Molecular Orbital Simulations of Metal 1s2p Resonant Inelastic X-ray Scattering

Iron Kβ X-ray Emission Spectroscopy: The Origin of Spectral Features from Atomic to Molecular Systems Using Multi-configurational Calculations

Kβ X-ray emission spectroscopy (XES) is widely used to fingerprint the local spin of transition-metal ions, including in pump-probe experiments, to identify excited states or in chemical and biological reactions to characterize short-lived intermediates. In this study, the spectra of ferrous and ferric complexes for various spin states were measured experimentally and described theoretically through restricted active space (RAS) calculations including dynamic correlations. Through the RAS calculations from simple atomic models to complex molecular systems, spectral effects such as the exchange interactions, crystal-field strength, and covalent orbital mixing were evaluated and discussed. The calculations find that only the spectral features of low-spin cases show a dependence on the crystal-field strength, particularly for ferrous low spin. The effect of the covalent orbital mixing strength on the first moment of the Kβ1,3 main line and the Kβ1,3-Kβ' energy splitting is quantitatively described. Clear relationships are found within a given nominal spin but less between different spin states, which calls for careful selection of reference spectra in future experiments. This study further advances our understanding of the correlation between changes in experimental spectral features and their corresponding electronic structure information.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements

A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.

Relativistic Multiconfigurational Ab Initio Calculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

We applied relativistic multiconfigurational all-electron ab initio calculations including the spin-orbit interaction to calculate the 3d4f resonant inelastic X-ray scattering (RIXS) map (3d3/2 → 5f5/2 U M4 absorption edge and 4f5/2 → 3d3/2 U Mβ emission) of uranyl (UO22+). The calculated data are in excellent agreement with experimental results and allow a detailed understanding of the observed features and an unambiguous assignment of all involved intermediate and final states. The energies corresponding to the maxima of the resonant emission and the non-resonant (normal) emission were determined with high accuracy, and the corresponding X-ray absorption near edge structure spectra extracted at these two positions were simulated and agree well with the measured data. With the high quality of our theoretical data, we show that the cause of the splitting of the three main peaks in emission is due to the fine structure splitting of the 4f orbitals induced through the trans di-oxo bonds in uranyl and that we are able to obtain direct information about the energy differences between the 5f and 4f orbitals: Δ5f δ/ϕ - 4f δ/ϕ, Δ5f π* - 4f π, and Δ5f σ* - 4f σ from the 3d4f RIXS map. RIXS maps contain a wealth of information, and ab initio calculations facilitate an understanding of their complex structure in a clear and transparent way. With these calculations, we show that the multiconfigurational protocol, which is nowadays applied as a standard tool to study the X-ray spectra of transition metal complexes, can be extended to the calculation of RIXS maps of systems containing actinides.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S₂ (ππ*) and S₁ (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N²) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering

Hard X-ray spectroscopy selectively probes metal sites in complex environments. Resonant inelastic X-ray scattering (RIXS) makes it is possible to directly study metal-ligand interactions through local valence excitations. Here multiconfigurational wavefunction simulations are used to model valence K pre-edge RIXS for three metal-hexacyanide complexes by coupling the electric dipole-forbidden excitations with dipole-allowed valence-to-core emission. Comparisons between experimental and simulated spectra makes it possible to evaluate the simulation accuracy and establish a best-modeling practice. The calculations give correct descriptions of all LMCT excitations in the spectra, although energies and intensities are sensitive to the description of dynamical electron correlation. The consistent treatment of all complexes shows that simulations can rationalize spectral features. The dispersion in the manganese(iii) spectrum comes from unresolved multiple resonances rather than fluorescence, and the splitting is mainly caused by differences in spatial orientation between holes and electrons. The simulations predict spectral features that cannot be resolved in current experimental data sets and the potential for observing d-d excitations is also explored. The latter can be of relevance for non-centrosymmetric systems with more intense K pre-edges. These ab initio simulations can be used to both design and interpret high-resolution X-ray scattering experiments.

HERFD-XANES probes of electronic structures of ironII/III carbene complexes

Iron centered N-heterocyclic carbene (Fe-NHC) complexes have shown long-lived excited states with charge transfer character useful for light harvesting applications. Understanding the nature of the metal-ligand bond is of fundamental importance to rationally tailor the properties of transition metal complexes. The high-energy-resolution fluorescence detected X-ray absorption near edge structure (HERFD-XANES) has been used to probe the valence orbitals of three carbene complexes, [Fe^II(bpy)(btz)₂](PF₆)₂ (bpy = 2,2'-bipyridine, btz = 3,3'-dimethyl-1,1'-bis(p-tolyl)-4,4'-bis(1,2,3-triazol-5-ylidene)), [Fe^III(btz)₃](PF₆)₃, and [Fe^III(phtmeimb)₂]PF₆ (phtmeimb = [phenyl(tris(3-methylimidazol-2-ylidene))borate]^-). The multiconfigurational restrict active space (RAS) approach has been used to simulate the metal K pre-edge X-ray absorption spectroscopy of these carbene complexes, and have reproduced the metal K pre-edge spectral features in terms of relative intensity and peak positions. The evident intensity difference between the Fe^II and the other two Fe^III complexes has been elucidated with different intensity mechanisms in the transition. The smaller splitting between the t_2g and e_g character peak for [Fe^III(btz)₃](PF₆)₃ has been observed in the experimental measurements and been reproduced in the RAS calculations. The results show how the combination of experimental HERFD-XANES measurements and ab initio RAS simulations can give quantitative evaluation of the orbital interactions between metal and ligands for such large and strongly interacting systems and thus allow to understand and predict properties of novel complexes.

Cr L-Edge X-ray Absorption Spectroscopy of CrIII(acac)3 in Solution with Measured and Calculated Absolute Absorption Cross Sections

X-ray absorption spectroscopy at the L-edge of 3d transition metals is widely used for probing the valence electronic structure at the metal site via 2p-3d transitions. Assessing the information contained in L-edge absorption spectra requires systematic comparison of experiment and theory. We here investigate the Cr L-edge absorption spectrum of high-spin chromium acetylacetonate Cr^III(acac)₃ in solution. Using a transmission flatjet enables determining absolute absorption cross sections and spectra free from X-ray-induced sample damage. We address the challenges of measuring Cr L absorption edges spectrally close to the O K absorption edge of the solvent. We critically assess how experimental absorption cross sections can be used to extract information on the electronic structure of the studied system by comparing our results of this Cr^III (3d³) complex to our previous work on L-edge absorption cross sections of Mn^III(acac)₃ (3d⁴) and Mn^II(acac)₂ (3d⁵). Considering our experimental uncertainties, the most insightful experimental observable for this d³(Cr^III)-d⁴(Mn^III)-d⁵(Mn^II) series is the L-edge branching ratio, and we discuss it in comparison to semiempirical multiplet theory and ab initio restricted active space calculations. We further discuss and analyze trends in integrated absorption cross sections and correlate the spectral shapes with the local electronic structure at the metal sites.

Direct Determination of Absolute Absorption Cross Sections at the L-Edge of Dilute Mn Complexes in Solution Using a Transmission Flatjet

The 3d transition metals play a pivotal role in many charge transfer processes in catalysis and biology. X-ray absorption spectroscopy at the L-edge of metal sites probes metal 2p-3d excitations, providing key access to their valence electronic structure, which is crucial for understanding these processes. We report L-edge absorption spectra of MnII(acac)2 and MnIII(acac)3 complexes in solution, utilizing a liquid flatjet for X-ray absorption spectroscopy in transmission mode. With this, we derive absolute absorption cross-sections for the L-edge transitions with peak magnitudes as large as 12 and 9 Mb for MnII(acac)2 and MnIII(acac)3, respectively. We provide insight into the electronic structure with ab initio restricted active space calculations of these L-edge transitions, reproducing the experimental spectra with excellent agreement in terms of shapes, relative energies, and relative intensities for the two complexes. Crystal field multiplet theory is used to assign spectral features in terms of the electronic structure. Comparison to charge transfer multiplet calculations reveals the importance of charge transfer in the core-excited final states. On the basis of our experimental observations, we extrapolate the feasibility of 3d transition metal L-edge absorption spectroscopy using the liquid flatjet approach in probing highly dilute biological solution samples and possible extensions to table-top soft X-ray sources.

Fingerprints of electronic, spin and structural dynamics from resonant inelastic soft X-ray scattering in transient photo-chemical species

We describe how inversion symmetry separation of electronic state manifolds in resonant inelastic soft X-ray scattering (RIXS) can be applied to probe excited-state dynamics with compelling selectivity. In a case study of Fe L3-edge RIXS in the ferricyanide complex Fe(CN)63-, we demonstrate with multi-configurational restricted active space spectrum simulations how the information content of RIXS spectral fingerprints can be used to unambiguously separate species of different electronic configurations, spin multiplicities, and structures, with possible involvement in the decay dynamics of photo-excited ligand-to-metal charge-transfer. Specifically, we propose that this could be applied to confirm or reject the presence of a hitherto elusive transient Quartet species. Thus, RIXS offers a particular possibility to settle a recent controversy regarding the decay pathway, and we expect the technique to be similarly applicable in other model systems of photo-induced dynamics.

Advanced X-ray Spectroscopic Methods for Studying Iron-Sulfur-Containing Proteins and Model Complexes

In this chapter, a brief overview of X-ray spectroscopic methods that may be utilized to obtain insight into the geometric and electronic structure of iron-sulfur proteins is provided. These methods include conventional methods, such as metal and ligand K-edge X-ray absorption, as well as more advanced methods including nonresonant and resonant X-ray emission. In each section, the basic information content of the spectra is highlighted and important experimental considerations are discussed. Throughout the chapter, recent applications to iron-sulfur-containing models and proteins are highlighted.

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 S and excited states with spin S' = S, S ± 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.

Spin-reversal energy barriers of 305 K for Fe2+ d6 ions with linear ligand coordination

A remarkably large magnetic anisotropy energy of 305 K is computed by quantum chemistry methods for divalent Fe²⁺ d⁶ substitutes at Li-ion sites with D_6h point-group symmetry within the solid-state matrix of Li₃N. This is similar to values calculated by the same approach and confirmed experimentally for linearly coordinated monovalent Fe¹⁺ d⁷ species, among the largest so far in the research area of single-molecule magnets. Our ab initio results therefore mark a new exciting exploration path in the search for superior single-molecule magnets, rooted in the configuration of d⁶ transition-metal ions with linear or quasilinear nearest-neighbor coordination. This d⁶ axial anisotropy may be kept robust even for symmetries lower than D_6h, provided the ligand and farther-neighbor environment is engineered such that the splitting remains large enough.

Orbital breathing effects in the computation of x-ray d-ion spectra in solids by ab initio wave-function-based methods

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d ⁹ cuprate Li₂CuO₂, for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d ⁿ electronic structures of group VI B to VIII B correlated oxide compounds.