Perspective: multi-configurational methods in bio-inorganic chemistry

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

TDDFT and the x-ray absorption spectrum of liquid water: Finding the "best" functional

We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333-7342 (2023)], in order to investigate which exchange-correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree-Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment.

Unveiling Hidden Shake-Up Features in the Uranyl M4-Edge Spectrum

The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.

GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

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.

Accessing metal-specific orbital interactions in C-H activation with resonant inelastic X-ray scattering

Photochemically prepared transition-metal complexes are known to be effective at cleaving the strong C-H bonds of organic molecules in room temperature solutions. There is also ample theoretical evidence that the two-way, metal to ligand (MLCT) and ligand to metal (LMCT), charge-transfer between an incoming alkane C-H group and the transition metal is the decisive interaction in the C-H activation reaction. What is missing, however, are experimental methods to directly probe these interactions in order to reveal what determines reactivity of intermediates and the rate of the reaction. Here, using quantum chemical simulations we predict and propose future time-resolved valence-to-core resonant inelastic X-ray scattering (VtC-RIXS) experiments at the transition metal L-edge as a method to provide a full account of the evolution of metal-alkane interactions during transition-metal mediated C-H activation reactions. For the model system cyclopentadienyl rhodium dicarbonyl (CpRh(CO)2), we demonstrate, by simulating the VtC-RIXS signatures of key intermediates in the C-H activation pathway, how the Rh-centered valence-excited states accessible through VtC-RIXS directly reflect changes in donation and back-donation between the alkane C-H group and the transition metal as the reaction proceeds via those intermediates. We benchmark and validate our quantum chemical simulations against experimental steady-state measurements of CpRh(CO)2 and Rh(acac)(CO)2 (where acac is acetylacetonate). Our study constitutes the first step towards establishing VtC-RIXS as a new experimental observable for probing reactivity of C-H activation reactions. More generally, the study further motivates the use of time-resolved VtC-RIXS to follow the valence electronic structure evolution along photochemical, photoinitiated and photocatalytic reactions with transition metal complexes.

Auger-Meitner and X-ray Absorption Spectra of Ethylene Cation: Insight into Conical Intersection Dynamics

We present a theoretical investigation of the near-edge X-ray absorption fine structure and the Auger-Meitner decay spectra of ethylene and its cation. Herein, we demonstrate that our method, coupled with the nuclear ensemble approach, successfully reproduces the natural bandwidth structure of the experimental resonant Auger-Meitner decay spectra of ethylene, which is not very well reproduced within the Franck-Condon approximation. Furthermore, we analyze the Auger-Meitner decay spectra of the ethylene cation in light of minimum energy conical intersection structures involving the two lowest cationic states (D1 and D0), providing valuable insights into the ultrafast D1/D0 relaxation dynamics. Our results suggest that Auger-Meitner electron spectroscopy can help elucidate the mechanism behind the initial 20 fs of the relaxation dynamics.

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.

Unraveling the variational breakdown of core valence separation calculations: Diagnostic and cure to the over relaxation error of double core hole states

The core valence separation (CVS) approximation is the most employed strategy to prevent the variational collapse of standard wave function optimization when attempting to compute electronic states bearing one or more electronic vacancies in core orbitals. Here, we explore the spurious consequences of this approximation on the properties of the computed core hole states. We especially focus on the less studied case of double core hole (DCH) states, whose spectroscopic interest has recently been rapidly growing. We show that the CVS error leads to a systematic underestimation of DCH energies, a property in stark contrast with the case of single core hole states. We highlight that the CVS error can then be interpreted as an over relaxation effect and design a new correction strategy adapted to these specificities.

Electronic Structure of the Complete Series of Gas-Phase Manganese Acetylacetonates by X-ray Absorption Spectroscopy

Metal centers in transition metal-ligand complexes occur in a variety of oxidation states causing their redox activity and therefore making them relevant for applications in physics and chemistry. The electronic state of these complexes can be studied by X-ray absorption spectroscopy, which is, however, due to the complex spectral signature not always straightforward. Here, we study the electronic structure of gas-phase cationic manganese acetylacetonate complexes Mn(acac)1-3+ using X-ray absorption spectroscopy at the metal center and ligand constituents. The spectra are well reproduced by multiconfigurational wave function theory, time-dependent density functional theory as well as parameterized crystal field and charge transfer multiplet simulations. This enables us to get detailed insights into the electronic structure of ground-state Mn(acac)1-3+ and extract empirical parameters such as crystal field strength and exchange coupling from X-ray excitation at both the metal and ligand sites. By comparison to X-ray absorption spectra of neutral, solvated Mn(acac)2,3 complexes, we also show that the effect of coordination on the L3 excitation energy, routinely used to identify oxidation states, can contribute about 40-50% to the observed shift, which for the current study is 1.9 eV per oxidation state.

Ferricyanide photo-aquation pathway revealed by combined femtosecond Kβ main line and valence-to-core x-ray emission spectroscopy

Reliably identifying short-lived chemical reaction intermediates is crucial to elucidate reaction mechanisms but becomes particularly challenging when multiple transient species occur simultaneously. Here, we report a femtosecond x-ray emission spectroscopy and scattering study of the aqueous ferricyanide photochemistry, utilizing the combined Fe Kβ main and valence-to-core emission lines. Following UV-excitation, we observe a ligand-to-metal charge transfer excited state that decays within 0.5 ps. On this timescale, we also detect a hitherto unobserved short-lived species that we assign to a ferric penta-coordinate intermediate of the photo-aquation reaction. We provide evidence that bond photolysis occurs from reactive metal-centered excited states that are populated through relaxation of the charge transfer excited state. Beyond illuminating the elusive ferricyanide photochemistry, these results show how current limitations of Kβ main line analysis in assigning ultrafast reaction intermediates can be circumvented by simultaneously using the valence-to-core spectral range.

Electron and ion spectroscopy of azobenzene in the valence and core shells

Azobenzene is a prototype and a building block of a class of molecules of extreme technological interest as molecular photo-switches. We present a joint experimental and theoretical study of its response to irradiation with light across the UV to x-ray spectrum. The study of valence and inner shell photo-ionization and excitation processes combined with measurement of valence photoelectron-photoion coincidence and mass spectra across the core thresholds provides a detailed insight into the site- and state-selected photo-induced processes. Photo-ionization and excitation measurements are interpreted via the multi-configurational restricted active space self-consistent field method corrected by second order perturbation theory. Using static modeling, we demonstrate that the carbon and nitrogen K edges of azobenzene are suitable candidates for exploring its photoinduced dynamics thanks to the transient signals appearing in background-free regions of the NEXAFS and XPS.

X-ray absorption of molecular cations-a new challenge for electronic structure theory

In this paper we put forward some historical notes on the development of computational chemistry toward applications of x-ray spectroscopies. We highlight some of the important contributions by Enrico Clementi as method and program developer and as a supporter of this branch of computational research. We bring up a modern example based on the very recent experimental development of x-ray absorption of cationic molecules. As we show this spectroscopy poses new challenges for electronic structure theory and the electron correlation problem.

Multireference Approach to Normal and Resonant Auger Spectra Based on the One-Center Approximation

A methodology to calculate the decay rates of normal and resonant Auger processes in atoms and molecules based on the One-Center Approximation (OCA), using atomic radial Auger integrals, is implemented within the restricted-active-space self-consistent-field (RASSCF) and the multistate restricted-active-space perturbation theory of second order (MS-RASPT2) frameworks, as part of the OpenMolcas project. To ensure an unbiased description of the correlation and relaxation effects on the initial core excited/ionized states and the final cationic states, their wave functions are optimized independently, whereas the Auger matrix elements are computed with a biorthonormalized set of molecular orbitals within the state-interaction (SI) approach. As a decay of an isolated resonance, the computation of Auger intensities involves matrix elements with one electron in the continuum. However, treating ionization and autoionization problems can be overwhelmingly complicated for nonexperts, because of many peculiarities, in comparison to bound-state electronic structure theory. One of the advantages of our approach is that by projecting the intensities on the atomic center bearing the core hole and using precalculated atomic radial two-electron integrals, the Auger decay rates can be easily obtained directly with OpenMolcas, avoiding the need to interface it with external programs to compute matrix elements with the photoelectron wave function. The implementation is tested on the Ne atom, for which numerous theoretical and experimental results are available for comparison, as well as on a set of prototype closed- and open-shell molecules, namely, CO, N₂, HNCO, H₂O, NO₂, and C₄N₂H₄ (pyrimidine).

Time-Resolved Optical Pump-Resonant X-ray Probe Spectroscopy of 4-Thiouracil: A Simulation Study

We theoretically monitor the photoinduced ππ* → nπ* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and nπ* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and nπ*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the nπ* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/nπ* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Soft x-ray signatures of ionic manganese-oxo systems, including a high-spin manganese(V) complex

Manganese-oxo species catalyze key reactions, including C–H bond activation or dioxygen formation in natural photosynthesis. To better understand relevant reaction intermediates, we characterize electronic states and geometric structures of [MnOn]+...

NEXAFS and MS-AES spectroscopy of the C 1s and Cl 2p excitation and ionization of chlorobenzene: Production of dicationic species

We report on single- and double-charge photofragment formation by synchrotron radiation, following C 1s core excitation and ionization and Cl 2p inner excitation and ionization of chlorobenzene, C₆H₅Cl. From a comparison of experimental near-edge X-ray absorption fine structure spectra and theoretical ab initio calculations, the nature of various core and inner shell transitions of the molecule and pure atomic features were identified. To shed light on the normal Auger processes following excitation or ionization of the molecule at the Cl 2p or C 1s sites, we addressed the induced ionic species formation. With energy resolved electron spectra and ion time-of-flight spectra coincidence measurements, the ionic species were correlated with binding energy regions and initial states of vacancies. We explored the formation of the molecular dication C₆H₅Cl²⁺, the analogue benzene dication C₆H₄²⁺, and the singly charged species produced by single loss of a carbon atom, C₅H_nCl⁺. The appearance and intensities of the spectral features associated with these ionic species are shown to be strongly site selective and dependent on the energy ranges of the Auger electron emission. Unexpected intensities for the analogue double charged benzene C₆H₄²⁺ ion were observed with fast Auger electrons. The transitions leading to C₆H₅Cl²⁺ were identified from the binding energy representation of high resolution electron energy spectra. Most C₆H₅Cl²⁺ ions decay into two singly charged moieties, but intermediate channels are opened leading to other heavy dicationic species, C₆H₄²⁺ and C₆H₄Cl²⁺, the channel leading to the first of these being much more favored than the other.

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.

Multi-reference approach to the computation of double core-hole spectra

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K^-2) are obtained for H₂O, N₂, CO, and C₂H_2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K^-2 shake-up spectra of H₂O and C₂H_2n molecules are here completely characterized for the first time.

Breaking inversion symmetry by protonation: experimental and theoretical NEXAFS study of the diazynium ion, N2H. Phys Chem Chem Phys 2021;23:17166-17176. [PMID: 34346432 DOI: 10.1039/d1cp02002a]

As an example of symmetry breaking in NEXAFS spectra of protonated species we present a high resolution NEXAFS spectrum of protonated dinitrogen, the diazynium ion N₂H⁺. By ab initio calculations we show that the spectrum consists of a superposition of two nitrogen 1s absorption spectra, each including a π* band, and a nitrogen 1s to H⁺ charge transfer band followed by a weak irregular progression of high energy excitations. Calculations also show that, as an effect of symmetry breaking by protonation, the π* transitions are separated by 0.23 eV, only slightly exceeding the difference in the corresponding dark (symmetry forbidden) and bright (symmetry allowed) core excitations of neutral N₂. By DFT and calculations and vibrational analysis, the complex π* excitation band of N₂H⁺ is understood as due to the superposition of the significantly different vibrational progressions of excitations from terminal and central nitrogen atoms, both leading to bent final state geometries. We also show computationally that the electronic structure of the charge transfer excitation smoothly depends on the nitrogen-proton distance and that there is a clear extension of the spectra going from infinity to close nitrogen-proton distance where fine structures show some, although not fully detailed, similarities. An interesting feature of partial localization of the nitrogen core orbitals, with a strong, non-monotonous, variation with nitrogen-proton distance could be highlighted. Specific effects could be unraveled when comparing molecular cation NEXAFS spectra, as represented by recently recorded spectra of N₂⁺ and CO⁺, and spectra of protonated molecules as represented here by the N₂H⁺ ion. Both types containing rich physical effects not represented in NEXAFS of neutral molecules because of the positive charge, whereas protonation also breaks the symmetry. The effect of the protonation on dinitrogen can be separated in charge, which extends the high-energy part of the spectrum, and symmetry-breaking, which is most clearly seen in the low-energy π* transition.

Site-specific generation of excited state wavepackets with high-intensity attosecond x rays

High-intensity attosecond x rays can produce coherent superpositions of valence-excited states through two-photon Raman transitions. The broad-bandwidth, high-field nature of the pulses results in a multitude of accessible excited states. Multiconfigurational quantum chemistry with the time-dependent Schrödinger equation is used to examine population transfer dynamics in stimulated x-ray Raman scattering of the nitric oxide oxygen and nitrogen K-edges. Two pulse schemes initiate wavepackets of different characters and demonstrate how chemical differences between core-excitation pathways affect the dynamics. The population transfer to valence-excited states is found to be sensitive to the electronic structure and pulse conditions, highlighting complexities attributed to the Rabi frequency. The orthogonally polarized two-color-pulse setup has increased selectivity while facilitating longer, less intense pulses than the one-pulse setup. Population transfer in the 1s → Rydberg region is more effective but less selective at the nitrogen K-edge; the selectivity is reduced by double core-excited states. Result interpretation is aided by resonant inelastic x-ray scattering maps.

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac-Coulomb(-Gaunt) Hamiltonian

We report an implementation of the core-valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH₃I, HX, and X^-, X = Cl-At) and xenon-containing (Xe, XeF₂) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac-Coulomb mean-field calculations (²DC^M), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations (²DCG^M) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.

An assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

The electronic structure and deexcitation pathways of an isolated metalloporphyrin ion resolved by metal L-edge spectroscopy

The local electronic structure of the metal-active site and the deexcitation pathways of metalloporphyrins are crucial for numerous applications but difficult to access by commonly employed techniques. Here, we applied near-edge X-ray absorption mass spectrometry and quantum-mechanical restricted active space calculations to investigate the electronic structure of the metal-active site of the isolated cobalt(iii) protoporphyrin IX cation (CoPPIX+) and its deexcitation pathways upon resonant absorption at the cobalt L-edge. The experiments were carried out in the gas phase, thus allowing for control over the chemical state and molecular environment of the metalloporphyrin. The obtained mass spectra reveal that resonant excitations of CoPPIX+ at the cobalt L3-edge lead predominantly to the formation of the intact radical dication and doubly charged fragments through losses of charged and neutral side chains from the macrocycle. The comparison between experiment and theory shows that CoPPIX+ is in a 3A2g triplet ground state and that competing excitations to metal-centred non-bonding and antibonding σ* molecular orbitals lead to distinct deexcitation pathways.

Equation-of-Motion Coupled-Cluster Theory to Model L-Edge X-ray Absorption and Photoelectron Spectra

We present an extension of the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing X-ray L-edge spectra, both in the absorption (XAS) and in the photoelectron (XPS) regimes. The approach is based on the perturbative evaluation of spin-orbit couplings using the Breit-Pauli Hamiltonian and nonrelativistic wave functions described by the fc-CVS-EOM-CCSD ansatz (EOM-CCSD within the frozen-core core-valence separated (fc-CVS) scheme). The formalism is based on spinless one-particle density matrices. The approach is illustrated by modeling XAS and XPS of several model systems ranging from Ar to small molecules containing sulfur and silicon.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Probing Solute-Solvent Interactions of Transition Metal Complexes Using L-Edge Absorption Spectroscopy

In order to tailor solution-phase chemical reactions involving transition metal complexes, it is critical to understand how their valence electronic charge distributions are affected by the solution environment. Here, solute-solvent interactions of a solvatochromic mixed-ligand iron complex were investigated using X-ray absorption spectroscopy at the transition metal L_2,3-edge. Due to the selectivity of the corresponding core excitations to the iron 3d orbitals, the method grants direct access to the valence electronic structure around the iron center and its response to interactions with the solvent environment. A linear increase of the total L_2,3-edge absorption cross section as a function of the solvent Lewis acidity is revealed. The effect is caused by relative changes in different metal-ligand-bonding channels, which preserve local charge densities while increasing the density of unoccupied states around the iron center. These conclusions are corroborated by a combination of molecular dynamics and spectrum simulations based on time-dependent density functional theory. The simulations reproduce the spectral trends observed in the X-ray but also optical absorption experiments. Our results underscore the importance of solute-solvent interactions when aiming for an accurate description of the valence electronic structure of solvated transition metal complexes and demonstrate how L_2,3-edge absorption spectroscopy can aid in understanding the impact of the solution environment on intramolecular covalency and the electronic charge distribution.

Origin of core-to-core x-ray emission spectroscopy sensitivity to structural dynamics

Recently, coherent structural dynamics in the excited state of an iron photosensitizer was observed through oscillations in the intensity of Kα x-ray emission spectroscopy (XES). Understanding the origin of the unexpected sensitivity of core-to-core transitions to structural dynamics is important for further development of femtosecond time-resolved XES methods and, we believe, generally necessary for interpretation of XES signals from highly non-equilibrium structures that are ubiquitous in photophysics and photochemistry. Here, we use multiconfigurational wavefunction calculations combined with atomic theory to analyze the emission process in detail. The sensitivity of core-to-core transitions to structural dynamics is due to a shift of the minimum energy metal-ligand bond distance between 1s and 2p core-hole states. A key effect is the additional contraction of the non-bonding 3s and 3p orbitals in 1s core-hole states, which decreases electron-electron repulsion and increases overlap in the metal-ligand bonds. The effect is believed to be general and especially pronounced for systems with strong bonds. The important role of 3s and 3p orbitals is consistent with the analysis of radial charge and spin densities and can be connected to the negative chemical shift observed for many transition metal complexes. The XES sensitivity to structural dynamics can be optimized by tuning the emission energy spectrometer, with oscillations up to ±4% of the maximum intensity for the current system. The theoretical predictions can be used to design experiments that separate electronic and nuclear degrees of freedom in ultrafast excited state dynamics.

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.

X-Ray Absorption Spectrum of the N_{2}^{+} Molecular Ion

The x-ray absorption spectrum of N_{2}^{+} in the K-edge region has been measured by irradiation of ions stored in a cryogenic radio frequency ion trap with synchrotron radiation. We interpret the experimental results with the help of restricted active space multiconfiguration theory. Spectroscopic constants of the 1σ_{u}^{-1} ^{2}Σ_{u}^{+} state, and the two 1σ_{u}^{-1}3σ_{g}^{-1}1π_{g} ^{2}Π_{u} states are determined from the measurements. The charge of the ground state together with spin coupling involving several open shells give rise to double excitations and configuration mixing, and a complete breakdown of the orbital picture for higher lying core-excited states.

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.

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy

Excited-state intramolecular hydrogen transfer (ESIHT) is a fundamental reaction relevant to chemistry and biology. Malonaldehyde is the simplest example of ESIHT, yet only little is known experimentally about its excited-state dynamics. Several competing relaxation pathways have been proposed, including internal conversion mediated by ESIHT and C[double bond, length as m-dash]C torsional motion as well as intersystem crossing. We perform an in silico transient X-ray absorption spectroscopy (TRXAS) experiment at the oxygen K-edge to investigate its potential to monitor the proposed ultrafast decay pathways in malonaldehyde upon photoexcitation to its bright S₂(ππ*) state. We employ both restricted active space perturbation theory and algebraic-diagrammatic construction for the polarization propagator along interpolated reaction coordinates as well as representative trajectories from ab initio multiple spawning simulations to compute the TRXAS signals from the lowest valence states. Our study suggests that oxygen K-edge TRXAS can distinctly fingerprint the passage through the H-transfer intersection and the concomitant population transfer to the S₁(nπ*) state. Potential intersystem crossing to T₁(ππ*) is detectable from reappearance of the double pre-edge signature and reversed intensities. Moreover, the torsional deactivation pathway induces transient charge redistribution from the enol side towards the central C-atom and manifests itself as substantial shifts of the pre-edge features. Given the continuous advances in X-ray light sources, our study proposes an experimental route to disentangle ultrafast excited-state decay channels in this prototypical ESIHT system and provides a pathway-specific mapping of the TRXAS signal to facilitate the interpretation of future experiments.

Vibrational wavepacket dynamics in Fe carbene photosensitizer determined with femtosecond X-ray emission and scattering

The non-equilibrium dynamics of electrons and nuclei govern the function of photoactive materials. Disentangling these dynamics remains a critical goal for understanding photoactive materials. Here we investigate the photoinduced dynamics of the [Fe(bmip)2]2+ photosensitizer, where bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine, with simultaneous femtosecond-resolution Fe Kα and Kβ X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS). This measurement shows temporal oscillations in the XES and XSS difference signals with the same 278 fs period oscillation. These oscillations originate from an Fe-ligand stretching vibrational wavepacket on a triplet metal-centered (3MC) excited state surface. This 3MC state is populated with a 110 fs time constant by 40% of the excited molecules while the rest relax to a 3MLCT excited state. The sensitivity of the Kα XES to molecular structure results from a 0.7% average Fe-ligand bond length shift between the 1 s and 2p core-ionized states surfaces.

Restricted active space simulations of the metal L-edge X-ray absorption spectra and resonant inelastic X-ray scattering: revisiting [CoII/III(bpy)3]2+/3+complexes

The metal L-edge spectra of cobalt compounds have been interpreted through restricted active space calculations.

The carbon and oxygen K-edge NEXAFS spectra of CO+

We present and analyze high resolution near edge X-ray absorption fine structure (NEXAFS) spectra of CO⁺ at the carbon and oxygen K-edges.