We report a detailed investigation of the importance of vibrational direct and interference effects in x-ray emission applied to water. We use the full Kramers–Heisenberg (KH) expression on a 2D grid with the two OH-stretches of a central water molecule as coordinates and solve for the relevant vibrational states, providing direct and interference terms. For two pentamer models, we show close agreement between high-level adiabatic diagrammatic construction and time-dependent density functional theory results, and apply to four larger 32-molecule clusters representing high- (HDL) and low-density liquid (LDL) and two intermediate structures. We find for HDL and LDL an initial split (without dynamics) of 0.6 eV, which is increased to 0.7 eV using the full KH expression, i.e., the observed split is dominated by the initial H-bonding. The importance of direct and interference contributions is different for HDL and LDL structures, where for HDL, the full spectrum is well represented by the direct contribution, while for LDL, the 3a1 is strongly enhanced in the direct spectrum, and the 1b1 has large interference contributions. In a recent attosecond x-ray pump/x-ray probe spectrum, only one 1b1 peak was observed together with a significantly increased intensity in the 3a1 region. We reassign the features due to molecules in asymmetric H-bond situations (1b1 peak) and molecules in tetrahedral H-bonding (3a1 intensity) in this experiment, where only direct terms contribute. To eliminate the need for precomputed potential energy surfaces, we show that a semi-classical approximation to the KH formalism gives excellent agreement, including vibrational fine-structure, with the full KH spectra for the four 32-molecule clusters.

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.

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.

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 similar to 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.

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 O-X 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.

The Gator program has been developed for computational spectroscopy and calculations of molecular properties using real and complex propagators at the correlated level of wave function theory. Currently, the focus lies on methods based on the algebraic diagrammatic construction (ADC) scheme up to the third order of perturbation theory. An auxiliary Fock matrix-driven implementation of the second-order ADC method for excitation energies has been realized with an underlying hybrid MPI/OpenMP parallelization scheme suitable for execution in high-performance computing cluster environments. With a modular and object-oriented program structure written in a Python/C++ layered fashion, Gator additionally enables time-efficient prototyping of novel scientific approaches, as well as interactive notebook-driven training of students in quantum chemistry.

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 -> pi* 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 similar to 10%, respectively, as compared to 0.3-0.6 eV and similar to 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.

ADC-connect (adcc) is a hybrid python/C++ module for performing excited state calculations based on the algebraic-diagrammatic construction scheme for the polarization propagator (ADC). Key design goal is to restrict adcc to this single purpose and facilitate connection to external packages, for example, for obtaining the Hartree-Fock references, plotting spectra, or modeling solvents. Interfaces to four self-consistent field codes have already been implemented, namely pyscf, psi4, molsturm, and veloxchem. The computational workflow, including the numerical solvers, is implemented in python, whereas the working equations and other expensive expressions are done in C++. This equips adcc with adequate speed, making it a flexible toolkit for both rapid development of ADC-based computational spectroscopy methods as well as unusual computational workflows. This is demonstrated by three examples. Presently, ADC methods up to third order in perturbation theory are available in adcc, including the respective core-valence separation and spin-flip variants. Both restricted or unrestricted Hartree-Fock references can be employed.

This article is categorized under: Software > Simulation Methods Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Quantum Chemistry

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 C-6 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.

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.