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

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

Alternative Pathway to Double-Core-Hole States

Excited double-core-hole states of isolated water molecules resulting from the sequential absorption of two x-ray photons have been investigated. These states are formed through an alternative pathway, where the initial step of core ionization is accompanied by the shake-up of a valence electron, leading to the same final states as in the core-ionization followed by core-excitation pathway. The capability of the x-ray free-electron laser to deliver very intense, very short, and tunable light pulses is fully exploited to identify the two different pathways.

Unraveling the variational breakdown of core valence separation calculations: Diagnostic and cure to the over relaxation error of double core hole states

The core valence separation (CVS) approximation is the most employed strategy to prevent the variational collapse of standard wave function optimization when attempting to compute electronic states bearing one or more electronic vacancies in core orbitals. Here, we explore the spurious consequences of this approximation on the properties of the computed core hole states. We especially focus on the less studied case of double core hole (DCH) states, whose spectroscopic interest has recently been rapidly growing. We show that the CVS error leads to a systematic underestimation of DCH energies, a property in stark contrast with the case of single core hole states. We highlight that the CVS error can then be interpreted as an over relaxation effect and design a new correction strategy adapted to these specificities.

3D space-confined Co0.85Se architecture with effective interfacial stress relaxation as anode material reveals robust and highly loading potassium-ion batteries

Conversion-type transition metal chalcogenide anodes could bring relatively high specific capacity in potassium ion storage due to multiple electron transport reactions, but often accompanying huge volume changes and resulting in low cycle life and rapid capacity fading.While electrode materials are closely packed, the contact at the interface during potassiation/depotassiation is similar to point-to-point contact, generating strong stress to make self-aggregation occur. In this work, we constructed a 3D carbon framework to confine Co_0.85Se nanocrystals in three-dimensional space, both fulfilling the requirements of the material's size in the nano-scale and providing the largest contact area for releasing stress. With this optimization, nitrogen-doped carbon confined Co_0.85Se nanocrystals (Co_0.85Se@NC) reach an ultra-stable cycle life over 4000 times with a specific capacity of 190.9 mA h g^-1 at 500 mA g^-1 and provide 155.6 mA h g^-1 at 10 A g^-1 in the rate capability test. It also renders the areal capacity up to 1.03 mA h cm^-2 at 500 mA g^-1 in the high-mass loading test. Furthermore, based on the finite element analysis, the 3D confinement strategy has the lowest interfacial stress, ensuring Co_0.85Se nanocrystals with high structural integrity. This strategy can relieve the stress issue in the conversion-type anode and demonstrate superior electrochemical performance even at high-loading mass electrodes.

Interpretation of Shakeup Mechanisms in Copper L-Shell Photoelectron Spectra

We report on an original full ab initio quantum molecular approach designed to simulate Cu 2p X-ray photoelectron spectra. The description includes electronic relaxation/correlation and spin-orbit coupling effects and is implemented within nonorthogonal sets of molecular orbitals for the initial and final states. The underlying mechanism structuring the Cu 2p photoelectron spectra is clarified thanks to a correlation diagram applied to the CuO₄C₆H₆ paradigm. This diagram illustrates how the energy drop of the Cu 3d levels following the creation of the Cu 2p core hole switches the nature of the highest singly occupied molecular orbital (H-SOMO) from dominant metal to dominant ligand character. It also reveals how the repositioning of the Cu 3d levels induces the formation of new bonding and antibonding orbitals from which shakeup mechanisms toward the relaxed H-SOMO operate. The specific nature, ligand → ligand and metal → ligand, of these excitations building the satellite lines is exposed. Our approach finally applied to the real Cu(acac)₂ system clearly demonstrates how a definite interpretation of the XPS spectra can be obtained when a correct evaluation of binding energies, intensities, and relative widths of the spectral lines is achieved.

Specific chemical bond relaxation unraveled by analysis of shake-up satellites in the oxygen single site double core hole spectrum of CO2

We recently developed [A. Ferté, et al., J. Phys. Chem. Lett., 2020, 11, 4359] a method to compute single site double core hole (ssDCH or K^-2) spectra. We refer to that method as NOTA+CIPSI. In the present paper this method is applied to the O K^-2 spectrum of the CO₂ molecule, and we use this as an example to discuss in detail its convergence properties. Using this approach, theoretical spectra in excellent agreement with the experimental one are obtained. Thanks to a thorough interpretation of the shake-up states responsible for the main satellite peaks and through comparison with the O K^-2 spectrum of CO, we can highlight the clear signature of the two non-equivalent carbon oxygen bonds in the oxygen ssDCH CO₂ dication.

Multi-reference approach to the computation of double core-hole spectra

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K^-2) are obtained for H₂O, N₂, CO, and C₂H_2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K^-2 shake-up spectra of H₂O and C₂H_2n molecules are here completely characterized for the first time.