Simulation Of X-ray Absorption Spectra Research Articles

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations.

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches.

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods’ performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@, X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L1 edges, and is capable of reproducing the splitting of the 1s1 (n + 1)p1 final states (n + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s1 (n + 2)p1 states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments.

Simulations of x-ray absorption spectra for CO desorbing from Ru(0001) with transition-potential and time-dependent density functional theory approaches.

The desorption of a carbon monoxide molecule from a Ru(0001) surface was studied by means of X-ray Absorption Spectra (XAS) computed with Transition Potential (TP-DFT) and Time Dependent (TD-DFT) DFT methods. By unraveling the evolution of the CO electronic structure upon desorption, we observed that at 2.3 Å from the surface, the CO molecule has already predominantly gas-phase character. While C 1s XAS is quite insensitive to changes in the C–O bond length, the O 1s excitation is very sensitive with the π* coming down in energy upon CO bond stretching, which competes with the increase in orbital energy due to the repulsive interaction with the metallic surface. We show in a systematic way that the TP-DFT method can describe the XAS rather well at the endpoints (chemisorbed and gas phase) but is affected by artificial charge transfer and/or incorrect spin treatment in the transition region in cases like CO, where there are low-lying π* orbitals and large exchange interactions between the core 1s and valence-acceptor π* orbitals. As an alternative, we demonstrate by comparing with experimental data that a linear response approach using TD-DFT employing common exchange-correlation functionals and finite-size clusters can yield a good description of the spectral evolution of the 1s → π* transition with correct spin and gas-to-chemisorbed chemical shifts in good agreement with experiment.

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory.

The simulation of X-ray absorption spectra requires both scalar and spin–orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac–Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange–correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee–Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.

PSIXAS: A Psi4 plugin for efficient simulations of X-ray absorption spectra based on the transition-potential and Δ-Kohn-Sham method.

Near edge X-ray absorption fine structure (NEXAFS) spectra and their pump-probe extension (PP-NEXAFS) offer insights into valence- and core-excited states. We present PSIXAS, a recent implementation for simulating NEXAFS and PP-NEXAFS spectra by means of the transition-potential and the Δ-Kohn-Sham method. The approach is implemented in form of a software plugin for the Psi4 code, which provides access to a wide selection of basis sets as well as density functionals. We briefly outline the theoretical foundation and the key aspects of the plugin. Then, we use the plugin to simulate PP-NEXAFS spectra of thymine, a system already investigated by others and us. It is found that larger, extended basis sets are needed to obtain more accurate absolute resonance positions. We further demonstrate that, in contrast to ordinary NEXAFS simulations, where the choice of the density functional plays a minor role for the shape of the spectrum, for PP-NEXAFS simulations the choice of the density functional is important. Especially hybrid functionals (which could not be used straightforwardly before to simulate PP-NEXAFS spectra) and their amount of "Hartree-Fock like" exact exchange affects relative resonance positions in the spectrum.

The simulation of X-ray absorption spectra from ground and excited electronic states using core-valence separated DFT/MRCI.

We present an extension of the combined density functional theory (DFT) and multireference configuration interaction (MRCI) method (DFT/MRCI) [S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999)] for the calculation of core-excited states based on the core-valence separation (CVS) approximation. The resulting method, CVS-DFT/MRCI, is validated via the simulation of the K-edge X-ray absorption spectra of 40 organic chromophores, amino acids, and nucleobases, ranging in size from CO2 to tryptophan. Overall, the CVS-DFT/MRCI method is found to yield accurate X-ray absorption spectra (XAS), with consistent errors in peak positions of ∼2.5-3.5 eV. Additionally, we show that the CVS-DFT/MRCI method may be employed to simulate XAS from valence excited states and compare the simulated spectra to those computed using the established wave function-based approaches [ADC(2) and ADC(2)x]. In general, each of the methods yields excited state XAS spectra in qualitative and often quantitative agreement. In the instances where the methods differ, the CVS-DFT/MRCI simulations predict intensity for transitions for which the underlying electronic states are characterized by doubly excited configurations relative to the ground state configuration. Here, we aim to demonstrate that the CVS-DFT/MRCI approach occupies a specific niche among numerous other electronic structure methods in this area, offering the ability to treat initial states of arbitrary electronic character while maintaining a low computational cost and comparatively black box usage.

Efficient calculation of X-ray absorption spectra using Chebyshev-Slepian filter diagonalisation.

The efficient, yet accurate, simulation of X-ray absorption spectra represents a significant challenge for ab initio electronic structure methods. Conventional approaches involve the explicit calculation of all core-excited states spanning the energy range of interest, even though only a small number of these states will contribute appreciably to the spectrum. We here report a different approach, based on a time-independent Chebyshev filter diagonalization scheme, which allows for the X-ray absorption spectrum to be computed without the explicit calculation of the core-excited eigenstates. Furthermore, in a subsequent postprocessing calculation, selected peaks may be analyzed via the calculation of natural transition orbitals, if desired. The scheme presented here is based on a refinement of the time-independent Chebyshev filter diagonalization approach. Previous formulations of this method have been characterized by a requirement for significant "user input" via the (sometimes unintuitive) tuning of various numerical parameters. To circumvent this, we introduce a new class of filters based on discrete prolate spheroidal sequences. We demonstrate that the resulting method, which we term Chebyshev-Slepian filter diagonalization, makes filter diagonalization essentially a black-box procedure. The Chebyshev-Slepian filter diagonalization method is implemented at the second-order algebraic diagrammatic construction level of theory and validated through the calculation of the X-ray absorption spectra of trifluoroacetonitrile and 1,4-benzoquinone.

Physical Properties, Exciton Analysis, and Visualization of Core-Excited States: An Intermediate State Representation Approach.

The theoretical simulation of X-ray absorption spectra is in general a challenging task. However, for small and medium-sized organic molecules, the algebraic diagrammatic construction scheme (ADC) for the polarization operator in combination with the core-valence separation approximation (CVS) has proven to yield core-excitation energies and transition moments with almost quantitative accuracy allowing for reliable construction of X-ray absorption spectra. Still, to understand core-excitation processes in detail, it is not sufficient to only compute energies, but also properties like static dipole moments and state densities are important as they provide deeper insight into the nature of core-excited states. Here, we present for the first time an implementation of the intermediate state representation (ISR) approach in combination with the CVS approximation (CVS-ISR), which gives, in combination with the CVS-ADC method, direct access to core-excited state properties. The performance of the CVS-ADC/CVS-ISR approach is demonstrated by means of small- and medium-sized organic molecules. Besides the calculation of core-excited state dipole moments, advanced analyses of core-excited state densities are performed using descriptors like exciton sizes and distances. Plotting electron and hole densities helps to determine the character of the state, and in particular, the investigation of detachment/attachment densities provides information about orbital relaxation effects that are crucial for understanding core excitations.

Simulation of X-ray absorption spectra with orthogonality constrained density functional theory.

Orthogonality constrained density functional theory (OCDFT) [F. A. Evangelista, P. Shushkov and J. C. Tully, J. Phys. Chem. A, 2013, 117, 7378] is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree-Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.

The role of Hartree–Fock exchange in the simulation of X-ray absorption spectra: A study of photoexcited [formula omitted

We present a theoretical analysis for the K- and L2/3-edge static and picosecond X-ray absorption spectra of [Fe(bpy)3]2+. Simulations of the pre-edge region at the Fe K-edge using time-dependent density functional theory demonstrate the importance of Hartree–Fock exchange within the exchange–correlation functional, especially when describing charge transfer and 1s→3d transitions. This becomes particularly relevant for range separated functionals, for which the incorporation of Hartree–Fock exchange at short range decreases the absolute error in the excitation energy usually observed using TD-DFT. Finally, we compute and interpret the L2/3-edge spectrum using the Restricted Open-Shell Configuration Interaction Singles method.

Simulations of X-ray absorption spectra: the effect of the solvent

We perform quantum mechanics/molecular mechanics molecular dynamics simulations on the [Pt(2)(P(2)O(5)H(2))(4)](4-) (abbreviated PtPOP) complex; in water, dimethylformamide and ethanol. These are used to calculate the ground state X-ray absorption spectrum of the complex. The structural parameters from X-ray spectra are usually extracted using a fit of the experimental data. In such simulations the solvent is neglected meaning that any effect of the local environment will be compensated for by structural changes of the solute, leading to possible discrepancies in the extracted structural parameters. Our simulations show a significant solvent effect on the spectra, which has important implications for the structural analysis of molecules in solution.

A computational study on the X-ray absorption spectrum of proton-ordered crystalline ice IX

The cluster model commonly used in the simulation of X-ray absorption spectra is examined for water in a crystalline environment. The proton-ordered crystalline ice IX was chosen as an example. Effects of the size of the quantum cluster, long-range electrostatic interactions and the quality of the atomic basis sets are examined in detail. It is found that both the size of the quantum cluster and the Madelung potential due to long-range electrostatic interactions in the ordered crystal strongly influence the calculated spectrum while the quality of the basis set only has a very minor effect. For ice IX, it is shown that the features observed in the pre- and near edge region are described reasonably well but the main and post-edge absorption profile is more difficult to reproduce.

Controlling Length of Gold Nanowires with Large-Scale: X-ray Absorption Spectroscopy Approaches to the Growth Process

By utilizing the X-ray absorption approach, the gold ions evolving from the Au−Cl complex to Au rods have been elucidated. The theoretical simulation of X-ray absorption spectra further revealed the evolution of gold and concluded that ultrafine small clusters of gold (Au13) formed after a reducing agent was added to the growth solution. A redesigned seed-assisted growth method, a serial addition of growth solution, was employed to achieve the goal of the consecutive support of gold. The development approach was found to successfully fabricate 1D gold nanorods/wires with a tunable size from 50 nm to 1.7 μm.