Core Electron Binding Energies Research Articles

Chemical space-informed machine learning models for rapid predictions of x-ray photoelectron spectra of organic molecules

Abstract We present machine learning models based on kernel-ridge regression for predicting X-ray photoelectron spec- tra of organic molecules originating from the ionization energies of 1s electrons in carbon (C), nitrogen (N), oxygen (O), and fluorine (F) atoms. We constructed training dataset through high-throughput calculations of core-electron binding energies (CEBEs) for 12,880 small organic molecules in the bigQM7ω dataset, employing the ∆-SCF formalism coupled with meta-GGA-DFT and a variationally converged basis set. The models are cost-effective, as they require the atomic coordinates of a molecule generated using universal force fields while estimating the target-level CEBEs corresponding to DFT-level equilibrium geometry. We explore transfer learning by utilizing the atomic environment feature vectors learned using a graph neural network framework in kernel-ridge regression. Additionally, we enhance accuracy using the ∆-machine learning framework by leveraging inexpensive baseline spectra derived from Kohn–Sham eigenvalues. Upon application to 208 com- binatorially substituted uracil molecules, larger than those in the training set, our analyses reveal that while the models may not yield quantitatively accurate predictions of CEBEs on a molecule-by-molecule basis, they do exhibit a strong linear correlation, which proves valuable for virtual high-throughput screening purposes. We present the dataset and models as the Python module, cebeconf, to facilitate further explorations.

All-electron first-principles GWΓ simulations for accurately predicting core-electron binding energies considering first-order three-point vertex corrections.

In the conventional GW method, the three-point vertex function (Γ) is approximated to unity (Γ ∼ 1). Here, we developed an all-electron first-principles GWΓ method beyond a conventional GW method by considering a first-order three-point vertex function (Γ(1) = 1 + iGGW) in a one-electron self-energy operator. We applied the GWΓ method to simulate the binding energies (BEs) of B1s, C1s, N1s, O1s, and F1s for 19 small-sized molecules. Contrary to the one-shot GW method [or G0W0(LDA)], which underestimates the experimentally determined absolute BEs by about 3.7eV for B1s, 5.1eV for C1s, 6.9eV for N1s, 7.8eV for O1s, and 5.8eV for F1s, the GWΓ method successfully reduces these errors by approximately 1-2eV for all the elements studied here. Notably, the first-order three-point vertex corrections are more significant for heavier elements, following the order of F > O > N > C > B1s. Finally, the computational cost analysis revealed that one term in the GWΓ one-electron self-energy operator, despite being computationally intensive, contributes negligibly (<0.1eV) to the C1s, N1s, O1s, and F1s.

Measurement of core electron binding energies of silver nanoparticles and their modeling with electron propagator calculations of silver clusters

Silver nanoparticles were synthesized by ionic exchange with zeolites and further reduction with hydrogen flux. Core electron binding energies were determined by X-ray photoelectron spectroscopy at different times of the reduction process. Electron propagator calculations of core electron binding energies were performed including scalar relativistic effects using effective core potentials and zero order regular approximation. Theoretical results were compared to the experiment to get insight into the origin of the experimental signals for carbon, oxygen, silicon, aluminum and silver. Small model molecules and zeolite fragments were used for the calculation of core electron binding energies. It is evidenced that although binding energies tend to converge, fluctuations of more than 1 eV are found for non-symmetric structures in neutral and cationic silver clusters. Detailed analysis shows that these fluctuations originate on the different coordination numbers of ionized silver atoms and charge fluctuations.

MP2-Based Composite Extrapolation Schemes Can Predict Core-Ionization Energies for First-Row Elements with Coupled-Cluster Level Accuracy.

X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into the chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires proper modeling of orbital relaxation and electron correlation upon core-ionization. This work systematically investigates basis set selection for extrapolation to the complete basis set limit of CEBEs from ΔMP2 and ΔCC energies across 94 K-edges in diverse organic molecules. We demonstrate that an alternative composite scheme using ΔMP2 in a large basis corrected by ΔCC-ΔMP2 difference in a small basis can quantitatively recover optimally extrapolated ΔCC CEBEs within 0.02 eV. Unlike ΔCC, MP2 calculations do not suffer from convergence issues and are computationally cheaper, and thus, the composite ΔMP2/ΔCC scheme balances accuracy and cost, overcoming limitations of solely using either method. We conclude by providing a comprehensive analysis of the choice of small and large basis sets for the composite schemes and provide practical recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio prediction of XPS data.

Solid solutions in disulfide systems Re(IV)S&lt;sub&gt;2&lt;/sub&gt;–Ti(IV)S&lt;sub&gt;2&lt;/sub&gt;, Re(IV)S&lt;sub&gt;2&lt;/sub&gt;–Mo(IV)S&lt;sub&gt;2&lt;/sub&gt;, and Re(IV)S&lt;sub&gt;2&lt;/sub&gt;–W(IV)S&lt;sub&gt;2&lt;/sub&gt;

Objectives. Chalcogenides of transition elements with low oxidation states, as well as their substituted derivatives, remain a poorly studied class of chemical compounds. Rhenium disulfide has many distinctive features and great application potential as a new twodimensional semiconductor. This is due to its unusual structure and unique anisotropic properties. The presence of weak interlayer bonding and a unique distorted octahedral (1T) structure suggests the possibility of creating new phases on its basis. The aim of this work is to obtain and study phases in systems Re(IV)S2–Ti(IV)S2, Re(IV)S2–Mo(IV)S2, and Re(IV)S2–W(IV)S2.Methods. The samples were obtained by high-temperature solid-phase ampoule synthesis in a vacuum. The study was carried out using X-ray phase analysis and X-ray photoelectron spectroscopy.Results. The regions of existence of solid solutions, intercalates and two-phase regions in the resulting systems were established.Diffraction patterns were obtained for the new phases and the crystal lattice parameters were calculated. Based on data relating to the binding energies of core electrons with the nucleus, the study showed the valence states of the elements after synthesis. The study also confirmed that all phases obtained as a result of synthesis contain transition elements in the oxidation state (IV).Conclusions. Intercalated solid solutions are formed in areas rich in rhenium, while in areas close to titanium and molybdenum disulfides, intercalated phases are attained. In the ReS2–WS2 system there is a region of solid solutions, including 30, 50, and 70 mol % rhenium disulfide. Their structure is a polymorphic modification of the structure of the original components. The presence of rhenium, molybdenum, and tungsten in these phases in the oxidation state (+IV) was confirmed. The data obtained on phase formation in dichalcogenide systems can be practically used in the creation of materials with unique electronic, magnetic, and optical properties with a wide range of applications.

Real-Space Pseudopotential Method for the Calculation of Third-Row Elements X-ray Photoelectron Spectroscopic Signatures.

X-ray photoelectron spectroscopy (XPS) is a powerful characterization technique that unveils subtle chemical environment differences via core-electron binding energy (CEBE) analysis. We extend the development of real-space pseudopotential methods to calculating 1s, 2s, and 2p3/2 CEBEs of third-row elements (S, P, and Si) within the framework of Kohn-Sham density-functional theory (KS-DFT). The new approach systematically prevents variational collapse and simplifies core-excited orbital selection within dense energy level distributions. However, careful error cancellation analysis is required to achieve accuracy comparable to all-electron methods and experiments. Combined with real-space KS-DFT implementation, this development enables large-scale simulations with both Dirichlet boundary conditions and periodic boundary conditions.

Peak Broadening in Photoelectron Spectroscopy of Amorphous Polymers: The Leading Role of the Electrostatic Landscape.

The broadening in photoelectron spectra of polymers can be attributed to several factors, such as light source spread, spectrometer resolution, the finite lifetime of the hole state, and solid-state effects. Here, for the first time, we set up a computational protocol to assess the peak broadening induced for both core and valence levels by solid-state effects in four amorphous polymers by using a combination of density functional theory, many-body perturbation theory, and classical polarizable embedding. We show that intrinsic local inhomogeneities in the electrostatic environment induce a Gaussian broadening of 0.2-0.7 eV in the binding energies of both core and semivalence electrons, corresponding to a full width at half-maximum (FWHM) of 0.5-1.7 eV for the investigated systems. The induced broadening is larger in acrylate-based than in styrene-based polymers, revealing the crucial role of polar groups in controlling the roughness of the electrostatic landscape in the solid matrix.

Characterization of peroxide on coal surface: A combined △SCF and XPS study

X‐ray photoelectron spectroscopy (XPS) is widely used to determine the composition of elements and oxygen‐containing functional groups. Accurate determination of core‐electron binding energies (CEBEs) is essential for identifying the types and contents of oxygen‐functional groups present on the surface of coal. The △SCF method has been carried out on CEBEs for an extensive series of oxygen‐containing organic systems encompassing the most common functionalities. The polymers for which experimental values are available for comparison demonstrate the adequacy of the treatment for describing CEBEs for the O1s core level. Therefore, a sound basis is provided for the discussion of CEBEs (O1s) for functionalities for which experimental values are not accurate or available, such as carbonyl, carboxyl, and peroxide. The results are applied to the XPS study of oxidized coal. The change law of peroxide and oxygen‐containing functional groups was discussed. The calculation method and results in this paper can provide a guide for readers to use XPS to study the oxidation of coal surfaces.

Tuning Pd-to-Ag Ratio to Enhance the Synergistic Activity of Fly Ash-Supported PdxAgy Bimetallic Nanoparticles.

Fly ash (FA)-supported bimetallic nanoparticles (PdxAgy/FA) with varying Pd:Ag ratios were prepared by coprecipitation of Pd and Ag involving in situ reduction of Pd(II) and Ag(I) salts in aqueous medium. All the supported nanoparticles were thoroughly characterized with the aid of powder X-ray diffraction (PXRD), X-ray photoelectron spectroscopy (XPS), electron microscopy (field emission scanning electron microscopy (FE-SEM) and transmission electron microscopy (TEM)), and elemental analyses, which include inductively coupled plasma-optical emission spectroscopy (ICP-OES) and energy-dispersive X-ray spectroscopy (EDS). A gradual broadening and shifting of PXRD peaks, ascribable to Ag, to higher angles with an increase in the Pd:Ag ratio affirms the alloying of interface between Pd and Ag nanoparticles. The coexistence of Pd and Ag was further confirmed by EDS elemental mapping as well as by the presence of bimetallic lattices on the FA surface, as evident from the high-resolution TEM analysis. The dependency of crystallite size and average size of bimetallic nanoparticles on Ag loading (mol %) was elucidated with the help of a combination of PXRD and TEM studies. Based on XPS analysis, the charge transfer phenomenon between contacting Pd-Ag sites could be evident from the shifting of 3d core electron binding energy for both Pd and Ag compared with monometallic Pd and Ag nanoparticles. Following a pseudo-first-order reaction kinetics, all the nanocatalysts were able to efficiently reduce 4-nitrophenol into 4-aminophenol in aqueous NaBH4. The superior catalytic performance of the bimetallic nanocatalysts (PdxAgy/FA) over their monometallic (Pd100/FA and Ag100/FA) analogues has been demonstrated. Moreover, the tunable synergistic effect of the bimetallic systems has been explored in detail by varying the Pd:Ag mol ratio in a systematic manner which in turn allowed us to achieve an optimum reaction rate (k = 1.050 min-1) for the nitrophenol reduction using a Pd25Ag75/FA system. Most importantly, all the bimetallic nanocatalysts explored here exhibited excellent normalized rate constants (K ≈ 6000-15,000 min-1 mmol-1) compared with other supported bimetallic Pd-Ag nanocatalysts reported in the literature.

Δ-based composite models for calculating x-ray absorption and emission energies

A practical ab initio composite method for modeling x-ray absorption and non-resonant x-ray emission is presented. Vertical K-edge excitation and emission energies are obtained from core-electron binding energies calculated with spin-projected ΔHF/ΔMP and outer-core ionization potentials/electron affinities calculated with electron propagator theory. An assessment of the combined methodologies against experiment is performed for a set of small molecules containing second-row elements.

Specific versus Nonspecific Solvent Interactions of a Biomolecule in Water.

Solvent interactions, particularly hydration, are vital in chemical and biochemical systems. Model systems reveal microscopic details of such interactions. We uncover a specific hydrogen-bonding motif of the biomolecular building block indole (C8H7N), tryptophan's chromophore, in water: a strong localized N-H···OH2 hydrogen bond, alongside unstructured solvent interactions. This insight is revealed from a combined experimental and theoretical analysis of the electronic structure of indole in aqueous solution. We recorded the complete X-ray photoemission and Auger spectrum of aqueous-phase indole, quantitatively explaining all peaks through ab initio modeling. The efficient and accurate technique for modeling valence and core photoemission spectra involves the maximum-overlap method and the nonequilibrium polarizable-continuum model. A two-hole electron-population analysis quantitatively describes the Auger spectra. Core-electron binding energies for nitrogen and carbon highlight the specific interaction with a hydrogen-bonded water molecule at the N-H group and otherwise nonspecific solvent interactions.

Combining the Δ-Self-Consistent-Field and GW Methods for Predicting Core Electron Binding Energies in Periodic Solids.

For the computational prediction of core electron binding energies in solids, two distinct kinds of modeling strategies have been pursued: the Δ-Self-Consistent-Field method based on density functional theory (DFT), and the GW method. In this study, we examine the formal relationship between these two approaches and establish a link between them. The link arises from the equivalence, in DFT, between the total energy difference result for the first ionization energy, and the eigenvalue of the highest occupied state, in the limit of infinite supercell size. This link allows us to introduce a new formalism, which highlights how in DFT─even if the total energy difference method is used to calculate core electron binding energies─the accuracy of the results still implicitly depends on the accuracy of the eigenvalue at the valence band maximum in insulators, or at the Fermi level in metals. We examine whether incorporating a quasiparticle correction for this eigenvalue from GW theory improves the accuracy of the calculated core electron binding energies, and find that the inclusion of vertex corrections is required for achieving quantitative agreement with experiment.

Intramolecular O···H Hydrogen Bonding of Salicylic Acid: Further Insights from O 1s XPS and 1H NMR Spectra Using DFT Calculations.

Intramolecular hydrogen bonding (HB) is a complex phenomenon that extends beyond a simple valence event, affecting the core electrons of a molecule. Salicylic acid (SA) and its conformers provide an excellent model compound for studying intramolecular HB as the proton donor (H) and acceptor (O) can be toggled by rotating the C-O and C-C bonds to form up to seven potential conformers through various HB. In this study, we computationally investigated intramolecular interactions in SA conformers with and without such HB, by examining their calculated O 1s core electron-binding energy (CEBE) and 1H NMR chemical shifts validated using recent measurements. The quantum mechanically stable SA conformers are fully defined by three rotatable bonds in the compound, which are abstracted as SA(η1η2η3) digital structures, where ηi = 0 if the ηi angles match the most stable SA conformer (000) and ηi = 1 otherwise. Our findings suggest that the stability is dominated by the appearance of the intergroup intramolecular HB of Hp···O (where O is in the carboxylic acid functional group and Hp is the phenolic proton in -OHp), and η3 serves as a switch of such HB. As a result, the (η1η20) SA conformers containing such Hp···O HB are more stable than other SA conformers (η1η21) without such the Hp···O HB. The present density functional theory calculations reveal that this Hp···O HB results in splitting of the O 1s CEBEs of two hydroxyl groups (-OH) by up to 1 eV and deshielding the Hp proton 1H NMR (δHp) up to 11.68 ppm for the (η1η20) conformers. Without such Hp···O HB, the O 1s XPS binding energies of two -OH groups will be closely located in the same band, and the 1H NMR chemical shift of the Hp atom will be as small as an 4.09 ppm SA conformer [SA-G(101)]. The present study indicates that the O 1s CEBE splitting between two -OH groups serves as an indicator of the presence of the Hp···O HB in SA conformers, which is also supported by the 1H NMR results.

Spatiotemporal Changes in Atomic and Molecular Architecture of Mineralized Bone under Pathogenic Conditions

Mechanisms responsible for spatiotemporal changes in the atomic-molecular architecture of the human femur in intact and osteoarthritis-affected areas were studied using high-resolution X-ray diffraction and spectroscopic techniques. Comparison of the experimental data demonstrates strong deviations of core electron-binding energies, lattice constants of hydroxyapatite crystal cells, linear sizes of crystallites, and degrees of crystallinity for both intact and osteoarthritic areas. The quantitative values of these characteristics and their standard deviations in each area are measured and presented. A systematic analysis of the site-dependent deviations was carried out within the framework of the 3D superlattice model. It is argued that the main mechanism responsible for the deviations arises primarily as a result of carbonization and catalytic reactions at the mineral-cartilage interface. The impact of the mechanism is enhanced in the vicinities of the area of sclerosed bone, but not inside the area where mechanical loads are maximum. Restoration of the atomic-molecular architecture of mineralized bone in the sclerosis area is revealed. Statistical aspects of the spatiotemporal changes in mineralized bone under pathogenic conditions are discussed.

Breakdown of the correlation between oxidation states and core electron binding energies at the sub-nanoscale

X-ray photoelectron spectroscopy is a powerful analytical tool to fingerprint the atomic oxidation state. However, the well-established trend that is found for bulk, ultra-thin films and surface oxides, which is usually characterized by an incremental binding energy shift upon increasing oxidation state, may not apply at the sub-nanoscale where reduced dimensionality and quantum size effects play a relevant role. Here we investigate through a combined experimental and theoretical approach the oxidation of size-selected Ag7 and Ag11 clusters supported on graphene, revealing an anomalous Ag 3d5/2 core level shift trend upon increasing O coverage. We show that the negative core level shift trend typical of Ag reverts back in the case of the highest Ag(III) oxidation state, an effect that is due to the peculiar electronic structure of Ag nano-oxides. Our results highlight the great care needed to extend at the zero-dimensional scale the knowledge acquired for the spectral interpretation of 3D and 2D materials.

XPS Core-Level Chemical Shift by Ab Initio Many-Body Theory.

X-ray photoemission spectroscopy (XPS) provides direct information on atomic composition and stoichiometry by measuring core-electron binding energies. Moreover, from the shift of the binding energy, the so-called chemical shift, the precise chemical type of bonds can be inferred, which brings additional information on the local structure. In this work, we present a theoretical study of the chemical shift first by comparing different theories, from Hartree-Fock and density functional theory to many-body perturbation theory approaches like the GW approximation and its static version (COHSEX). The accuracy of each theory is assessed with respect to a carbon 1s chemical shift experimental benchmark measured on a set of gas-phase molecules. More importantly, by decomposing the chemical shift into different contributions according to terms in the total Hamiltonian, classical electrostatics is identified as the major contributor to the chemical shift, one order of magnitude larger than the correlation.

Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization.

This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.

Electronic structure study of H3BXH3 (X═B, N and P) as hydrogen storage materials using calculated NMR and XPS spectra

Boron-based materials have been used for hydrogen storage applications owing to their high volumetric and gravimetric hydrogen density. The present study quantum mechanically investigates the electronic structures of three compounds: diborane (DB, B2H6), ammonia borane (AB, H3BNH3) and phosphine borane (PB, H3BPH3). The exploration is facilitated using calculated nuclear magnetic resonance (NMR) chemical shifts, together with outer valence ionisation potentials (IP) and core electron binding energy (CEBE). The findings show a distinct electronic structure for diborane, differing notably from AB and PB, which exhibit certain similarities. Noteworthy dissimilarities are observed in the chemical environments of the bridge hydrogens and terminal hydrogens in diborane, resulting in a substantial chemical shift difference of up to 5.31 ppm. Conversely, in AB and PB, two distinct sets of hydrogens emerge: protic hydrogens (Hp–N and Hp–P) and hydridic hydrogens (Hh–B). This leads to chemical shifts as small as 0.42 ppm in AB and as significant as 3.0 ppm in PB. The absolute isotropic NMR shielding constant (σB) of 11B in DB is 85.40 ppm, in contrast to 126.21 ppm in AB and 151.46 ppm in PB. This discrepancy indicates that boron in PB has the most robust chemical environment among the boranes. This assertion finds support in the calculated CEBE for B 1s of 196.53, 194.01 and 193.93 eV for DB, AB and PB respectively. It is clear that boron in PB is the most reactive atom. Ultimately, understanding the chemical environment of the boranes is pivotal in the context of dehydrogenation processes for boron-based hydrogen storage materials.

Observation of site-selective chemical bond changes via ultrafast chemical shifts

The concomitant motion of electrons and nuclei on the femtosecond time scale marks the fate of chemical and biological processes. Here we demonstrate the ability to initiate and track the ultrafast electron rearrangement and chemical bond breaking site-specifically in real time for the carbon monoxide diatomic molecule. We employ a local resonant x-ray pump at the oxygen atom and probe the chemical shifts of the carbon core-electron binding energy. We observe charge redistribution accompanying core-excitation followed by Auger decay, eventually leading to dissociation and hole trapping at one site of the molecule. The presented technique is general in nature with sensitivity to chemical environment changes including transient electronic excited state dynamics. This work provides a route to investigate energy and charge transport processes in more complex systems by tracking selective chemical bond changes on their natural timescale.

Resonant double-core excitations with ultrafast, intense X-ray pulses

Intense few-to-sub-femtosecond soft X-ray pulses can produce neutral, two-site excited double-core-hole states by promoting two core electrons to the same unoccupied molecular orbital. We theoretically investigate double nitrogen K-edge excitations of nitrous oxide (N 2 O) with multiconfigurational electronic structure calculations. We show that the second core-excitation energy is reduced with respect to its ground state value. A site-selective double core-excitation mechanism using intense few-femtosecond x-rays is investigated using time-dependent Schrödinger equation (TDSE) simulations. The subsequent two-step Auger–Meitner and two-electrons-one-electron decay spectra of the double core-excited states are analysed using a Mulliken population analysis of the multiconfirational wavefunctions. The change in the electron emission lineshape between the absorption of 1 or 2 photons in the resonant core-excitation is predicted by combining this approach with the TDSE simulations. We examine the possibility of resolving the double core-excited states with X-ray pump-probe techniques by calculating the chemical shifts of the core-electron binding energy of the core-excited states and decay products.