Pair Natural Orbital Restricted Open-Shell Configuration Interaction (PNO-ROCIS) Approach for Calculating X‑ray Absorption Spectra of Large Chemical Systems

In this work, the efficiency of first-principles calculations of X-ray absorption spectra of large chemical systems is drastically improved. The approach is based on the previously developed restricted open-shell configuration interaction singles (ROCIS) method and its parametrized version, based on a density functional theory (DFT) ground-state determinant ROCIS/DFT. The combination of the ROCIS or DFT/ROCIS methods with the well-known machinery of the pair natural orbitals (PNOs) leads to the new PNO-ROCIS and PNO-ROCIS/DFT variants. The PNO-ROCIS method can deliver calculated metal K-, L-, and M-edge XAS spectra orders of magnitude faster than ROCIS while maintaining an accuracy with calculated spectral parameters better than 1% relative to the original ROCIS method (referred to as canonical ROCIS). The method is of a black box character, as it does not require any user adjustments, while it scales quadratically with the system size. It is shown that for large systems, the size of the virtual molecular orbital (MO) space is reduced by more than 90% with respect to the canonical ROCIS method. This allows one to compute the X-ray absorption spectra of a variety of large “real-life” chemical systems featuring hundreds of atoms using a first-principles wave-function-based approach. Examples chosen from the fields of bioinorganic and solid-state chemistry include the Co K-edge XAS spectrum of aquacobalamin [H₂OCbl]⁺, the Fe L-edge XAS spectrum of deoxymyoglobin (DMb), the Ti L-edge XAS spectrum of rutile TiO₂, and the Fe M-edge spectrum of α-Fe₂O₃ hematite. In the largest calculations presented here, molecules with more than 700 atoms and cluster models with more than 50 metal centers were employed. In all the studied cases, very good to excellent agreement with experiment is obtained. It will be shown that the PNO-ROCIS method provides an unprecedented performance of wave-function-based methods in the field of computational X-ray spectroscopy

Restricted Open-Shell Configuration Interaction Cluster Calculations of the L‑Edge X‑ray Absorption Study of TiO₂ and CaF₂ Solids

X-ray metal L-edge spectroscopy has proven to be a powerful technique for investigating the electronic structure of transition-metal centers in coordination compounds and extended solid systems. We have recently proposed the Restricted Open-Shell Configuration Interaction Singles (ROCIS) method and its density functional theory variant (DFT/ROCIS) as methods of general applicability for interpreting such spectra. In this work, we apply the ROCIS and DFT/ROCIS methods for the investigation of cluster systems in order to interpret the Ca and Ti L-edge spectra of CaF₂ and TiO₂ (rutile and anatase), respectively. Cluster models with up to 23 metallic centers are considered together with the hydrogen saturation and embedding techniques to represent the extended ionic and covalent bulk environments of CaF₂ and TiO₂. The experimentally probed metal coordination environment is discussed in detail. The influence of local as well as nonlocal effects on the intensity mechanism is investigated. In addition, the physical origin of the observed spectral features is qualitatively and quantitatively discussed through decomposition of the dominant relativistic states in terms of leading individual 2p–3d excitations. This contribution serves as an important reference for future applications of ROCIS and DFT/ROCIS methods in the field of metal L-edge spectroscopy in solid-state chemistry

A Restricted Open Configuration Interaction with Singles Method To Calculate Valence-to-Core Resonant X‑ray Emission Spectra: A Case Study

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn–Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin <i>S</i> and excited states with spin <i>S</i>′ = <i>S</i>, <i>S</i> ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin–orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle–hole theories. In this work, the method is extended to the calculation of resonant VtC RXES [alternatively referred to as 1s-VtC resonant inelastic X-ray scattering (RIXS)] spectra. The complete Kramers–Dirac–Heisenerg equation is taken into account. Thus, state interference effects are treated naturally within this protocol. As a first application of this protocol, a computational study on the previously reported VtC RXES plane on a molecular managanese­(V) complex is performed. Starting from conventional X-ray absorption spectra (XAS), we present a systematic study that involves calculations and electronic structure analysis of both the XAS and non-resonant and resonant VtC XES spectra. The very good agreement between theory and experiment, observed in all cases, allows us to unravel the complicated intensity mechanism of these spectroscopic techniques as a synergic function of state polarization and interference effects. In general, intense features in the RIXS spectra originate from absorption and emission processes that involve nonorthogonal transition moments. We also present a graphical method to determine the sign of the interference contributions

Revisiting the Electronic Structure of FeS Monomers Using ab Initio Ligand Field Theory and the Angular Overlap Model

Iron–sulfur (FeS) proteins are universally found in nature with actives sites ranging in complexity from simple monomers to multinuclear sites from two up to eight iron atoms. These sites include mononuclear (rubredoxins), dinuclear (ferredoxins and Rieske proteins), trinuclear (e.g., hydrogenases), and tetranuclear (various ferredoxins and high-potential iron−sulfur proteins). The electronic structure of the higher-nuclearity clusters is inherently extremely complex. Hence, it is reasonable to take a bottom-up approach in which clusters of increasing nuclearity are analyzed in terms of the properties of their lower nuclearity constituents. In the present study, the first step is taken by an in-depth analysis of mononuclear FeS systems. Two different FeS molecules with phenylthiolate and methylthiolate as ligands are studied in their oxidized and reduced forms using modern wave function-based ab initio methods. The ab initio electronic spectra and wave function are presented and analyzed in detail. The very intricate electronic structure–geometry relationship in these systems is analyzed using ab initio ligand field theory (AILFT) in conjunction with the angular overlap model (AOM) parametrization scheme. The simple AOM model is used to explain the effect of geometric variations on the electronic structure. Through a comparison of the ab initio computed UV–vis absorption spectra and the available experimental spectra, the low-energy part of the many-particle spectrum is carefully analyzed. We show ab initio calculated magnetic circular dichroism spectra and present a comparison with the experimental spectrum. Finally, AILFT parameters and the ab initio spectra are compared with those obtained experimentally to understand the effect of the increased covalency of the thiolate ligands on the electronic structure of FeS monomers

Experimentally Quantifying Small-Molecule Bond Activation Using Valence-to-Core X‑ray Emission Spectroscopy

This work establishes the ability of valence-to-core X-ray emission spectroscopy (XES) to serve as a direct probe of N₂ bond activation. A systematic series of iron-N₂ complexes has been experimentally investigated and the energy of a valence-to-core XES peak was correlated with N–N bond length and stretching frequency. Computations demonstrate that, in a simple one-electron picture, this peak arises from the N₂ 2s2s σ* orbital, which becomes less antibonding as the N–N bond is weakened and broken. Changes as small as 0.02 Å in the N–N bond length may be distinguished using this approach. The results thus establish valence-to-core XES as an effective probe of small molecule activation, which should have broad applicability in transition-metal mediated catalysis

Measuring Spin-Allowed and Spin-Forbidden d–d Excitations in Vanadium Complexes with 2p3d Resonant Inelastic X‑ray Scattering

Spectroscopic probes of the electronic structure of transition metal-containing materials are invaluable to the design of new molecular catalysts and magnetic systems. Herein, we show that 2p3d resonant inelastic X-ray scattering (RIXS) can be used to observe both spin-allowed and (in the V^III case) spin-forbidden d–d excitation energies in molecular vanadium complexes. The spin-allowed d–d excitation energies determined by 2p3d RIXS are in good agreement with available optical data. In V­(acac)₃, a previously undetected spin-forbidden singlet state has been observed. The presence of this feature provides a ligand-field independent signature of V^III. It is also shown that d–d excitations may be obtained for porphyrin complexes. This is generally prohibitive using optical approaches due to intense porphyrin π-to-π* transitions. In addition, the intensities of charge-transfer features in 2p3d RIXS spectroscopy are shown to be a clear indication of metal–ligand covalency. The utility of 2p3d RIXS for future studies of complex inorganic systems is highlighted

Correlation Between Structural, Spectroscopic, and Reactivity Properties Within a Series of Structurally Analogous Metastable Manganese(III)–Alkylperoxo Complexes

Manganese–peroxos are proposed as key intermediates in a number of important biochemical and synthetic transformations. Our understanding of the structural, spectroscopic, and reactivity properties of these metastable species is limited, however, and correlations between these properties have yet to be established experimentally. Herein we report the crystallographic structures of a series of structurally related metastable Mn­(III)–OOR compounds, and examine their spectroscopic and reactivity properties. The four reported Mn­(III)–OOR compounds extend the number of known end-on Mn­(III)–(η¹-peroxos) to six. The ligand backbone is shown to alter the metal–ligand distances and modulate the electronic properties key to bonding and activation of the peroxo. The mechanism of thermal decay of these metastable species is examined via variable-temperature kinetics. Strong correlations between structural (O–O and Mn···N^py,quin distances), spectroscopic (E­(π_v*­(O–O) → Mn CT band), ν_O–O), and kinetic (Δ<i>H</i>^⧧ and Δ<i>S</i>^⧧) parameters for these complexes provide compelling evidence for rate-limiting O–O bond cleavage. Products identified in the final reaction mixtures of Mn­(III)–OOR decay are consistent with homolytic O–O bond scission. The N-heterocyclic amines and ligand backbone (Et vs Pr) are found to modulate structural and reactivity properties, and O–O bond activation is shown, both experimentally and theoretically, to track with metal ion Lewis acidity. The peroxo O–O bond is shown to gradually become more activated as the N-heterocyclic amines move closer to the metal ion causing a decrease in π-donation from the peroxo π_v*­(O–O) orbital. The reported work represents one of very few examples of experimentally verified relationships between structure and function

Correlation Between Structural, Spectroscopic, and Reactivity Properties Within a Series of Structurally Analogous Metastable Manganese(III)–Alkylperoxo Complexes

Manganese–peroxos are proposed as key intermediates in a number of important biochemical and synthetic transformations. Our understanding of the structural, spectroscopic, and reactivity properties of these metastable species is limited, however, and correlations between these properties have yet to be established experimentally. Herein we report the crystallographic structures of a series of structurally related metastable Mn­(III)–OOR compounds, and examine their spectroscopic and reactivity properties. The four reported Mn­(III)–OOR compounds extend the number of known end-on Mn­(III)–(η¹-peroxos) to six. The ligand backbone is shown to alter the metal–ligand distances and modulate the electronic properties key to bonding and activation of the peroxo. The mechanism of thermal decay of these metastable species is examined via variable-temperature kinetics. Strong correlations between structural (O–O and Mn···N^py,quin distances), spectroscopic (E­(π_v*­(O–O) → Mn CT band), ν_O–O), and kinetic (Δ<i>H</i>^⧧ and Δ<i>S</i>^⧧) parameters for these complexes provide compelling evidence for rate-limiting O–O bond cleavage. Products identified in the final reaction mixtures of Mn­(III)–OOR decay are consistent with homolytic O–O bond scission. The N-heterocyclic amines and ligand backbone (Et vs Pr) are found to modulate structural and reactivity properties, and O–O bond activation is shown, both experimentally and theoretically, to track with metal ion Lewis acidity. The peroxo O–O bond is shown to gradually become more activated as the N-heterocyclic amines move closer to the metal ion causing a decrease in π-donation from the peroxo π_v*­(O–O) orbital. The reported work represents one of very few examples of experimentally verified relationships between structure and function

Study of Iron Dimers Reveals Angular Dependence of Valence-to-Core X‑ray Emission Spectra

Transition-metal Kβ X-ray emission spectroscopy (XES) is a developing technique that probes the occupied molecular orbitals of a metal complex. As an element-specific probe of metal centers, Kβ XES is finding increasing applications in catalytic and, in particular, bioinorganic systems. For the continued development of XES as a probe of these complex systems, however, the full range of factors which contribute to XES spectral modulations must be explored. In this report, an investigation of a series of oxo-bridged iron dimers reveals that the intensity of valence-to-core features is sensitive to the Fe–O–Fe bond angle. The intensity of these features has a well-known dependence on metal–ligand bond distance, but a dependence upon bond angle has not previously been documented. Herein, we explore the angular dependence of valence-to-core XES features both experimentally and computationally. Taken together, these results show that, as the Fe–O–Fe angle decreases, the intensity of the Kβ″ feature increases and that this effect is modulated by increasing amounts of Fe <i>n</i>p mixing into the O 2s orbital at smaller bond angles. The relevance of these findings to the identification of oxygenated intermediates in bioinorganic systems is highlighted, with special emphasis given to the case of soluble methane monooxygenase

Measuring Spin-Allowed and Spin-Forbidden d–d Excitations in Vanadium Complexes with 2p3d Resonant Inelastic X‑ray Scattering

Spectroscopic probes of the electronic structure of transition metal-containing materials are invaluable to the design of new molecular catalysts and magnetic systems. Herein, we show that 2p3d resonant inelastic X-ray scattering (RIXS) can be used to observe both spin-allowed and (in the V^III case) spin-forbidden d–d excitation energies in molecular vanadium complexes. The spin-allowed d–d excitation energies determined by 2p3d RIXS are in good agreement with available optical data. In V­(acac)₃, a previously undetected spin-forbidden singlet state has been observed. The presence of this feature provides a ligand-field independent signature of V^III. It is also shown that d–d excitations may be obtained for porphyrin complexes. This is generally prohibitive using optical approaches due to intense porphyrin π-to-π* transitions. In addition, the intensities of charge-transfer features in 2p3d RIXS spectroscopy are shown to be a clear indication of metal–ligand covalency. The utility of 2p3d RIXS for future studies of complex inorganic systems is highlighted