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.

TREXIO: A file format and library for quantum chemistry.

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the hierarchical data format version 5 library, which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for Fortran, Python, and OCaml programming languages. In addition, a suite of tools have been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

Comparison of Many-Particle Representations for Selected Configuration Interaction: II. Numerical Benchmark Calculations.

The present work is the second part in our three-part series on the comparison of many-particle representations for the selected configuration interaction (CI) method. In this work, we present benchmark calculations based on our selected CI program called the iterative configuration expansion (ICE) that is inspired by the CIPSI method of Malrieu and co-workers (Malrieu J. Chem. Phys. 1973, 58, (12), 5745-5759). We describe the main parameters that enter in this algorithm and perform benchmark calculations on a set of 21 small molecules and compare ground state energies with full configuration interaction (FCI) results (FCI21 test set). The focus is the comparison of the performance of three different types of many-particle basis functions (MPBFs): (1) individual Slater determinants (DETS), (2) individual spin-adapted configuration state functions (CSFs), and (3) all CSFs of a given total spin that can be generated from spatial configurations (CFGs). An analysis of the cost of the calculation in terms of the number of wavefunction parameters and the energy error is evaluated for the DET-, CFG-, and CSF-based ICE. The main differences for the three many-particle basis representations show up in the number of wavefunction parameters and the rate of convergence toward the FCI limit with the thresholds of the ICE. Next, we analyze the best way to extrapolate the ICE energies toward the FCI results as a function of the thresholds. The efficiency of the extrapolation is investigated relative to the FCI21 test set as well as near FCI calculations on three moderately sized hydrocarbon molecules CH4, C2H4, and C4H6. Finally, we comment on the size-inconsistency error for the three many-particle representations and compare it with the error in the total energy. The implication for selected CI implementations with any of the three many-particle representations is discussed.

Comparison of many-particle representations for selected-CI I: A tree based approach.

The full configuration interaction (FCI) method is only applicable to small molecules with few electrons in moderate size basis sets. One of the main alternatives to obtain approximate FCI energies for bigger molecules and larger basis sets is selected CI. However, due to: (a) the lack of a well-defined structure in a selected CI Hamiltonian, (b) the potentially large number of electrons together with c) potentially large orbital spaces, a computationally and memory efficient algorithm is difficult to construct. In the present series of papers, we describe our attempts to address these issues by exploring tree-based approaches. At the same time, we devote special attention to the issue of obtaining eigenfunctions of the total spin squared operator since this is of particular importance in tackling magnetic properties of complex open shell systems. Dedicated algorithms are designed to tackle the CI problem in terms of determinant, configuration (CFG) and configuration state function many-particle bases by effective use of the tree representation. In this paper we describe the underlying logic of our algorithm design and discuss the advantages and disadvantages of the different many particle bases. We demonstrate by the use of small examples how the use of the tree simplifies many key algorithms required for the design of an efficient selected CI program. Our selected CI algorithm, called the iterative configuration expansion, is presented in the penultimate part. Finally, we discuss the limitations and scaling characteristics of the present approach.

Ligand Field Theory and Angular Overlap Model Based Analysis of the Electronic Structure of Homovalent Iron-Sulfur Dimers.

The electronic structure of multinuclear transition metal complexes is a highly challenging problem for quantum chemical methods. The problems to be solved for a successful analysis include the following: (1) many unpaired electrons leading to "highly entangled" wave functions that cannot be calculated by standard electronic structure methods, (2) drastic differences between the one-particle and many-particle spectra and a high density of low-lying states, and (3) the interpretation of such highly complex wave functions in chemical terms. In this work, we continue our research on oligonuclear clusters by presenting an in-depth analysis of the electronic structure of a prototypical iron-sulfur (Fe2S2) dimer. Accurate wave functions are obtained from a variety of advanced wave function based methods. The wave function results are interpreted in terms of an effective Hamiltonian that in turn is parametrized in terms of the angular overlap model (AOM) that provides the chemical insights that we are striving for. A hierarchical analysis allows us to interpret the local electronic structure in terms of the thiolate, sulfide ligands, and metal-metal interaction strengths. The many-particle spectrum is analyzed in terms of configurations involving ligand and metal centers. Finally, we are able to derive simple yet effective interpretations of ligand interaction strengths, the metal-metal interaction strength, and the low-lying many-particle spectrum of the Fe2S2 dimer.

Probing the Valence Electronic Structure of Low-Spin Ferrous and Ferric Complexes Using 2p3d Resonant Inelastic X-ray Scattering (RIXS).

Understanding the detailed electronic structure of transition metal ions is essential in numerous areas of inorganic chemistry. In particular, the ability to map out the many particle d-d spectrum of a transition metal catalyst is key to understanding and predicting reactivity. However, from a practical perspective, there are often experimental limitations on the ability to determine the energetic ordering, and multiplicity of all the excited states. These limitations derive in part from parity and spin-selection rules, as well as from the limited energy range of many standard laboratory instruments. Herein, we demonstrate the ability of 2p3d resonant inelastic X-ray scattering (RIXS) to obtain detailed insights into the many particle spectrum of simple inorganic molecular iron complexes. The present study focuses on low-spin ferrous and ferric iron complexes, including [FeIII/II(tacn)2]3+/2+ and [FeIII/II(CN)6]3-/4-. This series thus allows us to assess the contribution of d-count and ligand donor type, by comparing the purely σ-donating tacn ligand to the π-accepting cyanide. In order to highlight the conceptual difference between RIXS and traditional optical spectroscopy, we compare first RIXS results with UV-vis and magnetic circular dichroism spectroscopy. We then highlight the ability of 2p3d RIXS to (1) separate d-d transitions from charge transfer transitions and (2) to determine the many particle d-d spectrum over a much wider energy range than is possible by optical spectroscopy. Our experimental results are correlated with semiempirical multiplet simulations and ab initio complete active space self-consistent field calculations in order to obtain detailed assignments of the excited states. These results show that Δ S = 1, and possibly Δ S = 2, transitions may be observed in 2p3d RIXS spectra. Hence, this methodology has great promise for future applications in all areas of transition metal inorganic chemistry.

Revisiting the Electronic Structure of FeS Monomers Using ab Initio Ligand Field Theory and the Angular Overlap Model.

Iron-sulfur (FeS) proteins are universally found in nature with actives sites ranging in complexity from simple monomers to multinuclear sites from two up to eight iron atoms. These sites include mononuclear (rubredoxins), dinuclear (ferredoxins and Rieske proteins), trinuclear (e.g., hydrogenases), and tetranuclear (various ferredoxins and high-potential iron-sulfur proteins). The electronic structure of the higher-nuclearity clusters is inherently extremely complex. Hence, it is reasonable to take a bottom-up approach in which clusters of increasing nuclearity are analyzed in terms of the properties of their lower nuclearity constituents. In the present study, the first step is taken by an in-depth analysis of mononuclear FeS systems. Two different FeS molecules with phenylthiolate and methylthiolate as ligands are studied in their oxidized and reduced forms using modern wave function-based ab initio methods. The ab initio electronic spectra and wave function are presented and analyzed in detail. The very intricate electronic structure-geometry relationship in these systems is analyzed using ab initio ligand field theory (AILFT) in conjunction with the angular overlap model (AOM) parametrization scheme. The simple AOM model is used to explain the effect of geometric variations on the electronic structure. Through a comparison of the ab initio computed UV-vis absorption spectra and the available experimental spectra, the low-energy part of the many-particle spectrum is carefully analyzed. We show ab initio calculated magnetic circular dichroism spectra and present a comparison with the experimental spectrum. Finally, AILFT parameters and the ab initio spectra are compared with those obtained experimentally to understand the effect of the increased covalency of the thiolate ligands on the electronic structure of FeS monomers.

Engineering the magnetic coupling and anisotropy at the molecule-magnetic surface interface in molecular spintronic devices.

A challenge in molecular spintronics is to control the magnetic coupling between magnetic molecules and magnetic electrodes to build efficient devices. Here we show that the nature of the magnetic ion of anchored metal complexes highly impacts the exchange coupling of the molecules with magnetic substrates. Surface anchoring alters the magnetic anisotropy of the cobalt(II)-containing complex (Co(Pyipa)2), and results in blocking of its magnetization due to the presence of a magnetic hysteresis loop. In contrast, no hysteresis loop is observed in the isostructural nickel(II)-containing complex (Ni(Pyipa)2). Through XMCD experiments and theoretical calculations we find that Co(Pyipa)2 is strongly ferromagnetically coupled to the surface, while Ni(Pyipa)2 is either not coupled or weakly antiferromagnetically coupled to the substrate. These results highlight the importance of the synergistic effect that the electronic structure of a metal ion and the organic ligands has on the exchange interaction and anisotropy occurring at the molecule-electrode interface.

When a single hole aligns several spins: double exchange in organic systems.

The double exchange is a well-known and technically important phenomenon in solid state physics. Ionizing a system composed of two antiferromagnetically coupled high-spin units, the ground state of which is a singlet state, may actually produce a high-spin ground state. This work illustrates the possible occurrence of such a phenomenon in organic chemistry. The here-considered high-spin units are triangulenes, the ground state of which is a triplet. Bridging two of them through a benzene ring produces a molecular architecture of singlet ground state. A careful exploitation of a series of unrestricted density functional calculations enables one to avoid spin contamination in the treatment of the doublet states and shows that under ionization the system becomes of quartet multiplicity in its ground state. The possibility to align more than three spins from conjugated hydrocarbon polyradicals is explored, considering partially hydrogenated triangulenes. A dramatic example shows that ionization of a singlet ground state molecule may generate a decuplet.