A recursive formulation of one‐electron coupling coefficients for spin‐adapted configuration interaction calculations featuring many unpaired electrons

This work reports on a novel computational approach to the efficient evaluation of one-electron coupling coefficients as they are required during spin-adapted electronic structure calculations of the configuration interaction type. The presented approach relies on the equivalence of the representation matrix of excitation operators in the basis of configuration state functions and the representation matrix of permutation operators in the basis of genealogical spin eigenfunctions. After the details of this connection are established for every class of one-electron excitation operator, a recursive scheme to evaluate permutation operator representations originally introduced by Yamanouchi and Kotani is recapitulated. On the basis of this scheme we have developed an efficient algorithm that allows the evaluation of all nonredundant coupling coefficients for systems with 20 unpaired electrons and a total spin of S = 0 within only a few hours on a simple Desktop-PC. Furthermore, a full-CI implementation that utilizes the presented approach to one-electron coupling coefficients is shown to perform well in terms of computational timings for CASCI calculations with comparably large active spaces. More importantly, however, this work paves the way to spin-adapted and configuration driven selected configuration interaction calculations with many unpaired electrons.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

A configuration-based heatbath-CI for spin-adapted multireference electronic structure calculations with large active spaces

This work reports on a spin‐pure configuration‐based implementation of the heatbath configuration interaction (HCI) algorithm for selective configuration interaction. Besides the obvious advantage of being spin‐pure, the presented method combines the compactness of the configurational ansatz with the known efficiency of the HCI algorithm and a variety of algorithmic and conceptual ideas to achieve a high level of performance. In particular, through pruning of the selected configurational space after HCI selection by means of a more strict criterion, a more compact wavefunction representation is obtained. Moreover, the underlying logic of the method allows us to minimize the number of redundant matrix‐matrix multiplications while making use of just‐in‐time compilation to achieve fast diagonalization of the Hamiltonian. The critical search for 2‐electron connections within the configurational space is facilitated by a tree‐based representation thereof as suggested previously by Gopal et al. Usage of a prefix‐based parallelization and batching during the calculation of the PT2‐correction leads to a good load balancing and significantly reduced memory requirements for these critical steps of the calculation. In this way, the need for a semistochastic approach to the PT2 correction is avoided even for large configurational spaces. Finally, several test‐cases are discussed to demonstrate the strengths and weaknesses of the presented method.Peer Reviewe

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.</p

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N_2 and [Cu_2O_2(en)_2]^(2+) demonstrate some key properties of the method and indicate its capabilities

Insight into the X‐ray absorption spectra of Cu‐porphyrazines from electronic structure theory

Transition metal porphyrazines are a widely used class of compounds with applications in catalysis, organic solar cells, photodynamic therapy, and nonlinear optics. The most prominent members of that family of compounds are metallophtalocyanines, which have been the subject of numerous spectroscopic and theoretical studies. In this work, the electronic structure and X‐ray absorption characteristics of three Cu‐porphyrazine derivatives are investigated by means of modern electronic structure theory. More precisely, the experimentally observed N K‐edge and Cu L‐edge features are presented and reproduced by time‐dependent density functional theory, restricted open‐shell configuration interaction, and a restricted active space approach. Where possible, the calculations are used to interpret the observed spectroscopic features in terms of electronic transitions and, furthermore, to connect spectral differences to chemical variations. Part of the discussion of the computational results concerns the impact of various parameters and approximations that are used for the calculations, for example, the choice of active space

Two Allogons of an O2-activating Bis(disiloxido)ferrate(II) Accessible Selectively just by Variation of the Crystallization Temperature

Deprotonation of O(iPr2SiOH)2 (iPrLH2) with LiOtBu followed by reaction with FeCl2 in THF led to the complex [iPrL2Fe][Li(THF)2]2, 2, which represents a structural and spectroscopic model of the α‐Fe sites of Fe/ZSM‐5. Reaction with O2 in THF solution proceeds rather fast and is complete within 200 ms; an intermediate O2 adduct could not be identified by stopped‐flow methods. Cooling blue solutions of 2 to −80 °C led to the growth of blue crystals of 2⋅THF, the analysis of which by XRD revealed a FeO4 core that is somewhat distorted from planarity towards a tetrahedral structure. By contrast, cooling such solutions to −30 °C led to pink crystals of an allogon featuring a perfectly square planar FeO4 entity. Hence, 2 represents a unique case where two different structural isomers (allogons) can be crystallized from the same solvent selectively, controlled by the temperature. DFT calculations were performed to understand this finding.Peer Reviewe

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N_2 and [Cu_2O_2(en)_2]^(2+) demonstrate some key properties of the method and indicate its capabilities

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed

Electrochemistry and Reactivity of Chelation‐stabilized Hypervalent Bromine(III) Compounds

Hypervalent bromine(III) reagents possess a higher electrophilicity and a stronger oxidizing power compared to their iodine(III) counterparts. Despite the superior reactivity, bromine(III) reagents have a reputation of hard‐to‐control and difficult‐to‐synthesize compounds. This is partly due to their low stability, and partly because their synthesis typically relies on the use of the toxic and highly reactive BrF3 as a precursor. Recently, we proposed chelation‐stabilized hypervalent bromine(III) compounds as a possible solution to both problems. First, they can be conveniently prepared by electro‐oxidation of the corresponding bromoarenes. Second, the chelation endows bromine(III) species with increased stability while retaining sufficient reactivity, comparable to that of iodine(III) counterparts. Finally, their intrinsic reactivity can be unlocked in the presence of acids. Herein, an in‐depth mechanistic study of both the electrochemical generation and the reactivity of the bromine(III) compounds is disclosed, with implications for known applications and future developments in the field.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659European Regional Development Fund http://dx.doi.org/10.13039/501100008530HORIZON EUROPE European Research Council http://dx.doi.org/10.13039/100019180Estonian Research Competency Council http://dx.doi.org/10.13039/501100005189Peer Reviewe