Gaussian 09 (Gaussian, Wallingford, CT), Revision B.01.

10. Iikura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for gen-eralized-gradient-approximation exchange functionals. J Chem Phys 115:3540–3544.

11. Wong SD, et al. (2011) Nuclear resonance vibrational spectroscopy on the FeIV═O S ¼ 2

non-heme site in TMG3tren: Experimentally calibrated insights into reactivity. AngewChem Int Ed 50:3215–3218.

12. Mennucci B, Tomasi J (1997) Continuum solvation models: A new approach to theproblem of solute’s charge distribution and cavity boundaries. J Chem Phys106:5151–5158.

13. Mennucci B, Cancès E, Tomasi J (1997) Evaluation of solvent effects in isotropic andanisotropic dielectrics and in ionic solutions with a unified integral equation method:Theoretical bases, computational implementation, and numerical applications. J PhysChem B 101:10506–10517.

14. Cammi R, Mennucci B, Tomasi J (1999) Second-order Møller–Plesset Analytical deriva-tives for the polarizable continuum model using the relaxed density approach. J PhysChem A 103:9100–9108.

15. Cammi R, Mennucci B, Tomasi J (2000) Fast evaluation of geometries and properties ofexcited molecules in solution: A Tamm-Dancoff model with application to 4-dimethy-laminobenzonitrile. J Phys Chem A 104:5631–5637.

16. Tenderholt A (2007) QMForge, version 2.1. Available at http://qmforge.sourceforge.net.

17. Kieber-Emmons MT (2012) Lumo (Kieber-Emmons, Burlingame, CA).

18. Roos B, Taylor P (1980) A complete active space SCF method (CASSCF) using a densitymatrix formulated super-CI approach. Chem Phys 48:157–173.

19. Andersson K, Malmqvist P-A, Roos BO (1992) Second-order perturbation theory with acomplete active space self-consistent field reference function. J Chem Phys96:1218–1226.

20. Karlström G, et al. (2003) MOLCAS: A program package for computational chemistry.Comput Mat Sci 28:222–239.

21. Widmark P-O, Malmqvist P-A, Roos BO (1990) Density matrix averaged atomic natural

orbital (ANO) basis sets for correlated molecular wave functions. Theoret Chim Acta77:291–306.

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25. Heß BA, Marian CM, Wahlgren U, Gropen O (1996) A mean-field spin-orbit methodapplicable to correlated wavefunctions. Chem Phys Lett 251:365–371.

26. Roos BO, Andersson K (1995) Multiconfigurational perturbation theory with level shift—The Cr 2 potential revisited. Chem Phys Lett 245:215–223.

27. Forsberg N, Malmqvist P-A (1997) Multiconfiguration perturbation theory with ima-ginary level shift. Chem Phys Lett 274:196–204.

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Fig. S1. (A) Variable-temperature (VT) MCD spectrum of 5-mM sample of 1 in the NIR region, showing that: (i) The negative progression first increases in(negative) intensity with increasing temp, then decreases in (negative) intensity, and (ii) the positive progression initially increases in intensity with increasingtemp (Inset), then decreases in intensity with further increasing temp. Both temp-dependence behaviors indicate ðx; yÞ-pol. (Scheme S1). (B) Temp-dependencebehavior of MCD intensity in A taken at the energy indicated by an asterisk (*) where there is no overlap with any positive MCD intensity, overlaid with a redline simulating pure ðx; yÞ-pol. behavior, D of approximately 7.0 cm−1. (C) VT MCD spectrum of 10-mM sample of 1 showing the lowest-energy z-pol. Charge-transfer (CT) band, which starts off with large negative intensity at 2 K that decreases with increasing temp. (D) Temp-dependence behavior of C taken at (+),overlaid with a green line simulating pure z-pol. behavior, D of approximately 7.5 cm−1.

Fig. S2. Structure of 1 comparing DFT-calculated structural parameters with those obtained by X-ray crystallography (in brackets).

Fig. S3. TD-DFT–calculated (PCM, solvent ¼ CH3CN) state energies and intensities of lowest-energy excited states up to 35;000 cm−1. Dominant character andpolarization indicated. Note the ðx; yÞ-polarized Neq-based CT transition between the two lowest-energy oxo CT transitions; this is ruled out as the assignmentof the 23;500 cm−1 band in MCD by both its polarization as well as resonance Raman data taken towards the low-energy tail (514.5 nm ≈ 19;400 cm−1) of theband that show enhancement of the Fe─O stretching mode but no enhancement of Fe─N stretching modes (6).

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Fig. S4. Electronic spectrum simulated for first 15 S ¼ 2 CASPT2 states (Table S1). Spectrumwas modeled using a hybrid Gaussian distribution with bandwidths(FWHM) of 3;000 cm−1.

Fig. S5. (A) NIR abs spectrum showing a dip in continuum background profile; (B) Fano fit (orange line) of dip in NIR abs (Gaussian background subtractedto give black line). Instrument detector changeover in region indicated by (*) results in a spurious derivative feature in difference spectrum. (C) Fano analysisof sharp spin-forbidden transition in MCD (red line, obtained from subtraction of 5E-based MCD background intensity). Both the dip in abs and peak in MCDwere fit with Eq. S1 (vide supra).

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Fig. S6. (A) Nonrelativistic CASPT2 PES of the three lowest S ¼ 2 and the 10 lowest-energy S ¼ 1 states (number of states considered in C1 symmetry; these arethe states taken into account for SOC in Figs. 4B, column d and 5 C and D). Dominant electronic configurations of selected S ¼ 2 and S ¼ 1 states are displayedfor the ground-state equilibrium geometry (the orbital representations of which are shown in B). Note that the same electronic configuration may contributesignificantly to more than one electronic state. (B) MOs included in the active space of 16-in-11 CASPT2 calculations.

Fig. S7. PES of the 5A1 ground state, two lowest quintet excited states (LF 5E and oxo π → Fe dxz∕yz), and two triplet states interacting with LF 5E. In thisschematic picture, only the local strong SOC between 3E and 5E in the vicinity of the 5A1 equilibrium geometry is considered; otherwise, PES are calculated witha nonrelativistic CASPT2 approach.

Fig. S8. (A) CASPT2-calculated PES of self-decay of 1, in the vicinity of the TS. CI interaction of the two lowest S ¼ 2 states at low symmetry (C1) indicated bycolor gradient in both PES. Note that each state is represented here by one dominant electronic configuration. CI interaction of the FeIIIðS ¼ 5∕2Þ—oxylðpz; σÞstate (originating from 5A1) and one component of the FeIIIðS ¼ 5∕2Þ—oxylðpx; πÞ state (originating from the spectroscopically observed LF 5E state) occursalong the H-atom abstraction coordinate. CI mixing of both states results in a dominant FeIIIðS ¼ 5∕2Þ—oxylðpx; πÞ character of the ground state before the

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system reaches a TS (at the B3LYP level, Fe─O and O─H lengths are 1.77 Å and 1.22 Å, respectively). The alternative FeIIIðS ¼ 3∕2Þ—oxylðpx; πÞ pathway was notfound using CASPT2 calculations. However, it is worth mentioning that the corresponding CT oxo → Fe dxz∕yz (π�) state is predicted to be much higher in energy(28;700 cm−1) than the experimental value (19;500 cm−1). (B) CASPT2-calculated PES of THF σ-attack of 1 in the vicinity of the TS, showing that at the TS theelectronic structure can be described as having approximately 35% FeIIIðS ¼ 5∕2Þ—oxylðpx; σÞ character.

Fig. S9. Evolution of the two dominant electronic configurations contributing to the multiconfigurational CASPT2 wavefunction characters of each electronicstate (5A1 ground state, LF 5E). Percentages do not sum to 100% because of other electronic-configuration contributions not shown.

Fig. S10. DFT-calculated energy diagrams, in kcal∕mol of the reaction of 1 with itself (π-channel, Top) and with exogenous substrates (σ-channel, Bottom).Solvated (PCM, solv ¼ CH3CN) energies are shown in the order ΔE∕ΔH∕ΔG. Contributions to energy barriers (steric and electronic) are indicated in the middle(TS) column of each reaction coordinate. Stick figures represent structures at the three points of the reaction coordinates, with distances in Å. Note thatalthough the electronic barriers are almost the same for π-attack (Top, Left) and CH3NH2 σ-attack (Bottom, Left), the THF σ-attack electronic barrier (Bottom,Right) is slightly lower because of the weaker C─H bond. Also note that self-decay of the next-closest methyl group (Top, Right) is disfavored because of itshigher barrier.

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Table S1. Experimental and theoretical parameters for ligand-field d → d and oxo π → d CT excited states

Experimental MCD data CASPT2 calculations

ΔEvertic (cm−1)* SFe─O† νes;expcm−1‡ ΔQexp(Å)

§ ΔEverticcm−1¶ νes;calccm−1∥ ΔQcalc(Å)**

Ground state 0.0 - 820†† 0.0 0.0 940 0.0d → d 5E-based LCP 10700 2.8 710 0.13 13860 630 0.151st d → d 5E∕3E-based RCP 10460 3.5 620 0.16 13775 560 0.152nd d → d 3E∕5E-based RCP 12355 1.2 880 0.08 14100 1000 0.02CT oxo π → d RCP 19500 4.96 490 0.21 28714‡‡ 506 0.25

*Electronic vertical transition from 5A1 ground state to highest-intensity component of Franck–Condon progression.†Huang–Rhys factor determined from intensity distribution I0→n∕I0→0 ¼ ðSFe─OÞ.‡Frequency of excited-state Fe─O stretching mode (i.e., average spacing of vibronic progression).§Distortion of excited-state geometry along Fe─O stretching mode calculated from ΔQ ¼ SFe─O∕2π2μνes,where μ ¼ reduced mass of ðFe þ ligandÞ─O.

¶Electronic vertical transition from 5A1 ground state at CASPT2 equilibrium geometry (with Fe─O bond length of 1.6 Å).∥Estimated from, where k is obtained from fit of CASPT2 potential energy surfaces (PES; Fig. 5C) with third-order Taylor expansion.**The ΔQ taken as difference between equilibrium geometries of 5A1 state and excited state.††Taken from ref. 11.‡‡Taken from Table S2. Note that when the CASPT2 PES are instead fit to Morse potentials, the vibrational-level spacings decrease only slightlyfor the first seven quanta: The deviation of the 6 → 7 spacing from the 0 → 1 spacing is 5–10% (e.g., for the d → d 5E-based LCP state, the0 → 1 and 6 → 7 spacings are 553 and 521 cm−1, respectively).

Table S2. CASPT2 electronic energies of first 15 states (calculated for DFT-optimized C1 geometry with Fe─O ¼ 1.64 Å)

S ¼ 2 state ΔE∕cm−1 Dominant configuration in CI vector

SA-CASSCF(16-in-11)/MS-CASPT2; SA/MS over 15 states

root 1—Ground-state 0 63% σ2π2xzπ2

yzd 1xyd1

x 2y 2π�1xzπ�1

yzσ�0

root 2 π�→σ� 12,986 30% σ2π2xzπ2

yzd 1xyd1

x 2y 2π�0xzπ�1

yzσ�1 20% σ2πβxzπ2

yzd 1xyd1

x 2y 2π�1xzπ�1

yzσ�1

root 3 π�→σ� 12,998 31% σ2π2xzπ

βyzd 1

xyd1x 2y 2π�1

xzπ�1yzσ�1 30% σ2π2

xzπ2yzd 1

xyd1x 2y 2π�1

xzπ�0yzσ�1

root 4 π→π� 28,714 30% σ2π2xzπ1

yzd 1xyd1

x 2y 2π�2xzπ�1

yzσ�0 26% σ2π1xzπ2

yzd 1xyd1

x 2y 2π�1xzπ�2

yzσ�0

root 5 π→π� 28,741 29% σ2π2xzπ1

yzd 1xyd1

x 2y 2π�1xzπ�2

yzσ�0 28% σ2π1xzπ2

yzd 1xyd1

x 2y 2π�2xzπ�1

yzσ�0

root 6 π→π� 29,312 44% σ2π1xzπ2

yzd 1xyd1

x 2y 2π�1xzπ�2

yzσ�0 40% σ2π2xzπ1

yzd 1xyd1

x 2y 2π�2xzπ�1

yzσ�0

root 7 π→π� mixed with σ→σ� 30,034 25% σβπ2xzπ2

yzd 1xyd 1

x 2y 2π�1xzπ�1

yzσ�1 22% σ2π1xzπ2

yzd 1xyd 1

x 2y 2π�2xzπ�1

yzσ�0 20% σ2π2xzπ1

yzd1xyd 1

x 2y 2π�1xzπ�2

yzσ�0

root 8 d→σ� 30,954 28% σ2π2xzπ2

yzd 0xyd1

x 2y 2π�1xzπ�1

yzσ�1

root 9 d→σ� 30,980 29% σ2π2xzπ2

yzd 1xyd0

x 2y 2π�1xzπ�1

yzσ�1

root 10 π→d 34,136 55% σ2π1xzπ2

yzd 2xyd1

x 2y 2π�1xzπ�1

yzσ�0

root 11 π→d 34,281 46% σ2π2xzπ1

yzd 2xyd1

x 2y 2π�1xzπ�1

yzσ�0 33% σ2π1xzπ2

yzd 1xyd2

x 2y 2π�1xzπ�1

yzσ�0

root 12* π→d 34,301 59% σ2π1xzπ2

yzd 2xyd1

x 2y 2π�1xzπ�1

yzσ�0 19% σ2π2xzπ1

yzd 1xyd2

x 2y 2π�1xzπ�1

yzσ�0

root 13* π→d mixed with σ→σ� 34,680 29% σ2π1xzπ2

yzd 1xyd 2

x 2y 2π�1xzπ�1

yzσ�0 22% σβπ2xzπ2

yzd 1xyd 1

x 2y 2π�1xzπ�1

yzσ�1 22% σ2π2xzπ1

yzd2xyd 1

x 2y 2π�1xzπ�1

yzσ�0

root 14* σ→π� 37,275 79% σ1π2xzπ2

yzd 1xyd1

x 2y 2π�1xzπ�2

yzσ�0

root 15* σ→π� 37,369 79% σ1π2xzπ2

yzd 1xyd1

x 2y 2π�2xzπ�1

yzσ�0

For all states, dominant electronic configurations are displayed. Nomenclature for orbitals follows that of Fig. S1B. For corresponding simulated electronicspectrum, see Fig. S4. CI, configuration interaction.

Scheme S1. Splitting ofMs sublevels of an S ¼ 2 species with an applied fieldH. The z axis of the molecule is defined as its Zeeman axis. For z-pol. transitions inMCD, H is parallel to the ðx; yÞ plane; at 7 T, the MCD-activeMs ¼ −1 sublevel is lowest in energy, so there is MCD intensity at low temperature (temp), but withincreasing temp, the population of the Ms ¼ −1 sublevel decreases, whereas the populations of the Ms ¼ 0;þ1 sublevels increase. Because Ms ¼ 0 is MCDinactive andMs ¼ −1 produces MCD intensity of the opposite sign, the overall MCD intensity decreases as temp increases. For ðx; yÞ-pol. transitions, H is parallelto the z axis; at 7T, the MCD-inactiveMs ¼ 0 sublevel is lowest in energy; as temp increases, the MCD-activeMs ¼ −1 sublevel is populated, causing an increasein MCD intensity, but further increasing temp populates the Ms ¼ þ1 sublevel and produces MCD intensity of the opposite sign, thereby decreasing overallMCD intensity. Thus, z-pol. transitions start with high MCD intensity at low temp, and decrease with increasing temp, whereas ðx; yÞ-pol. transitions firstincrease in MCD intensity with increasing temp, then decrease at higher temp.

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Scheme S2. Two possible electronic structure descriptions of the TS for π-pathway reactivity: (Left) DFT produces a partial S ¼ 3∕2 FeIII species; (Right) CASPT2predicts a dominant contribution from an S ¼ 5∕2 FeIII species with an α-hole in an oxo π orbital.

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