Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

Spectroscopy of End-On Copper(II) Superoxido Complexes: A Wave Function-Based Analysis

Wave function methods are employed to analyze the ground and low-lying excited states of bipyramid trigonal copper(II) superoxido complexes, up to their characteristic ligand to metal charge transfer band. Several multireference methods have been combined to provide new insights into the interpretation of their experimental absorption spectra. We show that the intraligand transition on the dioxygen leads to a dark state. Among the results, we shall highlight the finding of doubly excited states in the region of the d-d transitions and the subtle interplay between Cu(I) and Cu(II) in the ground and excited states. Some of these findings could be obtained only with multireference methods.

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin-orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl6]3- and [Ce(IV)Cl6]2- complexes show that time-dependent density functional theory with approximate exchange-correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

Auger-Meitner and X-ray Absorption Spectra of Ethylene Cation: Insight into Conical Intersection Dynamics

We present a theoretical investigation of the near-edge X-ray absorption fine structure and the Auger-Meitner decay spectra of ethylene and its cation. Herein, we demonstrate that our method, coupled with the nuclear ensemble approach, successfully reproduces the natural bandwidth structure of the experimental resonant Auger-Meitner decay spectra of ethylene, which is not very well reproduced within the Franck-Condon approximation. Furthermore, we analyze the Auger-Meitner decay spectra of the ethylene cation in light of minimum energy conical intersection structures involving the two lowest cationic states (D1 and D0), providing valuable insights into the ultrafast D1/D0 relaxation dynamics. Our results suggest that Auger-Meitner electron spectroscopy can help elucidate the mechanism behind the initial 20 fs of the relaxation dynamics.

Time-Resolved X-ray Absorption Spectroscopy: An MCTDH Quantum Dynamics Protocol

Expressions for linear and nonlinear spectroscopy simulation in the X-ray window in which the time evolution of a photoexcited molecular system is treated via quantum dynamics are derived. By leveraging on the peculiar properties of core-excited/ionized states, first- and third-order response functions are recast in the limit of time-scale separation between the extremely short core-state lifetime and the (comparably longer) electronic-state transfer and nuclear vibrational motion. This work is a natural extension of Segatta et al. (J. Chem. Theory Comput. 2023, 19, 2075-2091), in which some of the present authors coupled MCTDH quantum dynamics to spectroscopy simulation at different levels of sophistication. Full quantum dynamics and approximate expressions are compared by simulating X-ray transient absorption spectroscopy at the carbon K-edge in the pyrene molecule.

Machine Learning-Based Screening for Potential Singlet Fission Chromophores: The Challenge of Imbalanced Data Sets

Excitation with one photon of a singlet fission (SF) material generates two triplet excitons, thus doubling the solar cell efficiency. Therefore, the SF molecules are regarded as new generation organic photovoltaics, but it is hard to identify them. Recently, it was demonstrated that molecules of low-to-intermediate diradical character (DRC) are potential SF chromophores. This prompts a low-cost strategy for finding new SF candidates by computational high-throughput workflows. We propose a machine learning aided screening for SF entrants based on their DRC. Our data set comprises 469 784 compounds extracted from the PubChem database, structurally rich but inherently imbalanced regarding DRC values. We developed well performing classification models that can retrieve potential SF chromophores. The latter (∼4%) were analyzed by K-means clustering to reveal qualitative structure-property relationships and to extract strategies for molecular design. The developed screening procedure and data set can be easily adapted for applications of diradicaloids in photonics and spintronics.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. 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.

Molecular Geometry and Electronic Structure of Copper Corroles

Copper corroles are known for their unique multiconfigurational electronic structures in the ground state, which arise from the transfer of electrons from the π orbitals of the corrole to the d-orbital of copper. While density functional theory (DFT) provides reasonably good molecular geometries, the determination of the ground spin state and the associated energetics is heavily influenced by functional choice, particularly the percentage of the Hartree-Fock exchange. Using extended multireference perturbation theory methods (XMS-CASPT2), the functional choice can be assessed. The molecular geometries and electronic structures of both the unsubstituted and the meso-triphenyl copper corroles were investigated. A minimal active space was employed for structural characterization, while larger active spaces are required to examine the electronic structure. The XMS-CASPT2 investigations conclusively identify the ground electronic state as a multiconfigurational singlet (S0) with three dominant electronic configurations in its lowest energy and characteristic saddled structure. In contrast, the planar geometry corresponds to the triplet state (T0), which is approximately 5 kcal/mol higher in energy compared to the S0 state for both the bare and substituted copper corroles. Notably, the planarity of the T0 geometry is reduced in the substituted corrole compared with that in the unsubstituted one. By analyzing the potential energy surface (PES) between the S0 and T0 geometries using XMS-CASPT2, the multiconfigurational electronic structure is shown to transition toward a single electron configuration as the saddling angle decreases (i.e., as one approaches the planar geometry). Despite the ability of the functionals to reproduce the minimum energy structures, only the TPSSh-D3 PES is reasonably close to the XMS-CASPT2 surface. Significant deviations along the PES are observed with other functionals.

The three kingdoms-Photoinduced electron transfer cascades controlled by electronic couplings

Excited states are the key species in photocatalysis, while the critical parameters that govern their applications are (i) excitation energy, (ii) accessibility, and (iii) lifetime. However, in molecular transition metal-based photosensitizers, there is a design tension between the creation of long-lived excited (triplet), e.g., metal-to-ligand charge transfer (3MLCT) states and the population of such states. Long-lived triplet states have low spin-orbit coupling (SOC) and hence their population is low. Thus, a long-lived triplet state can be populated but inefficiently. If the SOC is increased, the triplet state population efficiency is improved-coming at the cost of decreasing the lifetime. A promising strategy to isolate the triplet excited state away from the metal after intersystem crossing (ISC) involves the combination of transition metal complex and an organic donor/acceptor group. Here, we elucidate the excited state branching processes in a series of Ru(II)-terpyridyl push-pull triads by quantum chemical simulations. Scalar-relativistic time-dependent density theory simulations reveal that efficient ISC takes place along 1/3MLCT gateway states. Subsequently, competitive electron transfer (ET) pathways involving the organic chromophore, i.e., 10-methylphenothiazinyl and the terpyridyl ligands are available. The kinetics of the underlying ET processes were investigated within the semiclassical Marcus picture and along efficient internal reaction coordinates that connect the respective photoredox intermediates. The key parameter that governs the population transfer away from the metal toward the organic chromophore either by means of ligand-to-ligand (3LLCT; weakly coupled) or intra-ligand charge transfer (3ILCT; strongly coupled) states was determined to be the magnitude of the involved electronic coupling.

Are Actinyl Cations Good Probes for Structure Determination in Solution by NMR?

We report on NMR spectroscopy, CAS-based method calculations, and X-ray diffraction of An^V and An^VI complexes with a neutral and slightly flexible TEDGA ligand. After checking that pNMR shifts mainly arise from pseudocontact interactions, we analyze pNMR shifts considering the axial and rhombic anisotropy of the actinyl magnetic susceptibilities. The results are compared to those of a previous study performed on [An^VIO₂]²⁺ complexes with dipicolinic acid. It is shown that 5f² cations (Pu^VI and Np^V) make very good candidates for determining the structure of actinyl complexes in solution by ¹H NMR spectroscopy as shown by the invariance of the magnetic properties to the equatorial ligands, as opposed to the Np^VI complexes with a 5f¹ configuration.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

Adsorption energies on transition metal surfaces: towards an accurate and balanced description

Density functional theory predictions of binding energies and reaction barriers provide invaluable data for analyzing chemical transformations in heterogeneous catalysis. For high accuracy, effects of band structure and coverage, as well as the local bond strength in both covalent and non-covalent interactions, must be reliably described and much focus has been put on improving functionals to this end. Here, we show that a correction from higher-level calculations on small metal clusters can be applied to improve periodic band structure adsorption energies and barriers. We benchmark against 38 reliable experimental covalent and non-covalent adsorption energies and five activation barriers with mean absolute errors of 2.2 kcal mol^-1, 2.7 kcal mol^-1, and 1.1 kcal mol^-1, respectively, which are lower than for functionals widely used and tested for surface science evaluations, such as BEEF-vdW and RPBE.

Accurate computed singlet-triplet energy differences for cobalt systems: implication for two-state reactivity

Accurate singlet-triplet energy differences for cobalt and rhodium complexes were calculated by using several wave function methods, such as MRCISD, CASPT2, CCSD(T) and BCCD(T). Relaxed energy differences were obtained by considering the singlet and triplet complexes, each at the minimum of their potential energy surfaces. Active spaces for multireference calculations were carefully checked to provide accurate results. The considered systems are built by increasing progressively the first coordination sphere around the metal. We included in our set two CpCoX complexes (Cp = cyclopentadienyl, X = alkenyl ligand), which have been suggested as intermediates in cycloaddition reactions. Indeed, cobalt systems have been used for more than a decade as active species in this kind of transformations, for which a two-state reactivity has been proposed. Most of the considered systems display a triplet ground state. However, in the case of a reaction intermediate, while a triplet ground state was predicted on the basis of Density Functional Theory results, our calculations suggest a singlet ground state. This stems from the competition between the exchange term (stabilising the triplet) and the accessibility of an intramolecular coordination (stabilising the singlet). This finding has an impact on the general mechanism of the cycloaddition reaction. Analogous rhodium systems were also studied and, as expected, they have a larger tendency to electron pairing than cobalt species.

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).

Time-Resolved Optical Pump-Resonant X-ray Probe Spectroscopy of 4-Thiouracil: A Simulation Study

We theoretically monitor the photoinduced ππ* → nπ* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and nπ* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and nπ*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the nπ* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/nπ* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Photoionization Observables from Multi-Reference Dyson Orbitals Coupled to B-Spline DFT and TD-DFT Continuum

We present a theoretical model to compute the accurate photoionization dynamical parameters (cross-sections, asymmetry parameters and orbital, or cross-section, ratios) from Dyson orbitals obtained with the multi-state complete active space perturbation theory to the second order (MS-CASPT2) method. Our new implementation of Dyson orbitals in OpenMolcas takes advantage of the full Abelian symmetry point group and has the corrected normalization. The Dyson orbitals are coupled to an accurate description of the electronic continuum obtained with a multicentric B-spline basis at the DFT and TD-DFT levels. Two prototype diatomic molecules, i.e., CS and SiS, have been chosen due to their smallness, which hides important correlation effects. These effects manifest themselves in the appearance of well-characterized isolated satellite bands in the middle of the valence region. The rich satellite structures make CS and SiS the perfect candidates for a computational study based on our highly accurate MS-CASPT2/B-spline TD-DFT protocol.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the Equation of Motion Coupled Cluster Singles, Doubles and Perturbative Triples (EOM-CC3) method. Coupled to an accurate...

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

Relativistic Multiconfigurational Ab Initio Calculation of Uranyl 3d4f Resonant Inelastic X-ray Scattering

We applied relativistic multiconfigurational all-electron ab initio calculations including the spin-orbit interaction to calculate the 3d4f resonant inelastic X-ray scattering (RIXS) map (3d3/2 → 5f5/2 U M4 absorption edge and 4f5/2 → 3d3/2 U Mβ emission) of uranyl (UO22+). The calculated data are in excellent agreement with experimental results and allow a detailed understanding of the observed features and an unambiguous assignment of all involved intermediate and final states. The energies corresponding to the maxima of the resonant emission and the non-resonant (normal) emission were determined with high accuracy, and the corresponding X-ray absorption near edge structure spectra extracted at these two positions were simulated and agree well with the measured data. With the high quality of our theoretical data, we show that the cause of the splitting of the three main peaks in emission is due to the fine structure splitting of the 4f orbitals induced through the trans di-oxo bonds in uranyl and that we are able to obtain direct information about the energy differences between the 5f and 4f orbitals: Δ5f δ/ϕ - 4f δ/ϕ, Δ5f π* - 4f π, and Δ5f σ* - 4f σ from the 3d4f RIXS map. RIXS maps contain a wealth of information, and ab initio calculations facilitate an understanding of their complex structure in a clear and transparent way. With these calculations, we show that the multiconfigurational protocol, which is nowadays applied as a standard tool to study the X-ray spectra of transition metal complexes, can be extended to the calculation of RIXS maps of systems containing actinides.

NEXAFS and MS-AES spectroscopy of the C 1s and Cl 2p excitation and ionization of chlorobenzene: Production of dicationic species

We report on single- and double-charge photofragment formation by synchrotron radiation, following C 1s core excitation and ionization and Cl 2p inner excitation and ionization of chlorobenzene, C₆H₅Cl. From a comparison of experimental near-edge X-ray absorption fine structure spectra and theoretical ab initio calculations, the nature of various core and inner shell transitions of the molecule and pure atomic features were identified. To shed light on the normal Auger processes following excitation or ionization of the molecule at the Cl 2p or C 1s sites, we addressed the induced ionic species formation. With energy resolved electron spectra and ion time-of-flight spectra coincidence measurements, the ionic species were correlated with binding energy regions and initial states of vacancies. We explored the formation of the molecular dication C₆H₅Cl²⁺, the analogue benzene dication C₆H₄²⁺, and the singly charged species produced by single loss of a carbon atom, C₅H_nCl⁺. The appearance and intensities of the spectral features associated with these ionic species are shown to be strongly site selective and dependent on the energy ranges of the Auger electron emission. Unexpected intensities for the analogue double charged benzene C₆H₄²⁺ ion were observed with fast Auger electrons. The transitions leading to C₆H₅Cl²⁺ were identified from the binding energy representation of high resolution electron energy spectra. Most C₆H₅Cl²⁺ ions decay into two singly charged moieties, but intermediate channels are opened leading to other heavy dicationic species, C₆H₄²⁺ and C₆H₄Cl²⁺, the channel leading to the first of these being much more favored than the other.

In Silico Ultrafast Nonlinear Spectroscopy Meets Experiments: The Case of Perylene Bisimide Dye

Spectroscopy simulations are of paramount importance for the interpretation of experimental electronic spectra, the disentangling of overlapping spectral features, and the tracing of the microscopic origin of the observed signals. Linear and nonlinear simulations are based on the results drawn from electronic structure calculations that provide the necessary parameterization of the molecular systems probed by light. Here, we investigate the applicability of excited-state properties obtained from linear-response time-dependent density functional theory (TDDFT) in the description of nonlinear spectra by employing the pseudowavefunction approach and compare them with benchmarks from highly accurate RASSCF/RASPT2 calculations and with high temporal resolution experimental results. As a test case, we consider the prediction of femtosecond transient absorption and two-dimensional electronic spectroscopy of a perylene bisimide dye in solution. We find that experimental signals are well reproduced by both theoretical approaches, showing that the computationally cheaper TDDFT can be a suitable option for the simulation of nonlinear spectroscopy of molecular systems that are too large to be treated with higher-level RASSCF/RASPT2 methods.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S₂ (ππ*) and S₁ (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N²) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

Actinide arene-metalates: ion pairing effects on the electronic structure of unsupported uranium-arenide sandwich complexes

Addition of [UI₂(THF)₃(μ-OMe)]₂·THF (2·THF) to THF solutions containing 6 equiv. of K[C₁₄H₁₀] generates the heteroleptic dimeric complexes [K(18-crown-6)(THF)₂]₂[U(η⁶-C₁₄H₁₀)(η⁴-C₁₄H₁₀)(μ-OMe)]₂·4THF (118C6·4THF) and {[K(THF)₃][U(η⁶-C₁₄H₁₀)(η⁴-C₁₄H₁₀)(μ-OMe)]}₂ (1THF) upon crystallization of the products in THF in the presence or absence of 18-crown-6, respectively. Both 118C6·4THF and 1THF are thermally stable in the solid-state at room temperature; however, after crystallization, they become insoluble in THF or DME solutions and instead gradually decompose upon standing. X-ray diffraction analysis reveals 118C6·4THF and 1THF to be structurally similar, possessing uranium centres sandwiched between bent anthracenide ligands of mixed tetrahapto and hexahapto ligation modes. Yet, the two complexes are distinguished by the close contact potassium-arenide ion pairing that is seen in 1THF but absent in 118C6·4THF, which is observed to have a significant effect on the electronic characteristics of the two complexes. Structural analysis, SQUID magnetometry data, XANES spectral characterization, and computational analyses are generally consistent with U(iv) formal assignments for the metal centres in both 118C6·4THF and 1THF, though noticeable differences are detected between the two species. For instance, the effective magnetic moment of 1THF (3.74 μ_B) is significantly lower than that of 118C6·4THF (4.40 μ_B) at 300 K. Furthermore, the XANES data shows the U L_III-edge absorption energy for 1THF to be 0.9 eV higher than that of 118C6·4THF, suggestive of more oxidized metal centres in the former. Of note, CASSCF calculations on the model complex {[U(η⁶-C₁₄H₁₀)(η⁴-C₁₄H₁₀)(μ-OMe)]₂}²⁻ (1*) shows highly polarized uranium–arenide interactions defined by π-type bonds where the metal contributions are primarily comprised by the 6d-orbitals (7.3 ± 0.6%) with minor participation from the 5f-orbitals (1.5 ± 0.5%). These unique complexes provide new insights into actinide–arenide bonding interactions and show the sensitivity of the electronic structures of the uranium atoms to coordination sphere effects.

Use of Chatt metal-arene protocols with uranium leads to the synthesis of the first well-characterized, unsupported actinide–arenide sandwich complexes. The electronic structures of the actinide centres show a key sensitivity to ion pairing effects.

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.

Reactions of U+ with H2, D2, and HD Studied by Guided Ion Beam Tandem Mass Spectrometry and Theory

The kinetic energy-dependent reactions of the atomic actinide uranium cation (U⁺) with H₂, D₂, and HD were examined by guided ion beam tandem mass spectrometry. An average 0 K bond dissociation energy of D₀(U⁺ - H) = 2.48 ± 0.06 eV is obtained by analysis of the endothermic product ion cross sections. Quantum chemistry calculations were performed for comparison with experimental thermochemistry, including high-level CASSCF-CASPT2-RASSI calculations of the spin-orbit corrections. CCSD(T) and the CASSCF levels show excellent agreement with experiment, whereas B3LYP and PBE0 slightly overestimate and the M06 approach badly underestimates the bond energy for UH⁺. Theory was also used to investigate the electronic structures of the reaction intermediates and potential energy surfaces. The experimental product branching ratio for the reaction of U⁺ with HD indicates that these reactions occur primarily via a direct reaction mechanism, despite the presence of a deep-well for UH₂⁺ formation according to theory. The reactivity and hydride bond energy for U⁺ are compared with those for transition metal, lanthanide, and actinide cations, and periodic trends are discussed. These comparisons suggest that the 5f electrons on uranium are largely core and uninvolved in the reactive chemistry.

Toward an Accurate Ab Initio Description of Low-Lying Singlet Excited States of Polyenes

The low-lying excited states of carotenoids play a crucial role in many important biophysical processes such as photosynthesis. Most of these excited states are strongly correlated, which makes them both challenging for a qualitative ab initio description and an engaging model system for trying out emerging multireference methods. Among these methods, driven similarity renormalization group (DSRG) and its perturbative version (DSRG-MRPT2) are especially attractive in terms of both accuracy and moderate numerical complexity. In this paper, we applied density matrix renormalization group (DMRG) followed by DSRG-MRPT2 for the calculation of vertical and adiabatic excitation energies into the 2A_g^-, 1B_u^-, and 1B_u⁺ electronic states of polyenes containing from 8 to 13 conjugating double bonds acting as a model for natural carotenoids. It was shown that the DSRG flow parameter should be adjusted to ensure both the energy convergence with respect to it and the agreement with the experimental data. With the increased flow parameter, the proposed combination of methods provides a reasonable agreement with the experiment. The deviations of the adiabatic excitation energies are less than 1000 cm^-1 for the 2A_g^- and less than 3000 cm^-1 for the excited states of the B_u symmetry, which in terms of accuracy significantly outperforms the N-electron valence state perturbation theory. At the same time, DSRG-MRPT2 is shown to be robust with respect to variation of quality of the DMRG reference wave function such as the orbital optimization or the number of electronic states in the averaging.

EPR of Photoexcited Triplet-State Acceptor Porphyrins

The photoexcited triplet states of porphyrin architectures are of significant interest in a wide range of fields including molecular wires, nonlinear optics, and molecular spintronics. Electron paramagnetic resonance (EPR) is a key spectroscopic tool in the characterization of these transient paramagnetic states singularly well suited to quantify spin delocalization. Previous work proposed a means of extracting the absolute signs of the zero-field splitting (ZFS) parameters, D and E, and triplet sublevel populations by transient continuous wave, hyperfine measurements, and magnetophotoselection. Here, we present challenges of this methodology for a series of meso-perfluoroalkyl-substituted zinc porphyrin monomers with orthorhombic symmetries, where interpretation of experimental data must proceed with caution and the validity of the assumptions used in the analysis must be scrutinized. The EPR data are discussed alongside quantum chemical calculations, employing both DFT and CASSCF methodologies. Despite some success of the latter in quantifying the magnitude of the ZFS interaction, the results clearly provide motivation to develop improved methods for ZFS calculations of highly delocalized organic triplet states.

Ultrafast strong-field dissociation of vinyl bromide: An attosecond transient absorption spectroscopy and non-adiabatic molecular dynamics study

Attosecond extreme ultraviolet (XUV) and soft x-ray sources provide powerful new tools for studying ultrafast molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy (ATAS) to follow strong-field-initiated dynamics in vinyl bromide. Probing the Br M edge allows one to assess the competing processes in neutral and ionized molecular species. Using ab initio non-adiabatic molecular dynamics, we simulate the neutral and cationic dynamics resulting from the interaction of the molecule with the strong field. Based on the dynamics results, the corresponding time-dependent XUV transient absorption spectra are calculated by applying high-level multi-reference methods. The state-resolved analysis obtained through the simulated dynamics and related spectral contributions enables a detailed and quantitative comparison with the experimental data. The main outcome of the interaction with the strong field is unambiguously the population of the first three cationic states, D ₁, D ₂, and D ₃. The first two show exclusively vibrational dynamics while the D ₃ state is characterized by an ultrafast dissociation of the molecule via C-Br bond rupture within 100 fs in 50% of the analyzed trajectories. The combination of the three simulated ionic transient absorption spectra is in excellent agreement with the experimental results. This work establishes ATAS in combination with high-level multi-reference simulations as a spectroscopic technique capable of resolving coupled non-adiabatic electronic-nuclear dynamics in photoexcited molecules with sub-femtosecond resolution.

Temperature Dependence of 1 H Paramagnetic Chemical Shifts in Actinide Complexes, Beyond Bleaney's Theory: The AnVI O2 2+ -Dipicolinic Acid Complexes (An=Np, Pu) as an Example

Actinide +VI complexes ( A n V I = U V I , N p V I and P u V I ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, N p V I and P u V I complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹ H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans' method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the N p V I complex. The temperature dependence of the pNMR chemical shifts has a strong 1 / T contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the N p V I complex and a non-Kramers-doublet model for the P u V I complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.

Interpretation of photoelectron spectra of CoGen- (n = 4, 5) clusters by multiconfigurational RASPT2 calculations

The low-lying electronic states CoGe_n^-/0 (n = 4, 5) have been investigated with density functional theory and the state-of-the-art RASSCF/RASPT2 method to give assignments for the anion photoelectron spectra. The BP86 functional was employed to optimize the geometrical structures of the electronic states, while the RASSCF/RASPT2 was applied to calculate the single-point energies. With the RASSCF/RASPT2 approach, the active spaces are extended to a size of 21 orbitals for CoGe₄^-/0 and 24 orbitals for CoGe₅^-/0. The ground states of CoGe₄^-/0 are determined to be ³A″ and ²A″ of a trigonal bipyramidal structure in which the Co atom is situated at the equatorial corner of the bipyramid. The vertical detachment energies of the transitions from the anionic ground state to the neutral ²A″, 1⁴A″, ²A', 2⁴A″, 3⁴A″, 1⁴A', 2⁴A', and 6⁴A″ states are evaluated to be 2.29, 2.39, 2.60, 2.83, 3.17, 3.24, 3.47, and 4.00 eV. For the CoGe₅^-/0 clusters, the ground states are computed to be ¹A₁ and 1²A₂ of an octahedral structure. The vertical detachment energies of the removal of one electron from the anionic ground state to result in the 1²A₂, 1²A₁, 2²A₁, 1²B₁, 1²B₂, 4²B₁, 4²B₂, and 6²A₂ states are estimated to be 2.16, 2.79, 2.84, 3.06, 3.06, 3.59, 3.59, and 4.22 eV. All features in the photoelectron spectra of CoGe₄^- and CoGe₅^- are interpreted based on the computed electron detachment energies of the anionic ground states.

Multi- and single-reference methods for the analysis of multi-state peroxidation of enolates

In spite of being spin-forbidden, some enzymes are capable of catalyzing the incorporation of O₂(Σg-3) to organic substrates without needing any cofactor. It has been established that the process followed by these enzymes starts with the deprotonation of the substrate forming an enolate. In a second stage, the peroxidation of the enolate formation occurs, a process in which the system changes its spin multiplicity from a triplet state to a singlet state. In this article, we study the addition of O₂ to enolates using state-of-the-art multi-reference and single-reference methods. Our results confirm that intersystem crossing is promoted by stabilization of the singlet state along the reaction path. When multi-reference methods are used, large active spaces are required, and in this situation, semistochastic heat-bath configuration interaction emerges as a powerful method to study these multi-configurational systems and is in good agreement with PNO-LCCSD(T) when the system is well-represented by a single-configuration.

Parameterization of a linear vibronic coupling model with multiconfigurational electronic structure methods to study the quantum dynamics of photoexcited pyrene

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S₂ or S₅). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S₅, whose ultrafast deactivation mechanism was not yet clearly understood.

Manipulating Core Excitations in Molecules by X-Ray Cavities

Core excitations on different atoms are highly localized and therefore decoupled. By placing molecules in an x-ray cavity the core transitions become coupled via the exchange of cavity photons and form delocalized hybrid light-matter excitations known as core polaritons. We demonstrate these effects for the two inequivalent carbon atoms in 1,1-difluoroethylene. Polariton signatures in the x-ray absorption, two-photon absorption, and multidimensional four-wave mixing signals are predicted.

Bioinspired Nickel Complexes Supported by an Iron Metalloligand

Nature utilizes multimetallic sites in metalloenzymes to enable multielectron chemical transformations at ambient conditions and low overpotentials. One such example of multimetallic cooperativity can be found in the C-cluster of Ni-carbon monoxide dehydrogenase (CODH), which interconverts CO and CO₂. Toward a potential functional model of the C-cluster, a family of Ni-Fe bimetallic complexes was synthesized that contain direct metal-metal bonding interactions. The complexes were characterized by X-ray crystallography, various spectroscopies (NMR, EPR, UV-vis, Mössbauer), and theoretical calculations. The Ni-Fe bimetallic system has a reversible Fe(III)/Fe(II) redox couple at -2.10 V (vs Fc⁺/Fc). The Fe-based "redox switch" can turn on CO₂ reactivity at the Ni(0) center by leveraging the Ni→Fe dative interaction to attenuate the Ni(0) electron density. The reduced Ni(0)Fe(II) species mediated the formal two-electron reduction of CO₂ to CO, providing a Ni-CO adduct and CO₃^2- as products. During the reaction, an intermediate was observed that is proposed to be a Ni-CO₂ species.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

DFT Study on the Catalytic Activity of ALD-Grown Diiron Oxide Nanoclusters for Partial Oxidation of Methane to Methanol

Using density functional theory (DFT), we studied the catalytic activity of iron oxide nanoclusters that mimic the structure of the active site in the soluble form of methane monooxygenase (sMMO) for the partial oxidation of methane to methanol. Using N₂O as the oxidant, we consider a radical-rebound mechanism and a concerted mechanism for the oxidation of methane on either a bridging oxygen (O_b) or a terminal oxygen (O_t) active site. We find that the radical-rebound pathway is preferred over the concerted pathway by 40-50 kJ/mol, but the desorption of methanol and the regeneration of the oxygen site are found to be the highest barriers for the direct conversion of methane to methanol with these catalysts. As demonstrated by a population analysis, the O_x (x = b or t) site behaves as an oxygen radical during the H abstraction, and the [Fe⁺-O_x^-] site behaves as a Lewis acid-base pair during the concerted C-H cleavage. Molecular orbital decomposition analysis further demonstrates electron transfer during the oxidation and reduction steps of the reaction. High-level multireference calculations were also carried out to further assess the DFT results. Understanding how these systems behave during the proposed reaction pathways provides new insights into how they can be tuned for methane partial oxidation.

Boron-Doped Polycyclic Aromatic Hydrocarbons: A Molecular Set Revealing the Interplay between Topology and Singlet Fission Propensity

We demonstrate the relationship between the topology (the way in which the atoms are connected), open-shell character, and singlet fission (SF) propensity in a series of diboron-doped anthracenes and phenanthrenes. The study is performed by using high-level wave-function-based quantum-chemical calculations. The results show that the molecular topology plays a crucial role for the optical properties and, respectively, for the SF propensity of the studied compounds. The topology-derived correlations between the structure and properties are interpreted in the light of the Kekulé hydrocarbons concept and serve as molecular design guidelines for the discovery of new SF materials. Finally, several boron-doped polycyclic aromatic hydrocarbons are proposed as SF chromophores for organic solar cells.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

Following our previous work focusing on compounds containing up to 3 non-hydrogen atoms [J. Chem. Theory Comput. 2018, 14, 4360-4379], we present here highly accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. To obtain these energies, we use equation-of-motion/linear-response coupled cluster theory up to the highest technically possible excitation order for these systems (CC3, EOM-CCSDT, and EOM-CCSDTQ) and selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational n-electron valence state perturbation theory (NEVPT2) method. All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/aug-cc-pVQZ vertical excitation energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level methods with a typical deviation of ±0.04 eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse, and accurate set of more than 200 highly accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, n → π*, π → π*, ...). We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, CC3, and NEVPT2. The results of these benchmarks are compared to the available literature data.

Exploring the capabilities of optical pump X-ray probe NEXAFS spectroscopy to track photo-induced dynamics mediated by conical intersections

In the present contribution we introduce an accurate theoretical approach for the simulation of NEXAFS spectra of organic molecules, employing azobenzene as a test case.

A combined multi-reference pump-probe simulation method with application to XUV signatures of ultrafast methyl iodide photodissociation

UV pump-XUV/X-ray probe measurements have been successfully applied in the study of photo-induced chemical reactions. Although rich element-specific electronic structure information is accessible within XUV/X-ray (inner-shell) absorption spectra, it can be difficult to interpret the chemistry directly from the spectrum without supporting theoretical simulations. A multireference method to completely simulate UV pump-XUV/X-ray probe measurement has been developed and applied to study the methyl iodide photodissociation process. Multireference, fewest-switches surface hopping (FSSH) trajectories were used to explore the coupled electronic and ionic dynamics upon photoexcitation of methyl iodide. Interpretation of previous measurements is provided by associated multireference, restricted active space, inner-shell spectral simulations. This combination of multireference FSSH trajectories and XUV spectra provides an interpretation of transient features appearing in previous measurements within the first 100 fs after photoexcitation and validates the significant branching ratio in the final excited-state population. This methodology should prove useful for interpretation of the increasing number of inner-shell probe studies of molecular excited states or for directing new experiments toward interesting regions of the potential energy landscape.