A perturbation‐based super‐CI approach for the orbital optimization of a CASSCF wave function

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

Isolation and characterization of a triplet nitrene

Nitrene radical compounds are short-lived intermediates in a variety of nitrogen-involved transformations. They feature either a singlet or a triplet ground state, depending on the electronic properties of the substituents. Triplet nitrenes are highly reactive and their isolation in the condensed phase under ambient conditions is challenging. Here we report the synthesis and isolation of a triplet arylnitrene supported by a bulky hydrindacene ligand. The arylnitrene is fully characterized by various spectroscopic and structural techniques including electron paramagnetic resonance spectroscopy and single-crystal X-ray diffraction. Its high stability is largely attributed to the steric hindrance and effective electron delocalization provided by the supporting ligand. Electron paramagnetic resonance spectroscopy in conjunction with highly correlated wavefunction-based ab initio calculations provides support for a triplet ground state nitrene with axial zero-field splitting D = 0.92 cm-1 and vanishing rhombicity E/D = 0.002.

cis-Dihydroxylation by Synthetic Iron(III)-Peroxo Intermediates and Rieske Dioxygenases: Experimental and Theoretical Approaches Reveal the Key O-O Bond Activation Step

Dioxygen (O2) activation by iron-containing enzymes and biomimetic compounds generates iron-oxygen intermediates, such as iron-superoxo, -peroxo, -hydroperoxo, and -oxo, that mediate oxidative reactions in biological and abiological systems. Among the iron-oxygen intermediates, iron(III)-peroxo species are less frequently implicated as active intermediates in oxidation reactions. In this study, we present the combined experimental and theoretical investigations on cis-dihydroxylation reactions mediated by synthetic mononuclear nonheme iron-peroxo intermediates, demonstrating the importance of supporting ligands and metal centers in activating the peroxo ligand toward the O-O bond homolysis for the cis-dihydroxylation reactions. We found a significant ring size effect of the TMC ligand in [FeIII(O2)(n-TMC)]+ (TMC = tetramethylated tetraazacycloalkane; n = 12, 13, and 14) on the cis-dihydroxylation reactivity order: [FeIII(O2)(12-TMC)]+ > [FeIII(O2)(13-TMC)]+ > [FeIII(O2)(14-TMC)]+. Additionally, we found that only [FeIII(O2)(n-TMC)]+, but not other metal-peroxo complexes such as [MIII(O2)(n-TMC)]+ (M = Mn, Co, and Ni), is reactive for the cis-dihydroxylation of olefins. Using density functional theory (DFT) calculations, we revealed that electron transfer from the Fe dxz orbital to the peroxo σ*(O-O) orbital facilitates the O-O bond homolysis, with the O-O bond cleavage barrier well correlated with the energy gap between the frontier molecular orbitals of dxz and σ*(O-O). Further computational studies showed that the reactivity of the synthetic [FeIII(O2)(12-TMC)]+ complex is comparable to that of Rieske dioxygenases in cis-dihydroxylation, providing compelling evidence of the potential involvement of Fe(III)-peroxo species in Rieske dioxygenases. Thus, the present results significantly advance our understanding of the cis-dihydroxylation mechanisms by Rieske dioxygenases and synthetic nonheme iron-peroxo models.

Symmetry Breaking in a Triferrous Extended Metal Atom Chain

Semilocal and random phase approximation (RPA) density functional theory (DFT) and complete active space (CASSCF + NEVPT2) methodologies were applied to investigate a new class of extended metal atom chain (EMAC) complexes. A novel triferrous complex has been synthesized recently that does not utilize the usual 2,2'-dipyridylamine (dpa) ligand framework, which essentially always results in a tetragonal coordination environment and general formula M3(dpa)4X2, where X is an anion. Instead, the triferrous complex utilizes a dianionic, 2,6-bis(trimethylsilylamido)pyridine ligand (L2-) resulting in the formation of trigonal complexes with general formula Fe3L3. To better understand the electronic structure of this complex, calculations were utilized to explore the experimentally isolated Fe3L3, and a smaller theoretical complex, in order to compare and contrast with the traditional dpa-based EMACs. Due to the absence of anionic, axial ligands, the sigma nonbonding orbitals formed from the metal d orbitals are lower in energy than in the dpa complexes, and compete with the pi bonding orbitals for occupation in the Fe3L3 complex. While the idealized geometry of these complexes is D3h, a helical distortion of the ligands and subsequent electronic symmetry breaking due to Jahn-Teller distortions are predicted utilizing both semilocal and RPA DFT methods, ending in a C2 structure that closely matches the reported crystal structure. Predicted Mössbauer isomer shifts and ultraviolet/visible (UV/vis) spectra also agree with the experimental data available in the literature. Magnetic coupling constants also indicate ferromagnetic coupling between nearest neighbor irons. Two-dimensional (2D) potential energy surfaces were calculated for a range of fixed Fe-Fe bond lengths, revealing a flat potential energy surface over a wide range of Fe-Fe bond lengths and verifying the ability of RPA to act as a higher-level check on semilocal DFT results. In order to verify the predicted high-spin ground state, CASSCF + NEVPT2 was applied to selected molecular configurations and confirmed the predictions made by DFT. These calculations shed light on the physical ground state electron configuration of Fe3L3 and correlate this electronic configuration with the available experimental data.

Synergy of Experiment and Broadened Exploration of Ab Initio Calculations for Understanding of Lanthanide-Pentacyanidocobaltate Molecular Nanomagnets and Their Optical Properties

We present a synergistic experimental-theoretical methodology for the investigation of lanthanide-based single-molecule magnets (SMMs), demonstrated using the example of novel heterometallic molecules incorporating Nd3+/Ce3+ ions combined with three different, rarely explored, pentacyanidocobaltate(III) metalloligands, [CoIII(CN)5(azido/nitrito-N/iodido)]3-. The theoretical part of our approach broadens the exploration of ab initio calculations for lanthanide(III) complexes toward the convenient simulations of such physical characteristics as directional dependences of Helmholtz energy, magnetization, susceptibility, and their thermal and field evolution, as well as light absorption and emission bands. This work was conducted using newly designed SlothPy software (https://slothpy.org). It is introduced as an open-source Python library for simulating various physical properties from first-principles based on results of electronic structure calculations obtained within popular quantum chemistry packages. The computational results were confronted with spectroscopic and ac/dc-magnetic data, the latter analyzed using previously designed relACs software. The combination of experimental and computational methods gave insight into phonon-assisted magnetic relaxation mechanisms, disentangling them from the temperature-independent quantum tunneling of magnetization and emphasizing the role of local-mode processes. This study provides an understanding of the changes in lanthanide(III) magnetic anisotropy introduced with pentacyanidocobaltates(III) modifications, theoretically exploring also potential applications of reported compounds as anisotropy switches or optical thermometers.

Elucidation of the exchange interaction in photoexcited three-spin systems - a second-order perturbational approach

Photogenerated three-spin systems show great potential for applications in the field of molecular spintronics. In these systems, the exchange interaction in the electronically excited state dictates their magnetic properties. To design such molecules for specific applications, it is thus important to understand how the sign and magnitude of the exchange interaction can be controlled. For this purpose, we developed a perturbational approach, based on previous work by the groups of de Loth and Malrieu, that allows for the direct calculation of the exchange interaction and its individual contributions up to the second order and implemented it within the ORCA program package. Within this manuscript, we present the derivation of the individual second-order contributions, provide an overview of the implementation of the code and illustrate its performance. We show that, using this perturbational approach in combination with state-averaged orbitals from minimal active space calculations, accurate values for the exchange interaction can be computed for organic nitroxides. Further, we demonstrate that the weight of the ionic determinants in the orbital optimisation of the CASSCF procedure is crucial for the computation of accurate exchange couplings. In the case of photoexcited chromophore-radical systems, we find that the dynamic spin polarisation effect constitutes the most important contribution to the exchange interaction, whereby the sign of this contribution determines the sign of the exchange interaction.

Insights into dioxygen binding on metal centers: an ab initio multireference electronic structure analysis

Why does binding of dioxygen (O2) to metal centers, the initial step of O2 storage, transportation, and activation, almost inevitably induce metal-to-O2 single-electron transfer and generate superoxo (O2-˙) species, instead of genuine O02 adducts? To address this question, this study describes highly correlated wavefunction-based ab initio calculations using CASSCF/NEVPT2 (CASSCF = complete active space self-consistent field, and NEVPT2 = N-electron valence state second-order perturbation theory) approaches to explore the electronic-structure evolution of O2 association on Fe(II)(BDPP) (H2BDPP = 2,6-bis((2-(S)-diphenylhydroxylmethyl-1-pyrrolidinyl)methyl)pyridine) and Co(II)(BDPP) to produce S = 3 Fe(III)(BDPP)(O2-˙) (1) and Co(III)(BDPP)(O2-˙) (2). CASSCF/NEVPT2 calculations suggest that the processes furnishing 1 and 2 feature an avoided crossing resulting from interactions of two diabatic curves, of which one is characterized as Co(II) and Fe(II) centers interacting with a triplet O2 ligand and the other as Co(III) and Fe(III) centers bound to a superoxo ligand. In both cases, the avoided crossing induces a one-electron transfer from the divalent metal center to the incoming O2 ligand and leads to formation of trivalent metal-O2-˙ complexes. To facilitate the interpretation of complicated multireference wavefunctions, we formulated two-fragment spin eigenfunctions utilizing Clebsch-Gordan coefficients (CGCs) to rationalize computed spin populations on the metal centers and the O2 ligand and compared these results with usual valence bonding (VB) analyses. It turns out that both methods give the same results and are complementary to each other. Finally, the limitation of DFT approaches in describing complex electronic structures involving metal-ligand magnetic couplings is delineated.

A solution-processable benzothiazole-substituted formazanate zinc(II) complex designed for a robust resistive memory device

A novel mononuclear bis(formazanate)zinc complex (1) based on a redox-active 1-(benzothiazol-2-yl)-5-(2-benzoyl-4-chlorophenyl)-3-phenyl formazan ligand has been synthesized and characterized. Complex 1 was prepared by reacting one equivalent of Zn(OCOCH3)·2H2O with two equivalents of the corresponding formazan derivative. X-ray crystallography was employed to ascertain the solid-state structure of compound 1, and the analysis revealed a distorted octahedral geometry for the complex where the symmetrical ligands exhibit a preference for coordinating with the zinc center in the 'open' form, generating five-membered chelate rings. Moreover, cyclic voltammetry analysis reveals that complex 1 exhibits the capacity for electrochemical reduction as well as oxidation, resulting in the formation of radical anionic (L2Zn-) and dianionic (L2Zn2-) states as well as the oxidation state of 1. Additionally, the developed solution-processable complex 1 was employed as the fundamental building material for resistive switching memory applications. The [FTO/ZnIIL2(1)]/Ag RRAM device demonstrates exceptional resistive memory switching properties, with a substantial ION/IOFF ratio (103), low operational VSET and VRESET (0.9 V and -0.75 V) voltages, excellent endurance stability (100 cycles), and decent retention time (more than 2000 seconds). The findings presented in this study underscore the importance of redox-active formazanate metal complexes for creating promising memory storage devices.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

Linear, Electron-Rich Erbium Single-Molecule Magnet with Dibenzocyclooctatetraene Ligands

Judicious design of ligand scaffolds to highly anisotropic lanthanide ions led to substantial advances in molecular spintronics and single-molecule magnetism. Erbium-based single-molecule magnets (SMMs) are rare, which is attributed to the prolate-shaped ErIII ion requiring an equatorial ligand field for enhancing its single-ion magnetic anisotropy. Here, we present an electron-rich mononuclear Er SMM, [K(crypt-222)][Er(dbCOT)2], 1 (where dbCOT = dibenzocyclooctatetraene), that was obtained from a salt metathesis reaction of ErCl3 and K2dbCOT. The dipotassium salt, K2dbCOT, was generated through a two-electron reduction of the bare dbCOT0 ligand employing potassium graphite and was crystallized from DME to give the new solvated complex, [K(DME)]2[dbCOT]n, 2. 1 was analyzed through crystallography, electrochemistry, spectroscopy, magnetometry, and CASSCF calculations. The structure of 1 consists of an anionic metallocene complex featuring a linear (180.0°) geometry with an ErIII ion sandwiched between dianionic dbCOT ligands and an outer-sphere K+ ion encapsulated in 2.2.2-cryptand. Two pronounced redox events at negative potentials allude to the formation of a trianionic erbocene complex, [Er(dbCOT)2]3-, on the electrochemical time scale. 1 shows slow magnetic relaxation with an effective spin-reversal barrier of Ueff = 114(2) cm-1, which is close in magnitude to the calculated energies of the first and second excited states of 96.9 and 109.13 cm-1, respectively. 1 exhibits waist-constricted hysteresis loops below 4 K and constitutes the first example of an erbocene-SMM bearing fused aromatic rings to the central COT ligand. Notably, 1 comprises the largest COT scaffold implemented in erbocene SMMs, yielding the most electron-rich homoleptic erbium metallocene SMM.

Multireference and Coupled-Cluster Study of Dimethyltetroxide (MeO4Me) Formation and Decomposition

Peroxyl radicals (RO2) are important intermediates in the atmospheric oxidation processes. The RO2 can react with other RO2 to form reactive intermediates known as tetroxides, RO4R. The reaction mechanisms of RO4R formation and its various decomposition channels have been investigated in multiple computational studies, but previous approaches have not been able to provide a unified methodology that is able to connect all relevant reactions together. An apparent difficulty in modeling the RO4R formation and its decomposition is the involvement of open-shell singlet electronic states along the reaction pathway. Modeling such electronic states requires multireference (MR) methods, which we use in the present study to investigate in detail a model reaction of MeO2 + MeO2 → MeO4Me, and its decomposition, MeO4Me → MeO + O2 + MeO, as well as the two-body product complexes MeO···O2 + MeO and MeO···MeO + O2. The used MR methods are benchmarked against relative energies of MeO2 + MeO2, MeO4Me, and MeO + MeO + O2, calculated with CCSD(T)/CBS, W2X, and W3X-L methods. We found that the calculated relative energies of the overall MeO2 + MeO2 → MeO4Me → MeO + O2 + MeO reaction are very sensitive to the chosen MR method and that the CASPT2(22e,14o)-IPEA method is able to reproduce the relative energies obtained by the various coupled-cluster methods. Furthermore, CASPT2(22e,14o)-IPEA and W3X-L results show that the MeO···O2 product complex + MeO is lower in energy than the MeO···MeO complex + O2. The formation of MeO4Me is exothermic, and its decomposition is endothermic, relative to the tetroxide. Both the formation and decomposition reactions appear to follow pathways with no saddle points. According to potential energy surface scans of the decomposition pathway, the concerted cleavage of both MeO···O bonds in MeO4Me is energetically preferred over the corresponding sequential decomposition.

A closed-shell phenalenyl-based dinuclear iron(III) complex as a robust cathode for a one-compartment H2O2 fuel cell

Closed-shell phenalenyl (PLY) systems are increasingly becoming more attractive as building blocks for developing promising catalysts and electroactive cathode materials, as they have tremendous potential to accept electrons and participate in redox reactions. Herein, we report a PLY-based dinuclear [FeIII2(hmbh-PLY)3] complex, 1, and its utility as a cathode material in a H2O2 fuel cell. Complex 1 was synthesized from a new Schiff base ligand, (E)-9-(2-(2-hydroxy-3-methoxybenzylidene)hydrazineyl)-1H-phenalen-1-one, hmbh-PLYH2, designed using a PLY precursor, Hz-PLY. The newly derived ligand and complex 1 were characterized by various analytical techniques, including single-crystal X-ray diffraction (SCXRD). The cyclic voltammetry (CV) study revealed that complex 1 undergoes five electron reductions under an applied electric potential. When the electroactive complex 1 was employed as a cathode in a membrane-less one-compartment H2O2 fuel cell, with Ni foam as the corresponding anode, the designed fuel cell exhibited an exceptionally high peak power density (PPD) of 2.41 mW cm-2, in comparison with those of all the previously reported Fe-based molecular complexes. DFT studies were performed to gain reasonable insights into the two-electron catalytic reduction (pathway I) of H2O2 by the Fe-center of complex 1 and to explore the geometries, energetics of the electrocatalyst, reactive intermediates and transition states.

Effect of hydration equilibria on the relaxometric properties of Gd(III) complexes: new insights into old systems

We present a detailed relaxometric and computational investigation of three Gd(III) complexes that exist in solution as an equilibrium of two species with a different number of coordinated water molecules: [Gd(H2O)q]3+ (q = 8, 9), [Gd(EDTA)(H2O)q]- and [Gd(CDTA)(H2O)q]- (q = 2, 3). 1H nuclear magnetic relaxation dispersion (NMRD) data were recorded from aqueous solutions of these complexes using a wide Larmor frequency range (0.01-500 MHz). These data were complemented with 17O transverse relaxation rates and chemical shifts recorded at different temperatures. The simultaneous fit of the NMRD and 17O NMR data was guided by computational studies performed at the DFT and CASSCF/NEVPT2 levels, which provided information on Gd⋯H distances, 17O hyperfine coupling constants and the zero-field splitting (ZFS) energy, which affects electronic relaxation. The hydration equilibrium did not have a very important effect in the fits of the experimental data for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-, as the hydration equilibrium is largely shifted to the species with the lowest hydration number (q = 8 and 2, respectively). The quality of the analysis improves however considerably for [Gd(EDTA)(H2O)q]- upon considering the effect of the hydration equilibrium. As a result, this study provides for the first time an analysis of the relaxation properties of this important model system, as well as accurate parameters for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-.

Design and synthesis of a solution-processed redox-active bis(formazanate) zinc complex for resistive switching applications

In this paper, we report the synthesis and characterization of a mononuclear zinc complex (1) containing a redox-active bis(4-antipyrinyl) derivative of the 3-cyanoformazanate ligand. Complex 1 was readily obtained by refluxing zinc acetate with 3-cyano-1,5-(4-antipyrinyl)formazan (LH) in a methanolic solution. Single-crystal X-ray diffraction analysis of complex 1 shows that the formazanate ligands bind to the zinc center in a five-member chelate "open" form via the 1- and 4-positions of the 1,2,4,5-tetraazapentadienyl formazanate backbone leading to the formation of the mononuclear bis(formazanate) zinc complex exhibiting a distorted octahedral geometry. We also report the study of resistive-switching random access memory application of this solution-processable bis(formazanate) Zn(II) complex to facilitate the practical implementation of transition metal complex-based molecular memory devices. The complex demonstrated high conductance switching with a large ON-OFF ratio, good stability, and a long retention time. A trap-controlled space charge limited current mechanism is proposed for the observed resistive switching behavior of the device, wherein the role played by the [ZnIIL2] complex that comprises the extended redox-active conjugated ligand backbone is revealed by corroborating electrochemical studies, spectrochemical experiments, and DFT calculations. In addition to providing significant insights into the molecular design of transition metal complexes for memory applications, this study also presents the utilization of ZnIIL2 towards the realization of non-volatile resistive random access memory (RRAM) devices with inorganic/organic hybrid active layers that are highly cost-effective and sustainable. These devices exhibited multilevel switching and low current operation, both of which are desirable for advanced memory applications.

Characterizing the origin band spectrum of isoquinoline with resonance enhanced multiphoton ionization and electronic structure calculations

We report the experimental resonance enhanced multiphoton ionization spectrum of isoquinoline between 315 and 310 nm, along with correlated electronic structure calculations on the ground and excited states of this species. This spectral region spans the origin transitions to a π-π* excited state, which previous work has suggested to be vibronically coupled with a lower lying singlet n-π* state. Our computational results corroborate previous density functional theory calculations that predict the vertical excitation energy for the n-π* state to be higher than the π-π* state; however, we find an increase in the C-N-C angle brings the n-π* state below the energy of the π-π* state. The calculations find two out-of-plane vibrational modes of the n-π* state, which may be brought into near resonance with the π-π* state as the C-N-C bond angle increases. Therefore, the C-N-C bond angle may be important in activating vibronic coupling between the states. We fit the experimental rotational contour with a genetic algorithm to determine the excited state rotational constants and orientation of the transition dipole moment. The fits show a mostly in-plane polarized transition, and the projection of the transition dipole moment in the a-b plane is about 84° away from the a axis. These results are consistent with the prediction of our electronic structure calculations for the transition dipole moment of the π-π* excited state.

Mechanistic Understanding and Reactivity Analyses for the Photochemistry of Disubstituted Tetrazoles

The photolysis of tetrazoles has undergone extensive research. However, there are still some problems to be solved in terms of mechanistic understanding and reactivity analyses, which leaves room for theoretical calculations. Herein, multiconfiguration perturbation theory at the CASPT2//CASSCF level was employed to account for electron correction effects involved in the photolysis of four disubstituted tetrazoles. Based on calculations of vertical excitation properties and evaluations of intersystem crossing (ISC) efficiencies in the Frank-Condon region, the combination of space and electronic effects is found in maximum-absorption excitation. Two types of ISC (¹ππ* → ³nπ*, ¹ππ* → ³ππ*) are determined in disubstituted tetrazoles, and the obtained rates follow the El-Sayed rule. Through mapping three representative types of minimum energy profiles for the photolysis of 1,5-, and 2,5-disubstituted tetrazoles, a conclusion can be drawn that the photolysis of tetrazoles exhibits reactivity characteristic of bond-breaking selectivity. Kinetic evaluations show that the photogeneration of singlet imidoylnitrene operates predominately over that in the triplet state, which can be confirmed by a double-well model in the triplet potential energy surface of 1,5-disubstituted tetrazole. Similar mechanistic explorations and reactivity analyses were also applied to the photolysis of 2,5-disubstituted tetrazole to unveil fragmentation patterns of nitrile imine generation. All computational efforts allow us to better understand the photoreactions of disubstituted tetrazoles and to provide useful strategies for regulating their unique reactivity.

Redox Switching Behavior in Resistive Memory Device Designed Using a Solution-Processable Phenalenyl-Based Co(II) Complex: Experimental and DFT Studies

We herein report a novel square-planar complex [Co^IIL], which was synthesized using the electronically interesting phenalenyl-derived ligand LH₂ = 9,9'-(ethane-1,2-diylbis(azanediyl))bis(1H-phenalen-1-one). The molecular structure of the complex is confirmed with the help of the single-crystal X-ray diffraction technique. [Co^IIL] is a mononuclear complex where the Co(II) ion is present in the square-planar geometry coordinated by the chelating bis-phenalenone ligand. The solid-state packing of [Co^IIL] complex in a crystal structure has been explained with the help of supramolecular studies, which revealed that the π···π stacking present in the [Co^IIL] complex is analogous to the one present in tetrathiafulvalene/tetracyanoquinodimethane charge transfer salt, well-known materials for their unique charge carrier interfaces. The [Co^IIL] complex was employed as the active material to fabricate a resistive switching memory device, indium tin oxide/Co^IIL/Al, and characterized using the write-read-erase-read cycle. The device has interestingly shown a stable and reproducible switching between two different resistance states for more than 2000 s. Observed bistable resistive states of the device have been explained by corroborating the electrochemical characterizations and density functional theory studies, where the role of the Co^II metal center and π-conjugated phenalenyl backbone in the redox-resistive switching mechanism is proposed.

Characterization of the Fe(III)-Tiron System in Solution through an Integrated Approach Combining NMR Relaxometric, Thermodynamic, Kinetic, and Computational Data

The Fe(III)-Tiron system (Tiron = 4,5-dihydroxy-1,3-benzenedisulfonate) was investigated using a combination of ¹H and ¹⁷O NMR relaxometric studies at variable field and temperature and theoretical calculations at the DFT and NEVPT2 levels. These studies require a detailed knowledge of the speciation in aqueous solution at different pH values. This was achieved using potentiometric and spectrophotometric titrations, which afforded the thermodynamic equilibrium constants characterizing the Fe(III)-Tiron system. A careful control of the pH of the solution and the metal-to-ligand stoichiometric ratio allowed the relaxometric characterization of [Fe(Tiron)₃]^9-, [Fe(Tiron)₂(H₂O)₂]^5-, and [Fe(Tiron)(H₂O)₄]^- complexes. The ¹H nuclear magnetic relaxation dispersion (NMRD) profiles of [Fe(Tiron)₃]^9- and [Fe(Tiron)₂(H₂O)₂]^5- complexes evidence a significant second-sphere contribution to relaxivity. A complementary ¹⁷O NMR study provided access to the exchange rates of the coordinated water molecules in [Fe(Tiron)₂(H₂O)₂]^5- and [Fe(Tiron)(H₂O)₄]^- complexes. Analyses of the NMRD profiles and NEVPT2 calculations indicate that electronic relaxation is significantly affected by the geometry of the Fe³⁺ coordination environment. Dissociation kinetic studies indicated that the [Fe(Tiron)₃]^9- complex is relatively inert due to the slow release of one of the Tiron ligands, while the [Fe(Tiron)₂(H₂O)₂]^5- complex is considerably more labile.

Understanding the Exchange Interaction between Paramagnetic Metal Ions and Radical Ligands: DFT and Ab Initio Study on Semiquinonato Cu(II) Complexes

The exchange coupling, represented by the J parameter, is of tremendous importance in understanding the reactivity and magnetic behavior of open-shell molecular systems. In the past, it was the subject of theoretical investigations, but these studies are mostly limited to the interaction between metallic centers. The exchange coupling between paramagnetic metal ions and radical ligands has hitherto received scant attention in theoretical studies, and thus the understanding of the factors governing this interaction is lacking. In this paper, we use DFT, CASSCF, CASSCF/NEVPT2, and DDCI3 methods to provide insight into exchange interaction in semiquinonato copper(II) complexes. Our primary objective is to identify structural features that affect this magnetic interaction. We demonstrate that the magnetic character of Cu(II)-semiquinone complexes are mainly determined by the relative position of the semiquinone ligand to the Cu(II) ion. The results can support the experimental interpretation of magnetic data for similar systems and can be used for the in-silico design of magnetic complexes with radical ligands.

Calculation of exchange couplings in the electronically excited state of molecular three-spin systems

Photogenerated molecular three-spin systems, composed of a chromophore and a covalently bound stable radical, are promising candidates for applications in the field of molecular spintronics. Through excitation with light, an excited doublet state and a quartet state are generated, whereby their energy difference depends on the exchange interaction J TR between the chromophore triplet state (T) and the stable radical (R). In order to establish design rules for new materials to be used in molecular spintronics devices, it is of great importance to gain knowledge on the magnitude of J TR as well as the factors influencing J TR on a molecular level. Here, we present a robust and reliable computational method to determine excited state exchange couplings in three-electron-three-centre systems based on a CASSCF/QD-NEVPT2 approach. The methodology is benchmarked and then applied to a series of molecules composed of a perylene chromophore covalently linked to various stable radicals. We calculate the phenomenological exchange interaction J TR between chromophore and radical, which can be compared directly to the experiment, but also illustrate how the individual exchange interactions J ij can be extracted using an effective Hamiltonian that corresponds to the Heisenberg-Dirac-Van-Vleck Hamiltonian. The latter procedure enables a more detailed analysis of the contributions to the exchange interaction J TR and yields additional insight that will be invaluable for future design optimisation.

The nature of metal-metal bonding in Re-, Ru- and Os-corrole dimers

Studies of multiple bonding between transition metal complexes offer fundamental insight into the nature of bonding between metal ions and facilitate predictions of the physical properties and the reactivities of metal complexes containing metal-metal multiple bonds. Here we report a computational interrogation on the nature of the metal-metal bonding for neutral, oxidized, and reduced forms of dinuclear rhenium and osmium corrole complexes, [{Re[TpXPC]}2]0/1+/1- and [{Os[TpXPC]}2]0/1+/1-, using a complete active space self-consistent (CASSCF) methodology and density functional theory (DFT) calculations. For [{Re[TpXPC]}2]0, [{Ru[TpXPC]}2]0, and [{Os[TpXPC]}2]0, CASSCF calculations shows that the effective bond order is 3.29, 2.63, and 2.73, respectively. On their oxidized forms, [{Re[TpXPC]}2]1+, [{Ru[TpXPC]}2]1+, and [{Os[TpXPC]}2]1+ molecules, the results indicate an electron removal from a ligand-based orbital, where [{Re[TpXPC]}2]1+ gives slightly different geometry from its neutral form due to populating the δ* orbital. In this regard, the CASSCF calculations give an effective bond order of 3.25 which is slightly lower than in the [{Re[TpXPC]}2]0. On their reduced forms, the electron addition appears to be in the metal-based orbital for [{Re[TpXPC]}2]1- and [{Ru[TpXPC]}2]1- whereas in the ligand-based orbital for the Os-analogue which has no effect on the Os-Os bonding, an effective bond order of 3.18 and 2.17 is presented for the [{Re[TpXPC]}2]1- and [{Ru[TpXPC]}2]1-, respectively, within the CASSCF simulations. These results will further encourage theoreticians and experimentalists to design metalloporphyrin dimers with distinct metal-metal bonding.

A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions

In this work, we present a one-step second-order converger for state-specific (SS) and state-averaged (SA) complete active space self-consistent field (CASSCF) wave functions. Robust convergence is achieved through step restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid numerical instabilities, an exponential parameterization of variational configuration parameters is employed, which works with a nonredundant orthogonal complement basis. This is a common approach for SS-CASSCF and is extended to SA-CASSCF wave functions in this work. Our implementation is integral direct and based on intermediates that are formulated in either the sparse atomic-orbital or small active molecular-orbital basis. Thus, it benefits from a combination with efficient integral decomposition techniques, such as the resolution-of-the-identity or the chain-of-spheres for exchange approximations. This facilitates calculations on large molecules, such as a Ni(II) complex with 231 atoms and 5154 basis functions. The runtime performance of TRAH-CASSCF is competitive with the other state-of-the-art implementations of approximate and full second-order algorithms. In comparison with a sophisticated first-order converger, TRAH-CASSCF calculations usually take more iterations to reach convergence and, thus, have longer runtimes. However, TRAH-CASSCF calculations still converge reliably to a true minimum even if the first-order algorithm fails.

Exploiting the Fluxionality of Lanthanide Complexes in the Design of Paramagnetic Fluorine Probes

Fluorine-19 MRI is increasingly being considered as a tool for biomolecular imaging, but the very poor sensitivity of this technique has limited most applications. Previous studies have long established that increasing the sensitivity of ¹⁹F molecular probes requires increasing the number of fluorine nuclei per probe as well as decreasing their longitudinal relaxation time. The latter is easily achieved by positioning the fluorine atoms in close proximity to a paramagnetic metal ion such as a lanthanide(III). Increasing the number of fluorine atoms per molecule, however, is only useful inasmuch as all of the fluorine nuclei are chemically equivalent. Previous attempts to achieve this equivalency have focused on designing highly symmetric and rigid fluorinated macrocyclic ligands. A much simpler approach consists of exploiting highly fluxional lanthanide complexes with open coordination sites that have a high affinity for phosphated and phosphonated species. Computational studies indicate that Ln^III-TREN-MAM is highly fluxional, rapidly interconverting between at least six distinct isomers. In neutral water at room temperature, Ln^III-TREN-MAM binds two or three equivalents of fluorinated phosphonates. The close proximity of the ¹⁹F nuclei to the Ln^III center in the ternary complex decreases the relaxation times of the fluorine nuclei up to 40-fold. Advantageously, the fluorophosphonate-bound lanthanide complex is also highly fluxional such that all ¹⁹F nuclei are chemically equivalent and display a single ¹⁹F signal with a small LIS. Dynamic averaging of fluxional fluorinated supramolecular assemblies thus produces effective ¹⁹F MR systems.

The critical role of ligand topology: strikingly different properties of Gd(iii) complexes with regioisomeric AAZTA derivatives

Two regioisomeric Gd(III) complexes with heptadentate AAZTA-like ligands show different hydration state (q = 1 and 2) and astonishingly different thermodynamic stability and dissociation kinetics.

An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices

A factorization of the matrix elements of the Dyall Hamiltonian in N-electron valence state perturbation theory allowing their evaluation with a computational effort comparable to the one needed for the construction of the third-order reduced density matrix at the most is presented. Thus, the computational bottleneck arising from explicit evaluation of the fourth-order density matrix is avoided. It is also shown that the residual terms arising in the case of an approximate complete active space configuration interaction solution and containing even the fifth-order density matrix for two excitation classes can be evaluated with little additional effort by choosing again a favorable factorization of the corresponding matrix elements. An analogous argument is also provided for avoiding the fourth-order density matrix in complete active space second-order perturbation theory. Practical calculations indicate that such an approach leads to a considerable gain in computational efficiency without any compromise in numerical accuracy or stability.

First-Principles Study of Optical Absorption Energies, Ligand Field and Spin-Hamiltonian Parameters of Cr3+ Ions in Emeralds

Herein, we study the electronic structure, energies, and vibronic structure of optical d-d transitions of Cr³⁺ ions doped in beryl (Be₃Si₆Al₂O₁₈:Cr³⁺, emerald). A computational protocol is developed that combines periodic density functional theory (for modeling of the bulk crystalline lattice of emerald) and the multireference configuration interaction complete active space self-consistent field method supplemented with n-electron valence second-order perturbation theory (for the calculation of the energy levels, wave functions, and spin-Hamiltonian and ligand-field parameters of the trigonal Cr³⁺ centers in the [CrO₆]^9- clusters embedded in an extended point charge field). Ligand-field parameters were extracted from mapping the effective ligand-field Hamiltonian onto the full many-particle Hamiltonian from one side and from a direct fit to energies of computed d-d transitions on the other side. These have been analyzed using ab initio ligand-field theory. The quality of the theoretical predictions is critically assessed through a detailed comparison with the available experimental data.

Understanding the Effect of the Electron Spin Relaxation on the Relaxivities of Mn(II) Complexes with Triazacyclononane Derivatives

Investigating the relaxation of water ¹H nuclei induced by paramagnetic Mn(II) complexes is important to understand the mechanisms that control the efficiency of contrast agents used in diagnostic magnetic resonance imaging (MRI). Herein, a series of potentially hexadentate triazacyclononane (TACN) derivatives containing different pendant arms were designed to explore the relaxation of the electron spin in the corresponding Mn(II) complexes by using a combination of ¹H NMR relaxometry and theoretical calculations. These ligands include 1,4,7-triazacyclononane-1,4,7-triacetic acid (H₃NOTA) and three derivatives in which an acetate group is replaced by sulfonamide (H₃NO2ASAm), amide (H₂NO2AM), or pyridyl (H₂NO2APy) pendants. The analogue of H₃NOTA containing three propionate pendant arms (H₃NOTPrA) was also investigated. The X-ray structure of the derivative containing two acetate groups and a sulfonamide pendant arm [Mn(NO2ASAm)]^- evidenced six-coordination of the ligand to the metal ion, with the coordination polyhedron being close to a trigonal prism. The relaxivities of all complexes at 20 MHz and 25 °C (1.1-1.3 mM^-1 s^-1) are typical of systems that lack water molecules coordinated to the metal ion. The nuclear magnetic relaxation profiles evidence significant differences in the relaxivities of the complexes at low fields (<1 MHz), which are associated with different spin relaxation rates. The zero field splitting (ZFS) parameters calculated by using DFT and CASSCF methods show that electronic relaxation is relatively insensitive to the nature of the donor atoms. However, the twist angle of the two tripodal faces that delineate the coordination polyhedron, defined by the N atoms of the TACN unit (lower face) and the donor atoms of the pendant arms (upper face), has an important effect in the ZFS parameters. A twist angle close to the ideal value for an octahedral coordination (60°), such as that in [Mn(NOTPrA)]^-, leads to a small ZFS energy, whereas this value increases as the coordination polyhedron approaches to a trigonal prism.

Modern multireference methods and their application in transition metal chemistry

Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.

Electronic Structure of Ytterbium(III) Solvates-a Combined Spectroscopic and Theoretical Study

The wide range of optical and magnetic properties of lanthanide(III) ions is associated with their intricate electronic structures which, in contrast to lighter elements, is characterized by strong relativistic effects and spin-orbit coupling. Nevertheless, computational methods are now capable of describing the ladder of electronic energy levels of the simpler trivalent lanthanide ions, as well as the lowest energy term of most of the series. The electronic energy levels result from electron configurations that are first split by spin-orbit coupling into groups of energy levels denoted by the corresponding Russell-Saunders terms. Each of these groups are then split by the ligand field into the actual electronic energy levels known as microstates or sometimes m_J levels. The ligand-field splitting directly informs on the coordination geometry and is a valuable tool for determining the structure and thus correlating the structure and properties of metal complexes in solution. The issue with lanthanide complexes is that the determination of complex structures from ligand-field splitting remains a very challenging task. In this paper, the optical spectra-absorption, luminescence excitation, and luminescence emission-of ytterbium(III) solvates were recorded in water, methanol, dimethyl sulfoxide (DMSO), and N,N-dimethylformamide (DMF). The electronic energy levels, that is, the microstates, were resolved experimentally. Subsequently, density functional theory calculations were used to model the structures of the solvates, and ab initio relativistic complete active space self-consistent field calculations (CASSCF) were employed to obtain the microstates of the possible structures of each solvate. By comparing the experimental and theoretical data, it was possible to determine both the coordination number and solution structure of each solvate. In water, methanol, and N,N-dimethylformamide, the solvates were found to be eight-coordinated and have a square antiprismatic coordination geometry. In DMSO, the speciation was found to be more complicated. The robust methodology developed for comparing experimental spectra and computational results allows the solution structures of homoleptic lanthanide complexes to be determined.

Photodesorption mechanism of water on WO3(001) - a combined embedded cluster, computational intelligence and wave packet approach

In this work we investigate the mechanism of photodesorption of water from a WO3(001) surface by theoretical calculations, applying an embedded cluster model. Using the CASSCF method, we have calculated both the ground state as well as the energetically preferred charge-transfer state in three degrees of freedom of the water molecule on the surface. The calculated potential energy surfaces were afterwards fitted with a neural network optimized by a genetic algorithm. A final quantum dynamic wave packet study provided insight into the photodesorption mechanism.

Benchmarks for Electronically Excited States with CASSCF Methods

The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of Schreiber , M. ; et al. J. Chem. Phys. 2008 , 128 , 134110 . Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.

CASSCF linear response calculations for large open-shell molecules

The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.