The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron-Sulfur Cubanes

Quantum embedding for molecules using auxiliary particles - the ghost Gutzwiller Ansatz

Strong/static electronic correlation mediates the emergence of remarkable phases of matter, and underlies the exceptional reactivity properties in transition metal-based catalysts. Modeling strongly correlated molecules and solids calls for multi-reference Ansätze, which explicitly capture the competition of energy scales characteristic of such systems. With the efficient computational screening of correlated solids in mind, the ghost Gutzwiller (gGut) Ansatz has been recently developed. This is a variational Ansatz which can be formulated as a self-consistent embedding approach, describing the system within a non-interacting, quasiparticle model, yet providing accurate spectra in both low and high energy regimes. Crucially, small fragments of the system are identified as responsible for the strong correlation, and are therefore enhanced by adding a set of auxiliary orbitals, the ghosts. These capture many-body correlations through one-body fluctuations and subsequent out-projection when computing physical observables. gGut has been shown to accurately describe multi-orbital lattice models at modest computational cost. In this work, we extend the gGut framework to strongly correlated molecules, for which it holds special promise. Indeed, despite the asymmetric embedding treatment, the quasiparticle Hamiltonian effectively describes all major sources of correlation in the molecule: strong correlation through the ghosts in the fragment, and dynamical correlation through the quasiparticle description of its environment. To adapt the gGut Ansatz for molecules, we address the fact that, unlike in the lattice model previously considered, electronic interactions in molecules are not local. Hence, we explore a hierarchy of approximations of increasing accuracy capturing interactions between fragments and environment, and within the environment, and discuss how these affect the embedding description of correlations in the whole molecule. We will compare the accuracy of the gGut model with established methods to capture strong correlation within active space formulations, and assess the realistic use of this novel approximation to the theoretical description of correlated molecular clusters.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Dynamic Correlation on the Adaptive Sampling Configuration Interaction (ASCI) Reference Function: ASCI-DSRG-MRPT2

A balanced description of static and dynamic electron correlations is at the heart of quantum chemical methods. To obtain accurate results in strongly correlated systems using wave-function-based methods, a large active space is necessary to ensure correct descriptions of static correlations. Correcting the results for dynamic correlations is also necessary. In this work, we present implementations of second-order perturbation theory for dynamic correlations based on the adaptive sampling configuration interaction self-consistent field (ASCI-SCF) method. In particular, we implemented spin-free driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2). The extrapolation of the ASCI + PT2 energy based on the relaxed Hamiltonian in DSRG-MRPT2 gives a reasonable approximation of DSRG-MRPT2 based on CASSCF. We demonstrate the application of the ASCI-DSRG-MRPT2 method in evaluations of the spin-state energy gaps in iron porphyrins, polyacenes, and periacenes along with the reaction energies of methane oxidation by FeO+ and electrocyclic ring formation in cethrene.

Characterization of the Geometrical and Electronic Structures of the Active Site and Its Effects on the Surrounding Environment in Reduced High-Potential Iron-Sulfur Proteins Investigated by the Density Functional Theory Approach

The high-potential iron-sulfur protein (HiPIP) is an electron-transporting protein that functions in the photosynthetic electron-transfer system and possesses a cubane-type [4Fe-4S] cluster in the active center. Characterization of the geometrical and electronic structures of the [4Fe-4S] cluster leads to an understanding of the functions in HiPIP, which are expected to be influenced by the environment surrounding the [4Fe-4S] cluster. This work characterized the geometrical and electronic structures of the [4Fe-4S] cluster in the reduced HiPIP and evaluated their effects on the protein environment using the density functional theory (DFT) approach. DFT calculations showed that the structural asymmetry and spin delocalization between iron atoms allowed for the acquisition of a unique stable geometrical and electronic structure in the open-shell singlet. In addition, the formation of an Fe-Fe bond accompanying the spin delocalization was found to depend on the interatomic distance. A comparison of the calculated stable structures with and without consideration of the amino acids around the [4Fe-4S] cluster demonstrated that the surrounding amino acids stabilized the unique geometrical and electronic structure of the [4Fe-4S] cluster in HiPIP.

First-Principles Perspective on Gas Adsorption by [Fe4S4]-Based Metal-Organic Frameworks

[Fe₄S₄] or [4S-4Fe] clusters are responsible for storing and transferring electrons in key cellular processes and interact with their microenvironment to modulate their oxidation and magnetic states. Therefore, these clusters are ideal for the metal node of chemically and electromagnetically tunable metal-organic frameworks (MOFs). To examine the adsorption-based applications of [Fe₄S₄]-based MOFs, we used density functional theory calculations and studied the adsorption of CO₂, CH₄, H₂O, H₂, N₂, NO₂, O₂, and SO₂ onto [Fe₄S₄]⁰, [Fe₄S₄]²⁺, and two 1D MOF models with the carboxylate and 1,4-benzenedithiolate organic linkers. Our reaction kinetics and thermodynamics results indicated that MOF formation promotes the oxidative and hydrolytic stability of the [Fe₄S₄] clusters but decreases their adsorption efficiency. Our study suggests the potential industrial applications of these [Fe₄S₄]-based MOFs because of their limited capacity to adsorb CO₂, CH₄, H₂O, H₂, N₂, O₂, and SO₂ and high selectivity for NO₂ adsorption.

Review on the QM/MM Methodologies and Their Application to Metalloproteins

The multiscaling quantum mechanics/molecular mechanics (QM/MM) approach was introduced in 1976, while the extensive acceptance of this methodology started in the 1990s. The combination of QM/MM approach with molecular dynamics (MD) simulation, otherwise known as the QM/MM/MD approach, is a powerful and promising tool for the investigation of chemical reactions’ mechanism of complex molecular systems, drug delivery, properties of molecular devices, organic electronics, etc. In the present review, the main methodologies in the multiscaling approaches, i.e., density functional theory (DFT), semiempirical methodologies (SE), MD simulations, MM, and their new advances are discussed in short. Then, a review on calculations and reactions on metalloproteins is presented, where particular attention is given to nitrogenase that catalyzes the conversion of atmospheric nitrogen molecules N₂ into NH₃ through the process known as nitrogen fixation and the FeMo-cofactor.