Intrinsic glassy-metallic transport in an amorphous coordination polymer.

Conducting organic materials, such as doped organic polymers1, molecular conductors2,3 and emerging coordination polymers4, underpin technologies ranging from displays to flexible electronics5. Realizing high electrical conductivity in traditionally insulating organic materials necessitates tuning their electronic structure through chemical doping6. Furthermore, even organic materials that are intrinsically conductive, such as single-component molecular conductors7,8, require crystallinity for metallic behaviour. However, conducting polymers are often amorphous to aid durability and processability9. Using molecular design to produce high conductivity in undoped amorphous materials would enable tunable and robust conductivity in many applications10, but there are no intrinsically conducting organic materials that maintain high conductivity when disordered. Here we report an amorphous coordination polymer, Ni tetrathiafulvalene tetrathiolate, which displays markedly high electronic conductivity (up to 1,200 S cm-1) and intrinsic glassy-metallic behaviour. Theory shows that these properties are enabled by molecular overlap that is robust to structural perturbations. This unusual set of features results in high conductivity that is stable to humid air for weeks, pH 0-14 and temperatures up to 140 °C. These findings demonstrate that molecular design can enable metallic conductivity even in heavily disordered materials, raising fundamental questions about how metallic transport can exist without periodic structure and indicating exciting new applications for these materials.

Selective Cobalt-Mediated Formation of Hydrogen Peroxide from Water under Mild Conditions via Ligand Redox Non-Innocence.

Despite the broad importance of hydrogen peroxide (H2O2) in oxidative transformations, there are comparatively few viable routes for its production. The majority of commercial H2O2 is currently produced by the stepwise reduction of dioxygen (O2) via the anthraquinone process, but direct electrochemical formation from water (H2O) would have several advantages─namely, avoiding flammable gases or stepwise separations. However, the selective oxidation of H2O to form H2O2 over the thermodynamically favored product of O2 is a difficult synthetic challenge. Here, we present a molecular H2O oxidation system with excellent selectivity for H2O2 that functions both stoichiometrically and catalytically. We observe high efficiency for electrocatalytic H2O2 production at low overpotential with no O2 observed under any conditions. Mechanistic studies with both calculations and kinetic analyses from isolated intermediates suggest that H2O2 formation occurs in a bimolecular fashion via a dinuclear H2O2-bridged intermediate with an important role for a redox non-innocent ligand. This system showcases the ability of metal-ligand cooperativity and strategic design of the secondary coordination sphere to promote kinetically and thermodynamically challenging selectivity in oxidative catalysis.

Variable Peripheral Ligand Donation Tunes Electronic Structure and NIR II Emission in Tetrathiafulvalene Tetrathiolate Diradicaloids.

Near-infrared (NIR) lumiphores are promising candidates for numerous imaging, communication, and sensing applications, but they typically require large, conjugated scaffolds to achieve emission in this low-energy region. Due to the extended conjugation and synthetic complexity required, it is extremely difficult to tune the photophysical properties of these systems for desired applications. Here, we report facile tuning of deep NIR-emitting diradicaloid complexes through simple modification of peripheral ligands. These new lumiphores are rare examples of air-, acid-, and water-stable emissive diradicaloids. We apply a simple Hammett parameter-based strategy to tune the electron donation of the capping ligand across a series of commercially available triarylphosphines. This minor peripheral modification significantly alters the electronic structure, and consequently, the electrochemical, photophysical, and magnetic properties of the tetrathiafulvalene tetrathiolate (TTFtt)-based lumiphores. The resultant ∼100 nm absorption and emission range spans common laser lines and the desirable telecom region (ca. 1260-1550 nm). Furthermore, these lumiphores are sensitive to local dielectrics, distinguishing them as promising candidates for ratiometric imaging and/or barcoding in the deep NIR region.

Probing pH-Dependent Dehydration Dynamics of Mg and Ca Cations in Aqueous Solutions with Multi-Level Quantum Mechanics/Molecular Dynamics Simulations.

The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca2+ and Mg2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca2+ and Mg2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca2+ and Mg2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca2+ and Mg2+. Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.

Universal Generalization of Density Functional Theory for Static Correlation.

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Origin of Weak Magnetic Coupling in a Dimanganese(II) Complex Bridged by the Tetrathiafulvalene-Tetrathiolate Radical.

Magnetic exchange coupling (J) between different spin centers plays a crucial role in molecule-based magnetic materials. Direct exchange coupling between an organic radical and a metal is frequently stronger than superexchange through diamagnetic ligands, and the strategy of using organic radicals to engender desirable magnetic properties has been an area of active investigation. Despite significant advances and exciting bulk properties, the magnitude of J for radical linkers bridging paramagnetic centers is still difficult to rationally predict. It is thus important to elucidate the features of organic radicals that govern this parameter. Here, we measure J for the tetrathiafulvalene-tetrathiolate radical (TTFtt3-•) in a dinuclear Mn(II) complex. Magnetometry studies show that the antiferromagnetic coupling in this complex is much weaker than that in related Mn(II)-radical compounds, in contrast to what might be expected for the S-based chelating donor atoms of TTFtt. Experimental and computational analyses suggest that this small J coupling may be attributed to poor overlap between Mn- and TTFtt-based magnetic orbitals coupled with insignificant spin density on the coordinating S-atoms. These factors override any expected increase in J from the comparatively strong S-donors. This work elucidates the magnetic coupling properties of the TTFtt3-• radical for the first time and also demonstrates how multiple competing factors must be considered in rationally designing organic radical ligands for molecular-based magnetic compounds.

Generation and Aerobic Oxidative Catalysis of a Cu(II) Superoxo Complex Supported by a Redox-Active Ligand.

Cu systems feature prominently in aerobic oxidative catalysis in both biology and synthetic chemistry. Metal ligand cooperativity is a common theme in both areas as exemplified by galactose oxidase and by aminoxyl radicals in alcohol oxidations. This has motivated investigations into the aerobic chemistry of Cu and specifically the isolation and study of Cu-superoxo species that are invoked as key catalytic intermediates. While several examples of complexes that model biologically relevant Cu(II) superoxo intermediates have been reported, they are not typically competent aerobic catalysts. Here, we report a new Cu complex of the redox-active ligand tBu,TolDHP (2,5-bis((2-t-butylhydrazono)(p-tolyl)methyl)-pyrrole) that activates O2 to generate a catalytically active Cu(II)-superoxo complex via ligand-based electron transfer. Characterization using ultraviolet (UV)-visible spectroscopy, Raman isotope labeling studies, and Cu extended X-ray absorption fine structure (EXAFS) analysis confirms the assignment of an end-on κ1 superoxo complex. This Cu-O2 complex engages in a range of aerobic catalytic oxidations with substrates including alcohols and aldehydes. These results demonstrate that bioinspired Cu systems can not only model important bioinorganic intermediates but can also mediate and provide mechanistic insight into aerobic oxidative transformations.

Bright, Modular, and Switchable Near-Infrared II Emission from Compact Tetrathiafulvalene-Based Diradicaloid Complexes.

Near-infrared (NIR)-emitting molecules are promising candidates for biological sensing and imaging applications; however, many NIR dyes are large conjugated systems which frequently have issues with stability, solubility, and tunability. Here, we report a novel class of compact and tunable fluorescent diradicaloid complexes which are air-, water-, light-, and temperature-stable. These properties arise from a compressed π manifold which promotes an intense ligand-centered π-π transition in the NIR II (1000-1700 nm) region and which subsequently emits at ∼1200 nm. This emission is among the brightest known for monomolecular lumiphores with deep NIR II (>1100 nm) emission, nearly an order of magnitude brighter than the commercially available NIR II dye IR 26. Furthermore, this fluorescence is electrochemically sensitive, with efficient switching upon addition of redox agents. The brightness, stability, and modularity of this system distinguish it as a promising candidate for the development of new technologies built around NIR emission.

Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes.

The synthesis and design of organic biradicals with tunable singlet-triplet gaps have become the subject of significant research interest, owing to their possible photochemical applications and use in the development of molecular switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has been demonstrated to exhibit such organic biradical character in doubly ionized bimetallic complexes. In this article we use high-level ab initio calculations to interrogate the electronic structure of a series of TTFtt-bridged metal complexes, resolving the factors governing their biradical character and singlet-triplet gaps. We show that the degree of biradical character correlates with a readily measured experimental predictor, the central TTFtt C-C bond length, and that it may be described by a one-parameter model, providing valuable insight for the future rational design of TTFtt based biradical compounds and materials.

Elucidating the molecular orbital dependence of the total electronic energy in multireference problems.

The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference and dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investigated. Recent research has shown the ability of Kohn-Shan density functional theory to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here, we extend the search for optimal and more cost effective MOs to post-configuration-interaction [post-(CI)] methods, surveying the ability of the MOs obtained with various density functional theory (DFT) functionals, as well as Hartree-Fock and CC and MP calculations to accurately capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation to the dissociation of N2, the calculation of biradical singlet-triplet gaps, and the transition states of bicylobutane isomerization, we demonstrate that DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.

Accurate singlet-triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schrödinger equation.

The accurate description of biradical systems, and in particular the resolution of their singlet-triplet gaps, has long posed a major challenge to the development of electronic structure theories. Biradicaloid singlet ground states are often marked by strong correlation and, hence, may not be accurately treated by mainstream, single-reference methods such as density functional theory or coupled cluster theory. The anti-Hermitian contracted Schrödinger equation (ACSE), whose fundamental quantity is the two-electron reduced density matrix rather than the N-electron wave function, has previously been shown to account for both dynamic and strong correlations when seeded with a strongly correlated guess from a complete active space (CAS) calculation. Here, we develop a spin-averaged implementation of the ACSE, allowing it to treat higher multiplicity states from the CAS input without additional state preparation. We apply the spin-averaged ACSE to calculate the singlet-triplet gaps in a set of small main group biradicaloids, as well as the organic four-electron biradicals trimethylenemethane and cyclobutadiene, and naphthalene, benchmarking the results against other state-of-the-art methods reported in the literature.

Quantum-classical hybrid algorithm for the simulation of all-electron correlation.

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.

Reversible Switching of Organic Diradical Character via Iron-Based Spin-Crossover.

Organic diradicals are uncommon species that have been intensely studied for their unique properties and potential applicability in a diverse range of innovative fields. While there is a growing class of stable and well-characterized organic diradicals, there has been recent focus on how diradical character can be controlled or modulated with external stimuli. Here we demonstrate that a diiron complex bridged by the doubly oxidized ligand tetrathiafulvalene-2,3,6,7-tetrathiolate (TTFtt2-) undergoes a thermally induced Fe-centered spin-crossover which yields significant diradical character on TTFtt2-. UV-vis-near-IR, Mössbauer, NMR, and EPR spectroscopies with magnetometry, crystallography, and advanced theoretical treatments suggest that this diradical character arises from a shrinking TTFtt2- π-manifold from the Fe(II)-centered spin-crossover. The TTFtt2--centered diradical is predicted to have a singlet ground state by theory and variable temperature EPR. This unusual phenomenon demonstrates that inorganic spin transitions can be used to modulate organic diradical character.

Sparse non-orthogonal wave function expansions from the extension of the generalized Pauli constraints to the two-electron reduced density matrix.

Generalized Pauli constraints (GPCs) impose constraints in the form of inequalities on the natural orbital occupation numbers of the one electron reduced density matrix (1-RDM), defining the set of pure N-representable 1-RDMs, or 1-RDMs that can be derived from an N-electron wave function. Saturation of these constraints is termed "pinning" and implies a significant simplification of the N-electron wave function as the number of Slater determinants required to fully describe the system is reduced. Recent research has shown pinning to occur for the ground states of atoms and molecules with N = 3 and r = 6, where N is the number of electrons and r is the number of spin orbitals. For N = 4 and r = 8, however, pinning occurs not to the GPCs but rather to inequalities defining the pure N-representable two-electron reduced density matrices (2-RDMs). Using these more general inequalities, we derive a wave function ansatz for a system with four electrons in eight spin orbitals. We apply the ansatz to the isoelectronic series of the carbon atom and the dissociation of linear H4 where the correlation energies are recovered to fractions of a kcal/mol. These results provide a foundation for further developments in wave function and RDM theories based on "pinned" solutions, and elucidate a fundamental physical basis for the emergence of non-orthogonal bases in electronic systems of N ≥ 4.

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions.

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Characterizing the Mechanisms of Ca and Mg Carbonate Ion-Pair Formation with Multi-Level Molecular Dynamics/Quantum Mechanics Simulations.

The carbonate minerals of Ca and Mg are abundant throughout the lithosphere and have recently garnered significant research interest as possible long-term carbon sinks in the sequestration of atmospheric carbon dioxide. Nonetheless, an understanding of the atomic-level processes comprising their mineralization remains limited. Here, we characterize and contrast the mechanisms of contact ion-pair formation in aqueous Ca and Mg carbonate systems, which represents the most fundamental step leading to the formation of their mineral solids. Utilizing multilevel embedded correlated wavefunction-based ab initio molecular dynamics/quantum mechanics simulations, we characterize not only the dynamics of these processes but also factors arising from the electronic structure of the involved species, revealing further details of the fundamentally different mechanisms for the interconversion between the contact ion-pairs and solvent-shared ion-pairs of Ca versus Mg carbonate.

Tetrathiafulvalene-2,3,6,7-tetrathiolate linker redox-state elucidation via S K-edge X-ray absorption spectroscopy.

Sulfur K-edge XAS data provide a unique tool to examine oxidation states and covalency in electronically complex S-based ligands. We present sulfur K-edge X-ray absorption spectroscopy on a discrete redox-series of Ni-based tetrathiafulvalene tetrathiolate (TTFtt) complexes as well as on a 1D coordination polymer (CP), NiTTFtt. Experiment and theory suggest that Ni-S covalency decreases with oxidation which has implications for charge transport pathways.

Density Functional Theory Transformed into a One-Electron Reduced-Density-Matrix Functional Theory for the Capture of Static Correlation.

Density Functional Theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically transformed into a one-electron reduced-density-matrix (1-RDM) functional theory, which can address the limitations of DFT while retaining favorable computational scaling compared to wave function based approaches. In addition to relaxing the idempotency restriction on the 1-RDM in the kinetic energy term, we add a quadratic 1-RDM-based term to DFT's density-based exchange-correlation functional. Our approach, which we implement by quadratic semidefinite programming at DFT's computational scaling of O(r3), yields substantial improvements over traditional DFT in the description of static correlation in chemical structures and processes such as singlet biradicals and bond dissociations.

Comparison of Density-Matrix Corrections to Density Functional Theory.

Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work, we transformed DFT into a one-electron reduced density matrix theory (1-RDMFT) via the inclusion of a quadratic one-electron reduced density matrix (1-RDM) correction. Here, we combine our 1-RDMFT approach with different DFT functionals as well as Hartree-Fock to elucidate the method's dependence on the underlying functional selection. Furthermore, we generalize the information density matrix functional theory (iDMFT), recently developed as a correction to the Hartree-Fock method, by incorporating density functionals in place of the Hartree-Fock functional. We relate iDMFT mathematically to our approach and benchmark the two with a common set of functionals and systems.

Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming.

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems, and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the static correlation in DFT when frontier orbitals are degenerate by the means of using a semidefinite programming (SDP) approach to minimize the system energy as a function of the N-representable, non-idempotent 1-electron reduced density matrix. While showing greatly improved singlet-triplet gaps for local density approximation and generalized gradient approximation (GGA) functionals, the SDP procedure reveals flaws in modern meta and hybrid GGA functionals, which show no major improvements when provided with an accurate electron density.