Evaluating the Impact of the Tamm-Dancoff Approximation on X-ray Spectrum Calculations.

The impact of the Tamm-Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core-valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence-valence and valence-CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.

Room temperature X-ray absorption spectroscopy of metalloenzymes with drop-on-demand sample delivery at XFELs.

X-ray crystallography and X-ray spectroscopy using X-ray free electron lasers plays an important role in understanding the interplay of structural changes in the protein and the chemical changes at the metal active site of metalloenzymes through their catalytic cycles. As a part of such an effort, we report here our recent development of methods for X-ray absorption spectroscopy (XAS) at XFELs to study dilute biological samples, available in limited volumes. Our prime target is Photosystem II (PS II), a multi subunit membrane protein complex, that catalyzes the light-driven water oxidation reaction at the Mn4CaO5 cluster. This is an ideal system to investigate how to control multi-electron/proton chemistry, using the flexibility of metal redox states, in coordination with the protein and the water network. We describe the method that we have developed to collect XAS data using PS II samples with a Mn concentration of <1 mM, using a drop-on-demand sample delivery method.

Calibrating TDDFT Calculations of the X-ray Emission Spectrum of Liquid Water: The Effects of Hartree-Fock Exchange.

The structure and dynamics of liquid water continue to be debated, with insight provided by, among others, X-ray emission spectroscopy (XES), which shows a split in the high-energy 1b1 feature. This split is yet to be reproduced by theory, and it remains unclear if these difficulties are related to inaccuracies in dynamics simulations, spectrum calculations, or both. We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. A metric for evaluating the agreement between theoretical spectra termed the integrated absolute difference (IAD), which considers the integral of shifted difference spectra, is introduced and used to investigate the performance of different exchange-correlation functionals. We find that computed spectra of symmetric and asymmetric model water structures are strongly and differently influenced by the amount of Hartree-Fock exchange, with best agreement to reference spectra for ∼40-50%. Lower percentages tend to yield high density of contributing states, resulting in too broad features. The method introduced here is useful also for other spectrum calculations, in particular where the performance for ensembles of structures are evaluated.

Going around the Kok cycle of the water oxidation reaction with femtosecond X-ray crystallography.

The water oxidation reaction in photosystem II (PS II) produces most of the molecular oxygen in the atmosphere, which sustains life on Earth, and in this process releases four electrons and four protons that drive the downstream process of CO2 fixation in the photosynthetic apparatus. The catalytic center of PS II is an oxygen-bridged Mn4Ca complex (Mn4CaO5) which is progressively oxidized upon the absorption of light by the chlorophyll of the PS II reaction center, and the accumulation of four oxidative equivalents in the catalytic center results in the oxidation of two waters to dioxygen in the last step. The recent emergence of X-ray free-electron lasers (XFELs) with intense femtosecond X-ray pulses has opened up opportunities to visualize this reaction in PS II as it proceeds through the catalytic cycle. In this review, we summarize our recent studies of the catalytic reaction in PS II by following the structural changes along the reaction pathway via room-temperature X-ray crystallography using XFELs. The evolution of the electron density changes at the Mn complex reveals notable structural changes, including the insertion of OX from a new water molecule, which disappears on completion of the reaction, implicating it in the O-O bond formation reaction. We were also able to follow the structural dynamics of the protein coordinating with the catalytic complex and of channels within the protein that are important for substrate and product transport, revealing well orchestrated conformational changes in response to the electronic changes at the Mn4Ca cluster.

Structural evidence for intermediates during O2 formation in photosystem II.

In natural photosynthesis, the light-driven splitting of water into electrons, protons and molecular oxygen forms the first step of the solar-to-chemical energy conversion process. The reaction takes place in photosystem II, where the Mn4CaO5 cluster first stores four oxidizing equivalents, the S0 to S4 intermediate states in the Kok cycle, sequentially generated by photochemical charge separations in the reaction center and then catalyzes the O-O bond formation chemistry1-3. Here, we report room temperature snapshots by serial femtosecond X-ray crystallography to provide structural insights into the final reaction step of Kok's photosynthetic water oxidation cycle, the S3→[S4]→S0 transition where O2 is formed and Kok's water oxidation clock is reset. Our data reveal a complex sequence of events, which occur over micro- to milliseconds, comprising changes at the Mn4CaO5 cluster, its ligands and water pathways as well as controlled proton release through the hydrogen-bonding network of the Cl1 channel. Importantly, the extra O atom Ox, which was introduced as a bridging ligand between Ca and Mn1 during the S2→S3 transition4-6, disappears or relocates in parallel with Yz reduction starting at approximately 700 µs after the third flash. The onset of O2 evolution, as indicated by the shortening of the Mn1-Mn4 distance, occurs at around 1,200 µs, signifying the presence of a reduced intermediate, possibly a bound peroxide.

Solving response expressions in the ADC/ISR framework.

We present an implementation for the calculation of molecular response properties using the algebraic-diagrammatic construction (ADC)/intermediate state representation approach. For the second-order ADC model [ADC(2)], a memory-efficient ansatz avoiding the storage of double excitation amplitudes is investigated. We compare the performance of different numerical algorithms for the solution of the underlying response equations for ADC(2) and show that our approach also strongly improves the convergence behavior for the investigated algorithms compared with the standard implementation. All routines are implemented in an open-source Python library.

Core-hole delocalization for modeling x-ray spectroscopies: A cautionary tale.

The influence of core-hole delocalization for x-ray photoelectron, x-ray absorption, and x-ray emission spectrum calculations is investigated in detail using approaches including response theory, transition-potential methods, and ground state schemes. The question of a localized/delocalized vacancy is relevant for systems with symmetrically equivalent atoms, as well as near-degeneracies that can distribute the core orbitals over several atoms. We show that the issues relating to core-hole delocalization are present for calculations considering explicit core-hole states, e.g., when using a core-excited or core-ionized reference state or for fractional occupation numbers. As electron correlation eventually alleviates the issues, but even when using coupled-cluster single-double and perturbative triple, there is a notable discrepancy between core-ionization energies obtained with localized and delocalized core-holes (0.5 eV for the carbon K-edge). Within density functional theory, the discrepancy correlates with the exchange interaction involving the core orbitals of the same spin symmetry as the delocalized core-hole. The use of a localized core-hole allows for a reasonably good inclusion of relaxation at a lower level of theory, whereas the proper symmetry solution involving a delocalized core-hole requires higher levels of theory to account for the correlation effects involved in orbital relaxation. For linear response methods, we further show that if x-ray absorption spectra are modeled by considering symmetry-unique sets of atoms, care has to be taken such that there are no delocalizations of the core orbitals, which would otherwise introduce shifts in absolute energies and relative features.

Using core-hole reference states for calculating X-ray photoelectron and emission spectra.

For the calculation of core-ionization energies (IEs), X-ray photoelectron spectra (XPS), and X-ray emission spectra (XES), a commonly applied approach is to use non-Aufbau reference states with a core-hole as either final (IE and XPS) or initial (XES) state. However, such reference states can introduce numerical instabilities in post-HF methods, relating to the denominator of the energy corrections involved. This may become arbitrarily close to zero if a negative virtual orbital is present, e.g. a core-hole, leading to near-singularities. The resulting instabilities lead to severe convergence issues of the calculation schemes and, in addition, can strongly affect both energies and intensities, with oscillator strengths seen to reach values up to 4 × 107. For the K-edge we propose freezing the highest-energy virtual orbitals which contribute to any denominator below a threshold of 0.1 Hartree. Stable and reliable spectra are then produced, with minimal influence due to freezing energetically high-lying virtual orbitals (typically removing <5% of the total number of MOs). The developed protocol is here tested for Møller-Plesset perturbation theory and for the algebraic diagrammatic construction scheme for the polarization propagator, and it is also relevant for coupled cluster theory and other related methods.

XFEL serial crystallography reveals the room temperature structure of methyl-coenzyme M reductase.

Methyl-Coenzyme M Reductase (MCR) catalyzes the biosynthesis of methane in methanogenic archaea, using a catalytic Ni-centered Cofactor F430 in its active site. It also catalyzes the reverse reaction, that is, the anaerobic activation and oxidation, including the cleavage of the CH bond in methane. Because methanogenesis is the major source of methane on earth, understanding the reaction mechanism of this enzyme can have massive implications in global energy balances. While recent publications have proposed a radical-based catalytic mechanism as well as novel sulfonate-based binding modes of MCR for its native substrates, the structure of the active state of MCR, as well as a complete characterization of the reaction, remain elusive. Previous attempts to structurally characterize the active MCR-Ni(I) state have been unsuccessful due to oxidation of the redox- sensitive catalytic Ni center. Further, while many cryo structures of the inactive Ni(II)-enzyme in various substrates-bound forms have been published, no room temperature structures have been reported, and the structure and mechanism of MCR under physiologically relevant conditions is not known. In this study, we report the first room temperature structure of the MCRred1-silent Ni(II) form using an X-ray Free-Electron Laser (XFEL), with simultaneous X-ray Emission Spectroscopy (XES) and X-ray Diffraction (XRD) data collection. In celebration of the seminal contributions of inorganic chemist Dick Holm to our understanding of nickel-based catalysis, we are honored to announce our findings in this special issue dedicated to this remarkable pioneer of bioinorganic chemistry.

Effects of x-ray free-electron laser pulse intensity on the Mn K ß 1,3 x-ray emission spectrum in photosystem II-A case study for metalloprotein crystals and solutions.

In the last ten years, x-ray free-electron lasers (XFELs) have been successfully employed to characterize metalloproteins at room temperature using various techniques including x-ray diffraction, scattering, and spectroscopy. The approach has been to outrun the radiation damage by using femtosecond (fs) x-ray pulses. An example of an important and damage sensitive active metal center is the Mn4CaO5 cluster in photosystem II (PS II), the catalytic site of photosynthetic water oxidation. The combination of serial femtosecond x-ray crystallography and Kß x-ray emission spectroscopy (XES) has proven to be a powerful multimodal approach for simultaneously probing the overall protein structure and the electronic state of the Mn4CaO5 cluster throughout the catalytic (Kok) cycle. As the observed spectral changes in the Mn4CaO5 cluster are very subtle, it is critical to consider the potential effects of the intense XFEL pulses on the Kß XES signal. We report here a systematic study of the effects of XFEL peak power, beam focus, and dose on the Mn Kß1,3 XES spectra in PS II over a wide range of pulse parameters collected over seven different experimental runs using both microcrystal and solution PS II samples. Our findings show that for beam intensities ranging from ∼5 × 1015 to 5 × 1017 W/cm2 at a pulse length of ∼35 fs, the spectral effects are small compared to those observed between S-states in the Kok cycle. Our results provide a benchmark for other XFEL-based XES studies on metalloproteins, confirming the viability of this approach.

X-ray free-electron laser studies reveal correlated motion during isopenicillin N synthase catalysis.

Isopenicillin N synthase (IPNS) catalyzes the unique reaction of l-δ-(α-aminoadipoyl)-l-cysteinyl-d-valine (ACV) with dioxygen giving isopenicillin N (IPN), the precursor of all natural penicillins and cephalosporins. X-ray free-electron laser studies including time-resolved crystallography and emission spectroscopy reveal how reaction of IPNS:Fe(II):ACV with dioxygen to yield an Fe(III) superoxide causes differences in active site volume and unexpected conformational changes that propagate to structurally remote regions. Combined with solution studies, the results reveal the importance of protein dynamics in regulating intermediate conformations during conversion of ACV to IPN. The results have implications for catalysis by multiple IPNS-related oxygenases, including those involved in the human hypoxic response, and highlight the power of serial femtosecond crystallography to provide insight into long-range enzyme dynamics during reactions presently impossible for nonprotein catalysts.

XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π* Transitions.

The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities-in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange-correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2-0.3 eV and ∼10%, respectively, as compared to 0.3-0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.

Resonant X-ray emission spectroscopy from broadband stochastic pulses at an X-ray free electron laser.

Hard X-ray spectroscopy is an element specific probe of electronic state, but signals are weak and require intense light to study low concentration samples. Free electron laser facilities offer the highest intensity X-rays of any available light source. The light produced at such facilities is stochastic, with spikey, broadband spectra that change drastically from shot to shot. Here, using aqueous ferrocyanide, we show that the resonant X-ray emission (RXES) spectrum can be inferred by correlating for each shot the fluorescence intensity from the sample with spectra of the fluctuating, self-amplified spontaneous emission (SASE) source. We obtain resolved narrow and chemically rich information in core-to-valence transitions of the pre-edge region at the Fe K-edge. Our approach avoids monochromatization, provides higher photon flux to the sample, and allows non-resonant signals like elastic scattering to be simultaneously recorded. The spectra obtained match well with spectra measured using a monochromator. We also show that inaccurate measurements of the stochastic light spectra reduce the measurement efficiency of our approach.

Resonant X-ray emission spectroscopy from broadband stochastic pulses at an X-ray free electron laser.

Hard X-ray spectroscopy is an element specific probe of electronic state, but signals are weak and require intense light to study low concentration samples. Free electron laser facilities offer the highest intensity X-rays of any available light source. The light produced at such facilities is stochastic, with spikey, broadband spectra that change drastically from shot to shot. Here, using aqueous ferrocyanide, we show that the resonant X-ray emission (RXES) spectrum can be inferred by correlating for each shot the fluorescence intensity from the sample with spectra of the fluctuating, self-amplified spontaneous emission (SASE) source. We obtain resolved narrow and chemically rich information in core-to-valence transitions of the pre-edge region at the Fe K-edge. Our approach avoids monochromatization, provides higher photon flux to the sample, and allows non-resonant signals like elastic scattering to be simultaneously recorded. The spectra obtained match well with spectra measured using a monochromator. We also show that inaccurate measurements of the stochastic light spectra reduce the measurement efficiency of our approach.

Quantifying the error of the core-valence separation approximation.

For the calculation of core-excited states probed through X-ray absorption spectroscopy, the core-valence separation (CVS) scheme has become a vital tool. This approach allows us to target such states with high specificity, albeit introducing an error. We report the implementation of a post-processing step for CVS excitations obtained within the algebraic-diagrammatic construction scheme for the polarization propagator, which removes this error. Based on this, we provide a detailed analysis of the CVS scheme, identifying its accuracy to be dominated by an error balance between two neglected couplings, one between core and valence single excitations and the other between single and double core excitations. The selection of the basis set is shown to be vital for a proper description of both couplings, with tight polarizing functions being necessary for a good balance of errors. The CVS error is confirmed to be stable across multiple systems, with an element-specific spread for K-edge spectrum calculations of only about ±0.02 eV. A systematic lowering of the CVS error by 0.02 eV-0.03 eV is noted when considering excitations to extremely diffuse states, emulating ionization.

Complex excited state polarizabilities in the ADC/ISR framework.

We present the derivation and implementation of complex, frequency-dependent polarizabilities for excited states using the algebraic-diagrammatic construction for the polarization propagator (ADC) and its intermediate state representation. Based on the complex polarizability, we evaluate C6 dispersion coefficients for excited states. The methodology is implemented up to third order in perturbation theory in the Python-driven adcc toolkit for the development and application of ADC methods. We exemplify the approach using illustrative model systems and compare it to results from other ab initio methods and from experiments.

High-Resolution XFEL Structure of the Soluble Methane Monooxygenase Hydroxylase Complex with its Regulatory Component at Ambient Temperature in Two Oxidation States.

Soluble methane monooxygenase (sMMO) is a multicomponent metalloenzyme that catalyzes the conversion of methane to methanol at ambient temperature using a nonheme, oxygen-bridged dinuclear iron cluster in the active site. Structural changes in the hydroxylase component (sMMOH) containing the diiron cluster caused by complex formation with a regulatory component (MMOB) and by iron reduction are important for the regulation of O2 activation and substrate hydroxylation. Structural studies of metalloenzymes using traditional synchrotron-based X-ray crystallography are often complicated by partial X-ray-induced photoreduction of the metal center, thereby obviating determination of the structure of the enzyme in pure oxidation states. Here, microcrystals of the sMMOH:MMOB complex from Methylosinus trichosporium OB3b were serially exposed to X-ray free electron laser (XFEL) pulses, where the ≤35 fs duration of exposure of an individual crystal yields diffraction data before photoreduction-induced structural changes can manifest. Merging diffraction patterns obtained from thousands of crystals generates radiation damage-free, 1.95 Å resolution crystal structures for the fully oxidized and fully reduced states of the sMMOH:MMOB complex for the first time. The results provide new insight into the manner by which the diiron cluster and the active site environment are reorganized by the regulatory protein component in order to enhance the steps of oxygen activation and methane oxidation. This study also emphasizes the value of XFEL and serial femtosecond crystallography (SFX) methods for investigating the structures of metalloenzymes with radiation sensitive metal active sites.

Untangling the sequence of events during the S2 → S3 transition in photosystem II and implications for the water oxidation mechanism.

In oxygenic photosynthesis, light-driven oxidation of water to molecular oxygen is carried out by the oxygen-evolving complex (OEC) in photosystem II (PS II). Recently, we reported the room-temperature structures of PS II in the four (semi)stable S-states, S1, S2, S3, and S0, showing that a water molecule is inserted during the S2 → S3 transition, as a new bridging O(H)-ligand between Mn1 and Ca. To understand the sequence of events leading to the formation of this last stable intermediate state before O2 formation, we recorded diffraction and Mn X-ray emission spectroscopy (XES) data at several time points during the S2 → S3 transition. At the electron acceptor site, changes due to the two-electron redox chemistry at the quinones, QA and QB, are observed. At the donor site, tyrosine YZ and His190 H-bonded to it move by 50 µs after the second flash, and Glu189 moves away from Ca. This is followed by Mn1 and Mn4 moving apart, and the insertion of OX(H) at the open coordination site of Mn1. This water, possibly a ligand of Ca, could be supplied via a "water wheel"-like arrangement of five waters next to the OEC that is connected by a large channel to the bulk solvent. XES spectra show that Mn oxidation (τ of ∼350 µs) during the S2 → S3 transition mirrors the appearance of OX electron density. This indicates that the oxidation state change and the insertion of water as a bridging atom between Mn1 and Ca are highly correlated.

XANES and EXAFS of dilute solutions of transition metals at XFELs.

This work has demonstrated that X-ray absorption spectroscopy (XAS), both Mn XANES and EXAFS, of solutions with millimolar concentrations of metal is possible using the femtosecond X-ray pulses from XFELs. Mn XAS data were collected using two different sample delivery methods, a Rayleigh jet and a drop-on-demand setup, with varying concentrations of Mn. Here, a new method for normalization of XAS spectra based on solvent scattering that is compatible with data collection from a highly variable pulsed source is described. The measured XANES and EXAFS spectra of such dilute solution samples are in good agreement with data collected at synchrotron sources using traditional scanning protocols. The procedures described here will enable XFEL-based XAS on dilute biological samples, especially metalloproteins, with low sample consumption. Details of the experimental setup and data analysis methods used in this XANES and EXAFS study are presented. This method will also benefit XAS performed at high-repetition-rate XFELs such as the European XFEL, LCLS-II and LCLS-II-HE.