Mixed-valence Systems Research Articles

Ionic species representations for materials informatics

High-dimensional representations of the elements have become common within the field of materials informatics to build useful, structure-agnostic models for the chemistry of materials. However, the characteristics of elements change when they adopt a given oxidation state, with distinct structural preferences and physical properties. We explore several methods for developing embedding vectors of elements decorated with oxidation states. Graphs generated from 110 160 crystals are used to train representations of 84 elements that form 336 species. Clustering these learned representations of ionic species in low-dimensional space reproduces expected chemical heuristics, particularly the separation of cations from anions. We show that these representations have enhanced expressive power for property prediction tasks involving inorganic compounds. We expect that ionic representations, necessary for the description of mixed valence and complex magnetic systems, will support more powerful machine learning models for materials.

Theoretical insight into clocking in a molecular mixed-valence cell of quantum cellular automata through the vibronic approach.

In this article, we develop a vibronic theory of clocking in molecular quantum cellular automata (QCA). The clocking mechanism is considered for a trigonal trimeric mixed-valence (MV) system with one mobile electron, which is shown to act as the dimeric unit encoding binary information (Boolean states 0 or 1) coupled to a third redox center (Null state). The model includes the electron transfer between the three centers; vibronic coupling of the mobile charge with the "breathing" modes, forming a double degenerate Jahn-Teller vibration of the molecular triangle; and two electric fields, one collinear to the dimeric unit, which controls the binary states, and the other perpendicular to this unit, performing clocking. In the framework of the adiabatic approximation, the potential surface of the trimeric system has been studied and the condition determining switching and clocking has been analyzed in terms of the two controlling fields and the vibronic and transfer parameters. A thorough understanding of the site populations is achieved through the quantum-mechanical solution of the vibronic problem, maintaining the adiabatic condition for the controlling fields. It is shown that a MV trimer can act as a molecular clocked QCA cell, with favorable conditions being a positive electron transfer parameter and sufficiently strong vibronic coupling.

Mixed-valence system with near-infrared electrochromism of Fe(II)-based metal-organic coordination polymers

Near-infrared electrochromic materials have garnered great attention due to their potential applications in optical data storage and military camouflage. Herein, a networked metal-organic coordination polymer bearing multi-redox centra (Fe-MCP) was successfully prepared by coordination interaction of Fe ions with D-A-D-structure ligands through the liquid-liquid interface self-assembly strategy. The resultant uniform film exhibits improved NIR electrochromic attributed to the construction of mixed-valence system. Furthermore, a sandwich-structured electrochromic device was fabricated by combining Fe-MCP electrochromic layer, a gel composed of LiClO4, PMMA, and PC as the electrolyte layer, and anodically coloring PB as an ion storage layer. The resultant device illustrated an optical contrast of 31.4 % at 800 nm and 34.2 % at 1000 nm, a response speed of 4.0 s/8.3 s at 800 nm and 7.6 s/2.7 s at 1000 nm, and good cycling durability. The design principles proposed in this study provide a new insight for the preparation of high-performance NIR electrochromic materials.

Controlling Intramolecular and Intermolecular Electronic Coupling of Radical Ligands in a Series of Cobaltoviologen Complexes.

Controlling electronic coupling between multiple redox sites is of interest for tuning the electronic properties of molecules and materials. While classic mixed-valence (MV) systems are highly tunable, e.g., via the organic bridges connecting the redox sites, metal-bridged MV systems are difficult to control because the electronics of the metal cannot usually be altered independently of redox-active moieties embedded in its ligands. Herein, this limitation was overcome by varying the donor strengths of ancillary ligands in a series of cobalt complexes without directly perturbing the electronics of viologen-like redox sites bridged by the cobalt ions. The cobaltoviologens [1X-Co]n+ feature four 4-X-pyridyl donor groups (X = CO2Me, Cl, H, Me, OMe, NMe2) that provide gradual electronic tuning of the bridging CoII centers, while a related complex [2-Co]n+ with NHC donors supports exclusively CoIII states even upon reduction of the viologen units. Electrochemistry and IVCT band analysis indicate that the MV states of these complexes have electronic structures ranging from fully localized ([2-Co]4+; Robin-Day Class I) to fully delocalized ([1CO2Me-Co]3+; Class III) descriptions, demonstrating unprecedented control over electronic coupling without changing the identity of the redox sites or bridging metal. Additionally, single-crystal XRD characterization of the homovalent complexes [1H-Co]2+ and [1H-Zn]2+ revealed radical-pairing interactions between the viologen ligands of adjacent complexes, representing a type of through-space electronic coupling commonly observed for organic viologen radicals but never before seen in metalloviologens. The extended solid-state packing of these complexes produces 3D networks of radical π-stacking interactions that impart unexpected mechanical flexibility to these crystals.

Stable Spiro-Fused Diarylaminyl Radicals: A New Type of a Neutral Mixed-Valence System.

A new type of neutral mixed-valence system was synthesized using a facile one-pot procedure. The spiro-conjugated framework is additionally "fastened" with a biphenyl bridge, which does not directly participate in spin delocalization but makes the molecule stable and influences the reorganization energy and the energy barrier of the intramolecular electron transfer. The in-depth experimental and quantum-chemical study allowed determining the radicals as the Class II Robin-Day-mixed-valence systems. The structure of the radicals was confirmed by the X-ray data, which are relatively rare for Class II MV molecules. Advanced properties of the radicals, such as an ambipolar redox behavior and panchromatic absorption in the visible and NIR regions, along with their stability, make them of interest for materials science. All radicals demonstrate the SOMO-HOMO inversion phenomenon, which was supported by the DFT and the experimental study.

Structure of the normal state and origin of the Schottky anomaly in the correlated heavy-fermion superconductor UTe2

The recently discovered $\mathrm{U}{\mathrm{Te}}_{2}$ superconductor is regarded as a heavy-fermion mixed-valence system with very peculiar properties within the normal and superconducting (SC) states. It shows no signs of magnetic order, but has a strong anisotropy of magnetic susceptibility and SC critical field. In addition to a heavy-fermion-like behavior in the normal state, it exhibits a distinctive Schottky-type anomaly at $\ensuremath{\sim}12$ K and a characteristic excitations gap $\ensuremath{\sim}35\ensuremath{-}40$ K. Here, we show, by virtue of dynamical mean-field theory calculations with a quasiatomic treatment of electron correlations, that ab initio-derived crystal-field splitting of the $5{f}^{2}$ ionic configuration yields agreement with these experimental observations. A close analogy of the normal paramagnetic state of $\mathrm{U}{\mathrm{Te}}_{2}$ to that of $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ in the Kondo arrest scenario is revealed. We consider the impact of anisotropic superexchange interactions within the U-U structural dimer on magnetization and development of strong orbital and magnetic moment fluctuations in $\mathrm{U}{\mathrm{Te}}_{2}$.

Near-Infrared-I to III Absorption and Emission via Core Engineering of Open-shelled Organic Mixed-Valence Systems.

A novel class of agents was developed based on the core engineering of open-shelled organic mixed-valence (MV) systems, which enabled tunable absorption and emission across the NIR-I to III biowindow (700-1850nm) by adjusting the number of central nitrogen oxidation sites and the length of the conjugated bridge. Organic mixed-valence (MV) systems were synthesized through a one-step partial chemical oxidation of starburst oligoarylamines, with varying nitrogen oxidation sites and conjugated bridge lengths, including T4EPAn+ , TPDAn+ , and TMPBn+ . The absorption wavelength of the MV systems red-shifted clearly as the number of central nitrogen oxidation sites increased or the conjugated bridge length was prolonged. T4EPAn+ with one central nitrogen oxidation site exhibited fluorescence emission in the range of 900-1400nm, while TPDAn+ with two central nitrogen oxidation sites demonstrated strong heat generation capabilities. Additionally, the absorption peak of TMPBn+ with a biphenyl conjugated bridge reached up to 1610nm. Especially, these MV systems are highly stable for biological applications due to their high steric hindrance and hyperconjugation effect. These characteristics make MV systems promising candidates for constructing NIR-I/II/III emitters and photothermal agents, representing a significant advance towards developing the next generation of NIR-I to III agents. This article is protected by copyright. All rights reserved.

Terpyridine ruthenium–triarylamine asymmetrical mixed-valence systems: Syntheses, (Spectro) electrochemistry and theoretical calculations

A series of asymmetrical terpyridine ruthenium-TAA redox-active organometallic complexes was prepared and characterized. The bonding and electronic properties of these complexes were investigated by spectro-electrochemistry and theoretical calculations. Electrochemical results revealed that four complexes exhibited two successive single-electron redox processes, in which the first-step electrochemical behavior of tpyRu-ethynyl-TAA complexes occurred at the triarylamine moiety, the first-step based-metal oxidation of Cl-tpyRu-TAA complex was decided, and their half-wave potential difference ∆E decreased gradually. The near-infrared (NIR) spectroscopic results of mixed-valence states obtained by spectro-electrochemistry showed that they all have NIR multiple absorption characteristics. The maximum absorption wavelength of singly-oxidized tpyRu-ethynyl-TAA molecules redshifted with bridge conjugate extension, whereas Cl-tpyRu-TAA mixed-valence state only displayed weak absorption at high-energy region, as later confirmed by TDDFT calculation. The electron coupling parameters Hab obtained from the inter-valence charge transfer analysis of mixed-valence states by the Marcus–Hush theory decreased gradually with the extension of the bridge chain, consistent with the electrochemical results. In addition, DFT calculation reflected that the HOMO contribution in bridge chain of neutral molecules increased with the conjugate bridge extension, and the spin density distribution of mixed-valence states was mainly localized on the aryl bridge and NAr2 and featured the less metal character and hence less charge delocalization. The above results concluded that the degree of electronic coupling and the order of redox processes are greatly affected by conjugated bridge and the coordination model between terpyridine and ruthenium.

Origin of negative thermal expansion in strongly correlated f− electron systems

We have investigated the origin of the negative-thermal-expansion (NTE) phenomena observed in various strongly correlated $\mathit{f}\text{\ensuremath{-}}$electron systems, including Ce, Sm, and Yb rare-earth compounds and actinide element Pu. We have thoroughly surveyed existing nonmagnetic $\mathit{f}\text{\ensuremath{-}}$electron NTE materials and identified that the temperature ($T$)-induced valence transition plays an essential role in realizing the NTE in Sm- and Yb-based mixed-valence (MV) systems. We have discussed the contrasting thermal-expansion behaviors between (Sm, Yb)-based MV systems and their electron-hole symmetric counterparts (Ce, Eu)-based MV systems that exhibit positive-thermal-expansion (PTE) phenomena. We have also clarified the origin of intriguing thermal expansion behavior of Pu, which, upon cooling, reveals not only the NTE, but also the strong PTE. Finally, we have predicted the possible existence of an additional NTE feature in topological-Kondo-insulator (TKI) candidates of ${\mathrm{SmB}}_{6}$, g-SmS, and ${\mathrm{YbB}}_{12}$ in the low-$T$ regime where the TKI nature is expected to emerge.

Emergent Spin Frustration in Neutral Mixed-Valence 2D Conjugated Polymers: A Potential Quantum Materials Platform

Two-dimensional conjugated polymers (2DCPs)─organic 2D materials composed of arrays of carbon sp2 centers connected by π-conjugated linkers─are attracting increasing attention due to their potential applications in device technologies. This interest stems from the ability of 2DCPs to host a range of correlated electronic and magnetic states (e.g., Mott insulators). Substitution of all carbon sp2 centers in 2DCPs by nitrogen or boron results in diamagnetic insulating states. Partial substitution of C sp2 centers by B or N atoms has not yet been considered for extended 2DCPs but has been extensively studied in the analogous neutral mixed-valence molecular systems. Here, we employ accurate first-principles calculations to predict the electronic and magnetic properties of a new class of hexagonally connected neutral mixed-valence 2DCPs in which every other C sp2 nodal center is substituted by either a N or B atom. We show that these neutral mixed-valence 2DCPs significantly energetically favor a state with emergent superexchange-mediated antiferromagnetic (AFM) interactions between C-based spin-1/2 centers on a triangular sublattice. These AFM interactions are surprisingly strong and comparable to those in the parent compounds of cuprate superconductors. The rigid and covalently linked symmetric triangular AFM lattice in these materials thus provides a highly promising and robust basis for 2D spin frustration. As such, extended mixed-valence 2DCPs are a highly attractive platform for the future bottom-up realization of a new class of all-organic quantum materials, which could host exotic correlated electronic states (e.g., unusual magnetic ordering, quantum spin liquids).

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States.

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Electronic coupling and electron transfer in hydrogen-bonded mixed-valence compounds.

Electron transfer provided by hydrogen bonds represents a unique and highly significant area of research, as it has a crucial role to play in a wide variety of chemical and biological systems. The hydrogen-bonded mixed-valence system, in the form of donor-hydrogen bond-acceptor, provides an ideal platform for exploring thermally-induced electron transfer across this non-covalent unit. Over the past decades, ongoing progress has been made in this field. Here we critically assess some studies on the qualitative and quantitative evaluation of electronic coupling and thermal electron transfer across hydrogen bond interface. Additionally, selected experimental examples are discussed in terms of intervalence charge transfer, with particular attention paid to the proton-coupled and often overlooked proton-uncoupled electron transfer pathway in hydrogen-bonded mixed-valence systems. We further highlight the major limitations of this research area and suggest potential directions for future exploration.

Observation of an Alternate Charge-Polarization State in a One-Dimensional Pt-Pt-I Chain Compound with a Bulky Pendant Ligand.

A one-dimensional (1D) halogen-bridged dinuclear-metal complex (MMX-chain) exhibits various electronic states based on a mixed-valence metal-dimer system. This report deals with the synthesis and physical properties of a new MMX-chain with a bulky pendant ligand, Pt2 (mcc-HexCS2 )4 I (mcc-HexCS2 =trans-4-(methoxycarbonyl)cyclohexanedithiocarboxylate). The steric hindrance caused by the bulky substituent induces a strain in its 1D chain, achieving at ambient condition the first pure alternate charge-polarization (ACP) state (-Pt2+ -Pt3+ -I- -Pt3+ -Pt2+ -I- -), a kind of spin-Peierls state, as confirmed by X-ray diffraction and its conducting and magnetic properties. The strain effect is also manifested as a very large linear thermal expansion along the chain direction, which is quite different from conventional MMX-chains without a bulky ligand. The design of low-dimensional materials with ligand variations is expected to lead to the emergence of new electron-lattice coupled electronic states.

Cover Feature: Photoinduced Intervalence Charge Transfers: Spectroscopic Tools to Study Fundamental Phenomena and Applications (ChemPhysChem 20/2022)

The Cover Feature shows a molecule that forms, upon photon absorption, an excited state mixed valence system, which is characterized by a double-well potential energy surface. Inspection of the excited state with light reveals photoinduced intervalence charge transfers. More information can be found in the Concept by Alejandro Cadranel and co-workers.

Photoinduced Intervalence Charge Transfers: Spectroscopic Tools to Study Fundamental Phenomena and Applications

The front cover artwork is provided by Dr. Alejandro Cadranel's group at the University of Buenos Aires and the Friedrich-Alexander Universität Erlangen-Nürnberg. The image shows a ground state that forms, upon photon absorption, an excited state mixed valence system, which is characterized by a double-well potential energy surface. Inspection of the excited state with light reveals photoinduced intervalence charge transfers (cover design by Gonzalo Peñaloza). Read the full text of the Concept at 10.1002/cphc.202200384.

(Invited) Homo- and Heteromatallic Cyanide Bridged Networks and Derived Materials for Selected Electrochemical Applications Involving Enhanced Charge Transport and Storage

Hexacyanoferrates and related cyanometallates exhibit model electron transfer properties that are of importance to many electrochemical and related applications. In particular homo- and heterometallic cyanide bridged networks and derived materials have proven to exhibit very rich and diverse electrochemical properties. Their redox properties can be tuned by adjusting stoichiometry and oxidation state of the constituent metal centers, incorporation of interstitial ions, or preparation methods. Polynuclear cyanometallates are promising open-framework systems for low-cost electrochemical energy storage applications. Both soluble and insoluble analogues of Prussian blue have been explored as cathode materials with lithium, sodium, potassium, magnesium, calcium, and even zinc intercalated ionic carriers. Electrochromic devices are another promising area for employing the unique properties of cyanometallates. Prussian blue itself exhibits electrocatalytic properties toward hydrogen peroxide, and it has been used for biosensing and amperometric detection of glucose, L-cysteine, and glutamate. Also removal of radioactive cesium ions from contaminated water has been successfully achieved with Prussian blue and its metal substituted analogues.It is well-established that the choice of redox-active charge-storage material has a significant impact on the performance of a redox flow battery. The concentration of redox centers and their reaction kinetics have an influence on the available current densities and, thus, the power of the device. Remembering the requirement of good solubility of redox species, the semi-solid slurry approach (provided that the dispersion is homogeneous) represents another effective way to improve the volumetric capacity of the redox electrolyte (i.e. of the electrolyte with dissolved redox couples). An interesting approach to improve current densities involves application of circulating suspensions of electroactive materials. Prussian blue and its metal (Fe, Co, Ni, etc.) substituted analogues, which are electroactive mixed-valence inorganic systems, exhibit very rich and diverse electrochemistry. Their electrochemical properties that can be tuned through the variation of the material composition. Special attention will be paid to the formation of stable colloidal suspensions of truly mixed-valence fast-conducting Berlin Green, iron(III) hexacyanoferrate(III,II), together with multi-layered clay-like nickel(II) hexacyanoferrate(III) structures characterized by fast potassium counter-cation motion. It can be hypothesized that the proposed system could serve as the catholyte redox suspension containing large population of mixed-valence redox centers and capable of fast charge propagation and, consequently, yielding fairly large current densities. The materials can also be explored for sorption of large concentrations of Zn2+ ions and for the improvement of the Zn2+/Zn chemistry. While the application of Zn2+/Zn as the anode active system is well established in redox flow batteries, we are going to address and minimize limitations that include the efficiency of zinc deposition and the hydrogen evolution reaction taking place at the potentials where Zn is electrodeposited. The increase of current density could be achieved not only by reducing the viscosity of the electrolyte, thus accelerating charge-carrier transport, but also – by referencing to our experience with mixed-valent nickel hexacyanoferrate system as charge relay for dye-sensitized solar cells – through improvement of the dynamics of charge propagation by improving mobility of charge compensating counter-ions.

Effect of next to next-nearest-neighbor (NNNN) hopping interaction in mixed valence systems and study of the thermodynamic properties

The extended Falicov-Kimball model containing the next to next-nearest-neighbor hopping interaction (NNNN) is investigated using the exact diagonalization calculations in two dimensions. The f-electron density nf with the energy of f-level Ef is investigated using the allowable exact solutions. The temperature dependency of thermodynamical parameters such as specific heat(C) and entropy (S) are also studied here. The significant observations are (i) a discontinuous valence transition (insulator-to-metal) at a certain energy of f-level (Ec ) which varies with the value of NNNN interaction term (t 3), (ii) disorderedness of the system with the increasing value of t 3, (iii) the structures of single and double peaks in the specific heat versus temperature graphs varying with t 3 and E respectively.

Binuclear metal ruthenium complexes bridged by isomeric bis(ethynyl)pyridine: Syntheses, characterization and electronic coupling properties

Isomeric diruthenium complexes with bis(ethynyl)pyridine as bridge core [2,6-bis(ethynyl)pyridine (1), 3,5-bis(ethynyl)pyridine (2), 2,5-bis(ethynyl)pyridine (3)] were successfully prepared and characterized by 1H NMR, 13C NMR and elemental analysis. The electrochemical properties of complexes 1–3 were investigated by cyclic voltammetry (CV) and square-wave voltammetry (SWV), and different potential difference values were revealed and affected by N atom position and distance between redox metal centers. Electron absorption spectra showed that the absorption of the linear molecule 3 displayed a red shift relative to that of complexes 1 and 2. The broad near-infrared absorption characteristic of the singly-oxidized complex 3+ revealed the existence of a mixed-valence state, which can be classified as a class II mixed-valence system according to the intervalence charge transfer (IVCT) absorption parameter Hab and Г. These results indicated that 3 has higher conjugation and charge delocalization ability than isomers 1 and 2. Density functional theory (DFT) calculations spin density distribution analysis further confirmed the above results, and time-dependent DFT showed the NIR multi-absorption of complex 3+, and effectively attributed to Ru–CC→Ru IVCT absorption characteristics.

Photoinduced Intervalence Charge Transfers: Spectroscopic Tools to Study Fundamental Phenomena and Applications.

The exploitation of excited state chemistry for solar energy conversion or photocatalysis has been continuously increasing, and the needs of a transition to a sustainable human development indicate this trend will continue. In this scenario, the study of mixed valence systems in the excited state offers a unique opportunity to explore excited state electron transfer reactivity, and, in a broader sense, excited state chemistry. This Concept article analyzes recent contributions in the field of photoinduced mixed valence systems, i. e. those where the mixed valence core is absent in the ground state but created upon light absorption. The focus is on the utilization of photoinduced intervalence charge transfer bands, detected via transient absorption spectroscopy, as key tools to study fundamental phenomena like donor/acceptor inversion, hole delocalization, coexistence of excited states and excited state nature, together with applications in molecular electronics.

Intense Photoinduced Intervalence Charge Transfer in High-Valent Iron Mixed Phenolate/Carbene Complexes.

We report high‐valent iron complexes supported by N‐heterocyclic carbene (NHC)‐anchored, bis‐phenolate pincer ligands that undergo ligand‐to‐metal charge transfer (LMCT) upon photoexcitation. The resulting excited states – with a lifetime in the picosecond range – feature a ligand‐based, mixed‐valence system and intense intervalence charge transfer bands in the near‐infrared region. Upon oxidation of the complex, corresponding intervalence charge transfer absorptions are also observed in the ground state. We suggest that the spectroscopic hallmarks of such LMCT states provide useful tools to decipher excited‐state decay mechanisms in high‐valent NHC complexes. Our observations further indicate that NHC‐anchored, bis‐phenolate pincer ligands are not sufficiently strong donors to prevent the population of excited metal‐centered states in high‐valent iron complexes.