High-energy photoelectron C 1s and O 1s shake-up spectra of CO

GW Plus Cumulant Approach for Predicting Core-Level Shakeup Satellites in Large Molecules

Recently, the GW approach has emerged as a valuable tool for computing deep core-level binding energies as measured in X-ray photoemission spectroscopy. However, GW fails to accurately predict shakeup satellite features, which arise from charge-neutral excitations accompanying the ionization. In this work, we extend the GW plus cumulant (GW + C) approach to molecular 1s excitations, deriving conditions under which GW + C can be reliably applied to shakeup processes. We present an efficient implementation with O(N4) scaling with respect to the system size N, within an all-electron framework based on numeric atom-centered orbitals. We demonstrate that decoupling the core and valence spaces is crucial when using localized basis functions. Additionally, we meticulously validate the basis set convergence of the satellite spectrum for 65 spectral functions and identify the importance of diffuse augmenting functions. To assess the accuracy, we apply our GW + C scheme to π-conjugated molecules containing up to 40 atoms, predicting dominant satellite features within 0.5 eV of experimental values. For the acene series, from benzene to pentacene, we demonstrate how GW + C provides critical insights into the interpretation of experimentally observed satellite features.

Benchmark of GW Methods for Core-Level Binding Energies

The GW approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy. We present a comprehensive benchmark study of different GW methodologies (starting point optimized, partial and full eigenvalue-self-consistent, Hedin shift, and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three GW schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot GW calculations based on an optimized hybrid functional starting point, and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean absolute errors <0.2 eV the best results.

Predictions of Chemical Shifts for Reactive Intermediates in CO2 Reduction under Operando Conditions

The electroreduction of CO₂ into value-added products is a significant step toward closing the global carbon loop, but its performance remains far from meeting the requirement of any practical application. The insufficient understanding of the reaction mechanism is one of the major causes that impede future development. Although several possible reaction pathways have been proposed, significant debates exist due to the lack of experimental support. In this work, we provide opportunities for experiments to validate the reaction mechanism by providing predictions of the core-level shifts (CLS) of reactive intermediates, which can be verified by the X-ray photoelectron spectroscopy (XPS) data in the experiment. We first validated our methods from benchmark calculations of cases with reliable experiments, from which we reach consistent predictions with experimental results. Then, we conduct theoretical calculations under conditions close to the operando experimental ones and predict the C 1s CLS of 20 reactive intermediates in the CO₂ reduction reaction (CO₂RR) to CH₄ and C₂H₄ on a Cu(100) catalyst by carefully including solvation effects and applied voltage (U). The results presented in this work should be guidelines for future experiments to verify and interpret the reaction mechanism of CO₂RR.

Advanced Computation Method for Double Core Hole Spectra: Insight into the Nature of Intense Shake-up Satellites

Double core hole spectroscopy is an ideal framework for investigating photoionization shake-up satellites. Their important intensity in a single site double core hole (ssDCH) spectrum allows the exploration of the subtle mix of relaxation and correlation effects associated with the inherent multielectronic character of the shake-up process. We present a high-accuracy computation method for single photon double core-shell photoelectron spectra that combines a selected configuration interaction procedure with the use of non-orthogonal molecular orbitals to obtain unbiased binding energy and intensity. This strategy leads to the oxygen ssDCH spectrum of the CO molecule that is in excellent agreement with the experimental result. Through a combined wave function and density analysis, we highlight that the most intense shake-up satellites are characterized by an electronic reorganization that opposes the core hole-induced relaxation.

Accurate Absolute and Relative Core-Level Binding Energies from GW

We present an accurate approach to compute X-ray photoelectron spectra based on the GW Green's function method that overcomes the shortcomings of common density functional theory approaches. GW has become a popular tool to compute valence excitations for a wide range of materials. However, core-level spectroscopy is thus far almost uncharted in GW. We show that single-shot perturbation calculations in the G0W0 approximation, which are routinely used for valence states, cannot be applied for core levels and suffer from an extreme, erroneous transfer of spectral weight to the satellite spectrum. The correct behavior can be restored by partial self-consistent GW schemes or by using hybrid functionals with almost 50% of exact exchange as a starting point for G0W0. We also include relativistic corrections and present a benchmark study for 65 molecular 1s excitations. Our absolute and relative GW core-level binding energies agree within 0.3 and 0.2 eV with experiment, respectively.

Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction

The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.

Green's function coupled cluster formulations utilizing extended inner excitations

In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X _p (ω) and Y _q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N₂ and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.

Green's Function Coupled-Cluster Approach: Simulating Photoelectron Spectra for Realistic Molecular Systems

In this paper, we present an efficient implementation for the analytical energy-dependent Green's function coupled-cluster with singles and doubles (GFCCSD) approach with our first practice being computing spectral functions of realistic molecular systems. Because of its algebraic structure, the presented method is highly scalable and is capable of computing spectral function for a given molecular system in any energy region. Several typical examples have been given to demonstrate its capability of computing spectral functions not only in the valence band but also in the core-level energy region. Satellite peaks have been observed in the inner valence band and core-level energy region where a many-body effect becomes significant and the single particle picture of ionization often breaks down. The accuracy test has been carried out by extensively comparing the computed spectral functions by our GFCCSD method with experimental photoelectron spectra as well as the theoretical ionization potentials obtained from other methods. It turns out the GFCCSD method is able to provide a qualitative or semiquantitative level of description of ionization processes in both the core and valence regimes. To significantly improve the GFCCSD results for the main ionic states, a larger basis set can usually be employed, whereas the improvement of the GFCCSD results for the satellite states needs higher-order many-body terms to be included in the GFCC implementation.

C1s and O1s photoelectron satellite spectra of CO with symmetry-dependent vibrational excitations

The photoelectron shake-up satellite spectra that accompany the C1s and O1s main lines of carbon monoxide have been studied by a combination of high-resolution x-ray photoelectron spectroscopy and accurate ab initio calculations. The symmetry-adapted cluster-expansion configuration-interaction general-R method satisfactorily reproduces the satellite spectra over a wide energy region, and the quantitative assignments are proposed for the 16 and 12 satellite bands for C1s and O1s spectra, respectively. Satellite peaks above the pi(-1)pi(*) transitions are mainly assigned to the Rydberg excitations accompanying the inner-shell ionization. Many shake-up states, which interact strongly with three-electron processes such as pi(-2)pi(*2) and n(-2)pi(*2), are calculated in the low-energy region, while the continuous Rydberg excitations are obtained with small intensities in the higher-energy region. The vibrational structures of low-lying shake-up states have been examined for both C1s and O1s ionizations. The vibrational structures appear in the low-lying C1s satellite states, and the symmetry-dependent angular distributions for the satellite emission have enabled the Sigma and Pi symmetries to be resolved. On the other hand, the potential curves of the low-lying O1s shake-up states are predicted to be weakly bound or repulsive.

Charge transfer in the Cl−CO cluster induced by core ionization

Ab initio calculations of core-ionization spectra of the anion-molecule Cl-CO cluster are performed. Particular attention is paid to the investigation of charge-transfer screening processes accompanying core ionization of the CO molecule in the cluster. The charge-transfer processes are very efficient and favored by the presence of a low-lying unoccupied pi* orbital in CO capable of accepting an electron from Cl-. The O1s(-1) and C1s(-1) core-ionization spectra are calculated and compared. Both reveal a breakdown of the quasiparticle picture of core ionization caused by the charge-transfer processes. Remarkable differences between these two spectra are found which manifest themselves in distinct intensity distributions in the prominent low-energy spectral bands. The underlying reason for these differences is elucidated and linked with the preference of the pi* orbital to localize mainly on carbon. Core-ionization spectra of anion-molecule clusters are very sensitive to the type of the molecule involved as the comparative analysis of the O1s(-1) core-ionization spectra of the Cl-CO and Cl-H(2)O clusters show.