Static and Dynamic Electron Correlation in the Ligand Noninnocent Oxidation of Nickel Dithiolates

Unveiling the Low-Lying Spin States of [Fe3S4] Clusters via the Extended Broken-Symmetry Method

Photosynthetic water splitting, when synergized with hydrogen production catalyzed by hydrogenases, emerges as a promising avenue for clean and renewable energy. However, theoretical calculations have faced challenges in elucidating the low-lying spin states of iron-sulfur clusters, which are integral components of hydrogenases. To address this challenge, we employ the Extended Broken-Symmetry method for the computation of the cubane-[Fe3S4] cluster within the [FeNi] hydrogenase enzyme. This approach rectifies the error caused by spin contamination, allowing us to obtain the magnetic exchange coupling constant and the energy level of the low-lying state. We find that the Extended Broken-Symmetry method provides more accurate results for differences in bond length and the magnetic coupling constant. This accuracy assists in reconstructing the low-spin ground state force and determining the geometric structure of the ground state. By utilizing the Extended Broken-Symmetry method, we further highlight the significance of the geometric arrangement of metal centers in the cluster's properties and gain deeper insights into the magnetic properties of transition metal iron-sulfur clusters at the reaction centers of hydrogenases. This research illuminates the untapped potential of hydrogenases and their promising role in the future of photosynthesis and sustainable energy production.

Characterizing Excited States of a Copper-Based Molecular Qubit Candidate with Correlated Electronic Structure Methods

Molecular spins have a variety of potential advantages as qubits for quantum computation, such as tunability and well-understood design pathways through organometallic synthesis. Organometallic and heavy-metal-based molecular spin qubits can also exhibit rich electronic structures due to ligand field interactions and electron correlation. These features make consistent and reliable modeling of these species a considerable challenge for contemporary electronic structure techniques. Here, we elucidate the electronic structure of a Cu(II) complex analogous to a recently proposed room-temperature molecular spin qubit. Using active space methods to describe the electron correlation, we show the nuanced interaction between the metal d orbitals and ligand σ and π orbitals makes these systems challenging to model, both in terms of the delocalized spin density and the excited state ordering. We show that predicting the correct spin delocalization requires special consideration of the Cu d orbitals and that the excited state spectrum for the Cu(III) complex also requires the explicit inclusion of the π orbitals in the active space. These interactions are rather common in molecular spin qubit motifs and may play an important role in spin-decoherence processes. Our results may lend insight into future studies of the orbital interactions and electron delocalization of similar complexes.

Qubit Condensation for Assessing Efficacy of Molecular Simulation on Quantum Computers

Quantum computers may demonstrate significant advantages over classical devices, as they are able to exploit a purely quantum-mechanical phenomenon known as entanglement in which a single quantum state simultaneously populates two-or-more classical configurations. However, due to environmental noise and device errors, elaborate quantum entanglement can be difficult to prepare on modern quantum computers. In this paper, we introduce a metric based on the condensation of qubits to assess the ability of a quantum device to simulate many-electron systems. Qubit condensation occurs when the qubits on a quantum computer condense into a single, highly correlated particle-hole state. While conventional metrics like gate errors and quantum volume do not directly target entanglement, the qubit-condensation metric measures the quantum computer's ability to generate an entangled state that achieves nonclassical long-range order across the device. To demonstrate, we prepare qubit condensations on various quantum devices and probe the degree to which qubit condensation is realized via postmeasurement analysis. We show that the predicted ranking of the quantum devices is consistent with the errors obtained from molecular simulations of H₂ using a contracted quantum eigensolver.

Challenges for Variational Reduced-Density-Matrix Theory: Total Angular Momentum Constraints

The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum (J) and projection of total angular momentum (M_J) states in atomic systems described by nonrelativistic Hamiltonians, and it is shown that the approach exhibits serious deficiencies. Under ensemble N-representability constraints, v2RDM theory fails to retain the appropriate degeneracies among various J states for fixed spin (S) and orbital angular momentum (L), and for fixed L, S, and J, the manifold of M_J states is not necessarily degenerate. Moreover, a substantial energy error is observed for a system for which the two-electron reduced density matrix is exactly ensemble N-representable; in this case, the error stems from violations in pure-state N-representability conditions. Unfortunately, such violations do not appear to be good indicators of the reliability of energies from v2RDM theory in general. Several states are identified for which energy errors are near zero and yet pure-state conditions are clearly violated.

del Campo J. Charge delocalization error in Piris Natural Orbital Functionals

Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.

Near-Exact Nuclear Gradients of Complete Active Space Self-Consistent Field Wave Functions

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules.We show that the HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant error.The ability of HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems which require a larger active space than possible with complete active space self-consistent field (CASSCF).Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT).We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional.We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet-triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.

Complexation and redox chemistry of neptunium, plutonium and americium with a hydroxylaminato ligand

There is significant interest in ligands that can stabilize actinide ions in oxidation states that can be exploited to chemically differentiate 5f and 4f elements. Applications range from developing large-scale actinide separation strategies for nuclear industry processing to carrying out analytical studies that support environmental monitoring and remediation efforts. Here, we report syntheses and characterization of Np(iv), Pu(iv) and Am(iii) complexes with N-tert-butyl-N-(pyridin-2-yl)hydroxylaminato, [2-(^tBuNO)py]⁻(interchangeable hereafter with [(^tBuNO)py]⁻), a ligand which was previously found to impart remarkable stability to cerium in the +4 oxidation state. An[(^tBuNO)py]₄ (An = Pu, 1; Np, 2) have been synthesized, characterized by X-ray diffraction, X-ray absorption, ¹H NMR and UV-vis-NIR spectroscopies, and cyclic voltammetry, along with computational modeling and analysis. In the case of Pu, oxidation of Pu(iii) to Pu(iv) was observed upon complexation with the [(^tBuNO)py]⁻ ligand. The Pu complex 1 and Np complex 2 were also isolated directly from Pu(iv) and Np(iv) precursors. Electrochemical measurements indicate that a Pu(iii) species can be accessed upon one-electron reduction of 1 with a large negative reduction potential (E_1/2 = −2.26 V vs. Fc^+/0). Applying oxidation potentials to 1 and 2 resulted in ligand-centered electron transfer reactions, which is different from the previously reported redox chemistry of U^IV[(^tBuNO)py]₄ that revealed a stable U(v) product. Treatment of an anhydrous Am(iii) precursor with the [(^tBuNO)py]⁻ ligand did not result in oxidation to Am(iv). Instead, the dimeric complex [Am^III(μ₂-(^tBuNO)py)((^tBuNO)py)₂]₂ (3) was isolated. Complex 3 is a rare example of a structurally characterized non-aqueous Am-containing molecular complex prepared using inert atmosphere techniques. Predicted redox potentials from density functional theory calculations show a trivalent accessibility trend of U(iii) < Np(iii) < Pu(iii) and that the higher oxidation states of actinides (i.e., +5 for Np and Pu and +4 for Am) are not stabilized by [2-(^tBuNO)py]⁻, in good agreement with experimental observations.

The coordination modes and electronic properties of a strongly coordinating hydroxylaminato ligand with Np, Pu and Am were investigated.Complexes were characterized by a range of experimental and computational techniques.

Conductance Switching in an Organometallic Single-Electron Transistor Using Current-Constrained Reduced-Density Matrix Theory

We report switching of molecular conductance at finite bias in a binuclear organometallic complex and its cation which were previously experimentally analyzed at low voltages to see the signature of Kondo resonance. The variational reduced density matrix theory is applied to show that the system is strongly multireferenced especially in its charged form. We also study the molecular conductance of both forms using recently developed current-constrained two-electron reduced density matrix theory which is capable of handling strong electronic correlation. We compare the results against an uncorrelated 1-electron reduced density matrix version of conductance calculations using Hartree-Fock molecular orbitals. We observe that despite quantitative disagreements, the qualitative trend in the conductance is correctly predicted to be favorable for the cationic partner by both methods. We explain the results using the inherently high density of states for the low-lying excited states in the cationic partner which is also replicable from uncorrelated electronic structure methods. Our results not only indicate that the low-bias conductance trend is maintained even beyond the Kondo regime and produces quantitative agreement with that of the experiment but also identifies important physical markers that are responsible for the high conductance of the charged species.

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or nontrivial high-dimensional classical optimization. Here, we introduce a quantum solver of contracted eigenvalue equations, the quantum analog of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

A four-parameter system for rationalising the electronic properties of transition metal–radical ligand complexes

A heuristic four-parameter scheme captures and predicts the electronic properties of radical-ligand transition metal compounds, overcoming ligand specific descriptions.

Redox, transmetalation, and stacking properties of tetrathiafulvalene-2,3,6,7-tetrathiolate bridged tin, nickel, and palladium compounds

Here we report that capping the molecule TTFtt (TTFtt = tetrathiafulvalene-2,3,6,7-tetrathiolate) with dialkyl tin groups enables the isolation of a stable series of redox congeners and facile transmetalation to Ni and Pd. TTFtt has been proposed as an attractive building block for molecular materials for two decades as it combines the redox chemistry of TTF and dithiolene units. TTFttH₄, however, is inherently unstable and the incorporation of TTFtt units into complexes or materials typically proceeds through the in situ generation of the tetraanion TTFtt^4-. Capping of TTFtt^4- with Bu₂Sn²⁺ units dramatically improves the stability of the TTFtt moiety and furthermore enables the isolation of a redox series where the TTF core carries the formal charges of 0, +1, and +2. All of these redox congeners show efficient and clean transmetalation to Ni and Pd resulting in an analogous series of bimetallic complexes capped by 1,2-bis(diphenylphosphino)ethane (dppe) ligands. Furthermore, by using the same transmetalation method, we synthesized analogous palladium complexes capped by 1,1'-bis(diphenylphosphino)ferrocene (dppf) which had been previously reported. All of these species have been thoroughly characterized through a systematic survey of chemical and electronic properties by techniques including cyclic voltammetry (CV), ultraviolet-visible-near infrared spectroscopy (UV-vis-NIR), electron paramagnetic resonance spectroscopy (EPR), nuclear magnetic resonance spectroscopy (NMR) and X-ray diffraction (XRD). These detailed synthetic and spectroscopic studies highlight important differences between the transmetalation strategy presented here and previously reported synthetic methods for the installation of TTFtt. In addition, the utility of this stabilization strategy can be illustrated by the observation of unusual TTF radical-radical packing in the solid state and dimerization in the solution state. Theoretical calculations based on variational 2-electron reduced density matrix methods have been used to investigate these unusual interactions and illustrate fundamentally different levels of covalency and overlap depending on the orientations of the TTF cores. Taken together, this work demonstrates that tin-capped TTFtt units are ideal reagents for the installation of redox-tunable TTFtt ligands enabling the generation of entirely new geometric and electronic structures.

Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach

Excited-state energies are computed in the space of single-electron transitions from the ground state from only a knowledge of the two-electron reduced density matrix (2-RDM). Previous work developed and applied the theory to small molecular systems with accurate results, but applications to both larger and more correlated molecules were hindered by ill-conditioning of the effective eigenvalue problem. Here we improve the excited-spectra 2-RDM theory through a stable Hamiltonian-shifted regularization algorithm that removes the near singularities within the computation. The theory with ground-state 2-RDMs from the variational 2-RDM method is applied to the excited energies of strongly correlated molecules including the optical band gap of hydrogen and acene chains, the singlet-triplet splitting of nickel dithiolates, as well as the low-lying excited states of an optical dye. While single-excitation theories like CISD and TD-DFT underestimate band gaps and excited-state splittings, the 2-RDM theory yields band gap and excited-state splittings that are in good agreement with full configuration interaction and experiment where available.