Localized and delocalized topological modes of heat.

The topological physics has sparked intensive investigations into topological lattices in photonic, acoustic, and mechanical systems, powering counterintuitive effects otherwise inaccessible with usual settings. Following the success of these endeavors in classical wave dynamics, there has been a growing interest in establishing their topological counterparts in diffusion. Here, we propose an additional real-space dimension in diffusion, and the system eigenvalues are transformed from "imaginary" to "real." By judiciously tailoring the effective Hamiltonian with coupling networks, localized and delocalized topological modes are realized in heat transfer. Simulations and experiments in active thermal lattices validate the effectiveness of the proposed theoretical strategy. This approach can be applied to establish various topological lattices in diffusion systems, offering insights into engineering topologically protected edge states in dynamic diffusive scenarios.

Electron delocalization triggers nonradical Fenton-like catalysis over spinel oxides.

Nonradical Fenton-like catalysis offers opportunities to overcome the low efficiency and secondary pollution limitations of existing advanced oxidation decontamination technologies, but realizing this on transition metal spinel oxide catalysts remains challenging due to insufficient understanding of their catalytic mechanisms. Here, we explore the origins of catalytic selectivity of Fe-Mn spinel oxide and identify electron delocalization of the surface metal active site as the key driver of its nonradical catalysis. Through fine-tuning the crystal geometry to trigger Fe-Mn superexchange interaction at the spinel octahedra, ZnFeMnO4 with high-degree electron delocalization of the Mn-O unit was created to enable near 100% nonradical activation of peroxymonosulfate (PMS) at unprecedented utilization efficiency. The resulting surface-bound PMS* complex can efficiently oxidize electron-rich pollutants with extraordinary degradation activity, selectivity, and good environmental robustness to favor water decontamination applications. Our work provides a molecule-level understanding of the catalytic selectivity and bimetallic interactions of Fe-Mn spinel oxides, which may guide the design of low-cost spinel oxides for more selective and efficient decontamination applications.

How delocalized are the polyacenes?

In an attempt to quantify electron delocalization in polyacenes with up to 50 carbon atoms, we have performed self-consistent field calculations in which the π electrons are constrained to occupy highly localized molecular orbitals (HILOs) centered on a maximum of two, six or ten adjacent carbon atoms. We have also performed similar calculations on simple polyacene analogs consisting only of hydrogen atoms and exhibiting electron delocalization in the σ framework. We find that the energetic cost of localizing the π electrons in the polyacenes is roughly 60, 5 or 0.1 kJ/mol per ring atom for the two-, six- and ten-atom HILOs, respectively, and the use of these localized models overestimates the predicted hydrogenation energies of the acenes by roughly 50%, 4% and 0.1%, respectively. We conclude that the chemistry of polyacenes can be modeled well using highly localized descriptions of the π electrons.

Machine learning for accuracy in density functional approximations.

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Monodispersed Molecular Phthalocyanine with Sulfur-Driven Electron Delocalization for Enhanced Electrochemical Biosensing.

Heterogenizing the molecular catalysts on conductive scaffolds to achieve the isolated molecular dispersion and expected coordination structures is significant yet still challenging. Herein, a sulfur-driving strategy to anchor monodispersed cobalt phthalocyanine on nitrogen and sulfur co-doped graphene (NSG-CoPc) is demonstrated. Experimental and theoretical analysis prove that the incorporation of S dramatically improves the adsorption capability of NSG and evokes the monodispersion of the CoPc molecule, promoting the axial Co─N coordination and the electron delocalization of the Co catalytic center. Benefiting from the reduced activation energy barrier and boosted electron transfer, as well as the maximized active site utilization, NSG-CoPc exhibits outstanding H2O2 oxidization and sensing performance (used as a representative reaction). Moreover, the usage of NSG as a substrate can be readily extended to other metal (Ni, Cu, and Fe) phthalocyanine molecules with molecular-level dispersion. This work clarifies the mechanism of heteroatoms decoration and provides a new paradigm in devising monodispersed molecular catalysts with modulated chemical surroundings for broad applications.

A Self-Assembly-Induced Exciton Delocalization Strategy for Converting a Perylene Diimide Derivative from a Type-II to Type-I Photosensitizer.

Type-I photosensitizers have shown advantages in addressing the shortcomings of traditional oxygen-dependent type-II photosensitizers for the photodynamic therapy (PDT) of hypoxic tumors. However, developing type-I photosensitizers is yet a huge challenge because the type-II energy transfer process is much faster than the type-I electron transfer process. Herein, from the fundamental point of view, an effective approach is proposed to improve the electron transfer efficiency of the photosensitizer by lowering the internal reorganization energy and exciton binding energy via self-assembly-induced exciton delocalization. An example proof is presented by the design of a perylene diimide (PDI)-based photosensitizer (PDIMp) that can generate singlet oxygen (1O2) via a type-II energy transfer process in the monomeric state, but induce the generation of superoxide anion (O2˙-) via a type-I electron transfer process in the aggregated state. Significantly, with the addition ofcucurbit[6]uril (CB[6]), the self-assembled PDIMp can convert back to the monomeric state via host-guest complexation and consequently recover the generation of 1O2. The biological evaluations reveal that supramolecular nanoparticles (PDIMp-NPs) derived from PDIMp show superior phototherapeutic performance via synergistic type-I PDT and mild photothermal therapy (PTT) against cancer under either normoxia or hypoxia conditions.

Loosely Bounded Exciton with Enhanced Delocalization Capability Boosting Efficiency of Organic Solar Cells.

In organic solar cells (OSCs), electron acceptors have undergone multiple updates, from the initial fullerene derivatives, to the later acceptor-donor-acceptor type non-fullerene acceptors (NFAs), and now to Y-series NFAs, based on which efficiencies have reached over 19%. However, the key property responsible for further improved efficiency from molecular structure design is remained unclear. Herein, the material properties are comprehensively scanned by selecting PC71BM, IT-4F, and L8-BO as the representatives for different development stages of acceptors. For comparison, asymmetric acceptor of BTP-H5 with desired loosely bounded excitons is designed and synthesized. It's identified that the reduction of intrinsically exciton binding energy (Eb) and the enhancement of exciton delocalization capability act as the key roles in boosting the performance. Notably, 100 meV reduction in Eb has been observed from PC71BM to BTP-H5, correspondingly, electron-hole pair distance of BTP-H5 is almost two times over PC71BM. As a result, efficiency is improved from 40% of S-Q limit for PC71BM-based OSC to 60% for BTP-H5-based one, which achieves an efficiency of 19.07%, among the highest values for binary OSCs. This work reveals the confirmed function of exciton delocalization capability quantitatively in pushing the efficiency of OSCs, thus providing an enlightenment for future molecular design.

Aromaticity in Isoelectronic Analogues of Benzene, Carborazine and Borazine, from Electronic Structure and Magnetic Property.

Carborazine (B2C2N2H6) and borazine (B3N3H6) are isoelectronic analogues of benzene (C6H6). The aromatic character of borazine have basically reached a consensus after a long period of controversy, but the related properties of carborazine are even rarely reported. In this work, we systematically investigated the geometric structure, charge distribution, frontier molecular orbital characteristics, bonding, electronic delocalization, magnetic shielding effect, and induced ring current of carborazine and borazine, and compared the studied characteristics with those of benzene to determine the aromatic character of the two analogues. The combination of multiple properties shows that although they are isoelectronic, carborazine is evidently aromatic, while borazine only exhibits rather weak aromaticity. The C atom acting as a connecting bridge between B and N atoms in carborazine reduces the electronegativity difference on the molecular backbone and enhances the electronic delocalization over the conjugated path, which is the essence of the distinct disparity of aromaticity between carborazine and borazine.

Excited-State Dynamics in Segregated Donor-Acceptor Stacks Versus a Peri-Bisdonor-Acceptor System.

The investigation of impact of through-space/through-bond electronic interaction among chromophores on photoexcited-state properties has immense potential owing to the distinct emergent photophysical pathways. Herein, the photoexcited-state dynamics of homo-sorted π-stacked aggregates of a naphthalenemonoimide and perylene-based acceptor-donor (NI-Pe) system and a fork-shaped acceptor-bisdonor (NI-Pe2) system possessing integrally stacked peri-substituted donors was examined. Femtosecond transient absorption (fsTA) spectra of NI-Pe monomer recorded in chloroform displayed spectroscopic signatures of the singlet state of Pe; 1Pe*, the charge-separated state; NI-⋅-Pe+⋅, and the triplet state of Pe; 3Pe*. The examination of ultrafast excited-state processes of NI-Pe aggregate in chloroform revealed faster charge recombination ( τ C R a ${{\tau }_{CR}^{a}}$ =1.75 ns) than the corresponding monomer ( τ C R m ${{\tau }_{CR}^{m}}$ =2.46 ns) which was followed by observation of a broad structureless band attributed to an excimer-like state. The fork-shaped NI-Pe2 displayed characteristic spectroscopic features of the NI radical anion (λmax~450 nm) and perylene dimer radical cation (λmax~520 nm) upon photoexcitation in non-polar toluene solvent in the nanosecond transient absorption (nsTA) spectroscopy. The investigation highlights the significance of intrinsic close-stacked arrangement of donors in ensuring a long-lived photoinduced charge-separated state ( τ C R ${{\tau }_{CR}}$ =1.35 µs) in non-polar solvents via delocalization of radical cation between the donors.

Unraveling the Push-Pull Effect in Acenes, Polyenes and Polyynes.

Substituent effects (SEs) are fundamental for predicting molecular reactivity, while polyene, polyyne and acene derivatives are precursors to compounds with diverse applications. Computations were performed for Y-R-X systems, where reaction sites Y=NO2 and O- , substituents X=NO2 , CN, Cl, H, OH, NH2 , and spacers R=polyene, polyyne (n=1-5, 10 repeating units) and acene (up to tetracene). The cSAR (charge of the substituent active region) approach allowed to present, for the first time, quantitative relations describing the spacer's electron-donating and withdrawing properties as a function of n and the spacer type. The electronic properties of the X substituents depend on the type of spacer, its length and the Y group, which is an example of the reverse SE. To describe how the SE between Y and X weakens with n, two approaches were compared: cSAR and SESE (SE stabilization energy). The EDDB (electron density of delocalized bonds) characterize changes in electron delocalization in spacers due to the SE. A new approach - EDDB differential maps - allow to extract the effect of X substitution on the electron delocalization. The charges at spacer's C atoms correlate with cSAR; changes in the slopes confirm the charge transfer by resonance.

Can Aromaticity Be Evaluated Using Atomic Partitions Based on the Hilbert-Space?

Aromaticity is a fundamental concept in chemistry that explains the stability and reactivity of many compounds by identifying atoms within a molecule that form an aromatic ring. Reliable aromaticity indices focus on electron delocalization and depend on atomic partitions, which give rise to the concept of an atom-in-the-molecule (AIM). Real-space atomic partitions present two important drawbacks: a high computational cost and numerical errors, limiting some aromaticity measures to medium-sized molecules with rings up to 12 atoms. This restriction hinders the study of large conjugated systems like porphyrins and nanorings. On the other hand, traditional Hilbert-space schemes are free of the latter limitations but can be unreliable for the large basis sets required in modern computational chemistry. This paper explores AIMs based on three robust Hilbert-space partitions - meta-Löwdin, Natural Atomic Orbitals (NAO), and Intrinsic Atomic Orbitals (IAO) - which combine the advantages of real-space partitions without their disadvantages. These partitions can effectively replace real-space AIMs for evaluating the aromatic character. For the first time, we report multicenter index (MCI) and Iring values for large rings and introduce ESIpy, an open-source Python code for aromaticity analysis in large conjugated rings.

Electron and Spin Delocalization in [Co6 Se8 (PEt3 )6 ]0/+1 Superatoms.

Molecular clusters can function as nanoscale atoms/superatoms, assembling into superatomic solids, a new class of solid-state materials with designable properties through modifications on superatoms. To explore possibilities on diversifying building blocks, here we thoroughly studied one representative superatom, Co6 Se8 (PEt3 )6 . We probed its structural, electronic, and magnetic properties and revealed its detailed electronic structure as valence electrons delocalize over inorganic [Co6 Se8 ] core while ligands function as an insulated shell. 59 Co SSNMR measurements on the core and 31 P, 13 C on the ligands show that the neutral Co6 Se8 (PEt3 )6 is diamagnetic and symmetric, with all ligands magnetically equivalent. Quantum computations cross-validate NMR results and reveal degenerate delocalized HOMO orbitals, indicating aromaticity. Ligand substitution keeps the inorganic core nearly intact. After losing one electron, the unpaired electron in [Co6 Se8 (PEt3 )6 ]+1 is delocalized, causing paramagnetism and a delocalized electron spin. Notably, this feature of electron/spin delocalization over a large cluster is attractive for special single-electron devices.

New Perspectives on Delocalization Pathways in Aromatic Molecular Chameleons.

This study comprehensively analyzes the magnetically induced current density of polycyclic compounds labeled as "aromatic chameleons" since they can arrange their π-electrons to exhibit aromaticity in both the ground and the lowest triplet state. These compounds comprise benzenoid moieties fused to a central skeleton with 4n π-electrons and traditional magnetic descriptors are biased due to the superposition of local magnetic responses. In the S0 state, our analysis reveals that the molecular constituent fragments preserve their (anti)aromatic features in agreement with two types of resonant structures: one associated with aromatic benzenoids and the other with a central antiaromatic ring. Regarding the T1 state, a global and diatropic ring current is revealed. Our aromaticity study is complemented with advanced electronic and geometric descriptors to consider different aspects of aromaticity, particularly important in the evaluation of excited state aromaticity. Remarkably, these descriptors consistently align with the general features on the main delocalization pathways in polycyclic hydrocarbons consisting of fused 4n π-electron rings. Moreover, our study demonstrates an inverse correlation between the singlet-triplet energy difference and the antiaromatic character of the central ring in S0.

Theoretical Insights into Bifurcated Intramolecular Dihydrogen Bonds.

Two-ring intramolecular π-electron delocalization assisted dihydrogen bonds existing in (1Z,4Z)-1,4-dipentene-3-bora-1,5-diol and its symmetrically substituted derivatives have been analysed here since the MP2/6-311++G(d,p) calculations on these systems were performed. The influence of the coexistence of two intramolecular dihydrogen bonded rings in these molecular structures on properties of intramolecular dihydrogen bonds as well as on the π-electron delocalization within these rings was investigated. The comparison with corresponding structures of typical two-ring, so-called resonance-assisted, RAHB, systems was performed. The results of calculations show that such rings' coexistence leads to the weakening of dihydrogen bonds, similarly as for the typical two-ring RAHB systems. The Quantum Theory of ''Atoms in Molecules'' (QTAIM) was also applied here to get more details about the nature of dihydrogen bonds. Correlations between dihydrogen bond strength measures and other energetic, geometrical and topological parameters were also analysed. It was found that characteristics of bond critical points as well as of ring critical points are useful to estimate the strength of intramolecular dihydrogen bonds in two-ring dihydrogen bonded systems discussed here. The Natural Bond Orbital, NBO, approach parameters are also discussed as useful ones to describe properties of dihydrogen bonded systems.

Electron Delocalization Disentangles Activity-Selectivity Trade-Off of Transition Metal Phosphide Catalysts in Oxidative Desulfurization.

Breaking the activity-selectivity trade-off has been a long-standing challenge in catalysis. Here, we proposed a nanoheterostructure engineering strategy to overcome the trade-off in metal phosphide catalysts for the oxidative desulfurization (ODS) of fuels. Experimental and theoretical results demonstrated that electron delocalization was the key driver to simultaneously achieve high activity and high selectivity for the molybdenum phosphide (MoP)/tungsten phosphide (WP) nanoheterostructure catalyst. The electron delocalization not only promoted the catalytic pathway transition from predominant radicals to singlet oxygens in H2O2 activation but also simultaneously optimized the adsorption of reactants and intermediates on Mo and W sites. The presence of such dual-enhanced active sites ideally compensated for the loss of activity due to the nonradical catalytic pathway, consequently disentangling the activity-selectivity trade-off. The resulting catalyst (MoWP2/C) unprecedentedly achieved 100% removal of thiophenic compounds from real diesel at an initial concentration of 2676 ppm of sulfur with a high turnover frequency (TOF) of 105.4 h-1 and a minimal O/S ratio of 4. This work provides fundamental insight into the structure-activity-selectivity relationships of heterogeneous catalysts and may inspire the development of high-performance catalysts for ODS and other catalytic fields.

Substitution Effect of a Single Nitrogen Atom on π-Electronic Systems of Linear Polycyclic Aromatic Hydrocarbons (PAHs): Theoretically Visualized Coexistence of Mono- and Polycyclic π-Electron Delocalization.

We theoretically investigated the nitrogen substitution effect on the molecular structure and π-electron delocalization in linear nitrogen-substituted polycyclic aromatic hydrocarbons (N-PAHs). Based on the optimized molecular structures and magnetic field-induced parameters of fused bi- and tricyclic linear N-PAHs, we found that the local π-electron delocalization of subcycles (e.g., mono- and bicyclic constituent moieties) in linear N-PAHs is preserved, despite deviation from ideal structures of parent monocycles. The introduction of a fused five-membered ring with a pyrrolic N atom (N-5MR) in linear N-PAHs significantly perturbs the π-electronic condition of the neighboring fused six-membered ring (6MR). Monocyclic pyrrole exhibits substantial bond length alternations, strongly influencing the π-electronic systems of both the fused N-5MR and 6MR in linear N-PAHs, depending on the location of shared covalent bonds. A fused six-membered ring with a graphitic N atom in an indolizine moiety cannot generate monocyclic π-electron delocalization but instead contributes to the formation of polycyclic π-electron delocalization. This is evidenced by bifurcated diatropic ring currents induced by an external magnetic field. In conclusion, the satisfaction of Hückel's 4n + 2 rule for both mono- and polycycles is crucial for understanding the overall π-electron delocalization. It is crucial to consider the unique characteristics of the three types of substituted N atoms and the spatial arrangement of 5MR and 6MR in N-PAHs.

The Physical Mechanism of Linear and Nonlinear Optical Properties of Nanographene-Induced Chiral Inversion.

Based on density functional theory (DFT) and wave function analysis, the ultraviolet and visible spectrophotometry (UV-Vis) spectra and Raman spectra of 1-meso and 1-rac obtained by the chiral separation of chiral nanographenes are theoretically investigated. The electron excitation properties of 1-meso and 1-rac are studied by means of transition density matrix (TDM) and charge density difference (CDD) diagrams. The intermolecular interaction is discussed based on an independent gradient model based on Hirshfeld partition (IGMH). The interaction of 1-meso and 1-rac with the external environment is studied using the electrostatic potential (ESP), and the electron delocalization degree of 1-meso and 1-rac is studied based on the magnetically induced current under the external magnetic field. Through the chiral separation of 1-rac, two enantiomers, 1-(P, P) and 1-(M, M), were obtained. The electrical-magnetic interaction of the molecule is revealed by analyzing the electron circular dichroism (ECD) spectra of 1-meso, 1-(P, P) and 1-(M, M), the transition electric dipole moment (TEDM) and the transition magnetic dipole moment (TMDM). It is found that 1-(P, P) and 1-(M, M) have opposite chiral properties due to the inversion of the structure.

Enhanced Electron Delocalization Induced by Ferromagnetic Sulfur doped C3N4 Triggers Selective H2O2 Production.

For the 2D metal-free carbon catalysts, the atomic coplanar architecture enables a large number of pz orbitals to overlap laterally, thus forming π-electron delocalization, and the delocalization degree of the central atom dominates the catalytic activity. Herein, designing sulfur-doped defect-rich graphitic carbon nitride (S-Nv-C3N4) materials as a model, we propose a strategy to promote localized electron polarization by enhancing the ferromagnetism of ultra-thin 2D carbon nitride nanosheets. The introduction of sulfur (S) further promotes localized ferromagnetic coupling, thereby inducing long-range ferromagnetic ordering and accelerating the electron interface transport. Meanwhile, the hybridization of sulfur atoms breaks the symmetry and integrity of the unit structure, promotes electron enrichment and stimulating electron delocalization at the active site. This optimization enhances the *OOH desorption, providing a favorable kinetic pathway for the production of hydrogen peroxide (H2O2). Consequently, S-Nv-C3N4 exhibits high selectivity (>95 %) and achieves a superb H2O2 production rate, approaching 4374.8 ppm during continuous electrolysis over 300 hour. According to theoretical calculation and in situ spectroscopy, the ortho-S configuration can provide ferromagnetic perturbation in carbon active centers, leading to the electron delocalization, which optimizes the OOH* adsorption during the catalytic process.

Constructing π-π Superposition Effect of Tetralithium Naphthalenetetracarboxylate with Electron Delocalization for Robust Dual-Ion Batteries.

Organics are gaining significance as electrode materials due to their merits of multi-electron reaction sites, flexible rearrangeable structures and redox reversibility. However, organics encounter finite electronic conductivity and inferior durability especially in organic electrolytes. To circumvent above barriers, we propose a novel design strategy, constructing conductive network structures with extended π-π superposition effect by manipulating intermolecular interaction. Tetralithium 1,4,5,8-naphthalenetetracarboxylate (LNTC) interwoven by carbon nanotubes (CNTs) forms LNTC@CNTs composite firstly for Li-ion storage, where multiple conjugated carboxyls contribute sufficient Li-ion storage sites, the unique network feature enables electrolyte and charge mobility conveniently combining electron delocalization in π-conjugated system, and the enhanced π-π superposition effect between LNTC and CNTs endows laudable structural robustness. Accordingly, LNTC@CNTs maintain an excellent Li-ion storage capacity retention of 96.4 % after 400 cycles. Electrochemical experiments and theoretical simulations elucidate the fast reaction kinetics and reversible Li-ion storage stability owing to the electron delocalization and π-π superposition effect, while conjugated carboxyls are reversibly rearranged into enolates during charging/discharging. Consequently, a dual-ion battery combining this composite anode and expanded graphite cathode exhibits a peak specific capacity of 122 mAh g-1 and long cycling life with a capacity retention of 84.2 % after 900 cycles.

Tuning Electron Delocalization of Redox-Active Porous Aromatic Framework for Low-Temperature Aqueous Zn-K Hybrid Batteries with Air Self-Chargeability.

Air self-charging aqueous batteries promise to integrate energy harvesting technology and battery systems, potentially overcoming a heavy reliance on energy and the spatiotemporal environment. However, the exploitation of multifunctional air self-charging battery systems using promising cathode materials and suitable charge carriers remains challenging. Herein, for the first time, we developed low-temperature self-charging aqueous Zn-K hybrid ion batteries (AZKHBs) using a fully conjugated hexaazanonaphthalene (HATN)-based porous aromatic framework as the cathode material, exhibiting redox chemistry using K+ as charge carriers, and regulating Zn-ion solvation chemistry to guide uniform Zn plating/stripping. The unique AZKHBs exhibit the exceptional electrochemical properties in all-climate conditions. Most importantly, the large potential difference causes the AZKHBs discharged cathode to be oxidized using oxygen, thereby initiating a self-charging process in the absence of an external power source. Impressively, the air self-charging AZKHBs can achieve a maximum voltage of 1.15 V, an impressive discharge capacity (466.3 mAh g-1), and exceptional self-charging performance even at -40 °C. Therefore, the development of self-charging AZKHBs offers a solution to the limitations imposed by the absence of a power grid in harsh environments or remote areas.