Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment-A case study on V(IV)/V(III) complexes.

In this work, we present a combined experimental and theoretical study on the V L2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of VIVO(acac)2 and VIII(acac)3 prototype complexes. The recorded V L2,3-edge XAS and XMCD spectra are richly featured in both V L3 and L2 spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L2,3-edge XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin-orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S' = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.

X-ray Magnetic Circular Dichroism Spectroscopy Applied to Nitrogenase and Related Models: Experimental Evidence for a Spin-Coupled Molybdenum(III) Center.

Nitrogenase enzymes catalyze the reduction of atmospheric dinitrogen to ammonia utilizing a Mo-7Fe-9S-C active site, the so-called FeMoco cluster. FeMoco and an analogous small-molecule (Et4 N)[(Tp)MoFe3 S4 Cl3 ] cubane have both been proposed to contain unusual spin-coupled MoIII sites with an S(Mo)=1/2 non-Hund configuration at the Mo atom. Herein, we present Fe and Mo L3 -edge X-ray magnetic circular dichroism (XMCD) spectroscopy of the (Et4 N)[(Tp)MoFe3 S4 Cl3 ] cubane and Fe L2,3 -edge XMCD spectroscopy of the MoFe protein (containing both FeMoco and the 8Fe-7S P-cluster active sites). As the P-clusters of MoFe protein have an S=0 total spin, these are effectively XMCD-silent at low temperature and high magnetic field, allowing for FeMoco to be selectively probed by Fe L2,3 -edge XMCD within the intact MoFe protein. Further, Mo L3 -edge XMCD spectroscopy of the cubane model has provided experimental support for a local S(Mo)=1/2 configuration, demonstrating the power and selectivity of XMCD.

Comparison of multireference ab initio wavefunction methodologies for X-ray absorption edges: A case study on [Fe(II/III)Cl4]2-/1- molecules.

In this work, we present a detailed comparison of wavefunction-based multireference (MR) techniques for the prediction of transition metal L-edge X-ray absorption spectroscopy (XAS) using [Fe(II)Cl4]2- and [Fe(III)Cl4]1- complexes as prototypical test cases. We focus on the comparison of MR Configuration Interaction (MRCI) and MR Equation of Motion Coupled Cluster (MREOM-CC) methods, which are employed to calculate valence excitation as well as core to valence Fe L-edge XAS spectra of [Fe(II)Cl4]2- and [Fe(III)Cl4]1- complexes. The two investigated approaches are thoroughly analyzed with respect to their information content regarding (1) metal-ligand covalency, (2) ligand field splittings, (3) relativistic effects, (4) electron correlation, (5) energy distribution, and (6) intensity modulation of the experimentally observed spectral features. It is shown that at the level of MRCI calculations in both [Fe(II)Cl4]2- and [Fe(III)Cl4]1- cases, very good agreement with the experimental Fe L-edge XAS spectra is obtained provided that the employed active space is extended to include ligand-based orbitals in addition to metal-based molecular orbitals. It is shown that this is necessary in order to correctly describe the important σ- and π- Fe-Cl covalent interactions. By contrast, MREOM-CC calculations yield excellent agreement relative to experiment even with small active spaces. The efficiency of the employed MR computational protocols is thoroughly discussed. Overall, we believe that this study serves as an important reference for future developments and applications of MR methods in the field of X-Ray spectroscopy.

Ab Initio Wave Function-Based Determination of Element Specific Shifts for the Efficient Calculation of X-ray Absorption Spectra of Main Group Elements and First Row Transition Metals.

In this study, a detailed calibration of the performance of modern ab initio wave function methods in the domain of X-ray absorption spectroscopy (XAS) is presented. It has been known for some time that for a given level of approximation, for example, using time-dependent density functional theory (TD-DFT) in conjunction with a given basis set, there are systematic deviations of the calculated transition energies from their experimental values that depend on the functional, the basis set, and the chosen treatment of scalar relativistic effects. This necessitates a linear correlation for a given element/functional/basis set combination to be established before chemical applications can be performed. This is a laborious undertaking since it involves sourcing trustworthy experimental data, lengthy geometry optimizations, and detailed comparisons between theory and experiment. In this work, reference values for the element-specific shifts of all the first-row transition metal atoms and the main group elements C, N, O, F, Si, P, S, and Cl have been computed by using a protocol that is based on the complete active space configuration interaction in conjunction with second-order N-electron valence state perturbation theory (CASCI/NEVPT2). It is shown that by extrapolating the results to the basis set limit of the method and taking into account scalar relativistic effects via the second-order Douglas-Kroll-Hess (DKH2) corrections, the predicted element shifts are on average less than 0.75 eV across all the absorption edges and a very good agreement between theory and experiment in all the studied XAS cases is observed. The transferability of these errors to molecular systems is thoroughly investigated. The constructed CASCI/NEVPT2 database of element shifts is used to evaluate the performance and to automatically calibrate prior to comparison with the experiment two commonly used methods in X-ray spectroscopy, namely, DFT/Restricted open shell configuration interaction singles (DFT/ROCIS) and TD-DFT methods.

How Do Ring Size and π-Donating Thiolate Ligands Affect Redox-Active, α-Imino-N-heterocycle Ligand Activation?

Considerable effort has been devoted to the development of first-row transition-metal catalysts containing redox-active imino-pyridine ligands that are capable of storing multiple reducing equivalents. This property allows abundant and inexpensive first-row transition metals, which favor sequential one-electron redox processes, to function as competent catalysts in the concerted two-electron reduction of substrates. Herein we report the syntheses and characterization of a series of iron complexes that contain both π-donating thiolate and π-accepting (α-imino)-N-heterocycle redox-active ligands, with progressively larger N-heterocycle rings (imidazole, pyridine, and quinoline). A cooperative interaction between these complementary redox-active ligands is shown to dictate the properties of these complexes. Unusually intense charge-transfer (CT) bands, and intraligand metrical parameters, reminiscent of a reduced (α-imino)-N-heterocycle ligand (L•-), initially suggested that the electron-donating thiolate had reduced the N-heterocycle. Sulfur K-edge X-ray absorption spectroscopic (XAS) data, however, provides evidence for direct communication, via backbonding, between the thiolate sulfur and the formally orthogonal (α-imino)-N-heterocycle ligand π*-orbitals. DFT calculations provide evidence for extensive delocalization of bonds over the sulfur, iron, and (α-imino)-N-heterocycle, and TD-DFT shows that the intense optical CT bands involve transitions between a mixed Fe/S donor, and (α-imino)-N-heterocycle π*-acceptor orbital. The energies and intensities of the optical and S K-edge pre-edge XAS transitions are shown to correlate with N-heterocycle ring size, as do the redox potentials. When the thiolate is replaced with a thioether, or when the low-spin S = 0 Fe(II) is replaced with a high-spin S = 3/2 Co(II), the N-heterocycle ligand metrical parameters and electronic structure do not change relative to the neutral L0 ligand. With respect to the development of future catalysts containing redox-active ligands, the energy cost of storing reducing equivalents is shown to be lowest when a quinoline, as opposed to imidazole or pyridine, is incorporated into the ligand backbone of the corresponding Fe complex.

Iron L2,3-Edge X-ray Absorption and X-ray Magnetic Circular Dichroism Studies of Molecular Iron Complexes with Relevance to the FeMoco and FeVco Active Sites of Nitrogenase.

Herein, a systematic study of a series of molecular iron model complexes has been carried out using Fe L2,3-edge X-ray absorption (XAS) and X-ray magnetic circular dichroism (XMCD) spectroscopies. This series spans iron complexes of increasing complexity, starting from ferric and ferrous tetrachlorides ([FeCl4]-/2-), to ferric and ferrous tetrathiolates ([Fe(SR)4]-/2-), to diferric and mixed-valent iron-sulfur complexes [Fe2S2R4]2-/3-. This test set of compounds is used to evaluate the sensitivity of both Fe L2,3-edge XAS and XMCD spectroscopy to oxidation state and ligation changes. It is demonstrated that the energy shift and intensity of the L2,3-edge XAS spectra depends on both the oxidation state and covalency of the system; however, the quantitative information that can be extracted from these data is limited. On the other hand, analysis of the Fe XMCD shows distinct changes in the intensity at both L3 and L2 edges, depending on the oxidation state of the system. It is also demonstrated that the XMCD intensity is modulated by the covalency of the system. For mononuclear systems, the experimental data are correlated with atomic multiplet calculations in order to provide insights into the experimental observations. Finally, XMCD is applied to the tetranuclear heterometal-iron-sulfur clusters [MFe3S4]3+/2+ (M = Mo, V), which serve as structural analogues of the FeMoco and FeVco active sites of nitrogenase. It is demonstrated that the XMCD data can be utilized to obtain information on the oxidation state distribution in complex clusters that is not readily accessible for the Fe L2,3-edge XAS data alone. The advantages of XMCD relative to standard K-edge and L2,3-edge XAS are highlighted. This study provides an important foundation for future XMCD studies on complex (bio)inorganic systems.

Comparative electronic structures of nitrogenase FeMoco and FeVco.

An investigation of the active site cofactors of the molybdenum and vanadium nitrogenases (FeMoco and FeVco) was performed using high-resolution X-ray spectroscopy. Synthetic heterometallic iron-sulfur cluster models and density functional theory calculations complement the study of the MoFe and VFe holoproteins using both non-resonant and resonant X-ray emission spectroscopy. Spectroscopic data show the presence of direct iron-heterometal bonds, which are found to be weaker in FeVco. Furthermore, the interstitial carbide is found to perturb the electronic structures of the cofactors through highly covalent Fe-C bonding. The implications of these conclusions are discussed in light of the differential reactivity of the molybdenum and vanadium nitrogenases towards various substrates. Possible functional roles for both the heterometal and the interstitial carbide are detailed.

Experimental and theoretical correlations between vanadium K-edge X-ray absorption and Kß emission spectra.

A series of vanadium compounds was studied by K-edge X-ray absorption (XAS) and K[Formula: see text] X-ray emission spectroscopies (XES). Qualitative trends within the datasets, as well as comparisons between the XAS and XES data, illustrate the information content of both methods. The complementary nature of the chemical insight highlights the success of this dual-technique approach in characterizing both the structural and electronic properties of vanadium sites. In particular, and in contrast to XAS or extended X-ray absorption fine structure (EXAFS), we demonstrate that valence-to-core XES is capable of differentiating between ligating atoms with the same identity but different bonding character. Finally, density functional theory (DFT) and time-dependent DFT calculations enable a more detailed, quantitative interpretation of the data. We also establish correction factors for the computational protocols through calibration to experiment. These hard X-ray methods can probe vanadium ions in any oxidation or spin state, and can readily be applied to sample environments ranging from solid-phase catalysts to biological samples in frozen solution. Thus, the combined XAS and XES approach, coupled with DFT calculations, provides a robust tool for the study of vanadium atoms in bioinorganic chemistry.

X-ray Absorption and Emission Spectroscopic Studies of [L2Fe2S2](n) Model Complexes: Implications for the Experimental Evaluation of Redox States in Iron-Sulfur Clusters.

Herein, a systematic study of [L2Fe2S2](n) model complexes (where L = bis(benzimidazolato) and n = 2-, 3-, 4-) has been carried out using iron and sulfur K-edge X-ray absorption (XAS) and iron Kß and valence-to-core X-ray emission spectroscopies (XES). These data are used as a test set to evaluate the relative strengths and weaknesses of X-ray core level spectroscopies in assessing redox changes in iron-sulfur clusters. The results are correlated to density functional theory (DFT) calculations of the spectra in order to further support the quantitative information that can be extracted from the experimental data. It is demonstrated that due to canceling effects of covalency and spin state, the information that can be extracted from Fe Kß XES mainlines is limited. However, a careful analysis of the Fe K-edge XAS data shows that localized valence vs delocalized valence species may be differentiated on the basis of the pre-edge and K-edge energies. These findings are then applied to existing literature Fe K-edge XAS data on the iron protein, P-cluster, and FeMoco sites of nitrogenase. The ability to assess the extent of delocalization in the iron protein vs the P-cluster is highlighted. In addition, possible charge states for FeMoco on the basis of Fe K-edge XAS data are discussed. This study provides an important reference for future X-ray spectroscopic studies of iron-sulfur clusters.