Unveiling Hidden Shake-Up Features in the Uranyl M4-Edge Spectrum.

The M4,5-edge high energy resolution X-ray absorption near-edge structure (HR-XANES) spectra of actinyls offer valuable insights into the electronic structure and bonding properties of heavy-element complexes. To conduct a comprehensive spectral analysis, it is essential to employ computational methods that accurately account for relativistic effects and electron correlation. In this work, we utilize variational relativistic multireference configurational interaction methods to compute and analyze the X-ray M4-edge absorption spectrum of uranyl. By employing these advanced computational techniques, we achieve excellent agreement between the calculated spectral features and experimental observations. Moreover, the calculations unveil significant shake-up features, which arise from the intricate interplay between strongly correlated 3d core-electron and ligand excitations. This research provides important theoretical insights into the spectral characteristics of heavy-element complexes. Furthermore, it establishes the foundation for utilizing M4,5-edge spectroscopy as a means to investigate the chemical activities of such complexes. By leveraging this technique, we can gain a deeper understanding of the bonding behavior and reactivity of heavy-element compounds.

Uranium-Mediated Peroxide Activation and a Precursor toward an Elusive Uranium cis-Dioxo Fleeting Intermediate.

The activation of chalcogen-chalcogen bonds using organometallic uranium complexes has been well documented for S-S, Se-Se, and Te-Te bonds. In stark contrast, reports concerning the ability of a uranium complex to activate the O-O bond of an organic peroxide are exceedingly rare. Herein, we describe the peroxide O-O bond cleavage of 9,10-diphenylanthracene-9,10-endoperoxide in nonaqueous media, mediated by a uranium(III) precursor [((Me,AdArO)3N)UIII(dme)] to generate a stable uranium(V) bis-alkoxide complex, namely, [((Me,AdArO)3N)UV(DPAP)]. This reaction proceeds via an isolable, alkoxide-bridged diuranium(IV/IV) species, implying that the oxidative addition occurs in two sequential, single-electron oxidations of the metal center, including rebound of a terminal oxygen radical. This uranium(V) bis-alkoxide can then be reduced with KC8 to form a uranium(IV) complex, which upon exposure to UV light, in solution, releases 9,10-diphenylanthracene to generate a cyclic uranyl trimer through formal two-electron photooxidation. Analysis of the mechanism of this photochemical oxidation via density functional theory (DFT) calculations indicates that the formation of this uranyl trimer occurs through a fleeting uranium cis-dioxo intermediate. At room temperature, this cis-configured dioxo species rapidly isomerizes to a more stable trans configuration through the release of one of the alkoxide ligands from the complex, which then goes on to form the isolated uranyl trimer complex.

State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Benchmark and Perspectives.

Spin-orbit coupling (SOC) is an important driving force in photochemistry. In this work, we develop a perturbative spin-orbit coupling method within the linear response time-dependent density function theory framework (TDDFT-SO). A full state interaction scheme, including singlet-triplet and triplet-triplet coupling, is introduced to describe not only the coupling between the ground and excited states, but also between excited states with all couplings between spin microstates. In addition, expressions to compute spectral oscillator strengths are presented. Scalar relativity is included variationally using the second-order Douglas-Kroll-Hess Hamiltonian, and the TDDFT-SO method is validated against variational SOC relativistic methods for atomic, diatomic, and transition metal complexes to determine the range of applicability and potential limitations. To demonstrate the robustness of TDDFT-SO for large-scale chemical systems, the UV-Vis spectrum of Au25(SR)18 - is computed and compared to experiment. Perspectives on the limitation, accuracy, and capability of perturbative TDDFT-SO are presented via analyses of benchmark calculations. Additionally, an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.

Influencing Bonding Interactions of the Neptunyl (V, VI) Cations with Electron-Donating and -Withdrawing Groups.

Neptunium makes up the largest percentage of minor actinides found in spent nuclear fuel, yet separations of this element have proven difficult due to its rich redox chemistry. Developing new reprocessing techniques should rely on understanding how to control the Np oxidation state and its interactions with different ligands. Designing new ligands for separations requires understanding how to properly tune a system toward a desired trait through functionalization. Emerging technologies for minor actinide separations focus on ligands containing carboxylate or pyridine functional groups, which are desirable due to their high degree of functionalization. Here, we use DFT calculations to study the interactions of carboxylate and polypyridine ligands with the neptunyl cation [Np(V/VI)O2]+/2+. A systematic study is performed by varying the electronic properties of the carboxylate and polypyridine ligands through the inclusion of different electron-withdrawing and electron-donating R groups. We focus on how these groups can affect geometric properties, electronic structure, and bonding characterization as a function of the metal oxidation state and ligand character and discuss how these factors can play a role in neptunium ligand design principles.

Relativistic Effects in Modeling the Ligand K-Edge X-ray Absorption Near-Edge Structure of Uranium Complexes.

Accurate modeling of the complex electronic structure of actinide complexes requires full inclusion of relativistic effects. In this study, we examine the effect of explicit inclusion of spin-orbit coupling (SOC) versus scalar relativistic effects on the predicted spectra for heavy-element complexes. In this study, we employ a relativistic two-component Hamiltonian in the X2C form with all of the electrons in the system being considered explicitly to compare and contrast with previous studies that included the relativistic effects by means of relativistic effective core potentials (RECPs). A few uranium complexes are chosen as model systems. Comparison of the computed Cl K-edge X-ray absorption spectra with experimental data shows significantly improved agreement when a variational relativistic treatment of SOC is performed. In particular, we note the importance of SOC terms to obtain not only correct transition energies but also correct intensities for these heavy-element complexes because of the redistribution of ligand bonding character among the valence MOs. While RECPs generally agree well with all-electron scalar relativistic calculations, there are some differences in the predicted spectra of open-shell systems. These methods are still suitable for broad application to analyze the qualitative nature of transitions in X-ray absorption spectra, but caution is recommended for quantitative analysis, as SOC can be non-negligible for both open- and closed-shell heavy-element systems.

Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems.

Without rigorous symmetry constraints, solutions to approximate electronic structure methods may artificially break symmetry. In the case of the relativistic electronic structure, if time-reversal symmetry is not enforced in calculations of molecules not subject to a magnetic field, it is possible to artificially break Kramers degeneracy in open shell systems. This leads to a description of excited states that may be qualitatively incorrect. Despite this, different electronic structure methods to incorporate correlation and excited states can partially restore Kramers degeneracy from a broken symmetry solution. For single-reference techniques, the inclusion of double and possibly triple excitations in the ground state provides much of the needed correction. Formally, however, this imbalanced treatment of the Kramers-paired spaces is a multi-reference problem, and so methods such as complete-active-space methods perform much better at recovering much of the correct symmetry by state averaging. Using multi-reference configuration interaction, any additional corrections can be obtained as the solution approaches the full configuration interaction limit. A recently proposed "Kramers contamination" value is also used to assess the magnitude of symmetry breaking.

Relativistic Two-Component Multireference Configuration Interaction Method with Tunable Correlation Space.

The multiconfiguration nature of late-row (≥4th) elements and their molecular complexes, combined with significant relativistic effects, present large challenges for the accurate description of their electronic structure. To address these challenges and incorporate both relativistic and electron correlation effects, we present a two-component Kramers-unrestricted multireference configuration interaction method where relativistic effects are included variationally at the molecular orbital level via use of the "exact two-component" transformation of the solution of the one-electron modified Dirac equation. This method is developed within the restricted active space framework, allowing flexibility in both the choice of correlation space and the level of truncation of the excitation operator, as well as promoting the efficiency of generating and book-keeping unique electronic configurations. This method is applied to the study of fine structure splitting in selected p-block and d-block elements and is further applied to the study of the open-shell heavy-element uranium(V) ion.

Natural transition orbitals for complex two-component excited state calculations.

While the natural transition orbital (NTO) method has allowed electronic excitations from time-dependent Hartree-Fock and density functional theory to be viewed in a traditional orbital picture, the extension to multicomponent molecular orbitals such as those used in relativistic two-component methods or generalized Hartree-Fock (GHF) or generalized Kohn-Sham (GKS) is less straightforward due to mixing of spin-components and the inherent inclusion of spin-flip transitions in time-dependent GHF/GKS. An extension of single-component NTOs to the two-component framework is presented, in addition to a brief discussion of the practical aspects of visualizing two-component complex orbitals. Unlike the single-component analog, the method explicitly describes the spin and frequently obtains solutions with several significant orbital pairs. The method is presented using calculations on a mercury atom and a CrO2 Cl2 complex.

Theoretical investigation of quantum confinement on the Rashba effect in ZnO semiconductor nanocrystals.

Semiconducting nanocrystals have been the subject of intense research due to the ability to modulate the electronic and magnetic properties by controlling the size of the crystal, introducing dopants, and surface modification. While relatively simple models such as a particle in a sphere can work well to describe moderately sized quantum dots, this approximation becomes less accurate for very small nanocrystals that are strongly confined. In this work, we report all-electron, relativistic ab initio electronic structure calculations for a series of ZnO quantum dots in order to study the modulation of the Rashba effect. The impact and magnitude of spin-orbit coupling and crystalline anisotropy on the fine structure of the band-edge excitonic manifold are discussed.

Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory.

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L2,3-edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L2-L3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.

Variational Relativistic Two-Component Complete-Active-Space Self-Consistent Field Method.

The accurate description of the electronic structure of transition metals and their compounds can be complicated by both the large number of close-lying states that often have multiconfigurational nature and significant relativistic effects. In order to address these challenges we present a two-component complete-active-space self-consistent field method that includes scalar relativistic effects and one-electron spin-orbit coupling during the self-consistent wave function optimization procedure. These relativistic effects are included via an "exact two-component" transformation of the solution of the one-electron modified Dirac equation. The method is applied to the study of spin-orbit splitting of ground and low-lying excited states of main group elements and selected transition metals.

Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory.

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl4 and three transition metal complexes, TiCl4, CrO2Cl2, and [FeCl6]3-. Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems.

The time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard methods such as the Davidson algorithm for spectrally dense regions in the interior of the spectrum, as are common in X-ray absorption spectroscopy (XAS). More robust solvers, such as the generalized preconditioned locally harmonic residual (GPLHR) method, can alleviate this problem, but at the expense of higher average computational cost. A hybrid method is proposed which adapts to the problem in order to maximize computational performance while providing the superior convergence of GPLHR. In addition, a modification to the GPLHR algorithm is proposed to adaptively choose the shift parameter to enforce a convergence of states above a predefined energy threshold.

Model Order Reduction Algorithm for Estimating the Absorption Spectrum.

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.

Real time propagation of the exact two component time-dependent density functional theory.

We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.