X-ray Absorption Spectroscopy of VOCl3, CrO2Cl2, and MnO3Cl: An Experimental and Theoretical Study

Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.

Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.

Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods

The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

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.

Comparative Experimental and Theoretical Study of the Fe L2,3-Edges X-ray Absorption Spectroscopy in Three Highly Popular, Low-Spin Organoiron Complexes: [Fe(CO)5], [(η5-C5H5)Fe(CO)(μ-CO)]2, and [(η5-C5H5)2Fe]

The occupied and unoccupied electronic structures of three highly popular, closed shell organoiron complexes ([Fe(CO)₅], [(η⁵-C₅H₅)Fe(CO)(μ-CO)]₂, and [(η⁵-C₅H₅)₂Fe]) have been theoretically investigated by taking advantage of density functional theory (DFT) calculations coupled to the isolobal analogy ( Elian et al. Inorg. Chem. 1976 , 15 , 1148 ). The adopted approach allowed us to look into the relative role played by the ligand → Fe donation and the Fe → ligand back-donation in title molecules, as well as to investigate how CO- (terminal or bridging) and [(η⁵-C₅H₅)]^--based π* orbitals compete when these two ligands are simultaneously present as in [(η⁵-C₅H₅)Fe(CO)(μ-CO)]₂. Insights into the nature and the strength of the bonding between Fe and the C donor atoms have been gained by exploiting the Nalewajski-Mrozek bond multiplicity index ( Nalewajski et al. Int. J. Quantum Chem. 1994 , 51 , 187 ), which have been found especially sensitive even to tiny bond distance variations. The bonding picture emerging from ground state DFT results proved fruitful to guide the assignment of original, high-resolution, gas-phase L_2,3-edges X-ray absorption spectra of the title molecules, which have been modeled by the two-component relativistic time-dependent DFT including spin orbit coupling and correlation effects and taking advantage of the full use of symmetry. Assignments alternative to those reported in the literature for both [Fe(CO)₅] and [(η⁵-C₅H₅)₂Fe] are herein proposed. Despite the high popularity of the investigated molecules, the complementary use of symmetry, orbital, and spectroscopy allowed us to further look into the metal-ligand symmetry-restricted-covalency and the differential-orbital covalency, which characterize them.

An experimental and theoretical study of metallorganic coordination networks of tetrahydroxyquinone on Cu(111)

DFT modeling of STM and XAS evidences investigated the adsorption of THQ@Cu(111) that generates different ordered configurations at different temperatures.

The electronic properties of three popular high spin complexes [TM(acac)3, TM = Cr, Mn, and Fe] revisited: an experimental and theoretical study

The occupied and unoccupied electronic structures of three high spin TM(acac)₃ (TM = Cr, Mn, and Fe) complexes (I, II, and III, respectively) were studied by revisiting their literature vapour-phase He(i) and, when available, He(ii) photoemission (PE) spectra and by means of original near-edge X-ray absorption fine structure (NEXAFS) spectroscopic data recorded at the O K-edge (^OK-edge) and TM L_2,3-edges (^TML_2,3-edges). The assignments of the vapour-phase He(i)/He(ii) PE spectra were guided by the results of spin-unrestricted non-relativistic Slater transition state calculations, while the ^OK-edge and ^TML_2,3-edge spectroscopic pieces of evidence were analysed by exploiting the results of spin-unrestricted scalar-relativistic time-dependent density functional theory (DFT) and DFT/ROCIS calculations, respectively. Although the actual symmetry (D₃, in the absence of any Jahn-Teller distortion) of the title molecules allowed an extensive mixing between TM t_2g-like and e_g-like atomic orbitals, the use of the Nalewajski-Mrozek TM-O bond multiplicity index combined with a thorough analysis of the ground state (GS) outcomes allowed the assessment of the TM-O bond weakening associated with the progressive TM 3d-based e_g-like orbital filling. The experimental information provided by ^OK-edge spectra was rather poor; nevertheless, the combined use of symmetry, orbitals and spectra allowed us (i) to rationalise minor differences characterizing spectral features along the series, (ii) to quantify the contribution provided by the ligand-to-metal-charge-transfer (LMCT) excitations to the different spectral features, and (iii) to recognize the t_2g-/e_g-like nature of the TM 3d-based orbitals involved in LMCT transitions. As far as the ^TML_2,3-edge spectra and the DFT/ROCIS results were concerned, the lowest lying I^,IIL₃ spectral features included states having either the GS spin multiplicity (S(I) = 3/2, S(II) = 2) or, at higher excitation energies (EEs), states with ΔS = ±1. In contrast to that, only states with ΔS = 0, -1 significantly contributed to the IIIL₃ spectral pattern. Along the whole series, the L₃ higher EE side was systematically characterized by states involving ^TM2p → π₄ MLCT excitations; as such, coupled-single excitations with ΔS = 0 were involved in I and II, while single MLCT ^TM2p → π₄ transitions with ΔS = -1 were involved in III.

Electronic structure of CuTPP and CuTPP(F) complexes: a combined experimental and theoretical study II

CuTPP and CuTPP(F) thick films deposited on Au(111) have been studied by coupling NEXAFS spectroscopy at the ^C/N/FK-edges and ^CuL_2,3-edges and spin-unrestricted TD-DFT calculations.

Ab Initio Calculations of X-ray Spectra: Atomic Multiplet and Molecular Orbital Effects in a Multiconfigurational SCF Approach to the L-Edge Spectra of Transition Metal Complexes

A new ab initio approach to the calculation of X-ray spectra is demonstrated. It combines a high-level quantum chemical description of the chemical interactions and local atomic multiplet effects. We show here calculated L-edge X-ray absorption (XA) and resonant inelastic X-ray scattering spectra for aqueous Ni(2+) and XA spectra for a polypyridyl iron complex. Our quantum chemical calculations on a high level of accuracy in a post-Hartree-Fock framework give excellent agreement with experiment. This opens the door to reliable and detailed information on chemical interactions and the valence electronic structure in 3d transition-metal complexes also in transient excited electronic states. As we combine a molecular-orbital description with a proper treatment of local atomic electron correlation effects, our calculations uniquely allow, in particular, identifying the influence of interatomic chemical interactions versus intra-atomic correlations in the L-edge X-ray spectra.

Full potential x-ray absorption calculations using time dependent density functional theory

We report the implementation of a fully relativistic time dependent density functional theory (TDDFT) method for carrying out x-ray absorption spectroscopy calculations for extended systems. This is the first time that a TDDFT simulation of x-ray absorption in extended systems has featured a full potential ground state calculation. We prove that this unusual feature of the TDDFT implementation unequivocally yields improvement over the previous muffin-tin calculation methods.

Understanding the electronic structure of 4d metal complexes: from molecular spinors to L-edge spectra of a di-Ru catalyst

L(2,3)-edge X-ray absorption spectroscopy (XAS) has demonstrated unique capabilities for the analysis of the electronic structure of di-Ru complexes such as the blue dimer cis,cis-[Ru(III)(2)O(H(2)O)(2)(bpy)(4)](4+) water oxidation catalyst. Spectra of the blue dimer and the monomeric [Ru(NH(3))(6)](3+) model complex show considerably different splitting of the Ru L(2,3) absorption edge, which reflects changes in the relative energies of the Ru 4d orbitals caused by hybridization with a bridging ligand and spin-orbit coupling effects. To aid the interpretation of spectroscopic data, we developed a new approach, which computes L(2,3)-edges XAS spectra as dipole transitions between molecular spinors of 4d transition metal complexes. This allows for careful inclusion of the spin-orbit coupling effects and the hybridization of the Ru 4d and ligand orbitals. The obtained theoretical Ru L(2,3)-edge spectra are in close agreement with experiment. Critically, existing single-electron methods (FEFF, FDMNES) broadly used to simulate XAS could not reproduce the experimental Ru L-edge spectra for the [Ru(NH(3))(6)](3+) model complex nor for the blue dimer, while charge transfer multiplet (CTM) calculations were not applicable due to the complexity and low symmetry of the blue dimer water oxidation catalyst. We demonstrated that L-edge spectroscopy is informative for analysis of bridging metal complexes. The developed computational approach enhances L-edge spectroscopy as a tool for analysis of the electronic structures of complexes, materials, catalysts, and reactive intermediates with 4d transition metals.