Spin-flip dynamics in core-excited states in the basis of irreducible spherical tensor operators.

Recent experimental advances in ultrafast science have put different processes occurring on the electronic timescale below a few femtoseconds in focus. In the present theoretical work, we demonstrate how the transformation and propagation of the density matrix in the basis of irreducible spherical tensors can be conveniently used to study sub-few fs spin-flip dynamics in core-excited transition metal compounds. With the help of the Wigner-Eckart theorem, such a transformation separates the essential dynamical information from the geometric factors governed by the angular momentum algebra. We show that an additional reduction can be performed by the physically motivated truncation of the spherical tensor basis. In particular, depending on the degree of coherence, the ultrafast dynamics can be considered semi-quantitative in the notably reduced spherical basis when only the total populations of the basis states of the given spin are of interest. Such truncation should be especially beneficial when the number of high-spin basis states is vast, as it reduces computational costs.

Valence and Core Photoelectron Spectra of Aqueous I3- from Multi-Reference Quantum Chemistry.

The I3- molecule is known to undergo substantial structural reorganization upon solvation by a protic solvent, e.g., water. However, the details of this process are still controversially discussed in the literature. In the present study, we combined experimental and theoretical efforts to disentangle this controversy. The valence (5p), N4,5 (4d), and M4,5 (3d) edge photoelectron spectra were measured in an aqueous solution and computed using high-level multi-reference methods. Our previous publication mainly focused on obtaining reliable experimental evidence, whereas in the present article, we focused primarily on theoretical aspects. The complex electronic structure of I3- requires the inclusion of both static and dynamic correlation, e.g., via the multi-configurational perturbation theory treatment. However, the resulting photoelectron spectra appear to be very sensitive to problems with variational stability and intruder states. We attempted to obtain artifact-free spectra, allowing for a more reliable interpretation of experiments. Finally, we concluded that the 3d Photoelectron Spectrum (PES) is particularly informative, evidencing an almost linear structure with a smaller degree of bond asymmetry than previously reported.

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

A Multiconfigurational Wave Function Implementation of the Frenkel Exciton Model for Molecular Aggregates.

We present an implementation of the Frenkel exciton model into the OpenMolcas program package enabling calculations of collective electronic excited states of molecular aggregates based on a multiconfigurational wave function description of the individual monomers. The computational protocol avoids using diabatization schemes and, thus, supermolecule calculations. Additionally, the use of the Cholesky decomposition of the two-electron integrals entering pair interactions enhances the efficiency of the computational scheme. The application of the method is exemplified for two test systems, that is, a formaldehyde oxime and a bacteriochlorophyll-like dimer. For the sake of comparison with the dipole approximation, we restrict our considerations to situations where intermonomer exchange can be neglected. The protocol is expected to be beneficial for aggregates composed of molecules with extended π systems, unpaired electrons such as radicals or transition metal centers, where it should outperform widely used methods based on time-dependent density functional theory.

Can range-separated functionals be optimally tuned to predict spectra and excited state dynamics in photoactive iron complexes?

Density functional theory is an efficient computational tool to investigate photophysical and photochemical processes in transition metal complexes, giving invaluable assistance in interpreting spectroscopic and catalytic experiments. Optimally tuned range-separated functionals are particularly promising, as they were created to address some of the fundamental deficiencies present in approximate exchange-correlation functionals. In this paper, we scrutinize the selection of optimally tuned parameters and its influence on the excited state dynamics, using the example of the iron complex [Fe(cpmp)2]2+ with push-pull ligands. Various tuning strategies are contemplated based on pure self-consistent DFT protocols, as well as on the comparison with experimental spectra and multireference CASPT2 results. The two most promising sets of optimal parameters are then employed to carry out nonadiabatic surface-hopping dynamics simulations. Intriguingly, we find that the two sets lead to very different relaxation pathways and timescales. While the set of optimal parameters from one of the self-consistent DFT protocols predicts the formation of long-lived metal-to-ligand charge transfer triplet states, the set in better agreement with CASPT2 calculations leads to deactivation in the manifold of metal-centered states, in better agreement with the experimental reference data. These results showcase the complexity of iron-complex excited state landscapes and the difficulty of obtaining an unambiguous parametrization of long-range corrected functionals without experimental input.

Multireference Approach to Normal and Resonant Auger Spectra Based on the One-Center Approximation.

A methodology to calculate the decay rates of normal and resonant Auger processes in atoms and molecules based on the One-Center Approximation (OCA), using atomic radial Auger integrals, is implemented within the restricted-active-space self-consistent-field (RASSCF) and the multistate restricted-active-space perturbation theory of second order (MS-RASPT2) frameworks, as part of the OpenMolcas project. To ensure an unbiased description of the correlation and relaxation effects on the initial core excited/ionized states and the final cationic states, their wave functions are optimized independently, whereas the Auger matrix elements are computed with a biorthonormalized set of molecular orbitals within the state-interaction (SI) approach. As a decay of an isolated resonance, the computation of Auger intensities involves matrix elements with one electron in the continuum. However, treating ionization and autoionization problems can be overwhelmingly complicated for nonexperts, because of many peculiarities, in comparison to bound-state electronic structure theory. One of the advantages of our approach is that by projecting the intensities on the atomic center bearing the core hole and using precalculated atomic radial two-electron integrals, the Auger decay rates can be easily obtained directly with OpenMolcas, avoiding the need to interface it with external programs to compute matrix elements with the photoelectron wave function. The implementation is tested on the Ne atom, for which numerous theoretical and experimental results are available for comparison, as well as on a set of prototype closed- and open-shell molecules, namely, CO, N2, HNCO, H2O, NO2, and C4N2H4 (pyrimidine).

Probing the molecular structure of aqueous triiodide via X-ray photoelectron spectroscopy and correlated electron phenomena.

Liquid-microjet-based X-ray photoelectron spectroscopy was applied to aqueous triiodide solutions, I3-(aq.), to investigate the anion's valence- and core-level electronic structure, ionization dynamics, associated electron-correlation effects, and nuclear geometric structure. The roles of multi-active-electron (shake-up) ionization processes - with noted sensitivity to the solute geometric structure - were investigated through I3-(aq.) solution valence, I 4d, and I 3d core-level measurements. The experimental spectra were interpreted with the aid of simulated photoelectron spectra, built upon multi-reference ab initio electronic structure calculations associated with different I3-(aq.) molecular geometries. A comparison of the single-to-multi-active-electron ionization signal ratios extracted from the experimental and theoretical core-level photoemission spectra suggests that the ground state of the solute adopts a near-linear average geometry in aqueous solutions. This contrasts with the interpretation of time-resolved X-ray solution scattering studies, but is found to be fully consistent with the rest of the solution-phase I3-(aq.) literature. Comparing the results of low- and high-photon-energy photoemission measurements, we further suggest that the aqueous anion adopts a more asymmetric geometry at the aqueous-solution-gas interface than in the aqueous bulk.

RhoDyn: A ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules.

This article presents the program module RhoDyn as part of the OpenMOLCAS project intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework (ρ-TD-RASCI). The formalism allows for the treatment of spin-orbit coupling effects, accounts for nuclear vibrations in the form of a vibrational heat bath, and naturally incorporates (auto)ionization effects. Apart from describing the theory behind and the program workflow, the paper also contains examples of its application to the simulations of the linear L2,3 absorption spectra of a titanium complex, high harmonic generation in the hydrogen molecule, ultrafast charge migration in benzene and iodoacetylene, and spin-flip dynamics in the core excited states of iron complexes.

Site-Selective Real-Time Observation of Bimolecular Electron Transfer in a Photocatalytic System Using L-Edge X-Ray Absorption Spectroscopy*.

Time-resolved X-ray absorption spectroscopy has been utilized to monitor the bimolecular electron transfer in a photocatalytic water splitting system. This has been possible by uniting the local probe and element specific character of X-ray transitions with insights from high-level ab initio calculations. The specific target has been a heteroleptic [IrIII (ppy)2 (bpy)]+ photosensitizer, in combination with triethylamine as a sacrificial reductant and Fe3(CO)12 as a water reduction catalyst. The relevant molecular transitions have been characterized via high-resolution Ir L-edge X-ray absorption spectroscopy on the picosecond time scale and restricted active space self-consistent field calculations. The presented methods and results will enhance our understanding of functionally relevant bimolecular electron transfer reactions and thus will pave the road to rational optimization of photocatalytic performance.

Effect of chemical structure on the ultrafast spin dynamics in core-excited states.

Recent developments of the sources of intense and ultrashort x-ray pulses stimulate theoretical studies of phenomena occurring on ultrafast timescales. In the present study, spin-flip dynamics in transition metal complexes triggered by sub-femtosecond x-ray pulses are addressed theoretically using a density matrix-based time-dependent configuration interaction approach. The influence of different central metal ions and ligands on the character and efficiency of spin-flip dynamics is put in focus. According to our results, slight variations in the coordination sphere do not lead to qualitative differences in dynamics, whereas the nature of the central ion is more critical. However, the behavior in a row of transition metals demonstrates trends that are not consistent with general expectations. Thus, the peculiarities of spin dynamics have to be analyzed on a case-by-case basis.

Multi-reference protocol for (auto)ionization spectra: Application to molecules.

We present the application of the spherically averaged continuum model to the evaluation of molecular photoelectron and resonant Auger electron spectra. In this model, the continuum wave function is obtained in a numerically efficient way by solving the radial Schrödinger equation with a spherically averaged molecular potential. Different approximations to the Auger transition matrix element and, in particular, the one-center approximation are thoroughly tested against experimental data for the CH4, O2, NO2, and pyrimidine molecules. In general, this approach appears to estimate the shape of the photoelectron and autoionization spectra as well as the total Auger decay rates with reasonable accuracy, allowing for the interpretation of experimental results.

OpenMolcas: From Source Code to Insight.

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

Simulating vibronic spectra via Matsubara-like dynamics: Coping with the sign problem.

Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.

Erratum: Ultrafast Spin-State Dynamics in Transition-Metal Complexes Triggered by Soft-X-Ray Light [Phys. Rev. Lett. 118, 023001 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.023001.

Photoelectron shake-ups as a probe of molecular symmetry: 4d XPS analysis of I3- in solution.

A combination of multi-configurational restricted active space calculations with a Dyson orbital formalism has been applied for accurate simulations of 4d photo-electron spectra of the I3- molecular ion. The analysis based on the occupation numbers of natural orbitals allowed to predict and rationalize the spectral fingerprints of solvent-induced nuclear asymmetry. In particular, it demonstrates how the nuclear asymmetry directly causes an increase of shake-up intensity. The relative intensity of shake-up and main features of the I 4d XPS spectrum could therefore serve as a simplified experimental observable of structural asymmetry, complementary to changes in the shape of the main spectral features.

Quasi-classical approaches to vibronic spectra revisited.

The framework to approach quasi-classical dynamics in the electronic ground state is well established and is based on the Kubo-transformed time correlation function (TCF), being the most classical-like quantum TCF. Here we discuss whether the choice of the Kubo-transformed TCF as a starting point for simulating vibronic spectra is as unambiguous as it is for vibrational ones. Employing imaginary-time path integral techniques in combination with the interaction representation allowed us to formulate a method for simulating vibronic spectra in the adiabatic regime that takes nuclear quantum effects and dynamics on multiple potential energy surfaces into account. Further, a generalized quantum TCF is proposed that contains many well-established TCFs, including the Kubo one, as particular cases. Importantly, it also provides a framework to construct new quantum TCFs. Applying the developed methodology to the generalized TCF leads to a plethora of simulation protocols, which are based on the well-known TCFs as well as on new ones. Their performance is investigated on 1D anharmonic model systems at finite temperatures. It is shown that the protocols based on the new TCFs may lead to superior results with respect to those based on the common ones. The strategies to find the optimal approach are discussed.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy.

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

Ultrafast kinetics of linkage isomerism in Na2[Fe(CN)5NO] aqueous solution revealed by time-resolved photoelectron spectroscopy.

The kinetics of ultrafast photoinduced structural changes in linkage isomers is investigated using Na2[Fe(CN)5NO] as a model complex. The buildup of the metastable side-on configuration of the NO ligand, as well as the electronic energy levels of ground, excited, and metastable states, has been revealed by means of time-resolved extreme UV (XUV) photoelectron spectroscopy in aqueous solution, aided by theoretical calculations. Evidence of a short-lived intermediate state in the isomerization process and its nature are discussed, finding that the complete isomerization process occurs in less than 240 fs after photoexcitation.

Light-induced relaxation dynamics of the ferricyanide ion revisited by ultrafast XUV photoelectron spectroscopy.

Photoinduced charge transfer in transition-metal coordination complexes plays a prominent role in photosynthesis and is fundamental for light-harvesting processes in catalytic materials. However, revealing the relaxation pathways of charge separation remains a very challenging task because of the complexity of relaxation channels and ultrashort time scales. Here, we employ ultrafast XUV photoemission spectroscopy to monitor fine mechanistic details of the electron dynamics following optical ligand-to-metal charge-transfer excitation of ferricyanide in aqueous solution. XUV probe light with a time resolution of 100 fs, in combination with density functional theory employing the Dyson orbital formalism, enabled us to decipher the primary and subsequently populated electronic states involved in the relaxation, as well as their energetics on sub-picosecond timescales. We find strong evidence for the spin crossover followed by geometrical distortions due to vibronic interactions (Jahn-Teller effect) in the excited electronic states, rather than localization/delocalization dynamics, as suggested previously.

Nuclear Dynamical Correlation Effects in X-ray Spectroscopy from a Theoretical Time-Domain Perspective.

To date X-ray spectroscopy has become a routine tool that can reveal highly local and element-specific information on the electronic structure of atoms in complex environments. Here, we focus on nuclear dynamical correlation effects in X-ray spectra and develop a rigorous time-correlation function method employing ground state classical molecular dynamics simulations. The importance of nuclear correlation phenomena is demonstrated by comparison against the results from the conventional sampling approach performed on the same data set for gas phase water. In contrast to the first-order absorption, second-order resonant inelastic scattering spectra exhibit pronounced fingerprints of nuclear motions. The developed methodology is not biased to a particular electronic structure method and, owing to its generality, can be applied to, e.g., X-ray photoelectron and Auger spectroscopies.