Multi-edge X-ray Absorption Spectroscopy. 1. X-ray Absorption near

Article pubs.acs.org/JPCA

Multi-edge X‑ray Absorption Spectroscopy. 1. X‑ray Absorption nearEdge Structure Analysis of a Biomimetic Model of FeFe-Hydrogenase Logan J. Giles, Alexios Grigoropoulos, and Robert K. Szilagyi* Astrobiology Biogeocatalysis Research Center, Department of Chemistry and Biochemistry, Montana State University, Bozeman, Montana 59717, United States S Supporting Information *

ABSTRACT: In this work, we demonstrate the potential of multi-edge X-ray absorption near-edge structure (XANES) analysis in completely defining the ground state electronic structure of a prototypical biomimetic complex of the [2Fe]-subcluster of the catalytic H-cluster of FeFe-hydrogenase. The spectral features at the ionization thresholds for Fe, S, C, and O 1s (K-edge) and Fe 2p (L-edge) core electrons were considered simultaneously to obtain the atomic compositions of the unoccupied frontier molecular orbitals. A systematic error analysis was carried out at the most informative S K-edge for spectra collected by multiple detection methods, at various data collection temperatures, and different sample preparation protocols. As expected for the difference in bonding between bridging and terminal Fe−S(thiolate) coordination, the Fe−S bond is more covalent in the [2Fe]-biomimetic complex with formally iron(I) centers (36 ± 2% S character per Fe−S bond) than in the previously described [2Fe−2S] clusters (25 ± 3% S character per Fe−S bond) with formally iron(III) centers. An electron hole-based analysis of the pre-edge features at Fe K-, Fe L-, and S Kedges experimentally defines the composition of the first three frontier unoccupied molecular orbitals to contain 4% Fe 4p, 44% Fe 3d, and 24% S 3p contributions per electron hole, respectively. The complementary CO ligand contribution thus can be defined as 28% per electron hole. These experimental orbital covalency values are important in rationalizing redox properties, electrophilicity of the metals, or nucleophilicity of the ligands, and critically evaluating the absolute accuracy of electronic structure calculations.

1. INTRODUCTION X-ray absorption spectroscopy at multiple core electron ionization thresholds (multi-edge XAS) is an emerging new extension of a now well-established synchrotron-based spectroscopic technique.1 X-ray absorption near-edge spectroscopy (XANES)2 and extended X-ray absorption fine structure (EXAFS)3 analyses can provide electronic and geometric structural information, respectively, for a variety of coordination compounds with either para- or diamagnetic ground states in liquid, solution, frozen solution, solid powder, or crystalline form. A remarkable potential of collecting XAS data at multiple core electron ionization energies can be realized by the complementary information acquired from XANES and EXAFS analyses for developing a complete electronic and geometric structure description from a single spectroscopic technique and often for the same sample. Contemporary XAS techniques gained popularity from the widespread availability of synchrotron radiation-based, tunable X-rays that are generally classified as hard and soft X-rays. Due to the unique beamline instrumentation and importantly the information content, an intermediate energy range (“tender X-rays”) is also notable for the core excitation energy range of P, S, and Cl absorbers. The hard X-rays (above 4 keV) cause the excitation of n = 1 (K-edge) and n = 2 (L-edges) core electrons of first and third row transition metals, respectively, and beyond. The deep penetration of high energy X-rays allows for conventional transmission experiments in addition to fluorescence emission © 2012 American Chemical Society

and photoelectron ejection measurements. The soft X-rays (under 2 keV) cause the excitation of n = 2 core electrons of first row transition metals and the 1s core electrons of light (Z < 9) main group elements. The penetration of soft X-rays is limited and thus it can only probe the surface of samples. Moreover, the data collection requires an ultrahigh vacuum setup to avoid beam absorption by the atmosphere of the beam path or the sample chamber. The intermediate energy range or tender X-rays (about 2−4 keV) opened up an exciting field of research by providing an experimental tool for exciting the n = 1 core electrons of second row main group elements (P, S, Cl) as well as n = 2 core excitations of second row transition (Mo, Ru, Pd) metals.1,2,4 It is important to highlight that there is no other spectroscopic technique for S and Cl containing samples that can provide comparable structural information from direct measurements. A schematic representation of X-ray photon absorption, related excitation, and relaxation processes are summarized in Scheme 1, where important electronic structural changes that will be considered below for data analysis and interpretation are highlighted. The energy levels indicate electronic states; however, as described later, they can be regarded as occupied and unoccupied orbital energy levels. The formation of the core Received: April 24, 2012 Revised: November 10, 2012 Published: November 12, 2012 12280

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excitations.7 Therefore, the core excitation spectra for quantitative XANES analysis of the main group elements of the first (C, N, O) and the second row (S, P, Cl) are most commonly collected by measuring the electron yield or the fluorescence emission, respectively (see below). Furthermore, the different intensity of the fluorescence emission and the electron-yield signals is useful for separating the overlapping edges of the P, S, Cl K-edges and the Mo, Ru, Rh, Pd L-edges. For the above series of elements, the K-edges are proportionally more intense in fluorescence, but weaker in electron-yield detection and vice versa for the L-edges. In a multi-edge XAS measurement, the relaxation processes of the excited state (Scheme 1, panel 5) are recorded at multiple absorber edges in different energy ranges. Because, within a given molecule, the final states of the various core level excitations originate from the same unoccupied acceptor molecular orbital(s), the systematic determination of each absorber’s contribution maps out the complete atomic composition of the acceptor orbital(s). In a molecular orbital picture, these atomic compositions correspond to orbital coefficients, i.e., bond covalency, as commonly referred. The connection between the ground state orbital description and the experimentally observed excited states at core ionization thresholds or edges has already been established in past reviews.2,5,8 In brief, the acceptor molecular orbital for Fe−S bonding can be expressed as:

Scheme 1. Modeling of the Electronic Structural Effects of Absorption of X-rays Photons and the Origin of X-ray Absorption Spectral Intensities

hole (Scheme 1, panel 2) increases the effective nuclear charge (Zeff) of the absorber due to the reduced screening of the remaining electrons. Therefore, the energy of the occupied core and valence orbitals is lowered (panel 3). The localization of an excited electron to an unoccupied frontier orbital (panel 4) also lowers the energy of this acceptor orbital, however, to a smaller extent relative to the core orbital. The excited state (panel 4) has a short lifetime of approximately 10−18 to 10−21 s, estimated from the Heisenberg uncertainty principle. It relaxes back to the ground or other excited states in a radiative (fluorescence emission, ℏνF) or nonradiative (Auger electron ejection and other electron-yield processes, e−) process (panel 5).5 The transmission data are obtained from the reduced beam intensity (IT(ℏνi)) as the incident beam passes through the sample. Despite its simplicity, this molecular orbital-based description for the interaction of X-rays with chemical compounds in absorption spectroscopy1,2,4 is a practical model for describing the electronic state changes that are considered below in a detailed quantitative XANES analysis for the K- and L-edges. It is important to consider the energy dependence of the relaxation processes.6 The transmission detection is mainly limited by sample thickness. Using the ground powder-on-tape sample preparation protocol (see below), transmission data at lower energy than the Cl K-edge are practically unobtainable for conventional sample setup, whereas Auger decay dominates (70% yield or greater) for Z < 25 K-shell and Z < 78 L-shell

φA = β(a3dϕFe3d + a4sϕFe4s + a4pϕFe4p) − α(a3sϕS3s + a3pϕS3p + a3dϕS3d)

(1)

The experimental determination of the atomic orbitals coefficients an,l will be discussed later, where available. Similarly, the donor core orbital for Fe−S bonding can be expressed, with an ordering in energy for iron and sulfur core orbitals, as

Scheme 2. Comprehensive Transition Dipole Expressions for Multi-edge XANES Analysisa

The numbers in parentheses (Δn, Δl) indicate the change in the principal and the angular moment quantum numbers; a dash indicates forbidden transitions. a

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The χ2 coefficient is commonly referred as bond covalency from either the ligand or the metal point of view, depending on the 1s → np core excitation. D0 is the normalized area under a given spectral feature, 1/3 derives from angular part of the dipole integral, h is the number of electron holes in the acceptor orbital, and N is the number of absorber atoms. The I1s→np transition dipole integral is an empirical value that includes contributions from the beamline optics and the detector, the excited state lifetime broadening and the Zeff of the respective absorber. The transition dipole integral also depends on the sample preparation procedure, the selfabsorption effects in fluorescence detection mode and the accelerating potential or electronic bias in electron-yield/direct current detection mode. The extension of the above treatment for K-edge excitations is straightforward to metal L-edges. However, a key difference between the 1s → np transition-based K-edge and the 2p → nd transition-based L-edge spectra is that the latter splits into two edges. The lower energy LIII-edge corresponds to the 2p3/2 final state, whereas the higher energy LII-edge corresponds to the 2p1/2 final state.

∑ ϕFe 1s + ∑ ϕS 1s + ∑ ϕFe 2s + ∑ ϕFe 2p +

∑ ϕS 2s + ∑ ϕS 2p + ...

(2)

According to Fermi’s Golden Rule, the transition probability of an excitation from the donor orbital φD to the acceptor orbital φA is related to the square of a transition matrix element that describes the excitation and the density of the final states.9 In practice, this corresponds to the correlation of experimental intensity (D) or area under a given spectral feature with the transition probability between the ground and excited electronic states. The molecular orbital-based representation of core excited states is generally valid for classical coordination compounds, for example, Cu(II) or low spin Ni(II) ions and for 4d and 5d transition metals due to the negligible multiplet effects and mixing of excited and ground states. As these higher order electronic effects become important, this approximation and the corresponding assignments needs to be corrected accordingly, as it is presented below for the Fe L-edge analysis. In a multi-edge XAS analysis, we need to consider all possible combinations of the acceptor and donor orbitals. These can be summarized in a matrix representation of transition dipole expressions, as shown in Scheme 2. The first approximation is to neglect the integrals (off-diagonal terms in Scheme 2) between ligand core and metal valence orbitals and vice versa, because the core excitation is considered to be localized on the respective absorber.10 The various excitations can be divided into forbidden (s → s, p → p, d → d; Δl = 0 and indicated with the “−” sign in Scheme 2), electric dipole (s→p, p→d; Δl = +1 and p→s, d→p; Δl = −1), and electric quadrupole (s→d, d→s; Δl = ± 2) allowed transitions. The most intense spectral features are observed from the electric dipole allowed transitions where Δl = +1 (s → p and p → d) whereas the electric quadrupole allowed transitions (Δl = +2, s → d) are approximately an order of magnitude less intense.11 The electric dipole and quadrupole allowed excitations with Δl = −1 (p → s, d → p) and Δl = −2 (d → s) are expected to be approximately an additional order of magnitude weaker;11−13 hence they are rarely observed in XAS measurements. It is also important to consider the principal quantum number differences (Δn) for various dipole allowed excitations. Given that the probability of an excitation is proportional to the square of the transition dipole integral9 and that the dipole operator only operates on the radial part of the wave function, we can estimate that the magnitude of the core excitation dipole integral will be proportional to the square of the principal quantum number, “n”. Thus, the intensity difference for the various n − 1, n − 2, n − 3 transitions from Scheme 2 approximates an exponential relationship with a (Δn2)2 increase in transition probability. For example, the Fe K-edge 1s → 4p excitation with Δn = 3 will be approximately an order of magnitude more intense than the Fe LI-edge 2s → 4p with Δn = 2. In addition, the lower intensity of the LI-edge, compared with the K-edge, is further affected by the quantum yields of different experimental detection methods.6 Considering the electric dipole allowed transitions with the maximal Δn values for K-edges, the practical form of the transition dipole expression can be written for the metal and ligand K-edges as D0 =

1 h 2 χ I1s → n p 3N

D0 = DL III + DL II =

1 h 2 χ I2p → nd 3N

(4)

The normalized LIII and LII intensities (D0,L) have been intentionally omitted in eq 4, due to potential errors if the edges are normalized separately. The normalization of the Ledge spectra of the first row transition metals,5,8 in which the two L-edges are often overlapping, is not straightforward. For these absorbers, the separation of the LIII- and LII-edges is practically hindered by the magnitude of spin−orbit coupling of the corresponding 2p core hole final states. The spin−orbit coupling increases for the second row transition metals and above. Therefore, the independent normalization of each edge becomes feasible.14 However, the independent analysis of the two L-edges is still problematic. The 2J + 1 multiplicity of each 2p core hole final state dictates a 2:1 intensity ratio between the intensities of the LIII- and LII-edges, yet this ratio is practically never experimentally observed. Moreover, the LIII/LII ratio can vary from compound to compound, a fact that prohibits the use of separate transition dipole integrals for each of the L-edge. Admittedly, eq 4 omits the fine details of the electronic structure that originate from multiplet effects, because it involves the total normalized area of both L-edges to determine the total metal d contribution of the metal d orbitals. Nevertheless, the differential metal contribution to various orbitals and related multiplet states can actually be determined from the multi-edge treatment, as presented below in the Fe Ledge analysis section. To demonstrate the remarkable information content of multi-edge XAS analysis, we consider here the Fe2(pdt)(CO)6 complex (pdt = μ-S2C3H62−, Figure 1), which is a structural analogue of the catalytically active [2Fe]-subcluster of the FeFe-hydrogenase.15−17 In a forthcoming study, we will use this experimental approach to dissect the effects of various structural elements on the electronic structure of a large family of related [2Fe] biomimetic complexes of FeFe-hydrogenase.18−24 Fe2(pdt)(CO)6 is one of the simplest biomimetic models that contains three distinct types of chemical environments: a bridging dithiolate ligand, two low valent formally Fe(I) ions and six CO ligands, as can be seen in Figure 1. However, the quantitative analysis and fitting of its XAS features are remarkably convoluted. Without the multi-edge

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Scheme 3. Extended Molecular Orbital Diagram of Fe2(pdt)(CO)6a

Figure 1. Molecular structure from front (A) and side (B) views of the [Fe2(pdt)(CO)6] biomimetic model complex of the [2Fe]-subcluster of FeFe-hydrogenase (pdt = μ-[S(CH2)3S]2−).

XAS treatment, many aspects of its electronic structure would have remained undiscovered or even misinterpreted. The compound is readily available via a straightforward synthetic procedure25−27 and its crystal structure is known.22 Its IR spectrum exhibits three distinct absorption bands in the carbonyl stretching region in CH3CN or THF; 2072 cm−1 (medium), 2033 cm−1 (strong), and 1992 cm−1 (strong, broad)22,28 that indicate considerable Fe(I) → CO backdonation relative to the free CO stretching at 2143 cm−1. A detailed spectroscopic study presented its electronic absorption (UV−vis), magnetic circular dichroism (MCD), and resonance Raman (rR) spectra in combination with the electronic structure description from density functional theory (DFT) calculations.29 Its UV−vis spectrum28 shows an intense feature at 30 400 cm−1 with ε = 12 600 M−1 cm−1, which is assigned to the HOMO → LUMO transition as an indication of a covalent Fe−Fe bond. Absorption bands above 32 000 cm−1 were assigned to MLCT transitions from the Fe ions to the CO ligands. rR measurements with excitation at ∼19 500 cm−1 exhibit intense peaks at 205 and 356 cm−1 that were assigned to the totally symmetric Fe−Fe and Fe−S stretching modes. The rR spectrum of Fe2(pdt)(CO)6 also exhibits additional peaks in the 280−330 and 440−520 cm−1 range, which are the combination of nonsymmetric Fe−S stretching modes and Fe−C(O) stretching and Fe−C−O bending modes.30 These rR data allow for an estimate of the Fe−S bond strength relative to the classical, weak-field [Fe2S2(SEt)4]2− complex that has a diamond-shaped core but lacks an Fe−Fe covalent bond. The totally symmetric Fe−S stretching mode for [Fe2S2(SEt)4]2‑ is observed at 387 cm−1 (excitation at 17 600 cm−1).31 This indicates that the Fe−μS(sulfide) bond in the classical [2Fe− 2S] cluster is stronger than the Fe−μS(thiolate) bond in Fe2(pdt)(CO)6. The stronger Fe−μS(sulfide) bond defines an upper limit for the Fe−S bond covalency with 78 ± 7%.32 The corresponding terminal Fe−S(thiolate) bond covalency of the same [2Fe−2S] cluster was found to be 25 ± 3%,32 which can be considered as the lower limit for the bridging Fe−μS(thiolate) bond covalency in Fe2(pdt)(CO)6. From the traditional spectroscopic results and previous electronic structure calculations for Fe2(pdt)(CO)6, the coordination environment around each low valent Fe(I) site can be described as distorted octahedron. The t2g orbitals are fully occupied. Due to the Jahn−Teller distortion of the d7 pseudo-octahedral coordination, the eg orbitals are split into a singly occupied lower 3dz2 orbital and doubly unoccupied higher 3dx2−y2 for each Fe(I) site. Scheme 3 summarizes an expanded molecular orbital diagram adapted from reference 29. The HOMO and the LUMO are formed from the bonding and the antibonding combination of the above singly occupied Fe 3dz2 orbitals, respectively, with considerable S 3p character. The next two unoccupied frontier orbitals (LUMO+1 and LUMO +2) are the symmetric and asymmetric combinations of the

a

Adapted from ref 29.

vacant Fe(I) 3dx2−y2 orbitals, respectively, with less S 3p contributions. The following 12 CO π* orbitals have a considerable Fe 3d character from the t2g set18 and also some S 3p character, as discussed later. It is important to note that there is a significant mixing of approximately 12% total Fe 4p character into the LUMO as has been already proposed for a structurally similar Fe2(SMe)2(CO)6 complex with little to no 4s character,28 which will be important in the analysis of Fe Kedge data. As a complement to the above summarized conventional spectroscopic studies, we report here the XANES data that were collected on multiple occasions at different beamlines and using different detection methods in hard, tender, and soft Xray regions at the Fe K-, S K-, Fe L-, C K-, and O K-edges, respectively. The multi-edge XAS analysis allows for the definition of metal 4p, ligand 3p, and metal 3d orbital characters from the pre-edge feature intensities. With considering only the relative orbital compositions from electronic structure calculations, we were able to obtain an unambiguous fit to all the edges with self-consistent spectral interpretation. This would have not been possible if only a single edge was analyzed. Hence, multi-edge XAS has the potential to define a complete bonding description, directly from experiment. The C and O K-edges are also presented as a currently qualitative tool for extending this bonding description and aiding spectral assignments. This experimental electronic structure information can then be used for understanding the redox and acid/base properties of the studied compound in addition to the evaluation of the accuracy of electronic structure methods, such as density functional theory, the performance of basis sets and effective core potentials, and population analysis methods, which will be presented in a follow up paper.

2. EXPERIMENTAL METHODS 2.1. Sample Preparation. Fe2(pdt)(CO)6: The complex was synthesized as described in the literature.28 Additional samples were provided by collaborators (see Acknowledgments). Na2pdt: A solution of 0.6 g (14.3 mmol) of NaOH and 0.7 mL (7 mmol) of HS(CH2)3SH in 20 mL of dry, degassed MeOH was stirred for 12 h under N2. The solvent was removed, and the white residue was washed with Et2O. 1H 12283

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Figure 2. Data normalization steps for S K-edge (A) and (B) and Fe L-edge (C) and (D) spectra.

NMR (CD3OD): δH 2.5 (t, 4H, SCH2CH2CH2S), 1.8 (m, 2H, SCH2CH2CH2S).33 2.2. X-ray Absorption Measurements. Most of the XAS measurements were carried out at the Stanford Synchrotron Radiation Lightsource (SSRL) under storage ring (SPEAR 3) conditions of 300−80 mA current and 3 GeV energy. For the multi-edge treatment, beamlines (BL) 6-2 and 4-3 were utilized for the S K-edge energy region. BL 10-1 allowed for data collection in the soft X-ray region, for the Fe L-edge and C and O K-edge regions. BL 9-3 and BL 7-3 provided data at the Fe K-edge of the hard X-ray region. To evaluate the beamline and detector dependence of XAS data and thus the generality of the analysis method described here, we also collected S K-edge spectra at the Canadian Light Source (CLS) under a beam current of 250−130 mA and 2.9 GeV storage ring energy. Due to the volatility of the Fe2(pdt)(CO)6 complex, we had to utilize the He filled ambient chamber with fluorescence detection at the Soft X-ray Microcharacterization Beamline (SXRMB) 06B1-1 of CLS. BL 7-3 is a 20-pole and BL 9-3 is a 16-pole Wiggler beamline with a 2 T magnetic field, equipped with a Si(220) downward reflecting, double-crystal monochromator. Due to the high penetration of the hard X-rays, the transmission setup was utilized at these beamlines, for samples placed in a liquid helium cryostat and maintained at a constant temperature of ∼10 K. The beamline parameters were optimized at 8000 eV. The optimal sample concentration versus boron nitride matrix

was calculated by taking into account sample holder geometry and molar weight of the compound of interest using the program SAMPLE4 of EXAFSPAK. 34 The energy was calibrated using the first peak of the first derivative spectrum of an iron foil assigned to 7111.2 eV. Fe K-edge spectra were collected in the energy range of 6785−7985 eV. BL 6-2 is a 56-pole, 0.9 T and BL 4-3 is a 20-pole, 2.0 T Wiggler beamline equipped with a liquid N2 cooled Si(111) double-crystal monochromator. Both beamlines were optimized at 2740 eV. Na2S2O3·5H2O was used as a calibrant. The maximum of the pre-edge feature was set at 2472.02 eV. Sulfur K-edge spectra were collected in the energy range 2450−2740 eV using an unfocused beam in a He-purged beam path at both room temperature and ∼120 K for the solid samples and using either a multi-element Lytle (EXAFS Co) or a Passivated Implanted Planar Silicon (PIPS) fluorescence detector (CANBERRA). Partial electron-yield data were collected by a detector (EXAFS Co) equipped with a nickel grid at a 45 V collector potential. Solid samples were prepared in an anaerobic drybox, diluted in and ground together with boron nitride to minimize self-absorption and then mounted onto a sulfur-free Kapton tape. These samples, although not extremely air sensitive, were protected from oxidation and moisture during sample mounting by a thin polypropylene window. The SXRMB beamline at CLS provides access to an energy range comparable to those of BL 6-2 and BL 4-3 at SSRL. It is a bend magnet beamline with a water cooled Si(111) or 12284

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least three scans were collected and averaged to obtain an acceptable signal-to-noise ratio. If no radiation damage was present, the second scan generally looked already practically identical to the first. 2.3. X-ray Absorption Data Normalization Procedure. The three main steps in analyzing XAS data before the fitting of the spectral features are baseline subtraction, background correction, and normalization. The baseline subtraction and background correction are often done in a single step; however, in the case of dilute samples, detector and/or monochromator glitches, and sample chamber contamination, the collection of data for a blank sample holder and even an empty sample chamber is highly recommended (see top spectra in Figure 2A,C). The blank spectrum can correct for considerable differences between the slopes of the pre-edge and post-edge regions if it is subtracted from the sample spectrum. The background region of the raw or baseline subtracted data (middle spectrum in Figure 2A) is then fitted with a secondorder polynomial that is subtracted from the original data to get the background corrected data (bottom black line in Figure 2A). Two linear fits to the background (red line) and the postedge region (blue line) are used to generate constraints for the first derivative of a spline function (blue line in Figure 2B), which is then used to normalize the spectrum by scaling the S K-edge spline function (and not a data point of the spectrum) to 1.00 at 2490 eV. Figure 2C illustrates the data normalization steps taken for a representative Fe L-edge data of Fe2(pdt)(CO)6, which conceptually agree with those discussed for the S K-edge. A practical implementation for the background correction is to use the slope of linear fits as boundary conditions for the first derivative of a spline function that fits the post-edge region of 727−800 eV. The background corrected data were then normalized by setting the spline function to 1.0 at 800 eV as seen as in Figure 2D. 2.4. XANES Data Fitting. Fitting of the XANES region was achieved by using PeakFit v4.12 (Seasolve Software, Inc.) and the EDG_Fit program.34 Due to the overlapping spectral features, various fits are discussed using a range of combinations of Gaussian/Lorentzian peaks for the pre-edge regions. Initially, the data were fit by EDG_Fit34 due to the numerous examples from the literature,2 including relevant papers for the definition of the S 1s → 3p transition dipole integral.32,35−37 In these studies, the intensity of the pre-edge feature was estimated from the product of the peak amplitude and the half-height full line width. Instead of this approximation, we used the analytical area under the fit function of Gaussian+Lorentzian Amplitude from PeakFit, shown in eq 5

InSb(111) double-crystal monochromator with a collimating mirror before the monochromator and a torroidal focusing mirror. The beamline has UHV and He filled ambient endstation chambers for the XAS measurements. The former is equipped with electron-yield detector in the form of direct current measurement, multichannel plate, total fluorescence detector, and an energy selective, single element silicon drift detector. The ambient chamber, which was utilized in the given study, is equipped with a 4-element silicon drift detector (Vortex-ME4). The calibration and sample preparation procedures used at SXRMB are identical to those described above for BL 6-2 and BL 4-3 with the exception of using Kapton tape with Si containing adhesive, which gives a large background signal resulting in more than 30% detector deadtime. Instead, we used carbon tape with thin sample coverage and without any boronitride dilution. BL 10-1 is a 30-pole, 1.45 T Wiggler beamline, equipped with a 6 m spherical grating monochromator. For the Fe L-edge measurements, the 1000 lines/mm setting of the monochromator was used. Spectra were collected in the energy range 660−800 eV using an unfocused beam in ultrahigh vacuum (UHV). The beamline was optimized at 715 eV. Fe2O3 was used as a calibrant with a two-point calibration of the second feature of the LIII-edge and the first feature of the LII-edge set at 708.5 and 720.1 eV, respectively. The data were collected in electron-yield detection mode using a Channeltron (PHOTONIS) located approximately 3 cm away from the sample paddle and operating at 1800 V high voltage and 3000 V collector potentials. Attention: Due to the rapid sublimation of the Fe2(pdt)(CO)6 complex in the UHV chamber at room temperature, the sample can contaminate the chamber and the detector. The ground solid sample was pushed deeply into a carbon tape on a copper paddle and cooled using a liquid nitrogen finger Dewar. Even with the use of cryo-cooling, there was a thin layer of Fe2(pdt)(CO)6 deposited on the calibrant (Fe2O3) and the sample paddle. Furthermore, there is a considerable variation to the data if the spectra are collected at different exposure times to vacuum. The larger error bars of ∼10% found in the Fe L-edge spectra derive from the normalization of a weak edge jump and the presence of intense pre-edge features. If the sublimation is limited by the use of liquid N2 cooling, these error bars can be reduced to the expected value of ∼5%. In addition, radiation damage, which is generally more prominent for dilute solutions, was also observed at ∼700 eV for the solid sample. We also found that in the case of contamination of the incident beam grid/foil that introduces artifacts into the EY/I0 data, the direct use of the EY signal gives already reproducible data for quantitative analysis. However, it is more prudent to collect data for a blank carbon tape and use them for baseline subtraction (Figure 2). For the C and O K-edge measurements the 600 lines/mm setting was used for the grating monochromator at BL 10-1. Spectra were collected in the energy range 260−660 eV using an unfocused beam. Graphite was used as a calibrant with a one point calibration of the first feature, set at 284.7 eV. Fe2(pdt)(CO)6 was pushed directly into an indium foil, which was kept on a copper paddle and cooled using a liquid N2 finger Dewar. The data were collected only in electron-yield mode as described above for the Fe L-edge collection. The EY/ I0 signal had to be used for data normalization due to high curvature of the spectra. We also collected data for a blank indium foil for baseline subtraction due to the presence of an In2O3 layer on the surface of the foil. For all edge regions, at

f (E ) = ⎡ m ln 2 ⎛ E − E0 2 ⎞ ⎢ hhlw π exp⎝⎜ − 4 ln 2 hhlw ⎠⎟ + ⎢ A⎢ m ln 2 1−m + π hhlw ⎢ hhlw π ⎣

(

)

1−m E−E ⎤ ⎡ π hhlw⎣1 + hhlw0 ⎦

(

)

⎤ ⎥ ⎥ ⎥ ⎥ ⎦ (5)

where A is the amplitude of the peak, E0 is the peak position in eV, hhlw is the half-height full line-width in eV, and m is the line shape or Gaussian/Lorentzian mixing coefficient. To convert the previously published pre-edge intensities and transition dipole integrals, we need to consider a 27% increase to obtain the exact analytical area for m = 0.5 mixing relative to the approximation of D = (hhlw)A for a pseudo-Voigt line 12285

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neously, electron-yield (data set J) and fluorescence data collection can aid in the estimate of the self-absorption effect if a high enough collector potential is employed (∼200 V for the S K-edge) or direct current can be measured. BL 4-3 is a newer beamline at SSRL (data set G) replacing BL 6-2 (data set F) for XAS measurements in the tender X-ray energy region. The latter was used in the past for the main part of the quantitative XANES measurements at the S and Cl K-edges.2 A comparison between BL 6-2 and 4-3 for data sets F and G, respectively, revealed no significant differences in the spectra (see also Figure S4, Supporting Information). However, spectra collected at the SXRMB 06B1-1 beamline of CLS (date set K) consistently gave lower intensity fluorescence data despite the samples being prepared comparably thin to those at SSRL. After detector dead-time correction (see below, Figure S7, Supporting Information), the spectra from CLS became practically identical to those from SSRL, which further supports that the analysis presented here is not limited to a given beamline or facility. Effect of Sample Quality. In S K-edge XAS measurement, we need to consider the presence of additional absorber content in a sample, such as S containing counterions, or free uncoordinated ligands. Figure S5 (Supporting Information) shows the comparison of the normalized S K-edge spectra for Fe2(pdt)(CO)6 from three different laboratories (see Acknowledgment). It is notable that the peak energy positions and normalized intensities vary less than 0.1 eV for the major features, a value that matches the beamline’s resolution. The features above the ionization threshold are almost identical with slight differences observed only in data set B, due to modest sample decomposition during storage and handling, because data sets A and B were obtained for the same sample during different data collection trips. Radiation Damage. As contemporary synchrotron sources achieve lower emittance and higher flux for studying more dilute samples with smaller beam size, another important effect on the normalized data quality is radiation damage even for ground solid samples. We observed the signs of radiation damage as the storage ring (SPEAR at SSRL) was upgraded from a second to a third generation source in addition to the beam current at SSRL being increased from 100 to 300 mA. Notably, no sign of radiation damage was detected for spectra collected at CLS. Data collection at SSRL for Fe2(pdt)(CO)6 at room temperature resulted in considerable change in the S Kedge spectra, which was eliminated by a liquid He cryoflow setup. Figure 3A shows the characteristic progression of spectral changes at ambient temperature with fluorescence data collection using a Lytle detector. The radiation damage is significant, because the amplitude and the area under the preedge feature vary between the first and the third scans by 0.33 and 0.23 eV, respectively. Despite a visibly nonlinear change in the spectra presented in Figure 3A, we obtained practically identical spectra for the zero-exposure extrapolated data using either a linear or an exponential extrapolation method (Figure 3B and also in Figure S6, Supporting Information). In addition, both extrapolated spectra reproduced well the data collected for the sample at liquid He temperature (data set F). Simultaneous employment of fluorescence-yield and electron-yield detections can provide an additional tool for correcting for radiation damage. The electron-yield detection is more sensitive to radiation damage, because it only probes a few nanometers layer of the sample surface,7 in comparison to fluorescence detection, which probes a layer an order of

shape. It was necessary to move away from the latter simplification due to the transition envelop nature of the excitations for all the spectral features of Fe2(pdt)(CO)6. Thus, to obtain a consistent S 3p character of a metal−thiolate sulfur bond (M−St) with previous results,35,37 it was required to employ a 1.27 scaling factor for the IS 1s→3p transition dipole integral or the pre-edge peak intensities from past literature. A detailed critical evaluation of the results of various fitting procedures was carried out and summarized in Supporting Information (Figures S1−S2, Table S1, and pages S2−26). To obtain a reasonable fit for the ill-resolved rising-edge features, we used the free ligand spectrum of Na2pdt. The S−C bonding in the uncoordinated dithiolate salt and the coordinated ligand is remarkably similar.38 Therefore, the free ligand provides a reasonable estimate for the subtraction of ligand-based risingedge features from the spectrum of the complex. The entire rising-edge of the spectrum of Na2pdt was fitted by four pseudo-Voigt peaks and one Lorentzian cumulative function for the ionization threshold (Figure S2, Supporting Information) and then treated as a user defined function (UDF) in PeakFit. This UDF was allowed to shift in energy (E0) and scale (A) to match the rising-edge region of the Fe2(pdt)(CO)6 spectra. 2.5. Uncertainty and Error Analysis of the Normalized S K-Edge Spectra. As summarized in Table 1, we collected S Table 1. Summary of Sulfur (A−K) and Iron K-Edge (L and M) Spectra Used in This Study (FE, Fluorescence Emission; EY, Electron Yield; TM, Transmission) data set temp, K A B C D E F G H I J K L M

RT RT RT RT ∼120 ∼120 RT RT RT RT RT ∼11 ∼11

beamline

detectors

sample condition

6-2 6-2 6-2 6-2 6-2 6-2 4-3 4-3 4-3 4-3 SXRMB 9-3 7-3

Lytle FE Lytle FE Lytle FE Lytle FE Lytle FE Lytle FE Lytle FE PIPS FE Lytle FE EXAFSCO EY (45 V) Vortex 4E FE TM TM

crystallinea crystallinea powder crystallineb powder crystalline crystalline crystalline crystalline crystalline crystalline crystallinea powder

a

Samples provided by Prof. Pickett, University of East Anglia, U.K.. Sample provided by Prof. Heinekey, University of Washington, Seattle, WA.

b

K-edge spectra at three beamlines (BL 6-2 and BL 4-3 of SSRL, SXRMB 06B1-1 at CLS) for samples from three different synthetic batches, using three different detection methods (fluorescence using Lytle and PIPS detectors, electron-yield with a metal collector grid), and at two temperatures (ambient and liquid He cryoflow). This database provided us with a remarkable opportunity to compare and contrast the various sources of error in XAS data collection, data reduction, and spectral fitting. The slight variations among the normalized spectra (Figure S3, Supporting Information) with the exception of data set E are indicative of the generality of the quantitative electronic structure analysis from XAS presented here. Data set E was obtained for an intentionally thick sample, which gave the approximate lower limit of pre-edge and rising-edge intensities due to self-absorption of the fluorescence signal.39 Simulta12286

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Figure 3. Effect of radiation damage in S K-edge data (A); the comparison of linear and exponential extrapolated data to zero-exposure time, the average room temperature spectra without radiation damage correction and the data set F, which was collected at liquid He cryoflow temperature (B); effect of radiation damage in S K-edge data using fluorescence emission detection (C) and electron-yield detection (D); comparison of extrapolated data sets D, I, and J to no exposure, and of LHe cryoflow sample F (E; see also Figure S6, Supporting Information).

Detection Technique Influence on Data Quality. In addition to utilizing the differences among various detection techniques for correcting for radiation damage, it is also important to evaluate the data dependence on the detection method, as this can limit the transferability of transition dipole integrals. An earlier study on chloropalladium complexes discussed the need for a detection/beamline method dependent correction to the quantitative analysis of XANES features.40 The comparison of S K-edge spectra taken at BL 4-3 at room

magnitude thicker. Parts C and D of Figure S3 (Supporting Information) illustrate this difference and provide two different rates of radiation damage for extrapolating to the zero-exposure state. These corrections are critical to obtain the correct spectral intensity of the pre-edge features for an accurate quantitative analysis. The slightly lower intensity of the electron-yield data (data set J) relative to the fluorescence data set F is due to the detector being operated by a 45 V battery in partial electron-yield mode. 12287

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Figure 4. Energy position analysis of the XANES region of the normalized S K-edge spectra of (A) Fe2(pdt)(CO)6 and (B) Na2pdt: (C) and (D) first derivative spectra; (E) and (F) second derivative spectra.

temperature with different detectors is shown in Figure S7 (Supporting Information). The data sets overlay reasonably well with small differences between EY and FF data sets in the XANES region (Figure S7A, Supporting Information). Data set G was obtained with the older, three-element Lytle detector and is similar in the pre-edge region with data set H, collected with a PIPS detector. The intensity differences among the preedge and rising-edge features for the same sample, but with a newer, five-element Lytle detector (I) and simultaneous electron-yield detection (J) with 45 V potential between the

sample and a Ni collector grid can be rationalized by selfabsorption of the fluorescence signal for the thicker sample and the use of a smaller collector potential (45 V) than the ideal ∼200 V for total electron-yield detection, respectively. When the fluorescence data set K from CLS (Figure S4, Supporting Information) is corrected with the detector dead-time (9% at the most intense feature due to the large Fe fluorescence signal), the resulting spectrum becomes practically identical with SSRL data. 12288

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3. RESULTS AND ANALYSIS 3.1. S K-Edge XANES in the “Tender” X-ray Energy Range. The quantitative analysis of XANES pre-edge features is a direct approach to obtain experimental information about bond covalency, orbital composition, Zeff, and nucleo- or electrophilicity of an absorber. These can be directly used to understand and predict electronic and geometric structural features, and hence chemical reactivity. It is then critical to gauge the reproducibility and accuracy of XAS measurements, data normalization, and fitting procedures. Herein, we briefly summarize a systematic evaluation of key experimental factors, using Fe2(pdt)(CO)6 as a demonstrative example, that can have an effect on the data quality at the S K-edge region, such as data collection (sample preparation protocols, beamlines, sample mounting, detection methods, and sample temperature), data normalization, and fitting techniques. It is also important to highlight that Fe2(pdt)(CO)6 has a remarkably convoluted electronic structure that does not allow for a straightforward analysis like the one already reported for single electron holebased excitations.1,41 On the contrary, in the case of Fe2(pdt)(CO)6, we need to consider envelops of transitions that increase the uncertainty of the data analysis compared, for example, with the analysis of mononuclear Cu(II) complexes.41 Data Normalization. The normalization steps, as summarized in Figure 2, are implemented in the ADRP program.42 First we evaluated the dependence of the normalized data on the selected energy ranges for the background and the post-edge regions to obtain the second-order polynomials and spline functions, respectively. Figure S8 (Supporting Information) compares the results of three representative normalization protocols. The manual correction corresponds to the method that has been used in earlier S K-edge studies.2,43−45 ADRP-Go is an automated version of the ADRP program, which allows for a rapid data analysis using the best estimates for the polynomial fit energy ranges without any user interaction.42 As can be seen in Figure S8 (Supporting Information), the variations of spectral feature intensities remain small between the current and previously used normalization protocols. ADRP-Go introduces some error for the peak intensities (approximately 3%); however, it allows for a rapid qualitative comparison at the beamline immediately after data collection. Analysis of Energy Positions of XANES Features. Figure 4 summarizes the analysis steps for the most representative, normalized spectrum of Fe2(pdt)(CO)6 and the free ligand salt, Na2pdt. The XANES energy region of the complex can be separated at 2473 eV for the pre-edge and rising-edge regions. The inflection point along the rising-edge at 2473.5 eV (marked with a dot in Figure 4A) is obtained from the first derivative spectrum (Figure 4C). This energy position is often correlated with the Zeff of the S 1s core orbital. The minima of the second derivative spectrum (Figure 4E) define at least two features for each region (pre-edge, 2471.6 and 2472.2 eV; rising-edge, 2473.9, 2474.8, and 2475.4 eV). By considering the molecular orbital picture in Scheme 3, we expect to see excitations into the first thee unoccupied molecular orbitals that are the antibonding combination of the two Fe 3dz2 orbitals (LUMO) and the bonding and antibonding combination of the two Fe 3dx2−y2 orbitals (LUMO+1 and LUMO+2, respectively), with significant S 3p character. Furthermore, due to the low symmetry of the complex (C2v at most if the puckering of the dithiolate ring is neglected), there is also a possibility of mixing between the Fe−CO π* and S 3p orbitals. The S−C σ* and the

Rydberg S 4p orbitals are located at higher energy and partially mixed with the block of CO π* orbitals. The assignments of the latter two envelops of features are straightforward due to the availability of the free ligand spectrum. However, the ground state orbital energy levels in Scheme 3 allow for multiple assignments for the pre-edge and rising-edge features. One of the plausible interpretations is to consider the pre-edge features at 2471.6 and 2472.2 eV arising only from the first three Fe 3d-based orbitals. The rising-edge features at 2473.9 and 2474.8 eV then are due to the twelve CO π*, the C−S σ* orbitals, and at higher energy (2475.4 eV) the S 4pbased Rydberg orbitals. The latter can be taken as the approximate S 1s ionization threshold or edge jump position. An equally attractive explanation of the pre-edge features would be to assign the excitation of the S 1s core electron into the first fifteen LUMOs that correspond to the aforementioned Fe−Fe and Fe−S σ* and π* orbitals along with the twelve Fe−CO π* orbitals. In this case, the rising-edge features would have to be assigned to the transition from the S 1s core orbital to the S−C σ* orbitals and the S 4p Rydberg orbitals. The relative energy positions of the latter two transitions are consistent with the S K-edge spectra of other transition metal thiolates.4,46 However, as it will be discussed below, for all the Fe, C, and O K- and Fe L-edges, the multi-edge XAS treatment eliminates the latter assignment due to the well-defined energy separation of ∼2 eV between the first three Fe 3d-based and the upper twelve CObased orbitals. If available, the comparison with the free ligand salt spectrum can further aid the assignment of spectral features. The 1.6 eV shift of the rising-edge inflection points between the complex (2473.5 eV) and the free ligand (2471.9 eV) as shown in Figure 3C,D, respectively, is indicative of considerable S → Fe electron donation and thus reduced negative charge of the S absorbers of the dithiolate bridge in Fe2(pdt)(CO)6. These changes also correspond to an increase of Zeff(S) that lowers the energy of the core S 1s orbital and thus shifts up in energy all the spectral features of Fe2(pdt)(CO)6. Notably, the shift between the highest energy resolved features that were assigned to the S 1s→4p transition is only 1 eV, as shown in Figures 3E (2475.4 eV) and 3F (2474.4 eV), compared with the aforementioned 1.6 eV shift of the rising-edge inflection point. Taking into account that the unoccupied S 4p Rydberg orbitals do not significantly contribute to Fe−S bonding, the 0.6 eV difference can provide an estimate for the change in the Zeff(S) between the open conformation of the free ligand salt and the bridging dithiolate ligand in which the S···S distance is reduced (3.05 Å, Figure 1). The proximity of the two formally anionic S absorbers in Fe2(pdt)(CO)6 raises the energy of the S 3p-based donor orbitals due to ligand−ligand repulsion. This also contributes to the covalency of the Fe−S bonds, and thus, the increased S → Fe electron donation results in a larger shift of the S−C σ* features relative to the S 4p Rydberg orbitals. The absence of any low energy features below the rising-edge in the free ligand salt also supports our assignment that the pre-edge features in Figure 4A emerge only due to the presence of Fe−S bonds. The comparison of the S K-edge XAS spectra of the free and the coordinated bridging dithiolate ligand in Fe2(pdt)(CO)6 with previously reported free and coordinated terminal thiolate ligands,43 also reveals important electronic structure differences between the two coordination modes that need to be considered for estimating the S 1s→3p transition dipole integral (IS 1s→3p). The higher energy position of the 4p/edge position in the bridging dithiolate free ligand and the 12289

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Fe2(pdt)(CO)6 complex indicates that the transition dipole integral for the bridging thiolate, compared with the terminal thiolate, should be increased, as discussed below in the Fe−S bond covalency analysis section. Fitting of Pre-edge Features. To evaluate the variations in peak intensities as a function of various fitting methods, we used the EDG_FIT program as part of EXAFSPAK as a reference,34 because this fitting procedure has been used in a large set of previous S K-edge data.2,4 Due to the envelop nature of all transitions, the Gaussian/Lorentzian mixing coefficient (m) was allowed to deviate from 0.5, the value generally used for a pseudo-Voigt line shape of a single electron hole-based transition. In addition, the line widths were not linked to each other. In parallel, we obtained a similar fit using a more sophisticated fitting method in PeakFit (SEASOLVE). Although the fits from both EDG_FIT and PeakFit are visually similar as shown in Supporting Information (Figure S1), there are considerable differences in the intensities and the shapes of the transition envelopes (Table S1, Supporting Information). In brief, the main difference is observed in the fit done with EDG_Fit (Figure S1A, Supporting Information), in which the broad envelope that is related to the formally S 4p-based features subtracts ∼0.18 eV of intensity from the lower energy features. With respect to Fe−S bonding, the most important fitting parameters correspond to the first envelop of transitions. If all fits are considered (Table S1, Supporting Information), the normalized area of the pre-edge features ranges from 3.05 to 3.69 eV, with an average value of 3.42 ± 0.24 eV. This corresponds to an approximately 7% variation of the intensity of the spectral features describing Fe−S bonding. Considering the chemically most reasonable way of taking into account the rising-edge features (Figure 5 and “scaled and shifted” row in Table S1, Supporting Information) and expecting features due to small, but non-negligible mixing of S 3p character into the CO π* orbitals, repeated fitting of the pre-edge features with varied free-ligand energy positions introduces only 5% variation in the intensity of the two pre-edge features, with an average value of 3.69 ± 0.18 eV. Overall Error Analysis. We examine in this study the quantitative effects of sample quality, radiation damage, detector, and data normalization on the fitting parameters of the normalized pre-edge features using the chemically most reasonable rising-edge correction that is based on the subtraction of the free ligand spectrum (see above). The results are presented in Table 2. Data set E with strong self-absorption of the fluorescence signal shows a reduced pre-edge area of 3.47 eV, which is approximately 6% less than the average value of all data sets (3.74 ± 0.15 eV). The former value can be estimated to be the lower limit of pre-edge intensity using the chemically most reasonable normalization and fitting procedures (see above). Exclusion of data set E, as well as J that was not collected with the optimal detector set up, does not significantly affect the average pre-edge intensity that is now calculated at 3.73 ± 0.09 eV; however, the deviation is reduced to 4%. The effect of using samples from different laboratories (data sets B−D) introduces a deviation of ∼3% with an average value of 3.73 ± 0.11 eV. The radiation damage corrected data set D deviates by approximately 3% from data set G. The difference between beamline configurations (data sets F and G) is only approximately 1% for the area under the pre-edge transition envelope. The employment of different detectors (data sets G−

Figure 5. Fit to the pre-edge and rising-edge regions of the S K-edge spectrum of data set F (A) and to the pre-edge after rising-edge subtraction (B).

J) gives an average of 3.84 ± 0.10 eV with again approximately 4% deviation. On the basis of the above 10 different measurements, the overall range of peak intensity varies from 3.47 to 4.04 eV, which corresponds to a remarkable 9% variation with the lower limit being the sample that shows large self-absorption. However, as discussed above, the most reasonable spectra were obtained for data set F, which was collected with a cryoflow setup for a thin sample diluted in boron nitride with fluorescence detection. Experimental Fe−S Bond Covalency. The most representative total area under the pre-edge features of the S K-edge spectrum of Fe2(pdt)(CO)6 is 3.69 ± 0.18 eV, which corresponds to the total amount of S → Fe electron donation for the first three LUMOs with an approximately 5% uncertainty. To convert this number to orbital composition using eq 3, we need an estimate for the S 1s → 3p transition dipole integral (IS 1s→3p). Using the linear relationship of the transition dipole integral as a function of the S 4p/edge jump position,37 a value of IS 1s→3p = 15.2 eV is obtained for the edge jump position at 2475.4 eV (Figure 4C). This IS 1s→3p value converts the total analytical pre-edge area to 1.46 ± 0.07 electrons (e) total S 3p character for two S absorbers (N = 2) in six electron holes. Because the contribution of S 3s and 3d orbitals can be neglected in the given complex, we can use this number to define the covalency of each Fe−S bond. The bond covalency analysis for the [Fe2S2(SEt)4]2− and [Fe4S4(SEt)4]2− clusters defined 25 ± 3% and 41 ± 1% per each Fe−S(thiolate) bond, respectively.47−49 The comparable number for the 12290

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carbonyl groups forming the equatorial plane. The remaining terminal CO and a 3dz2-based Fe−Fe “banana” bond occupy the axial positions. Due to the noncentrosymmetric coordination environment of the Fe sites, the mixing of Fe 4pz and Fe 3d orbitals is not forbidden and estimated to be approximately 12% per orbital.50 Figure 6A shows two representative data sets collected at BL 7-3 and 9-3 at SSRL (Table 2, data sets L and M). The transmission spectra overlay well in the entire energy range. The pre-edge and rising-edge regions of the XANES spectra

Table 2. Fit Parameters to S K-Edge Data Sets A−J from Table 1, Where E0 is Peak Position, A is Amplitude, hhlw is the Half-Height Full Line Width, m is the Gaussian/ Lorentzian Line Shape Mixing Coefficient, and D0 is the Normalized Integrated Area/Intensity of the Envelope of Transitions for Pre-edge Featuresa data set

E0, eV

A

hhlw, eV

m

D0, eV

ΣD0, eV

A

2471.6 2472.3 2471.6 2472.2 2471.5 2472.2 2471.6 2472.2 2471.5 2472.2 2471.5 2472.2 2471.6 2472.2 2471.6 2472.2 2471.5 2472.2 2471.5 2472.0

1.47 0.98 1.67 1.27 1.58 1.22 1.62 1.25 1.29 1.07 1.53 1.23 1.53 1.22 1.46 1.09 1.55 1.05 0.92 1.49

1.03 1.17 0.88 0.98 0.96 1.07 0.91 1.04 0.97 1.09 0.89 1.01 0.90 1.04 1.03 1.11 1.00 1.10 0.97 1.52

0.59 0.01 0.32 0.54 0.37 0.29 0.38 0.20 0.25 0.16 0.20 0.28 0.32 0.14 0.46 0.08 0.46 0.00 0.02 0.72

1.86 1.78 2.00 1.55 2.03 1.79 1.97 1.87 1.76 1.71 1.96 1.73 1.87 1.86 1.94 1.84 2.00 1.81 1.40 2.65

3.64

B C D E F G H I J

3.55 3.82 3.84 3.47 3.69 3.73 3.78 3.81 4.04

a The fitting energy range was 2465−2474.5 eV for all data sets, and the fitting procedure of free ligand salt subtraction was used with shifting and scaling (see Table S1 and Figure S1D, Supporting Information).

formally four bonds in Fe2(pdt)(CO)6 is 36 ± 2%, which is remarkably more covalent than the [2Fe−2S] clusters and similar to the [4Fe−4S] clusters. The bridging nature of the dithiolate ligand and the presence of π-acceptor carbonyl ligands increases the covalency of the Fe−S bonds in Fe2(pdt)(CO)6. The total S 3p character can be distributed among the three Fe 3dz2-, 3dx2−y2-based LUMO−LUMO+2 orbitals to give ∼24 ± 2% S 3p character per electron hole on average. However, this equal distribution is not chemically reasonable due to the different LUMO compositions. A theoretical estimate for the relative amount of S 3p mixing with the Fe 3d orbitals from the molecular orbital picture (Scheme 3) is 15, 20, and 25% for LUMO−LUMO+2, respectively.29 Considering the relative S 3p characters, the experimental estimates for the differential orbital covalencies are 18 ± 3, 24 ± 3, and 30 ± 4% per electron hole for the first three LUMOs. 3.2. Fe K-Edge XANES in the Hard X-ray Energy Range. We present here a limited uncertainty analysis for the Fe K-edge XANES of the Fe2(pdt)(CO)6 complex due to its similarity in the source and nature of deviations among the sample preparation, detector and beamline dependence, and radiation damage to the S K-edge data. The edge jump at the Fe K-edge is intense with poorly resolved rising-edge features. A pre-edge feature at a metal K-edge is generally an order of magnitude weaker due to the electric quadrupole nature of a 1s → nd transition, relative to the electric dipole allowed 1s → (n + 1)p transitions.11 The geometry of each Fe site in Fe2(pdt)(CO)6 can be considered as distorted octahedral with two shared bridging thiolate S ligands and two terminal

Figure 6. Fe K-edge data of Fe2(pdt)(CO)6 for data sets L and M (Table 1) (A), the first derivative of data set M (B), and the second derivative of data set M (C) (see also Figure S9, Supporting Information). 12291

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show only little variation due to the slightly different concentration of the sample in the boron nitride matrix. An important parameter of the Fe K-edge XANES spectrum is the rising-edge inflection point at 7117.7 eV (marked with a dot in Figure 6A), which is an experimental measure of the Zeff(Fe) seen by the Fe 1s core orbital. This is obtained from the first maximum of the first derivative spectrum within the rising-edge region. The rising-edge inflection points of representative examples for formally metallic (Fe(0)), ferrous (Fe(II)F2), and ferric (Fe(III)F3) iron oxidation states are at 7111.2, 7122.1, and 7128.4 eV, respectively. Notably, the rising-edge of the Fe(I)2(pdt)(CO)6 complex features a shoulder as for the Fe(0) metal foil (Figure S10A, Supporting Information), which is absent for the FeF2 and FeF3 spectra. This may introduce some uncertainty in correlating rising-edge features with Zeff(Fe); however, an alternative assignment for the rising-edge inflection points shown by arrows in Figure S10B (Supporting Information) gives a chemically identical trend for the Fe(0)− Fe(I)−Fe(II)−Fe(III) series (7118.6, 7125.2, 7126.3, and 7132.4 eV, respectively). The similarity in rising-edge positions for the ferrous fluoride and the Fe2(pdt)(CO)6 complex is remarkable, because there is considerable Fe → CO back-donation, as indicated from the shift to lower energy of the v(CO) frequency in Fe2(pdt)(CO)6 (70−150 cm−1).22,28 In turn, this is expected to increase the Zeff(Fe) relative to that of the formal Fe(I) oxidation state. However, the covalent bonding with approximately 36% S character per Fe−S bond, as determined from the S K-edge XAS measurements presented above, compensates for the loss of Fe electron density due to back-donation. The intramolecular electron donation may also be described by a LL′CT mechanism, because overall the dithiolate ligand donates to the CO π* orbitals via the Fe centers. To demonstrate the benefit of multi-edge XAS treatment, it is important to note that the pre-edge region of the Fe K-edge shows two features that are separated by approximately 2 eV. This energy separation is analogous to the difference between the positions of the pre-edge and the rising-edge envelops in the S K-edge spectrum. Because both edges probe the same excited states originating from the same set of acceptor orbitals, the two spectral features can be correlated to each other. From the orbital picture in Scheme 3, the lower feature can be assigned to the Fe−S bonds, and the higher energy feature to the Fe−CO π* orbitals. At the S K-edge, the latter also show considerable S 3p character because they contain contributions from the S−C σ* orbitals. At the Fe K-edge, a comparison of the pre-edge peak areas after subtraction of the rising-edge (Figure 7B) shows a more intense first peak centered at 7112.6 eV with an area of 0.20 eV relative to the higher energy peak at 7114.5 eV with an area of 0.16 eV. The intensity differences of the two pre-edge features that are separated by 2.2 eV can be correlated with the relative Fe 4p mixing into the first three, Fe 3d-based LUMOs and the higher lying twelve Fe−CO π* orbitals. In comparison, tetrahedral [Fe(III)Cl4]− and [Fe(II)Cl4]2− complexes have pre-edge intensities of 0.26 and 0.16 eV,11 with approximately 0.17 and 0.10 e total Fe 4p mixing, respectively, into the vacant Fe 3d orbitals.11 The transition dipole integral (IFe 1s→4p) for these ionic compounds would then be approximately 4.6 eV. It is important to note that there is a considerable uncertainty (∼40%) in the transition dipole integral due to the inherent error of determining the reference 4p contribution for the Cs2CuCl4 complex and then using a

Figure 7. Fit to the pre-edge and rising-edge regions of the Fe K-edge spectrum of data set M (A) and to the pre-edge after rising-edge subtraction (B).

transition dipole integral expression as a function of metal effective nuclear charge to convert the Cu(II) value to Fe(II) and Fe(III).11 In addition, we anticipate a normalization error of 3% and a rising-edge subtraction/fitting error of 7% from the detailed S K-edge analysis above. Assuming a similarly small change in the transition dipole integral in going from Fe(III) to Fe(II) complexes and then to Fe(I) in the Fe2(pdt)(CO)6 complex, we can use eq 1 with D0 = 0.20 ± 0.02 eV and N = 2 to estimate the total Fe 4p contribution for 6 electron holes to be 0.26 ± 0.11 e. On the basis of relative pre-edge intensities, this converts to 0.21 ± 0.08 e Fe 4p mixing with the twelve Fe− CO π* orbitals. 3.3. Fe L-Edge XANES in the Soft X-ray Energy Range. The Fe L-edges represent a considerable departure from the Kedge features due to the intense pre-edge features in contrast to the small edge-jump, and the presence of two edges due to the spin−orbit coupling of the 2p5 core electron hole (J = 3/2 and 1/2 for LIII and LII-edges, respectively). In addition, there are significant technical differences in the experimental setup and data collection protocols among the L- and the K-edges, which also contribute to the need of different data normalization and fitting procedures. In the multi-edge XAS treatment, the metal L-edge features are essential, because they provide direct experimental information about the metal d character of the 12292

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LUMOs as a complement to the ligand p character from ligand K-edge measurements. From the above discussion of the S and Fe K-edge spectra of Fe2(pdt)(CO)6, we expect to see at least two groups of preedge features that can be correlated with the Fe 3dz2- and Fe 3dx2−y2-based first three LUMOs and the additional twelve Fe− CO π* orbitals. Spectral features at the metal L-edge corresponding to M → L back-donation have already been discussed for Fe, Cu, and Ni complexes.51−53 It is important to emphasize that the sum of the intensities of pre-edge features at both the LIII- and LII-edges is the chemically meaningful measure of the total Fe 3d character;51,54,55 however, the ground state orbital picture cannot always be directly mapped onto the L-edge spectrum. This is due to the non-negligible overlap between the core hole and the valence 3d orbitals and the multiplet effects involving the valence 3d orbitals. As can be seen in Figure 8A, the Fe L-edge spectrum is dominated by two pre-edge peaks for both LIII and LII regions. The peaks at the LIII-edge are centered at 708.4 and 710.4 eV. Both appear to have ill-resolved low energy shoulders, which show up in the second derivative spectrum at 707.8 and 709.7 eV. The unresolved shoulder at the higher energy side of the second pre-edge feature at ∼711.9 eV can be related to the weak Fe 2p → 4s transitions. This value also indicates the approximate position for the ionization threshold or the edge position. The 2 eV energy separation between the two groups of pre-edge features correlates well with the energy split of the spectral features at the S K- and Fe K-edges, thus demonstrating the power of multi-edge XAS in experimentally probing the same unoccupied frontier MOs from different energy ranges; however, the analysis of peak intensities below indicates that the excited state description cannot be directly correlated with the ground state molecular orbital picture due to multiplet effects. To model the LIII and LII-edge jumps, we initially fit the data with two arctangent functions, as described previously.51,54 The 2p-hole spin−orbit interaction was calculated to be 8.20 eV for Fe(II) or Fe(III) and this was scaled up by 3/2 to be approximately 12.3 eV in energy.56 The LIII ionization threshold of 707.7 eV for the Fe2(pdt)(CO)6 complex with formally Fe(I) sites can be extrapolated from the low-spin [Fe(III)(tacn)2]3+ (709.9 eV), [Fe(II)(tacn)2]2+ (708.5 eV) complexes, and metallic Fe0 (706.8 eV). However, this edge position gave considerable negative intensity after edge subtraction in the LIII pre-edge region. As detailed in the Supporting Information, we obtained reasonable edge-jump corrected data, which are summarized in Table 3 and Figure 9. Table 3 presents representative fits for the most reasonable edge subtracted data with respect to the m, ALII, and ELIII parameters. Variation in the slope parameter m from 0.1 to 1.0 introduces less than 2% deviation in the LIII, LII, and total Ledge area, respectively. Because all the fits are acceptable, this deviation can be considered as uncertainty due to the slope parameter (m). Using an intermediate value of m = 0.5 eV and keeping the LIII-edge position fixed at 710 eV, the deviations are 3−5% in the above order due to the change in the LIII-edge amplitude (ALIII) in the range of 0.7−0.9. As discussed above, the largest variations are found if the LIII-edge energy (ELIII) is varied while keeping the other parameters fixed in the range of 4−10%. From Figure 9, the 707−709 eV energy range of the LIII-edge can be fitted with two peaks, with an average area of 4.72 ±

Figure 8. Fe LIII- and LII-edge data of Fe2(pdt)(CO)6 (A), the first derivative of the Fe LIII/LII-edge (B), and the second derivative of the Fe LIII/LII-edge (C).

0.36 eV. The higher energy region of 709−712 eV at the LIIIedge can also be fitted using the minimal of two peaks with an average intensity of 11.65 ± 0.98 eV. Similarly, the LII-edge can be fitted with a minimum of two peaks for each feature leading to an average peak intensity of 2.54 ± 0.21 eV and 7.34 ± 0.34 eV for the 719−721.5 and 721.5−725 eV regions, respectively. By considering the total integrated intensity of each feature for both edges, as needed for eq 4, the total pre-edge intensities for the first and the second groups of excitations are 7.26 ± 0.50 and 19.0 ± 1.19 eV. 12293

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Table 3. Fitting Parameters of the Representative Fe L-Edge Pre-edge Features for Fe2(pdt)(CO)6 m/ALIII/ELIIIa

ELIII, eV

DLIII, eV

∑DLIII,eV

ELII, eV

DLII, eV

∑DLII,eV

D0, eV

DLIII/D0b

0.1/0.8/710

708.1 708.4 709.8 710.5 708.0 708.4 709.9 710.6 708.0 708.4 710.1 710.7 708.1 708.4 710.0 710.6 708.0 708.4 710.1 710.6 708.0 708.4 710.1 710.7 708.0 708.4 710.1 710.7

2.3 2.3 2.6 5.3 2.1 2.6 2.9 4.7 2.2 2.4 4.1 3.1 2.6 1.9 3.2 4.4 2.3 2.5 3.8 3.4 2.4 1.9 3.6 3.5 2.3 2.3 4.0 3.4

16.33

720.6 720.8 722.6 723.3 720.6 720.8 722.6 723.3 720.6 720.8 722.6 723.3 720.6 720.7 722.6 723.0 720.5 720.9 722.5 723.1 720.5 720.9 722.6 723.1 720.6 720.8 722.6 723.3

1.2 0.9 1.6 1.2 1.1 0.9 1.6 1.3 1.0 1.0 1.6 1.3 1.2 0.8 1.5 1.3 1.0 1.1 1.2 1.8 1.1 0.9 1.5 1.3 1.1 1.0 1.6 1.5

9.72

26.05

0.63

9.83

26.05

0.62

10.01

26.21

0.62

10.42

27.26

0.62

9.45

25.31

0.63

9.48

24.45

0.61

10.22

28.41

0.64

0.5/0.8/710

1.0/0.8/710

0.5/0.7/710

0.5/0.9/710

0.5/0.8/708

0.5/0.8/712

a

16.22

16.20

16.84

15.86

14.97

18.19

ALIII = 1 − ALII and ELII = ELIII + 12.3 eV. bIdeal ratio is 2/3.

We can obtain an estimate for the Fe 2p → 3d transition dipole integral from the literature, developed by Wasinger et al.,54 by taking the total L-edge intensity of 64.1 eV and correlating it with 4.01 e total Fe 3d character in the five lowest unoccupied frontier orbitals of [Fe(III)Cl4]−. Using eq 4, the integral IFe 2p→3d of 48.0 eV can be obtained for the high spin, ferric iron with N = 1 for h = 5 electron holes. Using this integral, the total Fe 3d character in the first 15 LUMOs of Fe2(pdt)(CO)6 can be estimated to be 3.3 ± 0.2 e for the total pre-edge intensity of 26.26 ± 1.6 eV from both L-edges. This can be broken equally into Fe 3d characters of 0.9 and 2.4 e for a total of 6 and 24 electron holes, respectively. From the S and Fe K-edges, we have seen that there is approximately 1.46 and 0.26 e total S 3p and Fe 4p characters in the first three LUMOs. Assuming negligible S 3s and 3d, Fe 4s contributions, this leaves approximately 4.28 e for the Fe 3d and the carbonyl ligand characters for LUMO−LUMO+2. This would correspond to an average of approximately 72% Fe 3d and CO σ/π* per electron hole. From earlier electronic structure calculations,22 the ratio of Fe 3d to carbonyl characters of these LUMOs is estimated to be 0.64. Thus, 44% electron hole composition can be correlated with to the Fe 3d character or total of 2.64 e for the three lowest energy LUMOs. This is about three times more as obtained from the intensity of the first group of pre-edge features (0.9 e). The low value of the experimental Fe 3d character relative to that expected from complementary pre-edge intensities at the S and Fe K-edges is indicative of two problems. First, the transition dipole integral may need to be adjusted because the effective nuclear charge seen by the Fe 2p orbitals of a low spin,

low valent Fe(I) is considerably lower relative to a high spin, ferric center. Second, and more important, the ground state electronic structure could not be directly mapped onto the Fe L-edge features. Even with adjusting the transition dipole integral, the relative ratios of the two pre-edge features and the Fe 3d characters between the first 3 and the next 12 LUMOs29 remains unreasonable. This indicates that we have not considered all the experimental intensity associated with the Fe 3d-based LUMO−LUMO+2; i.e., due to multiplet effects, the first three Fe 3d-based orbitals need to be split into two parts, where the higher energy part will overlap with the Fe− CO π* features. It is important to emphasize that this level of critical evaluation of spectral intensities would have not been possible without the complementarity of edge information from multi-edge XAS. Considering only relative values from previous electronic structure calculations for Fe2(pdt)(CO)6,29 the experimental 2.64 e contribution in the first three LUMOs need to be scaled by 1.45 to get an estimate for the Fe 3d character of the next twelve Fe−CO π* LUMOs. Thus, the total Fe 3d character (6.47 e) for the first 15 orbitals can now define a dipole integral of 24.4 eV for the low spin, low valent Fe(I) center. 3.3. C and O K-Edge XANES in the Soft X-ray Energy Range. To complete the experimental electronic structure for Fe2(pdt)(CO)6, we also collected the C and O K-edge spectra as shown in Figure 10. Due to the large background signal from stainless steel and oxide layers on the beamline components, we can only discuss the C and O K-edge XANES data in qualitative terms without a rigorous analysis of the spectral features and areas, as previously discussed for the S K-edge spectra. The 12294

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and 3 times more intense than7 the edge jump, respectively. Remarkably, both C and O ligand K-edge spectra exhibit a lower energy peak that is centered at 286.4 and 531.5 eV, respectively, approximately 2 eV below the intense pre-edge features. Although these peaks have weak intensities, they can be attributed to the excitation to the first three LUMOs. As discussed previously, this energy separation is very close to that found in the spectra of the S, Fe K- and Fe L-edges and associated with the Fe ← CO donation without the contributions of the 2s orbitals. Fitting of the collected data (Figure 11) reveals that the ratios of the pre-edge intensities are 1:51 and 1:21 for C and O, respectively. From the electronic structure calculations,22 a 1:11 ratio is estimated for the Cbased contributions to LUMO−LUMO+2 relative to the next 12 CO π*-based LUMOs. This ratio is calculated to be approximately 1:10 for the O-based contributions; however, the calculated ratios are based on total C and O characters without separating out the 2s and 2p contributions. Therefore, the higher amount of C and O 2s character relative to the 2p character of the first three Fe 3d-based LUMOs versus the pure 2p character of the CO π* orbitals can rationalize the deviation between the calculated and experimentally observed relative ratios.

4. CONCLUSIONS Using the example of a biomimetic model complex Fe2(pdt)(CO)6, we demonstrated the remarkable potential of employing a multi-edge X-ray absorption near-edge spectroscopic analysis in defining the complete atomic composition of unoccupied frontier orbitals, and thus the total bonding description of a transition metal complex with electron holes in its d-manifold. In addition to obtaining orbital composition from experiment, the multi-edge XANES approach can provide critical guidance in assigning ill-resolved features, because the same set of unoccupied orbitals are probed upon excitation, but from different core donor orbitals. The S K-edge data defined the total S 3p character of the first three Fe−S LUMOs. Using relative orbital compositions from electronic structure calculations, the total S character can be broken into differential orbital compositions. The complementarity of S 3p, Fe 4p, and Fe 3d contributions allows for the formulation of the complete electronic structure from experiment for the first 15 LUMO, as shown in Table 4. The electron hole compositions were obtained by using transition dipole integrals for the S 1s → 3p, Fe(I) 1s → 4p, and 2p → 3d excitations of 15.2, 4.6, and 24.4 eV, respectively. Furthermore, we carried out a systematic evaluation of sources for uncertainty in extracting quantitative orbital information from the XANES data. This was done in the most detailed way for the S K-edge considering variations in the data due to various detectors and different sample temperatures, preparation protocols, and experimental beamline stations. These data collection factors introduce a typical 4% variation in peak intensities with the worst case scenario being 9% off from the average value. The data normalization using the automated data reduction protocol (ADRP)42 introduces less than 3% variation in intensity. We found that the fitting procedure especially for the given case with an ill-resolved, envelope of transitions can be the source of a significant error of 12%. However, considering the chemically most reasonable protocol of subtracting the rising-edge and post-edge features of the free ligand or ionic ligand salt spectrum can reduce this error to a few percent. The Fe L-edges provide a challenge in

Figure 9. LIII-(A) and LII-edge (B) fits with m/ALII/ELIII parameters of 0.5 eV/0.2/708 eV fit of the edge-corrected Fe L-edge spectrum of Fe2(pdt)(CO)6.

optimization of data collection and beamline setup for quantitative data analysis is still in progress. Although the spectral features are reproducible, the normalization and fitting of the data are not unique. The background subtraction and normalization strongly depends on the type of spectrum used for baseline subtraction. Collecting data for the empty chamber, the sample paddle, or the indium foil used for sample mounting leads to significant differences in the final data after fitting. Moreover, the sublimation of the sample that is observed in ultrahigh vacuum (see warning in Experimental Methods Section) further complicates the C and O K-edge analysis. It is also important to consider that only the C and O 1s → 2p excitations are dipole allowed, and thus the non-negligible amount of mixing of 2s orbitals into the ground state electronic structure especially for carbon will not be observed. Specifically, we do not expect to see intense spectral features for the OC → Fe donation in the first three LUMOs of Fe2(pdt)(CO)6 due to the mixed 2s/2p character of the C-based lone pair (HOMO) of the CO ligand. In contrast, the 12 CO-based π* orbitals in Fe2(pdt)(CO)6 provide an intense pre-edge feature, because they are composed of only C and O 2p orbitals. As expected, both the C and O K-edge spectra have an intense feature centered at 287.1 and 533.2 eV, respectively (Figure 10). Similarly to the spectrum of the free gaseous or the chemisorbed carbon monoxide,7 these intense features, arising from C and O 1s to CO π* excitations, are approximately 10 12295

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Figure 10. Energy position analysis of the XANES region of the normalized C K-edge spectra (A) and O K-edge spectra (B) of Fe2(pdt)(CO)6: (C) and (D) first derivative spectra; (E) and (F) second derivative spectra.

fitting due to the overlapping spectral features. We developed a multiparameter fit-based uncertainty analysis that can be generalized to other transition metal L-edges as well. Simultaneous optimization of the edge jump slope, LII-edge amplitude, and LIII-edge energy position resulted in a range of acceptable fit parameters that can be used to extract intensity information from the pre-edge features at the L-edges. The ground state electronic structure-based pre-edge analysis had to

be abandoned for the Fe L-edge features due to multiplet effects. This was mandated by the complementarity of electronic structure information from all the other edges considered in this study. These qualitative and quantitative considerations of S K-, Fe K-, and Fe L-edges allows us to experimentally describe the electronic structure of the entire biomimetic spectrochemical series for the catalytic H-cluster of FeFe-hydrogenases and 12296

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ASSOCIATED CONTENT

S Supporting Information *

Details of quantitative XANES analysis for S K-edge spectra, user defined function for the free ligand salt spectrum, comparison of various normalization methods, normalized XANES spectra for data sets A−J with extended energy range, spectral differences among various beamlines, sample sources, detection technique, extended energy range spectra for Fe Kedges, reference Fe K-edge spectra for representative Fe(0), Fe(II), Fe(III) compounds, detailed Fe L-edge edge jump corrections, Fe L-edge spectrum of Fe(0) nanoparticles. This material is available free of charge via the Internet at http:// pubs.acs.org. In addition, all raw, normalized, and fitted spectra are available at our electronic Supporting Information database http://computational.chemistry.montana.edu/SI/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from the National Science Foundation CBET 0744820. NASA Astrobiology Institute Funded Astrobiology Biogeocatalysis Research Center Grant NNA08C-N85A. Portions of this research were conducted at the Stanford Synchrotron Radiation Laboratory (SSRL), a national user facility operated by Stanford University on behalf of the U.S. Department of Energy, Office of Basic Energy Sciences. The SSRL Structural Molecular Biology Program is supported by the Department of Energy, Office of Biological and Environmental Research, and by the National Institutes of Health, National Center for Research Resources, Biomedical Technology Program, and the National Institute of General Medical Sciences. Data collection described in this paper was also carried out at the Canadian Light Source, which is supported by the Natural Sciences and Engineering Research Council of Canada, the National Research Council Canada, the Canadian Institutes of Health Research, the Province of Saskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan. We thank the beamline scientists at SSRL, especially Dennis Nordlund, Curtis Troxel and Dan Brehmer for their support with the cryoflow setup at BL 10-1. Similarly, the guidance provided by beamline scientist Yongfeng Hu at CLS is appreciated. We also thank the technical assistance to Dr. David Gardenghi in continuously updating the ADRP program and Rhonda Barton for collecting the C and O K-edge data. We acknowledge the research groups of Prof. Chris Pickett, University of East Anglia, U.K., and Prof. D. Mike Heinekey, University of Washington, Seattle, for providing the Fe2(pdt)(CO)6 samples and Prof. Alex Smirnov, Dowling College, for the freshly made Fe nanoparticles.

Figure 11. Preliminary pre-edge fits to the normalized C K- (A) and O K-edge spectra (B) of Fe2(pdt)(CO)6.

Table 4. Experimental Electronic Structure of the Fe2(pdt)(CO)6 as Defined by Eq 1 from Multi-edge XANES Analysis at the S K-, Fe K-, and Fe L-Edgesa electron hole composition LUMO LUMO+1 LUMO+2 LUMO+3 ⋮ LUMO+14

S 3p %

Fe 3d %

Fe 4p %

24 ± 3

∼44

∼4

not resolved

∼32

∼2

S K-edge

Fe L-edge

Fe K-edge

a

Electron hole composition is half of the molecular orbital compositions for this diamagnetic complex.

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define the contributions of each structural feature to the structure and reactivity of this remarkable Fe cluster. In forthcoming publications, we will use the experimental electronic structure description from multi-edge XANES to calibrate ab initio wave function- and density functional theorybased electronic structure calculations for calculating molecular structure, H2 coordination and release, reduction potential, and protonation constants that are essential in mapping out the molecular mechanism of biomimetic and biological hydrogen gas uptake and evolution reactions.

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