N-Heterocyclic Carbene to Actinide d-Based π-bonding Correlates with Observed Metal–Carbene Bond Length Shortening Versus Lanthanide Congeners
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Results for “Mathematical methods”
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Tetracene Diacid Aggregates for Directing Energy Flow toward Triplet Pairs
Not Available
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Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons
The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ϵ $\mathbb{N}$). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, E g,exp ~ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.
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Single-Molecule Detection of the Encounter and Productive Electron Transfer Complexes of a Photosynthetic Reaction Center
Small, diffusible redox proteins play an essential role in electron transfer (ET) in respiration and photosynthesis, sustaining life on Earth by shuttling electrons between membrane-bound complexes via finely tuned and reversible interactions. Ensemble kinetic studies show transient ET complexes form in two distinct stages: an “encounter” complex largely mediated by electrostatic interactions, which subsequently, through subtle reorganization of the binding interface, forms a “productive” ET complex stabilized by additional hydrophobic interactions around the redox-active cofactors. Here, using single-molecule force spectroscopy (SMFS) we dissected the transient ET complexes formed between the photosynthetic reaction center-light harvesting complex 1 (RC-LH1) of Rhodobacter sphaeroides and its native electron donor cytochrome c 2 (cyt c 2 ). Importantly, SMFS resolves the distribution of interaction forces into low (~150 pN) and high (~330 pN) components, with the former more susceptible to salt concentration and to alteration of key charged residues on the RC. Thus, the low force component is suggested to reflect the contribution of electrostatic interactions in forming the initial encounter complex, whereas the high force component reflects the additional stabilization provided by hydrophobic interactions to the productive ET complex. Employing molecular dynamics simulations, we resolve five intermediate states that comprise the encounter, productive ET and leaving complexes, predicting a weak interaction between cyt c 2 and the LH1 ring near the RC-L subunit that could lie along the exit path for oxidized cyt c 2 . The multimodal nature of the interactions of ET complexes captured here may have wider implications for ET in all domains of life.
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Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits
High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition-metal complexes via optically detected magnetic resonance (ODMR) mechanisms analogous to the diamond-nitrogen-vacancy color center. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are π-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realize a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimize radical–radical interactions in the ground state, generating π-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarization. Furthermore, the molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular color centers.
Chemistry↗
Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys
The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC 1-x N x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al 1-x Ga x N. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC 1-x N x alloys as substrates for Al 1-x Ga x N. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III-N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. In conclusion, we also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.
36 MATERIALS SCIENCE↗
Structure and Synthesizability of Iron–Sulfur Metal–Organic Frameworks
Sulfur-based metal–organic frameworks (MOFs) and coordination polymers (CPs) are an emerging class of hybrid materials that have received growing attention due to their magnetic, conductive, and catalytic properties with potential applications in electrocatalysis and energy storage. In this work, we report a high-throughput virtual screening protocol to predict the synthesizability of candidate metal–sulfur MOFs/CPs by computing the thermodynamically stable structures resulting from a particular combination of metal cluster, linker, cation, and synthetic conditions. Free energies are computed by using all-atom classical mechanical thermodynamic integration. Low-free-energy structures are refined using ab initio density functional theory, and pair distribution functions and powder X-ray diffraction patterns are calculated to complement and guide experimental structure determination. We validate the computational approach by retrospective predictions of the stable structure produced by experimental syntheses, and a subsequent screen predicts Fe 4 S 4 -BDT–TPP as a new thermodynamically stable one-dimensional (1D) CP comprising a redox-active Fe 4 S 4 cluster, a 1,4-benzenedithiolate (BDT) linker, and a tetraphenylphosphonium (TPP) countercation. Furthermore, this material is experimentally synthesized, and the 1D chain structure of the crystal is confirmed using microcrystal electron diffraction. The computational screening pipeline is generically transferable to neutral and ionic MOFs/CPs comprising arbitrary metal clusters, linkers, cations, and synthetic conditions, and we make it freely available as an open source tool to guide and accelerate the discovery and engineering of novel porous materials.
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Electron Sextets as Optically Addressable Molecular Qubits: Triplet Carbenes
There is a growing demand in quantum information science and sensing for electron spin purification and readout via a spin-optical interface. This technique, known as optically detected magnetic resonance (ODMR), has been applied to diamond-NV centers and transition-metal complexes. Metal-free counterparts of these optically addressable spin qubits promise to be cheaper, more sustainable color centers with prolonged polarization lifetimes. However, progress has been hindered by the low ODMR signals of carbon-based π-diradicals, partly due to the lack of a ground singlet-to-triplet intersystem crossing (ISC). In this work, we propose exploring organic systems that are even more electron-deficient: electron sextets. Using triplet carbenes as an example, we illustrate how the ground singlet-triplet gap can be widened beyond thermal energy with the associated singlet-to-triplet ISC made available by vibronic effects. Through careful molecular engineering, this ISC can occur at a rate similar to and with an opposite spin selectivity from the excited-state ISC well-established in π-diradicals, unlocking a new ODMR pathway with potential signal gains. Persistent triplet carbenes are a renascent field, with multiple stable molecules being isolated in the past five years. To motivate further development of its emissive properties, we illustrate our design in three realistic carbene candidates that incorporate existing strategies for carbene stabilization. Furthermore, we believe that a new realm of quantum materials can be uncovered by expanding our scope toward stable electron sextets.
Carbene compounds↗
Reticular Structural Diversification of Zirconium Metal–Organic Frameworks Through Angular Ligand Configuration Control
Reticular chemistry offers practical guidelines for enlarging and enriching the arsenal of metal–organic frameworks (MOFs). However, reticular expansion to access mesoporous structures remains challenging due to limitations in achieving precise control over both the size and configuration during building units’ extension. Herein, we combine ligand isomerization and functionalization strategies to regulate the ligand configuration by systematically replacing aryl C–H groups with N atoms, resulting in angular dicarboxylate ligands with various symmetries. The assembly between a 4,4′-(pyridine-2,6-diyl)dibenzoic acid ligand (1N, C 2 symmetry) and 12-connected Zr 6 cluster leads to the formation of a pseudo ftw topology framework (NU-2611), where one pair of nose-to-nose 1N ligands resembles a tetra-topic ligand. When a 6,6′-(1,3-phenylene)dinicotinic acid ligand (2N, C S symmetry) was used, another pseudo ftw network NU-2612 was obtained with a 2-fold framework interpenetration. Interestingly, the planar [2,2′:6′,2″-terpyridine]-5,5″-dicarboxylic acid ligand (3N, C 2V symmetry) yielded an intriguing mesoporous Zr-MOF with kag topology. NU-2613 represents the first example of kag Zr-MOF designed to include large, well-defined mesopores. The diversity of these MOFs was further enhanced through post-synthetic metalation of linkers. Particularly, metalation of the chelating 3N ligand with Fe 3+ in NU-2613 enables efficient catalytic transformation within the functionalized channels. This work contributes insight into the reticular expansion of Zr-MOFs by finely-tuning the ligand planarity, advancing the structure diversification of mesoporous frameworks for specific applications.
Cluster chemistry↗
Mechanochemical Solid Form Screening of Zeolitic Imidazolate Frameworks Using Structure-Directing Liquid Additives
We demonstrate a systematic application of the mechanochemical liquid-assisted grinding (LAG) methodology to screen for forms of zinc imidazolate (ZnIm 2 ), of fundamental importance as the simplest member of the zeolitic imidazolate framework materials family. The exploration of 45 different liquid additives, selected based on their molecular structure and physicochemical properties has resulted in eight different ZnIm 2 topological forms, appearing in 13 crystallographically distinct solid forms (including two previously unknown forms of the crb (BCT) topology), amorphous phases, and the interrupted moc-Zn 4 Im 8 HIm. All prepared topological forms were also explored computationally, using dispersion-corrected periodic density functional theory (DFT) calculations, enabling the rationalization of screening outcomes, and setting the stage for future prediction of additive-directed metal–organic framework (MOF) synthesis. This first systematic exploration of LAG in screening for three-dimensional MOFs demonstrates the potential of the liquid additive to not only accelerate materials synthesis, but also to direct it toward topologically different MOFs. The discovery of novel forms of a material that already exhibits at least 21 crystallographically and functionally different forms provides a strong testimony on the power of mechanochemistry in metal–organic materials discovery.
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Dimensional Evolution Guides Property Control in the A n Cu 4– n TiS 4 Semiconductor Series
Through progressive reduction of the three-dimensional (3D) covalent network of Cu 4 TiS 4 , we isolate seven new members of the A n Cu 4–n TiS 4 family (A = alkali metal; n = 0–4), spanning 3D, 2D, 1D, and 0D structural fragments. The dimensional reduction is rational, as it preserves the edge-sharing connectivity between [CuS 4 ] 7– and [TiS 4 ] 4– tetrahedra across the series. This structural evolution is driven by the stepwise substitution of Cu with alkali metals, guiding the formation of fragments with reduced dimensionality. The effects of “n” and “A” on the crystal structures, stabilities, electronic structures, and optoelectronic properties are profound, demonstrating that the manipulation of alkali metal size and A n Cu 4–n TiS 4 stoichiometry enables predictable variations in structure and properties. For example, the n = 0 and n = 4 end members of the A n Cu 4–n TiS 4 family set the range of achievable band gaps with 2.00 eV for Cu 4 TiS 4 , 2.60 eV for Na 4 TiS 4 , and intermediate values for the n = 1–3 members. Notably, CsCu 3 TiS 4 exhibits exceptional air stability and congruent melting, with density functional theory (DFT) calculating moderate hole and electron effective masses in specific crystallographic directions (mh = 1.24m 0 , me = 0.87m 0 ). Additionally, A 3 CuTiS 4 (A = Na, K, Rb) displays direct band gap behavior and long photoluminescence lifetimes of 2.3–8.6 μs, and K 3 CuTiS 4 has a PLQY of 5.19%. These findings underscore the potential of the A n Cu 4–n TiS 4 family for applications in optoelectronics and demonstrate widely applicable design concepts that unveil rational stoichiometries within a given composition space to generate a series of crystal structures related through an evolving covalent dimensionality that corresponds to a predictable electronic structure and property progression.
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Dimensional Reduction Guides Electronic Structure Evolution in the A n Cu 4–n SnS 4 Semiconductor Series
The search for new functional materials with tunable properties remains a central challenge in chemistry, particularly for applications in energy and electronics. In this work, we present a framework for predictive crystal design in alkali metal chalcogenides that enables controlled dimensional reduction of a parent covalent motif, yielding a broad range of electronic structures, which systematically evolve from one parent to the other. We present 11 new members of the A n Cu 4–n SnS 4 family (A = alkali metal; n = 0–4), which reduce the three-dimensional (3D) covalent network of Cu 4 SnS 4 into various 3D, 2D, 1D, and 0D [Cu 4–n SnS 4 ] n− motifs through the substitution of Cu with alkali metals of various radii. The end members of the family set the range in achievable band gaps at 0.99 eV for fully covalent Cu 4 SnS 4 (n = 0) and 3.38 eV for K 4 SnS 4 (n = 4) with 0D [SnS 4 ] n− tetrahedra. As the dimensionality of [Cu 4–n SnS 4 ] n− systematically reduces within A n Cu 4–n SnS 4 (n = 1–3), a stepwise increase in band gap energy occurs through a gradual decrease in the energy of the valence band maximum and an increase in the conduction band minimum, with an increase in the effective masses of charge carriers. Furthermore, irrespective of the alkali metal, the thermal stability decreases with decreasing [Cu 4–n SnS 4 ] n− dimensionality within the quaternary members. Most importantly, we demonstrate that predictable crystal structure and property evolution for a given composition space is possible by deriving a general formula based on substituting the covalent metals of a parent structure with alkali metals.
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Alkali-Metal Interlocking of 2D V 4 O 10 Sheets Defines Discretized Interlayer Shear Relationships
Low-dimensional materials manifest structural anisotropy, quantum confinement, and tightly bound excitonic states, which make them attractive building blocks that can be assembled within three-dimensional laterally stitched heterostructures, stacked van der Waals solids, and complex moiré superlattices. Ion intercalation in the galleries between layered materials provides a means of modifying interlayer separation and coupling, but it is also known to drive the shearing of the layers. In this article, we explore the distinct ligand coordination environments afforded by vanadyl oxygens of singular [V 4 O 10 ] sheets and examine how the size, polarizability, and stoichiometry of Group I cations sandwiched between such layers determine the interlocking of the sheets in stacked structures. Based on the topochemical insertion of alkali-metal ions into the layered λ-V 2 O 5 , we identify seven types of guest ion coordination sites discretized into four distinct regimes of interlayer shear in units of half octahedral widths. The coordination preferences of intercalated cations govern how they interlock 2D [V 4 O 10 ] sheets and engender specific shear conformations. We present evidence that static and dynamic disorder in guest ion arrangement modulate the magnetic structure of the intercalated compounds based on electrostatic polarization, localization of charge and spin density, and lattice distortion. The results illustrate the use of topochemical ion insertion to modulate stacking relationships and magnetic transition characteristics.
36 MATERIALS SCIENCE↗
Torsional Flexibility Tuning of Hexa-Carboxylate Ligands to Unlock Distinct Topological Access to Zirconium Metal–Organic Frameworks
Zirconium-based metal–organic frameworks (Zr-MOFs) exhibit remarkable structural diversity and functionality. However, uncovering new topological types within this family remains a considerable challenge today. Herein, we report two new hexa-topic ligands designed through the introduction of torsional flexibility, which enable the construction of two Zr-MOFs featuring rare network topologies. The (4,4′,4″,4‴,4‴′,4‴′′-((2-carboxybenzene-1,3,5-triyl)tris(9H-carbazole-9,3,6-triyl))hexabenzoic acid ligand (BTCH)) was obtained by replacing the rigid triptycene core in the H6PET-1 ligand (4,4′,4″,4‴,4‴′,4‴′′-(9,10-dihydro-9,10-[1,2]benzenoanthracene-2,3,6,7,14,15-hexayl)hexabenzoic acid) with a benzene-tricarbazole unit. Owing to its torsionally flexible core that allows rotational freedom to the arms, this ligand directs the construction of NU-2620 (NU represents Northwestern University), a Zr-MOF with 8-connected Zr6 clusters and the rare nuh topology. Further flexibilization of the carbazole units to benzene rings yielded the even more torsionally flexible 5′,5‴-bis(4-carboxyphenyl)-5″-(4,4″-dicarboxy-[1,1′:3′,1″-terphenyl]-5′-yl)-[1,1′:3′,1″:3″,1‴:3‴,1‴′-quinquephenyl]-4,4‴′-dicarboxylic acid ligand (CCTT), which forms NU-2630 featuring 6-connected clusters and the pcu topology. Both frameworks exhibit good chemical stability, prompting evaluation of their performance in CO2 photoreduction catalysis. Under low-concentration CO2 conditions, NU-2620 displays markedly higher catalytic activity than its benzene-based analogue, NU-2630, thanks to the abundance of photoactive carbazole units within its structure. These results demonstrate that introducing torsional flexibility in high-connected linkers can unlock access to new topologies and accelerates the reticular expansion of Zr-MOFs.
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Derivation and Decoration of Nets with Trigonal-Prismatic Nodes: A Unique Route to Reticular Synthesis of Metal–Organic Frameworks
Quests for advanced functionalities in metal–organic frameworks (MOFs) inevitably encounter increasing complexity in their tailored framework architectures, accompanied by heightened challenges with their geometric design. Herein, we demonstrate the feasibility of rationally exploiting topological prediction as a blueprint for predesigned MOFs. A new triangular frusta secondary building unit (SBU), {Zn 4 (tz) 3 }, was bridged by three TDC 2– fragments to initially form a trigonal prismatic node, {Zn 8 (tz) 6 (TDC) 3 } (Htz = 1 H -1,2,3-triazole and H 2 TDC = 2,5-thiophenedicarboxylic acid). Furthermore, the trigonal prism unit can be considered as a double SBU derived from triply bound triangular frusta. By considering theoretical derived nets for linking this trigonal-prismatic node with ditopic, tritopic, and tetratopic linkers, we have synthesized and characterized a new family of MOFs that adopt the decorated lon , jea , and xai nets, respectively. Pore sizes have also been successively increased within TPMOF- n family, which facilitates heterogeneous biomimetic catalysis with Fe–porphyrin-based TPMOF-7 as a catalyst.
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Tuning the Surface Chemistry of Metal Organic Framework Nodes: Proton Topology of the Metal-Oxide-Like Zr 6 Nodes of UiO-66 and NU-1000
Some metal organic frameworks (MOFs) incorporate nodes that are nanoscale metal oxides, and the hydroxycontaining functional groups on them provide opportunities for introducing catalytic sites with precisely defined structures. Investigations have been done to understand the structures of these groups on nodes and node vacancies, because, in prospect, atomic-scale modulation of the composition, areal density, and/or siting of the groups would open up possibilities for exquisite tuning of the siting and performance of subsequently anchored catalytic units (e.g., single metal ions, pairs of metal ions, or well-defined metal-ion-containing clusters). In this work we have combined infrared (IR) spectroscopy and density functional theory (DFT) to demonstrate tuning of these sites, namely, hydrogen-bonded OH/OH 2 groups on the Zr 6 nodes of the MOFs UiO-66 and NU-1000 via the intermediacy of node methoxy (or ethoxy) groups formed from methanol (or ethanol). Methoxy (or ethoxy) groups on node vacancy sites are converted to a structure incorporating one vacant Zr site and one terminal OH group per face by reaction with water. Our results highlight how the combination of DFT and IR spectroscopy facilitates the determination of the identity and chemistry of the functional groups on MOF node vacancies and defect sites.
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Co-assembly of Peptide Amphiphiles and Lipids into Supramolecular Nanostructures Driven by Anion–π Interactions
Co-assembly of binary systems driven by specific non-covalent interactions can greatly expand the structural and functional space of supramolecular nanostructures. We report here on the self-assembly of peptide amphiphiles and fatty acids driven primarily by anion–π interactions. The peptide sequences investigated were functionalized with a perfluorinated phenylalanine residue to promote anion–π interactions with carboxylate headgroups in fatty acids. These interactions were verified here by NMR and circular dichroism experiments as well as investigated using atomistic simulations. Positioning the aromatic units close to the N-terminus of the peptide backbone near the hydrophobic core of cylindrical nanofibers leads to strong anion–π interactions between both components. With a low content of dodecanoic acid in this position, the cylindrical morphology is preserved. However, as the aromatic units are moved along the peptide backbone away from the hydrophobic core, the interactions with dodecanoic acid transform the cylindrical supramolecular morphology into ribbon-like structures. Increasing the ratio of dodecanoic acid to PA leads to either the formation of large vesicles in the binary systems where the anion–π interactions are strong, or a heterogeneous mixture of assemblies when the peptide amphiphiles associate weakly with dodecanoic acid. Furthermore, our findings reveal how co-assembly involving designed specific interactions can drastically change supramolecular morphology and even cross from nano to micro scales.
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Packing Guidelines for Optimizing Singlet Fission Matrix Elements in Noncovalent Dimers
Not provided.
Chemistry↗