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

Web-CONEXS: an inroad to theoretical X-ray absorption spectroscopy

Accurate analysis of the rich information contained within X-ray spectra usually calls for detailed electronic structure theory simulations. However, density functional theory (DFT), time-dependent DFT and many-body perturbation theory calculations increasingly require the use of advanced codes running on high-performance computing (HPC) facilities. Consequently, many researchers who would like to augment their experimental work with such simulations are hampered by the compounding of nontrivial knowledge requirements, specialist training and significant time investment. To this end, we present Web-CONEXS, an intuitive graphical web application for democratizing electronic structure theory simulations. Web-CONEXS generates and submits simulation workflows for theoretical X-ray absorption and X-ray emission spectroscopy to a remote computing cluster. In the present form, Web-CONEXS interfaces with three software packages: ORCA, FDMNES and Quantum ESPRESSO, and an extensive materials database courtesy of the Materials Project API. These software packages have been selected to model diverse materials and properties. Web-CONEXS has been conceived with the novice user in mind; job submission is limited to a subset of simulation parameters. This ensures that much of the simulation complexity is lifted and preliminary theoretical results are generated faster. Web-CONEXS can be leveraged to support beam time proposals and serve as a platform for preliminary analysis of experimental data.

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

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.

Evaluation of cobalt complexes with tripod ligands for zinc finger targeting

We report the ability of Co^II and Co^III complexes of tri(2-pyridylmethyl)amine and N,N-di(2-pyridylmethyl)glycinate to disrupt zinc fingers.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy

Quantum dynamics simulations are used to simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom.

Revisiting the Dependence of Cu K-Edge X-ray Absorption Spectra on Oxidation State and Coordination Environment

X-ray absorption spectroscopy (XAS) at the Cu K-edge is an important tool for probing the properties of copper centers in transition-metal chemistry and catalysis. However, the interpretation of experimental XAS spectra requires a detailed understanding of the dependence of spectroscopic features on the local geometric and electronic structure, which can be established by theoretical X-ray spectroscopy. Here, we present a systematic computational study of the Cu K-edge XAS spectra of selected Cu complexes based on time-dependent density-functional theory in combination with a molecular orbital analysis of the relevant transitions. For a series of Cu ammine model complexes as well as a comprehensive test set of 12 Cu(I) and 5 Cu(II) complexes, we revisit the dependence of the pre-edge region in Cu K-edge XAS spectra on oxidation state and coordination geometry. While our calculations confirm earlier experimental assignments, we can also reveal additional signatures of the ligand orbitals and identify the underlying orbital interactions. The comprehensive picture revealed by this study will provide a reliable basis for the interpretation of in situ Cu K-edge XAS spectra of catalytic intermediates.

Nonadiabatic effects in electronic and nuclear dynamics

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.

NEXAFS spectroscopy of ionic liquids: experiments versus calculations

Experimental N 1s and S 1s NEXAFS spectra are compared to TD-DFT calculated spectra for 12 ionic liquids.

Tracking reaction dynamics in solution by pump–probe X-ray absorption spectroscopy and X-ray liquidography (solution scattering)

TRXL and TRXAS are powerful techniques for real-time probing of structural and electronic dynamics of photoinduced reactions in solution phase.

Probing spin–vibronic dynamics using femtosecond X-ray spectroscopy

Ultrafast pump-probe spectroscopy within the X-ray regime is now possible owing to the development of X-ray Free Electrons Lasers (X-FELs) and is opening new opportunities for the direct probing of femtosecond evolution of the nuclei, the electronic and spin degrees of freedom. In this contribution we use wavepacket dynamics of the photoexcited decay of a new Fe(ii) complex, [Fe(bmip)₂]²⁺ (bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)pyridine), to simulate the experimental observables associated with femtosecond Fe K-edge X-ray Absorption Near-Edge Structure (XANES) and X-ray emission (XES) spectroscopy. We show how the evolution of the nuclear wavepacket is translated into the spectroscopic signal and the sensitivity of these approaches for following excited state dynamics.

Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method

The intensities and relative energies of metal K pre-edge features are sensitive to both geometric and electronic structures.

Quantum Chemical Calculations of X-ray Emission Spectroscopy

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time-dependent density functional theory (TDDFT), and resolution of the identity single excitation configuration interaction with second-order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation, removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s orbitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment; however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth-order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range corrected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B(66)LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, acetone, dimethyl sulfoxide, and CF3Cl in good agreement with experiment.

Element-specific characterization of transient electronic structure of solvated Fe(II) complexes with time-resolved soft X-ray absorption spectroscopy

Polypyridyl transition-metal complexes are an intriguing class of compounds due to the relatively facile chemical designs and variations in ligand-field strengths that allow for spin-state changes and hence electronic configurations in response to external perturbations such as pressure and light. Light-activated spin-conversion complexes have possible applications in a variety of molecular-based devices, and ultrafast excited-state evolution in these complexes is of fundamental interest for understanding of the origins of spin-state conversion in metal complexes. Knowledge of the interplay of structure and valence charge distributions is important to understand which degrees of freedom drive spin-conversion and which respond in a favorable (or unfavorable) manner. To track the response of the constituent components, various types of time-resolved X-ray probe methods have been utilized for a broad range of chemical and biological systems relevant to catalysis, solar energy conversions, and functional molecular devices. In particular, transient soft X-ray spectroscopy of solvated molecules can offer complementary information on the detailed electronic structures and valence charge distributions of photoinduced intermediate species: First-row transition-metal L-edges consist of 2p-3d transitions, which directly probe the unoccupied valence density of states and feature lifetime broadening in the range of 100 meV, making them sensitive spectral probes of metal-ligand interactions. In this Account, we present some of our recent progress in employing picosecond and femtosecond soft X-ray pulses from synchrotron sources to investigate element specific valence charge distributions and spin-state evolutions in Fe(II) polypyridyl complexes via core-level transitions. Our results on transient L-edge spectroscopy of Fe(II) complexes clearly show that the reduction in σ-donation is compensated by significant attenuation of π-backbonding upon spin-crossover. This underscores the important information contained in transient metal L-edge spectroscopy on changes in the 3d orbitals including oxidation states, orbital symmetries, and covalency, which largely define the chemistry of these complexes. In addition, ligand K-edge spectroscopy reveals the "ligand view" of the valence charge density by probing 1s-2p core-level transitions at the K-edge of light elements such as nitrogen, carbon, and oxygen. In the case of Fe(II) spin-conversion complexes, additional details of the metal-ligand interactions can be obtained by this type of X-ray spectroscopy. With new initiatives in and construction of X-ray free-electron laser sources, we expect time-resolved soft X-ray spectroscopy to pave a new way to study electronic and molecular dynamics of functional materials, thereby answering many interesting scientific questions in inorganic chemistry and material science.

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.

Dynamic structure elucidation of chemical reactivity by laser pulses and X-ray probes

Visualising chemical reactions by X-ray methods is a tantalising prospect. New light sources provide the prospect for studying atomic, electronic and energy transfers accompanying chemical change by X-ray spectroscopy and inelastic scattering. Here we assess how this adventure can illuminate inorganic and catalytic chemistry. In particular X-ray inelastic scattering provides a means of exploiting X-ray free electron lasers, as a parallel to laser Raman spectroscopy.

Nonadiabatic molecular dynamics simulations: synergies between theory and experiments

Recent developments in nonadiabatic dynamics enabled ab inito simulations of complex ultrafast processes in the condensed phase. These advances have opened new avenues in the study of many photophysical and photochemical reactions triggered by the absorption of electromagnetic radiation. In particular, theoretical investigations can be combined with the most sophisticated femtosecond experimental techniques to guide the interpretation of measured time-resolved observables. At the same time, the availability of experimental data at high (spatial and time) resolution offers a unique opportunity for the benchmarking and the improvement of those theoretical models used to describe complex molecular systems in their natural environment. The established synergy between theory and experiments can produce a better understanding of new ultrafast physical and chemical processes at atomistic scale resolution. Furthermore, reliable ab inito molecular dynamics simulations can already be successfully employed as predictive tools to guide new experiments as well as the design of novel and better performing materials. In this paper, I will give a concise account on the state of the art of molecular dynamics simulations of complex molecular systems in their excited states. The principal aim of this approach is the description of a given system of interest under the most realistic ambient conditions including all environmental effects that influence experiments, for instance, the interaction with the solvent and with external time-dependent electric fields, temperature, and pressure. To this end, time-dependent density functional theory (TDDFT) is among the most efficient and accurate methods for the representation of the electronic dynamics, while trajectory surface hopping gives a valuable representation of the nuclear quantum dynamics in the excited states (including nonadiabatic effects). Concerning the environment and its effects on the dynamics, the quantum mechanics/molecular mechanics (QM/MM) approach has the advantage of providing an atomistic (even though approximated) description of the solvent molecules, which is crucial for the characterization of all ultrafast relaxation phenomena that depend on the geometrical arrangement at the interface between a molecule and the solvent, for example, the hydrogen bond network. After a short description of the TDDFT-based implementation of Ehrenfest and trajectory surface hopping dynamics, I will present applications in different domains of molecular chemistry and physics: the analysis and the understanding of (time-resolved) X-ray absorption spectra, the interpretation of the ultrafast relaxation dynamics of photoexcited dyes in solution, and the design of specific laser pulses (capable of inducing desired chemical reactions) using local control theory.

Probing the electronic and geometric structure of ferric and ferrous myoglobins in physiological solutions by Fe K-edge absorption spectroscopy

We present an iron K-edge X-ray absorption study of carboxymyoglobin (MbCO), nitrosylmyoglobin (MbNO), oxymyoglobin (MbO2), cyanomyoglobin (MbCN), aquomet myoglobin (metMb) and unligated myoglobin (deoxyMb) in physiological media. The analysis of the XANES region is performed using the full-multiple scattering formalism, implemented within the MXAN package. This reveals trends within the heme structure, absent from previous crystallographic and X-ray absorption analysis. In particular, the iron-nitrogen bond lengths in the porphyrin ring converge to a common value of about 2 Å, except for deoxyMb whose bigger value is due to the doming of the heme. The trends of the Fe-Nε (His93) bond length is found to be consistent with the effect of ligand binding to the iron, with the exception of MbNO, which is explained in terms of the repulsive trans effect. We derive a high resolution description of the relative geometry of the ligands with respect to the heme and quantify the magnitude of the heme doming in the deoxyMb form. Finally, time-dependent density functional theory is used to simulate the pre-edge spectra and is found to be in good agreement with the experiment. The XAS spectra typically exhibit one pre-edge feature which arises from transitions into the unoccupied dσ and dπ - πligand* orbitals. 1s → dπ transitions contribute weakly for MbO2, metMb and deoxyMb. However, despite this strong Fe d contribution these transitions are found to be dominated by the dipole (1s → 4p) moment due to the low symmetry of the heme environment.

High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory

X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core-hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas-Kroll-Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD-XAS to complex catalytic systems.

Photooxidation and photoaquation of iron hexacyanide in aqueous solution: A picosecond X-ray absorption study

We present a picosecond Fe K-edge absorption study of photoexcited ferrous and ferric hexacyanide in water under 355 and 266 nm excitation. Following 355 nm excitation, the transient spectra for the ferrous and ferric complexes exhibit a red shift of the edge reflecting an increased electron density at the Fe atom. For the former, an enhanced pre-edge transition is also observed. These observations are attributed to the aquated [Fe(CN)5OH2](3-) species, based on quantum chemical calculations which also provide structural parameters. Upon 266 nm excitation of the ferric complex, a transient reminiscent of the aquated species is observed (appearance of a pre-edge feature and red shift of the edge) but it is different from that obtained under 355 nm excitation. This points to a new reaction channel occurring through an intermediate state lying between these two excitation energies. Finally, 266 nm excitation of the ferrous species is dominated by the photooxidation channel with formation of the ferric complex as main photoproduct. However, we observe an additional minor photoproduct, which is identical to the 266 nm generated photoproduct of the ferric species, suggesting that under our experimental conditions, the pump pulse photooxidises the ferrous complex and re-excites the primary ferric photoproduct.