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

General Spin-Restricted Open-Shell Configuration Interaction Approach: Application to Metal K-Edge X-ray Absorption Spectra of Ferro- and Antiferromagnetically Coupled Dimers

In this work, we present a generalized implementation of the previously developed restricted open-shell configuration interaction singles (ROCIS) family of methods. The new method allows us to treat high-spin (HS) ferro- as well as antiferromagnetically (AF) coupled systems while retaining the total spin as a good quantum number. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion (ICE) method, which is able to tackle general configuration interaction (CI) problems on the basis of spin-adapted configuration state functions (CSFs). While ICE is designed to work in restricted orbital spaces, the new general-spin ROCIS (GS-ROCIS) method is designed to be applicable to larger molecules by employing a prototyping strategy. This new method can be applied to closed-shell, high-spin open-shell, as well as antiferromagnetic reference CSFs. In addition, GS-ROCIS can be combined with the pair natural orbital (PNO) machinery in the form of the PNO-GS-ROCIS method. With this extension, one can drastically reduce the required virtual space in the vicinity of the involved core orbitals, leading to computational savings of several orders of magnitude with negligible (<1%) loss in accuracy. To demonstrate the use of the new methodology, the metal K pre-edge X-ray absorption excitation problem of an antiferromagnetically coupled copper model dimer was investigated. By first analyzing a model copper dimer, it is shown that even for the minimum core excitation problem that involves the two antiferromagnetically coupled singly occupied orbitals and one virtual orbital, the resulting GS-ROCIS and broken-symmetry configuration interaction singles (BS-CIS) spectra may differ in terms of the number, energy position, and relative intensity of the computed bands. Furthermore, the methodology was validated to perform equally well in computing the K-edge spectra of antiferromagnetic nickel oxide dimers and mixed-valence cobalt oxide trimers. Collectively, the present development represents an important methodological advance in the application of theoretical X-ray spectroscopy.

Benchmark Study of Core-Ionization Energies with the Generalized Active Space-Driven Similarity Renormalization Group

X-ray photoelectron spectroscopy (XPS) is a powerful experimental technique for probing the electronic structure of molecules and materials; however, interpreting XPS data requires accurate computational methods to model core-ionized states. This work proposes and benchmarks a new approach based on the generalized active space-driven similarity renormalization group (GAS-DSRG) for calculating core-ionization energies and treating correlation effects at the perturbative and nonperturbative levels. We tested the GAS-DSRG across three data sets. First, the vertical core-ionization energies of small molecules containing first-row elements are evaluated. GAS-DSRG achieves mean absolute errors below 0.3 eV, which is comparable to high-level coupled cluster methods. Next, the accuracy of GAS-DSRG is evaluated for larger organic molecules using the CORE65 data set, with the DSRG-MRPT3 level yielding a mean absolute error of only 0.34 eV for 65 core-ionization transitions. Insights are provided into the treatment of static and dynamic correlation, the importance of high-order perturbation theory, and notable differences from density functional theory in the predicted energy ordering of core-ionized states for specific molecules. Finally, vibrationally resolved XPS spectra of diatomic molecules (CO, N2, and O2) are simulated, showing excellent agreement with experimental data.

Web-CONEXS: an inroad to theoretical X-ray absorption spectroscopy

Accurate analysis of the rich information contained within X-ray spectra usually calls for detailed electronic structure theory simulations. However, density functional theory (DFT), time-dependent DFT and many-body perturbation theory calculations increasingly require the use of advanced codes running on high-performance computing (HPC) facilities. Consequently, many researchers who would like to augment their experimental work with such simulations are hampered by the compounding of nontrivial knowledge requirements, specialist training and significant time investment. To this end, we present Web-CONEXS, an intuitive graphical web application for democratizing electronic structure theory simulations. Web-CONEXS generates and submits simulation workflows for theoretical X-ray absorption and X-ray emission spectroscopy to a remote computing cluster. In the present form, Web-CONEXS interfaces with three software packages: ORCA, FDMNES and Quantum ESPRESSO, and an extensive materials database courtesy of the Materials Project API. These software packages have been selected to model diverse materials and properties. Web-CONEXS has been conceived with the novice user in mind; job submission is limited to a subset of simulation parameters. This ensures that much of the simulation complexity is lifted and preliminary theoretical results are generated faster. Web-CONEXS can be leveraged to support beam time proposals and serve as a platform for preliminary analysis of experimental data.

Interpreting the Cu-O2 Antibonding Nature in Two Cu-O2 Complexes from Cu L-Edge X-ray Absorption Spectra

Cu-O2 structures play important roles in bioinorganic chemistry and enzyme catalysis, where the bonding between the Cu and O2 parts serves as a fundamental research concern. Here, we performed a multiconfigurational study on the copper L2,3-edge X-ray absorption spectra (XAS) of two copper enzyme model complexes to gain a better understanding of the antibonding nature from the clearly interpreted structure-spectroscopy relation. We obtained spectra in good agreement with the experiments by using the restricted active space second-order perturbation theory (RASPT2) method, which facilitated reliable chemical analysis. Spectral feature interpretations were supported by computing the spin-orbit natural transition orbitals. All major features were assigned to be mainly from Cu 2p to antibonding orbitals between Cu 3d and O2 π*, Cu 3d-πO-O* (type A), and a few also to mixed antibonding/bonding orbitals between Cu 3d and O2 π, Cu 3d ± πO-O (type M). Our calculations provided a clear illustration of the interactions between Cu 3d and O2 π*/π orbitals that are carried in the metal L-edge XAS.

A Combined Wave Function and Density Functional Approach for K-Edge X-ray Absorption Near-Edge Spectroscopy: A Case Study of Hydrated First-Row Transition Metal Ions

The prediction of X-ray absorption spectra (XAS) of transition metal complexes has important and broad application areas in chemistry and biology. In this letter, we have investigated the predictive ability of multiconfiguration pair-density functional theory (MC-PDFT) for X-ray absorption spectra by calculating the metal K pre-edge features of aquated 3d transition metal ions in common oxidation states. MC-PDFT results were compared with experimentally measured spectra as well as analyzed against results from restricted active-space second-order perturbation theory (RASPT2) and time-dependent density functional theory (TDDFT). As expected, TDDFT performs well for excited states that can be accurately represented by singly excited configurations but fails for excited states where higher order excitations become important. On the other hand, both RASPT2 and MC-PDFT provide quantitatively accurate results for all excited states irrespective of their character. While core-level spectroscopy with RASPT2 is accurate, it is computationally expensive. Our results show that MC-PDFT performs equally well with significantly lower computational cost and is an encouraging alternate approach for X-ray spectroscopies.

A study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group

This work examines the accuracy and precision of x-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the x-ray absorption benchmark of organic molecule (XABOOM) set, consisting of 116 transitions from mostly organic molecules [Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32 eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

Fitting Multiplet Simulations to L-Edge XAS Spectra of Transition-Metal Complexes Using an Adaptive Grid Algorithm

A new methodology based on an adaptive grid algorithm followed by an analysis of the ground state from the fit parameters is presented to analyze and interpret experimental XAS L_2,3-edge data. The fitting method is tested first in a series of multiplet calculations for d⁰-d⁷ systems and for which the solution is known. In most cases, the algorithm is able to find the solution, except for a mixed-spin Co²⁺ O_h complex, where it instead revealed a correlation between the crystal field and the electron repulsion parameters near spin-crossover transition points. Furthermore, the results for the fitting of previously published experimental data sets on CaO, CaF₂, MnO, LiMnO₂, and Mn₂O₃ are presented and their solution discussed. The presented methodology has allowed the evaluation of the Jahn-Teller distortion in LiMnO₂, which is consistent with the observed implications in the development of batteries, which use this material. Moreover, a follow-up analysis of the ground state in Mn₂O₃ has demonstrated an unusual ground state for the highly distorted site which would be impossible to optimize in a perfect octahedral environment. Ultimately, the presented methodology can be used in the analysis of X-ray absorption spectroscopy data measured at the L_2,3-edge for a large number of materials and molecular complexes of first-row transition metals and can be expanded to the analysis of other X-ray spectroscopic data in future studies.

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

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.

cis-[(η5-C5H5)Fe(η1-CO)(μ-CO)]2, the poor relative between cis and trans tautomers. A theoretical study of the gas-phase Fe L3-edge and C and O K-edge XAS of trans-/cis-[(η5-C5H5)Fe(η1-CO)(μ-CO)]2

The relative stability of trans-[(η⁵-C₅H₅)Fe(η¹-CO)(μ-CO)]₂ (trans-I) and cis-I tautomers in a vacuum and in solvents with different dielectric constants (ε) has been investigated by exploiting density functional theory (DFT). Theoretical results indicate that, in agreement with experimental evidence, trans-I is more stable than cis-I in a vacuum (∼1.5 kcal mol^-1; ε = 1), while the opposite is true in media with ε > 7. Differently from solution, DFT outcomes pertaining to the vapor-phase cis-I ⇆ trans-I equilibrium at T = 368 K, the temperature at which the Fe L_2,3-edges and the C and O K-edge X-ray absorption spectroscopy (XAS) data of I have been recorded, ultimately indicate the trans-I predominance (∼93%). Compositions, oscillator strengths (f) and excitation energy (EE) values of cis-I transitions substantially mirror those of trans-I; nevertheless, the weighted cis-If(EE) distributions negligibly contribute to the diverse simulated XA spectra of I.

Efficient and low-scaling linear-response time-dependent density functional theory implementation for core-level spectroscopy of large and periodic systems

We discuss our implementation of linear-response time-dependent density functional theory (LR-TDDFT) for core level near-edge absorption spectroscopy. The method is based on established LR-TDDFT approaches to X-ray absorption spectroscopy (XAS) with additional accurate approximations for increased efficiency. We validate our implementation by reproducing benchmark results at the K-edge and showing that spin-orbit coupling effects at the L_2,3-edge are well described. We also demonstrate that the method is suitable for extended systems in periodic boundary conditions and measure a favorable sub-cubic scaling of the calculation cost with system size. We finally show that GPUs can be efficiently exploited and report speedups of up to a factor 2.

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 L_2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of V^IVO(acac)₂ and V^III(acac)₃ prototype complexes. The recorded V L_2,3-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 L_2,3-edge XAS and XMCD spectra of the V^IVO(acac)₂ and V^III(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 V^IVO(acac)₂ and V^III(acac)₃ complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.

Electronic Structure of Aqueous [Co(bpy)3]2+/3+ Electron Mediators

We report on the electronic structure of cobalt(II) tris-2,2'-bipyridine and cobalt(III) tris-2,2'-bipyridine in aqueous solution using resonant inelastic X-ray scattering (RIXS) spectroscopy at the Co L-edge and N K-edge resonances. Partial fluorescence yield X-ray absorption spectra at both edges were obtained by signal integration of the respective RIXS spectra. Experiments are complemented by calculations of the X-ray absorption spectra for high- and low-spin configurations using density functional theory/restricted open-shell configuration interaction singles and time-dependent density functional theory methods. We find that linear combinations of the simulated X-ray absorption spectra for different spin states reproduce the experimental spectra. Best agreement is obtained for measurements at the Co L-edge, for both samples. For cobalt(II) tris-2,2'-bipyridine, our combined experimental and computational study reveals ∼40% low-spin and ∼60% high-spin state components. Much stronger low-spin character is found for cobalt(III) tris-2,2'-bipyridine, ∼80% low spin and ∼20% high spin. Prominent energy-loss features in the Co RIXS spectra are indicative of d-d excitations and charge-transfer excitations due to strong mixing between metal and ligand orbitals in both complexes. Analysis of N 1s RIXS data reveals the emission from metal dominated orbitals in the valence region, supporting the strong metal-ligand mixing.