Unraveling intrinsic correlation effects with angle-resolved photoemission spectroscopy.

Interaction effects can change materials properties in intriguing ways, and they have, in general, a huge impact on electronic spectra. In particular, satellites in photoemission spectra are pure many-body effects, and their study is of increasing interest in both experiment and theory. However, the intrinsic spectral function is only a part of a measured spectrum, and it is notoriously difficult to extract this information, even for simple metals. Our joint experimental and theoretical study of the prototypical simple metal aluminum demonstrates how intrinsic satellite spectra can be extracted from measured data using angular resolution in photoemission. A nondispersing satellite is detected and explained by electron-electron interactions and the thermal motion of the atoms. Additional nondispersing intensity comes from the inelastic scattering of the outgoing photoelectron. The ideal intrinsic spectral function, instead, has satellites that disperse both in energy and in shape. Theory and the information extracted from experiment describe these features with very good agreement.

Ab Initio Multiplet-Plus-Cumulant Approach for Correlation Effects in X-Ray Photoelectron Spectroscopy.

The treatment of electronic correlations in open-shell systems is among the most challenging problems of condensed matter theory. Current approximations are only partly successful. Ligand-field multiplet theory has been widely successful in describing intra-atomic correlation effects in x-ray spectra, but typically ignores itinerant states. The cumulant expansion for the one-electron Green's function has been successful in describing shake-up effects but ignores atomic multiplets. More complete methods, such as dynamic mean-field theory can be computationally demanding. Here, we show that separating the dynamic Coulomb interactions into local and longer-range parts with ab initio parameters yields a combined multiplet-plus-cumulant approach that accounts for both local atomic multiplets and satellite excitations. The approach is illustrated in transition metal oxides and explains the multiplet peaks, charge-transfer satellites, and distributed background features observed in XPS experiment.

Advanced calculations of X-ray spectroscopies with FEFF10 and Corvus.

The real-space Green's function code FEFF has been extensively developed and used for calculations of X-ray and related spectra, including X-ray absorption (XAS), X-ray emission (XES), inelastic X-ray scattering, and electron energy-loss spectra. The code is particularly useful for the analysis and interpretation of the XAS fine-structure (EXAFS) and the near-edge structure (XANES) in materials throughout the periodic table. Nevertheless, many applications, such as non-equilibrium systems, and the analysis of ultra-fast pump-probe experiments, require extensions of the code including finite-temperature and auxiliary calculations of structure and vibrational properties. To enable these extensions, we have developed in tandem a new version FEFF10 and new FEFF-based workflows for the Corvus workflow manager, which allow users to easily augment the capabilities of FEFF10 via auxiliary codes. This coupling facilitates simplified input and automated calculations of spectra based on advanced theoretical techniques. The approach is illustrated with examples of high-temperature behavior, vibrational properties, many-body excitations in XAS, super-heavy materials, and fits of calculated spectra to experiment.

Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra.

We present a combined equation of motion coupled-cluster cumulant Green's function approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS) and x-ray photoemission spectra. The method is based on a factorization of the transition amplitude in the time domain, which leads to a convolution of an effective one-body absorption spectrum and the core-hole spectral function. The spectral function characterizes intrinsic losses in terms of shake-up excitations and satellites using a cumulant representation of the core-hole Green's function that simplifies the interpretation. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

Corvus: a framework for interfacing scientific software for spectroscopic and materials science applications.

Corvus, a Python-based package designed for managing workflows of physical simulations that utilize multiple scientific software packages, is presented. Corvus can be run as an executable script with an input file and automatically generated or custom workflows, or interactively, in order to build custom workflows with a set of Corvus-specific tools. Several prototypical examples are presented that link density functional, vibrational and X-ray spectroscopy software packages and are of interest to the synchrotron community. These examples highlight the simplification of complex spectroscopy calculations that were previously limited to expert users, and demonstrate the flexibility of the Corvus infrastructure to tackle more general problems in other research areas.

The effect of self-consistent potentials on EXAFS analysis.

A theory program intended for use with extended X-ray-absorption fine structure (EXAFS) spectroscopy and based on the popular FEFF8 is presented. It provides an application programming interface designed to make it easy to integrate high-quality theory into EXAFS analysis software. This new code is then used to examine the impact of self-consistent scattering potentials on EXAFS data analysis by methodical testing of theoretical fitting standards against a curated suite of measured EXAFS data. For each data set, the results of a fit are compared using a well characterized structural model and theoretical fitting standards computed both with and without self-consistent potentials. It is demonstrated that the use of self-consistent potentials has scant impact on the results of the EXAFS analysis.

Finite Temperature Green's Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter.

We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W, and improves on the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate T. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.

Dynamical effects in electron spectroscopy.

One of the big challenges of theoretical condensed-matter physics is the description, understanding, and prediction of the effects of the Coulomb interaction on materials properties. In electronic spectra, the Coulomb interaction causes a renormalization of energies and change of spectral weight. Most importantly, it can lead to new structures, often called satellites. These can be linked to the coupling of excitations, also termed dynamical effects. State-of-the-art methods in the framework of many-body perturbation theory, in particular, the widely used GW approximation, often fail to describe satellite spectra. Instead, approaches based on a picture of electron-boson coupling such as the cumulant expansion are promising for the description of plasmon satellites. In this work, we give a unified derivation of the GW approximation and the cumulant expansion for the one-body Green's function. Using the example of bulk sodium, we compare the resulting spectral functions both in the valence and in the core region, and we discuss the dispersion of quasi-particles and satellites. We show that self-consistency is crucial to obtain meaningful results, in particular, at large binding energies. Very good agreement with experiment is obtained when the intrinsic spectral function is corrected for extrinsic and interference effects. Finally, we sketch how one can approach the problem in the case of the two-body Green's function, and we discuss the cancellation of various dynamical effects that occur in that case.

Lattice model of resonant inelastic x-ray scattering in metals: relation of a strong core hole to the x-ray edge singularity.

We show how the classic approach of Nozières and di Domenicis for treating the edge singularity in x-ray absorption and emission can be generalized to treat the more complex case of the resonant inelastic x-ray scattering (RIXS) process, including effects of the intermediate states involved therein in the presence of the core hole. We solve our lattice model essentially exactly (numerically) to obtain a novel form of edge singularity at the RIXS threshold energy. Our RIXS spectrum naturally includes both the well and poorly screened spectral components and their dispersions and allows its separation into pair and multiple-pair excitations.

Dynamic structural disorder in supported nanoscale catalysts.

We investigate the origin and physical effects of "dynamic structural disorder" (DSD) in supported nano-scale catalysts. DSD refers to the intrinsic fluctuating, inhomogeneous structure of such nano-scale systems. In contrast to bulk materials, nano-scale systems exhibit substantial fluctuations in structure, charge, temperature, and other quantities, as well as large surface effects. The DSD is driven largely by the stochastic librational motion of the center of mass and fluxional bonding at the nanoparticle surface due to thermal coupling with the substrate. Our approach for calculating and understanding DSD is based on a combination of real-time density functional theory/molecular dynamics simulations, transient coupled-oscillator models, and statistical mechanics. This approach treats thermal and dynamic effects over multiple time-scales, and includes bond-stretching and -bending vibrations, and transient tethering to the substrate at longer ps time-scales. Potential effects on the catalytic properties of these clusters are briefly explored. Model calculations of molecule-cluster interactions and molecular dissociation reaction paths are presented in which the reactant molecules are adsorbed on the surface of dynamically sampled clusters. This model suggests that DSD can affect both the prefactors and distribution of energy barriers in reaction rates, and thus can significantly affect catalytic activity at the nano-scale.

Nonstoichiometric intensities in core photoelectron spectroscopy.

X-ray photoemission spectroscopy is used in a great variety of research fields; one observable is the sample's stoichiometry. The stoichiometry can be deduced based on the expectation that the ionization cross sections for innershell orbitals are independent of the molecular composition. Here we used chlorine-substituted ethanes in the gas phase to investigate the apparent carbon stoichiometry. We observe a nonstoichiometric ratio for a wide range of photon energies, the ratio exhibits x-ray-absorption fine structure spectroscopy (EXAFS)-like oscillations and hundreds of eV above the C1s ionization approaches a value far from 1. These effects can be accounted for by considering the scattering of the outgoing photoelectron, which we model by multiple-scattering EXAFS calculations, and by considering the effects of losses due to monopole shakeup and shakeoff and to intramolecular inelastic scattering processes.

Real-Time Equation-of-Motion CCSD Cumulant Green's Function.

Many-body excitations in X-ray photoemission spectra have been difficult to simulate from first principles. We have recently developed a cumulant-based one-electron Green's function method using the real-time coupled-cluster-singles equation-of-motion approach (RT-EOM-CCS) that provides a general framework for treating these problems. Here we extend this approach to include double excitations in the ground-state energy and in the coupled cluster amplitudes, which have been implemented using subroutines generated by the Tensor Contraction Engine (TCE). As in the case of the singles approximation, RT-EOM-CCSD yields a nonperturbative cumulant form of the Green's function in terms of the time-dependent cluster amplitudes, adding nonlinear corrections to the traditional cumulant forms. The extended approach is applied to the core-hole spectral function for small molecular systems. We find that, when core-optimized basis sets are used, the doubles contributions reduce the mean absolute errors in the core binding energies of the 10e systems from 0.8 to 0.3 eV. They also significantly improve the quasiparticle-satellite gap by reducing its overestimation from about 3-5 to about 0-1 eV in CH4, NH3, and H2O, and also improving the overall shape of the satellite features. Finally, we demonstrate the application of the new implementation to the larger, classical XPS ESCA series of molecules and show that the singles approximation can be paired with a modest basis set to study carbon speciation.

The status of strontium in biological apatites: an XANES investigation.

Osteoporosis represents a major public health problem and increases patient morbidity through its association with fragility fractures. Among the different treatments proposed, strontium-based drugs have been shown to increase bone mass in postmenopausal osteoporosis patients and to reduce fracture risk. While the localization of Sr(2+) cations in the bone matrix has been extensively studied, little is known regarding the status of Sr(2+) cations in natural biological apatite. In this investigation the local environment of Sr(2+) cations has been investigated through XANES (X-ray absorption near-edge structure) spectroscopy in a set of pathological and physiological apatites. To assess the localization of Sr(2+) cations in these biological apatites, numerical simulations using the ab initio FEFF9 X-ray spectroscopy program have been performed. The complete set of data show that the XANES part of the absorption spectra may be used as a fingerprint to determine the localization of Sr(2+) cations versus the mineral part of calcifications. More precisely, it appears that a relationship exists between some features present in the XANES part and a Sr(2+)/Ca(2+) substitution process in site (I) of crystal apatite. Regarding the data, further experiments are needed to confirm a possible link between the relationship between the preparation mode of the calcification (cellular activity for physiological calcification and precipitation for the pathological one) and the adsorption mode of Sr(2+) cations (simple adsorption or insertion). Is it possible to draw a line between life and chemistry through the localization of Sr in apatite? The question is open for discussion. A better structural description of these physiological and pathological calcifications will help to develop specific therapies targeting the demineralization process in the case of osteoporosis.

Equation-of-Motion Coupled-Cluster Cumulant Green's Function for Excited States and X-Ray Spectra.

Green's function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green's function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green's function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green's function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green's function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH3.

Real-Time Coupled-Cluster Approach for the Cumulant Green's Function.

Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Here, we develop the cumulant form of the one-electron Green's function using a real-time coupled-cluster equation-of-motion approach, in an extension of our previous study (Rehr J.; et al. J. Chem. Phys. 2020, 152, 174113). The approach yields a nonperturbative expression for the cumulant in terms of the solution to a set of coupled first-order, nonlinear differential equations. The method thereby adds nonlinear corrections to traditional cumulant methods, which are linear in the self-energy. The approach is applied to the core-hole Green's function and is illustrated for a number of small molecular systems. For these systems, we find that the nonlinear contributions yield significant improvements, both for quasiparticle properties such as core-level binding energies and for inelastic losses that correspond to satellites observed in photoemission spectra.

Charge-transfer satellites and chemical bonding in photoemission and x-ray absorption of SrTiO3 and rutile TiO2: Experiment and first-principles theory with general application to spectroscopic analysis.

First-principles, real-time-cumulant, and Bethe-Salpeter-equation calculations fully capture the detailed satellite structure that occurs in response to the sudden creation of the core hole in both photoemission and x-ray absorption spectra of the transition-metal compounds SrTiO3 and rutile TiO2. Analysis of the excited-state, real-space charge-density fluctuations betrays the physical nature of these many electron excitations that are shown to reflect the materials' solid-state electronic structure and chemical bonding. This first-principles development of the cumulant-based core hole spectral function is generally applicable to other systems and should become a standard tool for all similar spectroscopic analysis going beyond the quasiparticle physics of the photoelectric effect.

Core hole processes in x-ray absorption and photoemission by resonant Auger-electron spectroscopy and first-principles theory.

Electron-core hole interactions are critical for proper interpretation of core-level spectroscopies commonly used as analytical tools in materials science. Here we utilize resonant Auger-electron spectroscopy to uniquely identify exciton, shake, and charge-transfer processes that result from the sudden creation of the core hole in both x-ray-absorption and photoemission spectra. These effects are captured for the transition-metal compounds SrTiO3 and MoS2 by fully ab initio, combined real-time cumulant, and Bethe-Salpeter equation approaches to account for core hole dynamics and screening. Atomic charges and excited-state electron-density fluctuations reflect materials' solid-state electronic structure, loss of translational symmetry around the core hole, and breakdown of the sudden approximation. They also demonstrate competition between long- and short-range screening in a solid.

Many-Pole Model of Inelastic Losses Applied to Calculations of XANES.

Conventional Kohn-Sham band-structure methods for calculating deep-core x-ray spectra typically neglect photoelectron self-energy effects, which give rise to an energy-dependent shift and broadening of the spectra. Here an a posteriori procedure is introduced to correct for these effects. The method is based on ab initio calculations of the GW self-energy using a many-pole model and a calculation of the dielectric function in the long wavelength limit using either the FEFF8 real-space Green's function code, or the AI2NBSE interface between the National Institute of Standards and Technology (NIST) Bethe-Salpeter equation solver (NBSE) and the ABINIT pseudopotential code. As an example the method is applied to core level x-ray spectra of LiF and MgAl2O4 calculated using (respectively) OCEAN, an extension of the AI2NBSE code for core level excitations, and the PARATEC pseudopotential code with the core-hole treated using a super-cell. The method satisfactorily explains the discrepancy between experiment and calculations.

The local electronic structure of alpha-Li3N.

New theoretical and experimental investigations of the occupied and unoccupied local electronic densities of states (DOS) are reported for alpha-Li(3)N. Band-structure and density-functional theory calculations confirm the absence of covalent bonding character. However, real-space full-multiple-scattering (RSFMS) calculations of the occupied local DOS find less extreme nominal valences than have previously been proposed. Nonresonant inelastic x-ray scattering, RSFMS calculations, and calculations based on the Bethe-Salpeter equation are used to characterize the unoccupied electronic final states local to both the Li and N sites. There is a good agreement between experiment and theory. Throughout the Li 1s near-edge region, both experiment and theory find strong similarities in the s-and p-type components of the unoccupied local final DOS projected onto an orbital angular momentum basis (l-DOS). An unexpected, significant correspondence exists between the near-edge spectra for the Li 1s and N 1s initial states. We argue that both spectra are sampling essentially the same final DOS due to the combination of long core-hole lifetimes, long photoelectron lifetimes, and the fact that orbital angular momentum is the same for all relevant initial states. Such considerations may be generally applicable for low atomic number compounds.