Cluster embedding of ionic systems: Point charges and extended ions

On the choice of shape and size for truncated cluster-based X-ray spectral simulations of 2D materials

Truncated cluster models represent an effective way for simulating X-ray spectra of 2D materials. Here we systematically assessed the influence of two key parameters, the cluster shape (honeycomb, rectangle, or parallelogram) and size, in X-ray photoelectron (XPS) and absorption (XAS) spectra simulations of three 2D materials at five K-edges (graphene, C 1s; C3N, C/N 1s; h-BN, B/N 1s) to pursue the accuracy limit of binding energy (BE) and spectral profile predictions. Several recent XPS experiments reported BEs with differences spanning 0.3, 1.5, 0.7, 0.3, and 0.3 eV, respectively. Our calculations favor the honeycomb model for stable accuracy and fast size convergence, and a honeycomb with ~10 nm side length (120 atoms) is enough to predict accurate 1s BEs for all 2D sheets. Compared to all these experiments, predicted BEs show absolute deviations as follows: 0.4-0.7, 0.0-1.0, 0.4-1.1, 0.6-0.9, and 0.1-0.4 eV. A mean absolute deviation of 0.3 eV was achieved if we compare only to the closest experiment. We found that the sensitivity of computed BEs to different model shapes depends on systems: graphene, sensitive; C3N, weak; h-BN, very weak. This can be attributed to their more or less delocalized π electrons in this series. For this reason, a larger cluster size is required for graphene than the other two to reproduce fine structures in XAS. The general profile of XAS shows weak dependence to model shape. Our calculations provide optimal parameters and accuracy estimations that are useful for X-ray spectral simulations of general graphene-like 2D materials.

General embedded cluster protocol for accurate modeling of oxygen vacancies in metal-oxides

The O vacancy (Ov) formation energy, EOv, is an important property of a metal-oxide, governing its performance in applications such as fuel cells or heterogeneous catalysis. These defects are routinely studied with density functional theory (DFT). However, it is well-recognized that standard DFT formulations (e.g., the generalized gradient approximation) are insufficient for modeling the Ov, requiring higher levels of theory. The embedded cluster method offers a promising approach to compute EOv accurately, giving access to all electronic structure methods. Central to this approach is the construction of quantum(-mechanically treated) clusters placed within suitable embedding environments. Unfortunately, current approaches to constructing the quantum clusters either require large system sizes, preventing application of high-level methods, or require significant manual input, preventing investigations of multiple systems simultaneously. In this work, we present a systematic and general quantum cluster design protocol that can determine small converged quantum clusters for studying the Ov in metal-oxides with accurate methods, such as local coupled cluster with single, double, and perturbative triple excitations. We apply this protocol to study the Ov in the bulk and surface planes of rutile TiO2 and rock salt MgO, producing the first accurate and well-converged determinations of EOv with this method. These reference values are used to benchmark exchange–correlation functionals in DFT, and we find that all the studied functionals underestimate EOv, with the average error decreasing along the rungs of Jacob’s ladder. This protocol is automatable for high-throughput calculations and can be generalized to study other point defects or adsorbates.

Origin of the complex main and satellite features in Fe 2p XPS of Fe2O3

Although the origin and assignment of the complex XPS features of the cations in ionic compounds has been the subject of extensive theoretical work, agreement with experimental observations remains insufficient for unambiguous interpretation. This paper presents a rigorous ab initio treatment of the main and satellite features in the Fe 2p XPS of Fe₂O₃. This has been possible using a unique methodology for the selection of orbitals that are used to form the ionic wavefunctions. This orbital selection makes it possible to treat both the angular momentum coupling of the open shell core and valence electrons as well the shake excitations from the closed shell orbitals associated with the O ligands into the valence open shell orbitals associated with the Fe 3d shell. This allows the character of the ionic states in terms of the occupations of the open shell core and valence orbitals and of the contributions of 2p_1/2 and 2p_3/2 ionization to the XPS intensities to be determined. Our analysis gives strong evidence that many body effects are essential for a correct description of the ionic states and, in general the states cannot be described by a single configuration over the open shell orbitals. An important consequence is that the Fe 2p XPS intensity in most of the features arises from small contributions from the ionization to many, tens to hundreds, of often unresolved ionic states. While the usual understanding of the lower binding energy main and satellite features as being dominantly from 2p_3/2 ionization is confirmed, this is not the case for the higher binding energy features where 2p_1/2 and 2p_3/2 ionization and shake excitations in the valence space mix strongly. Furthermore, we have been able to show that a very large fraction, 88%, of the total Fe 2p XPS intensity is contained in a relatively small binding energy range of ∼35 eV. This is relevant if one wants to extract the stoichiometry of Fe₂O₃ from Fe 2p/O 1s intensity ratios. Similar considerations about the importance of many-body effects are likely to be relevant for other ionic compounds as well.

Computational and Spectroscopic Tools for the Detection of Bond Covalency in Pu(IV) Materials

Plutonium is used as a major component of new-generation nuclear fuels and of radioisotope batteries for Mars rovers, but it is also an environmental pollutant. Plutonium clearly has high technological and environmental importance, but it has an extremely complex, not well-understood electronic structure. The level of covalency of the Pu 5f valence orbitals and their role in chemical bonding are still an enigma and thus at the frontier of research in actinide science. We performed fully relativistic quantum chemical computations of the electronic structure of the Pu⁴⁺ ion and the PuO₂ compound. Using four different theoretical tools, it is shown that the 5f orbitals have very little covalent character although the 5f(_7/2) a_2u orbital with the highest orbital energy has the greatest extent of covalency in PuO₂. It is illustrated that the Pu M_4,5 edge high-energy resolution X-ray absorption near-edge structure (Pu M_4,5 HR-XANES) spectra cannot be interpreted in terms of dipole selection rules applied between individual 3d and 5f orbitals, but the selection rules must be applied between the total wavefunctions for the initial and excited states. This is because the states cannot be represented by single determinants. They are shown to involve major redistributions on the 5f electrons over the different 5f orbitals. These redistributions could be viewed as shake-up-like excitations in the 5f shell from the lowest orbital energy from J = 5f(_5/2) into higher orbital energy J = 5f(_7/2). We show that the second peak in the Pu M₄ edge and the high-energy shoulder of the Pu M₅ edge HR-XANES spectra probe the 5f(_7/2) a_2u orbital; thus, these spectral features are expected to change upon bond variations. We describe theoretical and spectroscopy tools, which can be applied for all actinide elements in materials with cubic structure.

Combined multiplet theory and experiment for the Fe 2p and 3p XPS of FeO and Fe2O3

The Al K alpha, 1486.6 eV, based x-ray photoelectron spectroscopy (XPS) of Fe 2p and Fe 3p for Fe(III) in Fe₂O₃ and Fe(II) in FeO is compared with theoretical predictions based on ab initio wavefunctions that accurately treat the final, core-hole, multiplets. The principal objectives of this comparison are to understand the multiplet structure and to evaluate the use of both the 2p and 3p spectra in determining oxidation states. In order to properly interpret the features of these spectra and to use the XPS to provide atomistic insights as well as atomic composition, it is necessary to understand the origin of the multiplet energies and intensities. The theoretical treatment takes into account the ligand field and spin-orbit splittings, the covalent mixing of ligand and Fe 3d orbitals, and the angular momentum coupling of the open shell electrons. These effects lead to the distribution of XPS intensity into a large number of final, ionic, states that are only partly resolved with energies spread over a wide range of binding energies. For this reason, it is necessary to record the Fe 2p and 3p XPS spectra over a wide energy range, which includes all the multiplets in the theoretical treatment as well as additional shake satellites. We also evaluate the effects of differing assumptions concerning the extrinsic background subtraction, to make sure our experimental spectrum may be fairly compared to the theory. We conclude that the Fe 3p XPS provides an additional means for distinguishing Fe(III) and Fe(II) oxidation states beyond just using the Fe 2p spectrum. In particular, with the use of the Fe 3p XPS, the depth of the material probed is about 1.5 times greater than for the Fe 2p XPS. In addition, a new type of atomic many-body effect that involves excitations into orbitals that have Fe f,ℓ = 3, symmetry has been shown to be important for the Fe 3p XPS.

Covalency in Fe2O3 and FeO: Consequences for XPS satellite intensity

The covalent character of the interaction between the metal cation and the oxygen ligands has been examined for two Fe oxides with different nominal oxidation states, Fe(II)O, and Fe(III)₂O₃. The covalent character is examined for the initial, ground state configuration and for the ionic states involving the removal of a shallow core, Fe 3p, and a deep core, Fe 2p, electron. The covalency is assessed based on novel theoretical analyses of wave functions for the various cases. It is found that the covalency is considerably different for different oxidation states and for different ionized and non-ionized configurations. The changes in covalency for the ions are shown to be responsible for important changes in relaxation energies for X-Ray Photoelectron Spectroscopy (XPS) spectra and in the intensity lost from main XPS peaks to shake satellites. While these consequences are not observables themselves, they are important for the interpretation of the XPS spectra, in particular, for efforts to extract stoichiometries of these iron oxides from XPS data. This is a finding likely applicable across various 3d transition metal oxide materials.