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We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core–Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states. [ABSTRACT FROM AUTHOR]

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations. [ABSTRACT FROM AUTHOR]

The characteristic x-ray emission direction of a material indicates the direction of the bonding orbitals and spatial symmetry of the electron orbitals. Accordingly, the intensity of x-ray emission, which varies with the direction of emission and crystal orientation, provides crucial information regarding anisotropic electronic structures. This study utilized angle-resolved soft x-ray emission spectroscopy (SXES) on a layered material, NaAlSi, to ascertain the spatial distribution of the valence electrons. Distinct alterations in the spectral intensity distributions were observed in the Al–L2,3 and Si–L2,3 spectra with respect to the emission angle. To interpret the anisotropic SXES spectra, the spatial distribution of each valence electronic state was simulated using first-principle calculations. Although the anisotropic emission intensity could not explain the symmetry of the spatial distributions of the isolated s and d atomic orbitals, the anisotropy of the SXES spectra could be interpreted as the spatial distribution of these orbitals when hybridized with p orbitals. Furthermore, the spectral structure corresponding to the electronic states near the Fermi level reflected the characteristics of the d orbitals. Therefore, angle-resolved SXES measurements can effectively discern the spatial distribution of hybridized electron orbitals with specific energy levels, which could enhance techniques related to electron distribution analysis, with potential applications in material science and electronic structure characterization. [ABSTRACT FROM AUTHOR]

Many low-cost or semiempirical quantum mechanical-based electronic structure methods suffer from the use of unpolarized minimal atomic orbital (AO) basis sets. In this work, we overcome this limitation by a fully DFT variationally optimized, adaptive minimal basis set consistently available for the elements up to radon (Z = 86). The new key feature is to make the linear coefficients of the primitive Gaussians in a contracted AO dependent on the effective atomic charge of the atom in the molecule, i.e., each symmetry-unique atom obtains its "own" specifically adapted basis functions. In this way, the physically important "breathing" of the AOs in a molecule with (a) atomic charge (expansion/contraction for anionic/cationic states) and (b) the number of close-lying bonded neighbor atoms is accounted for. The required atomic charges are obtained from a specially developed extended Hückel type Hamiltonian and the coordination numbers from the molecule geometry. Proper analytical derivatives of the resulting adaptive basis functions can easily be derived. Moreover, the basis functions are electric field-dependent, thus improving the description of, e.g., dipole moments and polarizabilities. The new basis set termed q-vSZP (charge dependent valence single-ζ, polarized) is thoroughly benchmarked for atomic/molecular and thermochemical properties compared to standard minimal and double-ζ basis sets at the DFT level with the accurate ωB97X-D4 functional. It is shown that q-vSZP is clearly superior to existing minimal basis sets, often reaching double-ζ quality or even better results. We expect it to be the optimal choice in future semiempirical quantum mechanical methods. [ABSTRACT FROM AUTHOR]

A well-known theorem of Sabidussi shows that a simple G -arc-transitive graph can be represented as a coset graph for the group G. This pivotal result is the standard way to turn problems about simple arc-transitive graphs into questions about groups. In this paper, the Sabidussi representation is extended to arc-transitive, not necessarily simple graphs which satisfy a local-finiteness condition: namely graphs with finite valency and finite edge-multiplicity. The construction yields a G -arc-transitive coset graph Cos (G , H , J) , where H , J are stabilisers in G of a vertex and incident edge, respectively. A first major application is presented concerning arc-transitive maps on surfaces: given a group G = 〈 a , z 〉 with | z | = 2 and | a | finite, the coset graph Cos (G , 〈 a 〉 , 〈 z 〉) is shown, under suitable finiteness assumptions, to have exactly two different arc-transitive embeddings as a G -arc-transitive map (V , E , F) (with V , E , F the sets of vertices, edges and faces, respectively), namely, a G-rotary map if | a z | is finite, and a G-bi-rotary map if | z z a | is finite. The G -rotary map can be represented as a coset geometry for G , extending the notion of a coset graph. However the G -bi-rotary map does not have such a representation, and the face boundary cycles must be specified in addition to incidences between faces and edges. In addition a coset geometry construction is given of a flag-regular map (V , E , F) for non necessarily simple graphs. For all of these constructions it is proved that the face boundary cycles are simple cycles precisely when the given group acts faithfully on V ∪ F. Illustrative examples are given for graphs related to the n -dimensional hypercubes and the Petersen graph. [ABSTRACT FROM AUTHOR]

High-TC ferro-/ferrimagnetic quadruple perovskites constitute an important class of oxides that has garnered a lot of research attention in recent times, but their synthesis is commonly achieved under high-pressure conditions. Thus, the development of high-TC quadruple perovskites that can be synthesized under ambient pressure can be a key to the above problem. Herein, we report ambient pressure synthesis of a series of new A-site ordered quadruple perovskites, LnCu3Mn1+xTi3−xO12 (Ln = La, Nd; x = 0, 0.3), by coupled aliovalent-cation manipulation in CaCu3Ti4O12. The effect of smaller lanthanide Nd incorporation in place of La has been investigated. Furthermore, 30% mixed valency of Mn per Mn3+ has been introduced in place of Ti4+ following similar strategies adopted to achieve giant magnetoresistive manganites La0.7A0.3MnO3 (A = Ca, Sr, Ba) from LaMnO3. Mn is present in the 3+ state for x = 0 and in a mixed valent state (3+ and 4+) for x = 0.3, whereas Cu exists in the 2+ state in all the compounds. While LaCu3MnTi3O12 and LaCu3Mn1.3Ti2.7O12 show the onset of ferrimagnetic order at ∼60 and 110 K, respectively, the corresponding Nd analogs, NdCu3MnTi3O12 and NdCu3Mn1.3Ti2.7O12, exhibit enhanced TC's of ∼80 and 140 K, respectively. This work reveals an effective strategy of mixed-valent Mn incorporation in the B-sublattice and smaller rare-earth cation incorporation to achieve higher ferrimagnetic ordering temperatures in quadruple perovskites. [ABSTRACT FROM AUTHOR]

Nonsymmetrical oxygen-bridged binuclear copper centers have been proposed and modeled as intermediates and transition states in several C-H oxidation pathways, leading to the postulation that structural dissymmetry enhances the reactivity of the bridging oxygen. However, experimentally characterizing the structure and reactivity of these transient species is remarkably challenging. Here, we report the high-pressure synthesis of a metastable nonsymmetrical dicopper-µ-oxo compound with exceptional reactivity toward the mono-oxygenation of aliphatic C-H bonds. The nonequivalent coordination environment of copper stabilizes localized mixed valency and greatly enhances the hydrogen atom abstraction activity of the bridging oxygen, enabling room-temperature hydroxylation of methane under pressure. These findings highlight the role of dissymmetry in the reactivity of binuclear copper centers and demonstrate precise control of molecular structures by mechanical means. [ABSTRACT FROM AUTHOR]

Cluster aggregation states are thermodynamically favored at the subnanoscale, for which an inverse growth from nanoparticles to clusters may be realized on subnanometer supports. Herein, we develop Au‐polyoxometalate‐layered double hydroxide (Au‐POM‐LDH) sub‐1 nm nanosheets (Sub‐APL) based on the above strategy, where sub‐1 nm Au clusters with negative valence are generated by the in situ disintegration of Au nanoparticles on POM‐LDH supports. Sub‐1 nm Au clusters with ultrahigh surface atom ratios exhibit remarkable efficiency for glutathione (GSH) depletion. The closely connected sub‐1 nm Au with negative valence and POM hetero‐units can promote the separation of hole‐electrons, resulting in the enhanced reactive oxygen species (ROS) generation under ultrasound (US). Besides, the reversible redox of Mo in POM is able to deplete GSH and trigger chemodynamic therapy (CDT) simultaneously, further enhancing the oxidative stress. Consequently, the Sub‐APL present 2‐fold ROS generation under US and 7‐fold GSH depletion compared to the discrete Au and POM‐LDH mixture. Therefore, the serious imbalance of redox in the TME caused by the sharp increase of ROS and rapid decrease of GSH leads to death of tumor ultimately. [ABSTRACT FROM AUTHOR]

Leukocytes interact with other cells using cell surface receptors. The largest group of such receptors are non-catalytic tyrosine phosphorylated receptors (NTRs), also called immunoreceptors. NTR signalling requires phosphorylation of cytoplasmic tyrosine residues by SRC-family tyrosine kinases. How ligand binding to NTRs induces this phosphorylation, also called NTR triggering, remains controversial, with roles suggested for size-based segregation, clustering, and mechanical force. Here we exploit a recently developed cell-surface generic ligand system to explore the ligand requirements for NTR triggering. We examine the effect of varying the ligand's length, mobility and valency on the activation of representative members of four NTR families: SIRPβ1, Siglec 14, NKp44 and TREM-1. Increasing the ligand length impairs activation via NTRs, despite enhancing cell-cell conjugation, while varying ligand mobility has little effect on either conjugation or activation. Increasing the valency of the ligand, while enhancing cell-cell conjugation, does not enhance activation at equivalent levels of conjugation. These findings are more consistent with a role for size-based segregation, rather than mechanical force or clustering, in NTR triggering, suggesting a role for the kinetic-segregation model. Using a generic ligand system, we show that activation via immunoreceptors is dependent on the size, but not the valency or mobility, of their cell surface ligand. This suggests that they trigger using the kinetic segregation mechanism. [ABSTRACT FROM AUTHOR]

Reconstruction‐engineered electrocatalysts with enriched high active Ni species for urea oxidation reaction (UOR) have recently become promising candidates for energy conversion. However, to inhibit the over‐oxidation of urea brought by the high valence state of Ni, tremendous efforts are devoted to obtaining low‐value products of nitrogen gas to avoid toxic nitrite formation, undesirably causing inefficient utilization of the nitrogen cycle. Herein, we proposed a mediation engineering strategy to significantly boost high‐value nitrite formation to help close a loop for the employment of a nitrogen economy. Specifically, platinum‐loaded nickel phosphides (Pt‐Ni2P) catalysts exhibit a promising nitrite production rate (0.82 mol kWh−1 cm−2), high stability over 66 h of Zn‐urea‐air battery operation, and 135 h of co‐production of nitrite and hydrogen under 200 mA cm−2 in a zero‐gap membrane electrode assembly (MEA) system. The in situ spectroscopic characterizations and computational calculations demonstrated that the urea oxidation kinetics is facilitated by enriched dynamic Ni3+ active sites, thus augmenting the "cyanate" UOR pathway. The C−N cleavage was further verified as the rate‐determining step for nitrite generation. [ABSTRACT FROM AUTHOR]

Let ᴦ be a distance-regular graph with valency k and diameter D ≥ 3. It has been shown that for a fixed real number α > 2, if ᴦ has at most αk vertices, then there are only finitely many such graphs, except for the cases where (D = 3 and ᴦ is imprimitive) and (D = 4 and ᴦ is antipodal and bipartite). And there is a classification for α ≤3. In this paper, we further study such distance-regular graphs for α > 3. Let β ≥ 3 be an integer, and let ᴦ be a distance-regular graph with valency k, diameter D ≥ 3 and at most βk + 1 vertices. Note that if D ≥ β+1, then ᴦ must have at least βk + 2 vertices. Thus, the assumption that ᴦ has at most βk + 1 vertices implies that D ≤ β. We focus on the case where D = β and provide a classification of distance-regular graphs having at most Dk + 1 vertices. [ABSTRACT FROM AUTHOR]

Targeted protein degradation is an emergent and rapidly evolving therapeutic strategy. In particular, biologics-based targeted degradation modalities (bioPROTACs) are relatively under explored compared to small molecules. Here, we investigate how target affinity, cellular localization, and valency of bioPROTACs impact efficacy of targeted degradation of the oncogenic phosphatase src-homology 2 containing protein tyrosine phosphatase-2 (SHP2). We identify bivalent recruitment of SHP2 by bioPROTACs as a broadly applicable strategy to improve potency. Moreover, we demonstrate that SHP2-targeted bioPROTACs can effectively counteract gainof-function SHP2 mutants present in cancer, which are otherwise challenging to selectively target with small molecule constructs. Overall, this study demonstrates the utility of bioPROTACs for challenging targets, and further explicates design principles for therapeutic bioPROTACs. [ABSTRACT FROM AUTHOR]

We report the experimental observations of the physical properties enhancement for the (Ni-Co)-doped ZnO films under a photodoping mechanism by UV irradiation. The elemental, structural, and morphological properties confirm that the photodoping mechanism in the (Ni-Co)-doped ZnO films is more successful than the traditional doping mechanism. The doping mechanism of the transparent conducting oxides under UV irradiation generates oxygen vacancies near the metal atoms, reducing the valency of metal ions while leaving dopant ions intact in the films. Therefore, the dopant ions occupy metal sites in the transparent conducting oxides, which enhances the physical properties of the doped transparent conducting oxides. Additionally, the effect of the photodoping mechanism on the bandgap energy, electrical conductivity, and photoconductivity is higher than the effect of the traditional doping mechanism. Finally, we can conclude that the physical properties of the Ni-, Co-, and (Ni-Co)-doped ZnO films are enhanced by using the photodoped method compared to those of the traditional doping method. Therefore, we suggest using the photodoping mechanism in the doped transparent conducting oxide film instead of the traditional doping mechanism. [ABSTRACT FROM AUTHOR]

We construct finitely generated Engel branch groups, answering a question of Fernández‐Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non‐nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case. [ABSTRACT FROM AUTHOR]

Despite the fact that most quantum chemistry basis sets are designed for accurately modeling valence chemistry, these general-purpose basis sets continue to be widely used to model core-dependent properties. Core-specialized basis sets are designed with specific features to accurately represent the behavior of the core region. This design typically incorporates Gaussian primitives with higher exponents to capture core behavior effectively, as well as some decontraction of basis functions to provide flexibility in describing the core electronic wave function. The highest Gaussian exponent and the degree of contraction for both s- and p-basis functions effectively characterize these design aspects. In this study, we compare the design and performance of general-purpose basis sets against several literature-based basis sets specifically designed for three core-dependent properties: J coupling constants, hyperfine coupling constants, and magnetic shielding constants (used for calculating chemical shifts). Our findings consistently demonstrate a significant reduction in error when employing core-specialized basis sets, often at a marginal increase in computational cost compared to the popular 6-31G** basis set. Notably, for expedient calculations of J coupling, hyperfine coupling, and magnetic shielding constants, we recommend the use of the pcJ-1, EPR-II, and pcSseg-1 basis sets, respectively. For higher accuracy, the pcJ-2, EPR-III, and pcSseg-2 basis sets are recommended. [ABSTRACT FROM AUTHOR]

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photo-induced chemical transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C4H3IS) is performed. The dynamics are experimentally monitored with a femtosecond extreme ultraviolet (XUV) probe that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations and the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Gradual absorption changes up to ∼0.5 to 1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160 ± 30 fs. Comparison of spectral intensities and energies with the calculations identifies an iodine dissociation pathway initiated by a predominant π → π* excitation. In contrast, initial excitation to a nearby n⟂ → σ* state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the π → π* state is followed by contraction of the C–I bond, enabling a nonadiabatic transition to a dissociative π → σ C − I * state. For the subsequent fragmentation, a relatively narrow bond-length region along the C–I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly occupied molecular orbitals on the two fragments. [ABSTRACT FROM AUTHOR]

AbstractA finite group G is an exact product of two subgroups A and B if G = AB and A∩B={1G}. In this paper, for all odd numbers k≥3, using the theory of skew morphisms and associated extended power functions, we present a classification of exact products of a cyclic group and a dihedral group D2k. As an application the regular generalized Cayley maps of odd valency over cyclic groups are classified. [ABSTRACT FROM AUTHOR]

Single‐atom catalysts (SACs) have recently become highly attractive for selective hydrogenation reactions owing to their remarkably high selectivity. However, compared to their nanoparticle counterparts, atomically dispersed metal atoms in SACs often show inferior activity and are prone to aggregate under reaction conditions. Here, by theoretical calculations, we show that tuning the local electronic structures of metal anchor sites on g‐C3N4 by doping B atoms (BCN) with relatively lower electronegativity allows achieving zero‐valence Pd SACs with reinforced metal‐support orbital hybridizations for high stability and upshifted Pd 4d orbitals for high activity in H2 activation. The precise synthesis of Pd SACs on BCN supports with varied B contents substantiated the theoretical prediction. A zero‐valence Pd1/BCN SAC was achieved on a BCN support with a relatively low B content. It exhibited much higher stability in a H2 reducing environment, and more strikingly, a hydrogenation activity, approximately 10 and 34 times greater than those high‐valence Pd1/g‐C3N4 and Pd1/BCN with a high B content, respectively. [ABSTRACT FROM AUTHOR]

Zirconolite ceramics have been proven to be a promising matrix for high-level waste immobilization, especially for minor actinides. In this study, a series of CaZr 1-2x REE 2x Ti 2-x Mo x O 7 (REE = Nd, Sm, Gd, Ho, Yb) samples were prepared to investigate the formation of zirconolite REE as surrogates of minor actinides and Mo6+ as charge compensator. Synchrotron and in-house powder X-ray diffraction (XRD), X-ray absorption near edge spectroscopy (XANES), and scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDX) were used to study their solid solubility, phase evolution, and structural details. XRD results show that the formation of zirconolite-2M can be up to x = 0.15 in the CaZr 1-2x Nd 2x Ti 2-x Mo x O 7 samples when co-existence of 2 M and 4 M was observed at x = 0.20 and 0.25. The "yellow phase" appears when x exceeds 0.4. The phase evolutions of CaZr 1-2x Sm 2x Ti 2-x Mo x O 7 , CaZr 1-2x Gd 2x Ti 2-x Mo x O 7 , CaZr 1-2x Ho 2x Ti 2-x Mo x O 7 and CaZr 1-2x Yb 2x Ti 2-x Mo x O 7 solid solutions are similar to each other: (1) zirconolite-2M in x = 0.05 and 0.10; (2) co-existence of 2 M and 4 M and then formation of 4 M phase from x = 0.15 to 0.25; (3) formation of "yellow phase" and pyrochlore when x ≥ 0.30. Interestingly, perovskite exits in all the ceramic samples, and its lattice parameters slightly change when increasing the dopants. Rietveld refinement results reveal that Sm/Ho mainly incorporates into 8f (Wyckoff position) Zr-sites while Mo replaces the 8f (Wyckoff position) Ti-sites. XANES results further confirm the occupation of Mo in TiO5 coordination environments. Furthermore, there is a considerable amount of Sm/Ho incorporated into 8f Ca-sites, demonstrating a different substitution mechanism from the preliminary design. [ABSTRACT FROM AUTHOR]

The impurity sulfur in lead–zinc-bearing hematite–limonite ore mainly exists in the form of galena, sphalerite, pyrite, and natural sulfur, and deep reduction roasting–low intensity magnetic separation does not effectively remove sulfur in a low valence state, which affects the quality of iron ore concentrate. Thereby, the desulfurization mechanism of the oxidative roasting process was investigated via XRD, TG, microscopy, thermodynamics, electron probe micro-analysis–energy-dispersive spectroscopy (EPMA-EDS) analyses. It is noted that hematite–limonite ore contains the valuable components of Fe2O3 (59.72 wt.%), SiO2 (15.43 wt.%), which are 46.32% of total of Fe, with a numerous number of impurities such as S (3.34 wt.%), Pb (1.50% wt.%), Zn (1.25% wt.%), etc. Microscopic identification revealed a complex relationship between hematite, pyrite, galena, sphalerite, and silica inclusions. Therefore, optimal roasting conditions were 60 min and 1050°C, respectively, where the total desulfurization rate was 92.33%, with the desulfurization rate of low valent sulfur reaching 98.64%. Meanwhile, thermodynamic and XRD analyses showed that pyrite was oxidized to ferrous oxide, magnetite, and hematite, etc., sphalerite was oxidized to zinc oxide, while galena was oxidized to lead oxide, and the difficulty of removing products such as PbO·PbSO4, and PbSO4 is noted [ABSTRACT FROM AUTHOR]

Single‐atom catalysis involves loading the active metal onto the carrier's surface as a single‐atom. This atom is primarily bonded to the carrier surface through hetero‐atom bonding. It is important to note that the coordination environment of the metal atoms may not be the same when each dispersed active metal atom has an identical coordination environment on the carrier's surface. The utilization of single‐atom catalysts (SACs) doesn't strictly imply that a solitary metal atom with zero valency functions as the active core. Singular atoms can also engage in distant interactions with other atoms or clusters of atoms on the substrate, like electron transfer, and frequently demonstrate specific charges. The main reason for the high activity of the catalyst is the remote (i.e., long‐range) interaction of the active atom with the surrounding coordination atoms. For this reason, the study of the mechanism of long‐range interactions between multiple single‐atom sites and between single‐atom sites and atomic cluster sites has become an important and urgent task in the design and regulation of single‐atom catalyst performance. [ABSTRACT FROM AUTHOR]

Thermodynamic calculations and thermal analysis tests were performed to investigate the thermodynamic and kinetic behaviors of the carbothermal reduction of vanadium-titanium magnetite w(C)/w(O) and basicity on the carbothermal reduction process of vanadium-titanium magnetite based on the HIsmelt process. Thermodynamic analysis showed that the addition of basicity promoted the reduction of vanadium-titanium magnetite, and the reaction onset temperature gradually increased with the decrease of the valence states of the elements V, Ti and Fe in the product. Increasing the amount of carbon assigned to the system gradually increased the mass fractions of metal Fe and Fe3C and raised the mass fractions of Ti, V and their low valence compounds at equilibrium. Increasing the basicity had less effect on the Fe, V and Ti fractions of the equilibrium system. The results of kinetic tests showed that the maximum reduction degree and maximum reaction rate of the reduction reaction by increasing w(C)/w(O) and basicity increased, the apparent activation energy and the finger front factor decreased, and the reaction mechanism function of the non-isothermal kinetic reduction process was f(α) = (3/2)(1−α)4/3[(1−α)−1/3−1] −1 belonging to the three-dimensional Z-L-T diffusion model. [ABSTRACT FROM AUTHOR]

C−H metalation is the most efficient method to prepare aryl–zinc and –aluminium complexes that are ubiquitous nucleophiles. Virtually all C−H metalation routes to form Al/Zn organometallics require stoichiometric, strong Brønsted bases with no base‐catalyzed reactions reported. Herein we present a catalytic in amine/ammonium salt (Et3N/[(Et3N)H]+) C−H metalation process to form aryl‐zinc and aryl‐aluminium complexes. Key to this approach is coupling an endergonic C−H metalation step with a sufficiently exergonic dehydrocoupling step between the ammonium salt by‐product of C−H metalation ([(Et3N)H]+) and a Zn−H or Al−Me containing complex. This step, forming H2/MeH, makes the overall cycle exergonic while generating more of the reactive metal electrophile. Mechanistic studies supported by DFT calculations revealed metal‐specific dehydrocoupling pathways, with the divergent reactivity due to the different metal valency (which impacts the accessibility of amine‐free cationic metal complexes) and steric environment. Notably, dehydrocoupling in the zinc system proceeds through a ligand‐mediated pathway involving protonation of the β‐diketiminate Cγ position. Given this process is applicable to two disparate metals (Zn and Al), other main group metals and ligand sets are expected to be amenable to this transition metal‐free, catalytic C−H metalation. [ABSTRACT FROM AUTHOR]

Zeta potential refers to the electrokinetic potential present in colloidal systems, exerting significant influence on the diverse properties of nano-drug delivery systems. The impact of the dielectric constant on the zeta potential and charge inversion of highly charged colloidal particles immersed in a variety of solvents spanning from polar, such as water, to nonpolar solvents and in the presence of multivalent salts was investigated through primitive Monte Carlo (MC) model simulations. Zeta potential, ξ , is decreased with the decreasing dielectric constant of the solvent and upon further increase in the salinity and the valency of the salt. At elevated levels of salt, the colloidal particles become overcharged in all solvents. As a result, their apparent charge becomes opposite in sign to the stoichiometric charge. This reversal of charge intensifies until reaching a saturation point with further increase in salinity. [ABSTRACT FROM AUTHOR]

A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive. For a semisymmetric graph Γ of order 2 p 3 , p a prime, it is well known that Γ is bipartite with two biparts having equal size. The complete classification of such graphs has been given for the full automorphism group Aut (Γ) acting unfaithfully on at least one bipart of Γ , which shows that there is only one infinite family of such graphs with valency p 2. The graphs of this kind have been determined when Aut (Γ) acts faithfully and primitively on at least one bipart of Γ , and thus there is only one remaining case for classifying such graphs of valency p 2 , Aut (Γ) acting faithfully and imprimitively on both biparts of Γ , which is dealt with in this paper. As a result, there is only one infinite family of semisymmetric graphs of order 2 p 3 with valency p 2. [ABSTRACT FROM AUTHOR]

Studying the relationship between electronic structure and activity helps to understand the catalytic mechanism since the catalytic combustion is a redox reaction dominated by electron transfer. Herein, we regulated the electron energy and O p-band center of La-based perovskite catalysts by a facile method of changing the B-site ion (B = Co, Mn, Fe). The crystal structure, morphology, reducibility, element valence distribution, and catalytic properties of prepared catalysts were characterized. Combining with DFT calculation, it was found that the low electron energy in (110) facets of LaCoO3/SiO2 catalyst contributes to the formation of reactive oxygen species and high-valence Co3+ ions. The highest oxygen adsorption activation capacity of LaCoO3/SiO2 originates from a moderate location of the O p-band center with respect to the Fermi level. As expected, the LaCoO3/SiO2 sample shows higher n-butylamine oxidation activity than that of LaMnO3/SiO2 and LaFeO3/SiO2. This work provides different insights into understanding the activity of La-based perovskite catalysts for oxidation reactions. [ABSTRACT FROM AUTHOR]

Topological indices are molecular descriptors associated with the physical, chemical, and biological properties of the molecules. The main goal of this paper is to explore some mathematical properties of generalized irregular neighborhood related descriptor. Also, the particular cases of these descriptors are calculated for the molecular structure of some basic polycyclic aromatic hydrocarbons (PAHs) along with statistical analysis. [ABSTRACT FROM AUTHOR]

Silicon is one of the most important components of electronic devices. Surface passivation of a silicon wafer is an active area of research. The Si(OH)2 sites of partially oxidized silicon surface could exist as hydroxylated [Si(OH)2] or hydrated silanone [SiO∙(OH2)]. The previously reported disiladicarbene (cAAC)2Si2 has been reacted here with water to obtain elusive, hydrated silanone (3) co-crystallized with its silanol analog (2) in a 1:3 molar ratio. The mass spectrometric characterization of acyclic silanone, followed by the isolation and characterization of the zwitterionic hydrated silanone, has been achieved. The detailed energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) calculations revealed that the central Si(O)OH unit of the hydrated silanone possesses a covalent electron sharing σ- and a dative σ-bonds (CL−Si, Si←CL) with hydrogen-containing cyclic alkyl(amino) carbene ligands. These two bonds are stabilized by 49% coulombic interaction and 47.8% orbital interaction. The presence of N-atoms at the hydrogenated and/or protonated carbene part (cAACH/cAACH2) has reduced the stability of these species. The electron pair on the N-atom of the cAACH unit displays a sort of anomeric effect relevant to the cyclic form of the sugar molecule. A disiladicarbene containing two Si(0) centres reacts with water to produce a mixture of co-crystallized products in a 3:1 molar ratio. EDA-NOCV analyses further analysed the bonding and stability of zwitterionic-hydrate-silanone to probe the nature of chemical bonds in it. This species has further been characterized by ES-MS spectrometry. [ABSTRACT FROM AUTHOR]

NiFe-based electrocatalysts will experience dynamical surface reconstruction during oxygen evolution reaction (OER) process, and the derived metal (oxy)hydroxide hybrids on the surface have been considered as the actual active species for OER. Tremendous efforts have been dedicated to understanding the surface reconstruction, but there is rare research on recognizing the origin of improved performance derived from anion species of substrate. Herein, the OER electrocatalytic characteristics were tuned with different anions in NiFe-based catalyst, using NiFe-based oxides/nitride/sulfide/selenides/phosphides (NiFeX, X = O, N, S, Se, and P) as the model materials. The combination of X-ray photoelectronic spectroscopy, electrochemical tests, operando spectroscopic characterizations, and density functional theory (DFT) calculations, reveals that anion with lower electronegativity in NiFe-based catalyst leads to higher conductivity and delayed valence transition of Ni sites, as well as optimized adsorption behavior towards oxygen intermediates, contributing to enhanced OER performance. Accordingly, NiFeP electrocatalyst demonstrates an ultralow overpotential of 265 mV at 20 mA·cm−2 for OER, as well as long-term stability. This work not only offers further insights into the effect of anionic electronegativity on the intrinsic OER electrocatalytic properties of NiFe-based electrocatalyst but also provides guide to design efficient non-noble metal-based electrocatalysts for water oxidation. [ABSTRACT FROM AUTHOR]

Boron cluster sheets are two-dimensional boron atom-based formations called borophene. They are similar to the two-dimensional sheet known as graphene, which is composed of carbon atoms arranged in a hexagonal lattice. The unique electrical, mechanical, and thermal properties of borophene make it a sought-after substance for a variety of uses, such as catalysis, energy storage, and electronics. There are two ways to manufacture borophene: chemical vapor deposition and molecular beam epitaxy. Vertex-edge valency-based topological descriptors are a great example of a molecular descriptor that provides information on the connection of atoms in a molecule. These descriptions are based on the notion that a node's value in a molecular network is the sum of the valency of those atoms that are directly connected to that node. In this article, we discussed some novel vertex-edge (ve) and edge-vertex (ev) topological descriptors and found their formulations for the boron cluster or borophene sheets. Also, we show the numerical and graphical comparison of these descriptors in this article. [ABSTRACT FROM AUTHOR]

Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials. [ABSTRACT FROM AUTHOR]

We study some learnability problems in the family of Categorial Dependency Grammars (CDG), a class of categorial grammars defining dependency structures. CDG is a formal system, where types are attached to words, combining the classical categorial grammars' elimination rules with valency pairing rules defining non-projective (discontinuous) dependencies; very importantly, the elimination rules are naturally extended to the so called "iterated dependencies" expressed by a specific type constructor and related elimination rules. This paper first reviews key points on negative results: even the rigid (one type per word) CDG cannot be learned neither from function/argument structures, nor even from dependency structures themselves. Such negative results prove the impossibility to define a learning algorithm for these grammar classes. Nevertheless, we show that the CDG satisfying reasonable and linguistically valid conditions on the iterated dependencies are incrementally learnable in the limit from dependency structures. We provide algorithms and also discuss these aspects for recent variants of the formalism that allow the inference of CDG from linguistic treebanks. [ABSTRACT FROM AUTHOR]

[Display omitted] The structure of MnO 2 was modified by constructing the composites CeO 2 / MnO 2 via a facile hydrothermal method. The catalytic performance of optimal composite (Mn-Ce10) in peroxymonosulfate (PMS) activation for the degradation of bisphenol A (BPA) is approximately three times higher than that of MnO 2 alone. The average valence of manganese in CeO 2 /MnO 2 is lowered compared to MnO 2 , which induces the generation of more free radicals, such as OH and SO 4 •−. In addition, the composite exhibits a higher concentration of oxygen vacancies than MnO 2 , facilitating bonding with PMS to produce more singlet oxygen (1O 2). Moreover, the incorporation of CeO 2 activates the lattice oxygen of MnO 2 , improving its oxidative ability. Consequently, approximately 48% of BPA decomposition in 10min is attributed to direct oxidation in the Mn-Ce10/PMS system, whereas only 36% occurs in 30min for the MnO 2 /PMS system. Simulation results confirm weakened Mn-O covalency and elongated Mn-O bonds due to the activation of lattice oxygen in CeO 2 /MnO 2 , demonstrating that PMS tends to be adsorbed on the composite rather than on MnO 2. This work establishes a relationship between lattice oxygen and the degradation pathway, offering a novel approach for the targeted regulation of catalytic oxidation. [ABSTRACT FROM AUTHOR]

In search for structural features that enable the control of the valence isomerization of the fluxional bullvalene, a bullvalene‐bis(harmane) conjugate is identified that acts as chelating ligand in complexes with metal ions. Spectrometric titrations show that this ligand forms 1 : 1 complexes with Ag+, Cu+, Cu2+, and Zn2+. Most importantly, detailed NMR‐spectroscopic analysis at different temperatures reveals that the complexation with Ag+ strongly affects the dynamic isomerization of the bullvalene unit of the ligand such that only one predominant valence isomer is formed, even at 5 °C. Detailed 1H‐NMR‐spectroscopic studies disclose an increased barrier (~11 kJ mol−1) of the Cope rearrangement. Furthermore, the addition of hexacyclene displaces the Ag+ from the complex, so that the valence isomerization is accelerated and an equilibrium with two predominant isomers is formed. In turn, repeated addition of Ag+ regains the complex with the restrained isomerization of the bullvalene unit. This method to control the valence isomerism by straightforward chemical stimuli may be used to simplify structural analysis at elevated temperatures, i. e. a feature not available so far with bullvalenes, and it may be employed as functional element in dynamic supramolecular assemblies. [ABSTRACT FROM AUTHOR]

Extending Lee-Schoenfeld & Diewald’s (2017) corpus investigation and formal analysis of lehren (‘teach’) to the other four German double-accusative verbs, abfragen, abhören (both meaning ‘quiz/test’), kosten (‘cost’), and fragen (‘ask’), we show that each verb follows its own individual path to overriding the highly marked ACC > ACC pattern, with the latest usage data revealing notably different results as to the verbs’ most typical syntactic patterns, meaning variants, and contextual features. Specifically, we propose that this small group of verbs makes use of three different “strategies” for avoiding the ACC > ACC pattern: (i) change of major valency frame from a ditransitive to a monotransitive pattern (abhören and abfragen), (ii) limiting the second object to primarily a clausal or prepositional one (fragen), and (iii) semantic diversification / polysemy combined with different preferences as to the valency pattern per meaning (kosten). We back up these claims by comparing the usage patterns of the verbs in four time periods between 1800 and 2010 via corpus analyses using DWDS (Digitales Wörterbuch der deutschen Sprache, https://www.dwds.de/). We also present the results of a synchronic search using the German web corpus deTenTen. [ABSTRACT FROM AUTHOR]

Autonomous verbs in Irish are special verb forms incompatible with the surface realization of a subject. Previous studies have suggested to postulate empty categories such as pro, PRO or expletive pro to fill the subject position (cf. Stenson 1989; McCloskey 2007; Bondaruk/ Charzyńska-Wóicjk 2003), thus rejecting the idea that these verbs might be classified as completely subjectless. A series of syntactic tests bear out the hypothesis that, at least for Irish, these verbs behave as actually lacking a subject. I first suggest correlating this state of affairs to the fact that, with autonomous verbs, no argument role to be promoted to subject position is selected at the valency level, although it is "implied" in the unfolding of the event. Secondly, I argue that both valency reduction and syntactic non-realization of an argument role is driven by information structural constraints; notably, the focal nature of autonomous verbs (as advocated elsewhere, cf. Nolan 2012) causes the subject (together with the argument role it is associated with) to be informationally downgraded, thereby leading to its suppression in the sentence. The position held in this paper is that autonomous verbs of the Irish type epitomize an interesting phenomenon of semantic-pragmatic interface, with the pragmatic level of the utterance "mediating" between the semantic and the syntactic level; in such a perspective, the pragmatic (information structural) level of an utterance would determine either the number and type of argument roles a verb can take in a particular discourse context (cf. DuBois 1987; Goldberg 2006) and their syntactic encoding. [ABSTRACT FROM AUTHOR]

Cobalt dioxolenes are a well-known class of switchable coordination compounds showing intramolecular electron transfer, which is always accompanied by a spin state change at the cobalt center. Here, we present the first example of thermally switchable cobalt bis-dioxolenes where intramolecular electron transfer seems to take place, but the spin state change is suppressed. This leads to the detection of thermal transition between a common ls-CoIII(SQ˙−)(Cat2−) and an extremely rare ls-CoII(SQ˙−)2 electronic state (hs – high-spin, ls – low-spin, SQ˙− – benzosemiquinonate(1−) radical and Cat2− – catecholate(2−)). Parallel to the present work, a similar work but on cobalt mono-dioxolenes has just appeared (Chem. Eur. J., 2023, 29, e202300091), suggesting thermal transition between ls-CoIII(Cat2−) and ls-CoII(SQ˙−) electronic states. [ABSTRACT FROM AUTHOR]

The Kazakh anthroponymicon during its centuries-old history did not experience serious pressure from religious and state institutions and therefore is characterized by a high degree of non-formalization. It has preserved the ancient traditions of naming, which are based on cultural and gender stereotypes: firstly, the preference for the birth of a male baby; and secondly, the birth of a boy child that is considered as a gift of higher sacred powers. This article explores a group of male anthroponyms formed as a result of the addition of substantive forms and the verbs tuu 'to be born', kelu 'to come', and beru 'to give'. They retain syntactic relations that go back to the original sentence: propositional semantics and actant models. Complex two-part anthroponyms belong to polypropositive structures; the primary proposition for all of them is the proposition 'A child was born'. Further, depending on the semantics and valency of the verbal component, there are situations of a reward, a birth time with different actants. In the surface structure of the anthroponym, depending on the relevance for those who give the name, in addition to the predicate, actants of various types are verbalized, such as agent, patient, and donor. In addition to the dictum content, the considered names include modal meanings: an evaluative mode, intention, which are expressed implicitly. Names-wishes and names-thanksgiving are distinguished depending on the intention. [ABSTRACT FROM AUTHOR]

BaBiO3 has attracted a lot of research attention since it was discovered as the parent compound for the high-Tc superconducting BaPbxBi1–xO3 and Ba1–xKxBiO3. In its pure state, BaBiO3 is an insulator due to the presence of a breathing distortion of the BiO6 octahedra. The distortion is attributed to the valency of Bi in the compound being charge-ordered in the form of Bi3+ and Bi5+ along the lattice, resulting in alternating expanded or contracted BiO6 octahedra. The interaction between the electronic properties and the thickness of the thin film is crucial to study. We conducted a thorough study to investigate the effect of the thickness reduction of BaBiO3-δ grown on SrTiO3-buffered Si substrates on the optical properties as well as the Bi electronic structure of the thin films. We conclude that modifications in the valency of Bi in the ultra-thin film regime result in an optically conducting layer. [ABSTRACT FROM AUTHOR]

The interfacial structure of a silicon grain boundary (Si-GB) plays a decisive role on its chemical functionalization and has implications in diverse physical–chemical properties of the material. Therefore, the GB interface is particularly relevant when the material is employed in high performance technological applications. Here, we studied from first principles the role of GB interface by providing an atomistic understanding of two different Σ 3{112} Si-GB models. These models are (1 × 1) and (1 × 2) Σ 3{112} Si-GBs, which lead to different structural reconstruction. Starting from these two models, we have shown that geometry optimization has an important role on the structural reconstruction of the GB interface and, therefore, on its properties. For this reason, we discussed different methodologies to define an optimal relaxation protocol. The influence of the local structures in (1 × 1) and (1 × 2) models has also been investigated in the presence of vacancies where different light impurities of different valency (C, N, H, O) can segregate. We studied how local structures in (1 × 1) and (1 × 2) models are modified by the presence of vacancies and impurities. These structural modifications have been correlated with the changes of the energetics and electronic properties of the GBs. The behavior of (1 × 1) and (1 × 2) models was demonstrated to be significantly different. The interaction with vacancies and the segregation of C, N, H, and O are significantly different depending on the type of local structures present in Σ 3{112} Si-GB. [ABSTRACT FROM AUTHOR]

Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in human-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. We study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their out- puts such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP’16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks. [ABSTRACT FROM AUTHOR]

Comprehensive Summary: Developing highly efficient and low‐cost electrocatalysts towards oxygen evolution reaction (OER) is essential for practical application in water electrolyzers and rechargeable metal‐air batteries. Although Fe‐based oxyhydroxides are regarded as state‐of‐the‐art non‐noble OER electrocatalysts, the origin of performance enhancement derived from Fe doping remains a hot topic of considerable discussion. Herein, we demonstrate that in situ generated Fe vacancies in the pristine CoFeOOH catalyst through a pre‐conversion process during alkaline OER result from dynamic Fe dissolution, identifying the origin of Fe‐vacancy‐induced enhanced OER kinetics. Density functional theory (DFT) calculations and experimental results including X‐ray absorption fine‐structure spectroscopy, in situ UV‐Vis spectroscopy, and in situ Raman spectroscopy reveal that the Fe vacancies could significantly promote the d‐band center and valence states of adjacent Co sites, alter the active site from Fe atom to Co atom, accelerate the formation of high‐valent active Co4+ species, and reduce the energy barrier of the potential‐determining step, thereby contribute to the significantly enhanced OER performance. [ABSTRACT FROM AUTHOR]

Comprehensive Summary: Developing highly efficient and low‐cost electrocatalysts towards oxygen evolution reaction (OER) is essential for practical application in water electrolyzers and rechargeable metal‐air batteries. Although Fe‐based oxyhydroxides are regarded as state‐of‐the‐art non‐noble OER electrocatalysts, the origin of performance enhancement derived from Fe doping remains a hot topic of considerable discussion. Herein, we demonstrate that in situ generated Fe vacancies in the pristine CoFeOOH catalyst through a pre‐conversion process during alkaline OER result from dynamic Fe dissolution, identifying the origin of Fe‐vacancy‐induced enhanced OER kinetics. Density functional theory (DFT) calculations and experimental results including X‐ray absorption fine‐structure spectroscopy, in situ UV‐Vis spectroscopy, and in situ Raman spectroscopy reveal that the Fe vacancies could significantly promote the d‐band center and valence states of adjacent Co sites, alter the active site from Fe atom to Co atom, accelerate the formation of high‐valent active Co4+ species, and reduce the energy barrier of the potential‐determining step, thereby contribute to the significantly enhanced OER performance. [ABSTRACT FROM AUTHOR]

We report a spectroscopic and computational study that investigates the absorption spectra of Bi(III) complexes, which often show an absorption band in the UV region (∼270–350 nm) due to 6sp ← 6s transitions. We investigated the spectra of three simple complexes, [BiCl5]2−, [BiCl6]3− and [Bi(DMSO)8]3+, which show absorption maxima at 334, 326 and 279 nm due to 3P1 ← 1S0 transitions. Theoretical calculations based on quasi-degenerate N-electron valence perturbation theory to second order (QD-NEVPT2) provide an accurate description of the absorption spectra when employing CAS(2,9) wave functions. We next investigated the absorption spectra of the [Bi(NOTA)] complex (H3NOTA = 1,4,7-triazacyclononane-1,4,7-triacetic acid), which forms ternary complexes [Bi(NOTA)X]− (X = Cl, Br or I) in the presence of excess halide in aqueous solutions. Halide binding has an important impact on the position of the 3P1 ← 1S0 transition, which shifts progressively to longer wavelengths from 282 nm ([Bi(NOTA)]) to 298 nm (X = Cl), 305 nm (X = Br) and 325 nm (X = I). Subsequent QD-NEVPT2 calculations indicate that this effect is related to the progressive stabilization of the spin–orbit free states associated with the 6s16p1 configuration on increasing the covalent character of the metal–ligand(s) bonds, rather than with significant differences in spin–orbit coupling (SOC). These studies provide valuable insight into the coordination chemistry of Bi(III), an ion with increasing interest in targeted alpha therapy due to the possible application of bismuth isotopes bismuth-212 (212Bi, t1/2 = 60.6 min) and bismuth-213 (213Bi, t1/2 = 45.6 min). [ABSTRACT FROM AUTHOR]

Suppose that G is a finite group and S is a non-empty subset of G such that e ∉ S and S -1 ⊆ S. Suppose that Cay(G, S) is the Cayley graph whose vertices are all elements of G and two vertices x and y are adjacent if and only if xy -1 ∈ S. In this paper, we introduce the generalized Cayley graph denoted by Caym(G,S) that is a graph with vertex set consists of all column matrices Xm which all components are in G and two vertices Xm and Ym are adjacent if and only if Xm[(Ym) -1 ] t ∈ M(S), where Ym -1 is a column matrix that each entry is the inverse of similar entry of Ym and M(S) is m × m matrix with all entries in S, [Y -1 ] t is the transpose of Y-1 and m ≥ 1. We aim to determine the structure of Caym(G,S) when G is the dihedral group of order 2n and L S |= 3 for every m ≥ 2, n ≥ 3. [ABSTRACT FROM AUTHOR]

In the two-component relativistic density functional theory, the picture change error (PCE), which originates from insufficient transformation of operators, should be corrected. In this study, we examine the PCE in the fractional occupation number (FON) state based on the spin-free infinite-order two-component Hamiltonian. The PCE for the total and orbital energy changes is estimated with respect to the FON electrons of the highest occupied molecular orbital and 1s core orbital in noble gas atoms. PCE is significant in core orbitals in heavy elements but relatively small in light elements and valence orbitals. The delocalization error, which can be represented by the total energy deviation from the behavior of the exact energy, is overestimated by the lack of picture change correction of the two-electron operator and underestimated by that of the density operator. Corresponding to these results, the PCE influences the value of orbital energies and slope of orbital energy change to FON. [ABSTRACT FROM AUTHOR]

The effect of TiW substitution on the microwave dielectric performances of MgNb 2 O 6 ceramics prepared via solid-state reaction has been investigated using Raman scattering spectroscopy, microscopic morphology analysis, and complex chemical bond theory. The dielectric permittivity is mainly affected by porosity, molecular polarizability and crystal vibrations. The Q × f value is mainly determined by the bond covalency of the Nb–O bond and the FWHM value of the Raman spectrum. In addition, τ f value is mainly affected by the bond valence of the Nb–O bond. This research demonstrates that a moderate amount of (TiW)5+ not only reduces the sintering temperature (from 1460 °C to 1340 °C) and lowers the dielectric loss, but also improves the temperature stability. The composition (x = 0.01) exhibits excellent properties: ε r = 20.67, Q × f = 117,660 GHz, and τ f = −45.73 ppm/°C, providing a promising candidate for 5 G electronic devices. [ABSTRACT FROM AUTHOR]

Equilibrium Sn isotope fractionation properties between aqueous Sn (2+, 4+) species and Sn-bearing minerals are the key to using tin isotopes to trace the transportation, enrichment, and precipitation of tin in various geological processes. However, the application of Sn isotope geochemistry has been impeded by the absence of equilibrium Sn isotopic fractionation factors between Sn-bearing minerals and fluid and between mineral pairs. In this contribution, we conducted first-principles calculations based on the density functional theory to obtain the equilibrium Sn isotopic fractionation factors between aqueous Sn complexes and minerals. For Sn-bearing complexes in solution, the reduced partition function ratios (β) are determined by taking snapshots from the molecular dynamics trajectories and computing the average β of the snapshots based on the lowest energy atomic coordinates. For Sn-bearing minerals, static first-principles periodic density functional theory methods are performed. The results show that the β factors decrease in the sequence of malayaite (s) S n 4 + > cassiterite (s) S n 4 + > S n 4 + C l 4 H 2 O 2 (a q) > S n 2 + F 3 (a q) − > S n 2 + (O H) 2 (a q) > S n 2 + C O 3 (a q) > stannite (s) S n 4 + > S n 2 + C l 3 (a q) − . The predicted Sn isotope fractionation follows several distinct patterns. (1) For minerals, the Sn isotope fractionations (1000lnαminerals-stannite) of cassiteritestannite and malayaite-stannite mineral pairs are controlled by the properties of elements coordinating with tin, and the equilibrium Sn isotope fractionation factors between mineral pairs are large enough to make them powerful Sn isotope thermometers. (2) For Sn-bearing aqueous species, the β values of tin (4+) complexes are remarkably larger than those of all aqueous Sn2+ species, indicating that higher valence tin is preferentially enriched heavy tin isotopes. For aqueous Sn2+ species, the aqueous species with shorter bonds are more-enriched in heavy Sn isotopes than those with longer bonds. When both the valence state and bond length are different, the valence state is the main factor controlling tin isotope fractionation. (3) During the precipitation of various Sn2+ aqueous complexes into cassiterite or malayaite, heavy Sn isotopes tend to be enriched in minerals, while there are two situations for the precipitation of Sn2+ complexes into stannite. When Sn is transported in hydrothermal solution as Sn2+Cl3–, stannite precipitation leads to the enrichment of light tin isotopes in the residual solution and late minerals. On the contrary, other S n 2 + species S n 2 + F 3 − , S n 2 + (O H) 2 and S n 2 + C O 3 that precipitate as stannite will result in the enrichment of heavy tin isotopes in the residual solutions. In addition, the direct precipitation of Sn4+ complexes into cassiterite, malayaite, or stannite also produces considerable tin isotope fractionation. During precipitation, Sn4+ aqueous complexes form cassiterite or malayaite, and heavy Sn isotopes tend to be enriched in minerals; whereas when aqueous Sn4+ species are precipitated into stannite, heavy Sn isotopes are enriched in the residual fluid and late minerals. The calculated results are essential for further understanding the mechanisms of Sn isotopic fractionation in various Sn-involved geological processes. [ABSTRACT FROM AUTHOR]

The electrocatalytic NO3− reduction reaction (NO3RR) to NH3 provides a promising pathway for ambient NH3 synthesis and environmental pollution treatment. Cu and its oxides are recognized as effective NO3RR electrocatalysts due to their favorable d-orbital energy levels and superior kinetics. In this work, mixed-valence Cu-based catalysts with tunable valence states were constructed via an inorganic salt-induced MOF-derived strategy. Notably, optimized Cu–CuxO/C-0.3 featured a Cu/Cu2O heterostructure and demonstrated the lowest Cu valence state. The resulting Cu/Cu2O heterointerface facilitated electron transfer and increased the density of electrochemically active sites, leading to an enhanced faradaic efficiency of 81.4% and a remarkable yield rate of 13.38 mg h−1 cm−2 (ca. 2.39 mol h−1 gcat.−1) at −0.8 V vs. RHE. This work presents insights for designing multi-phase heterostructured NO3RR catalysts and emphasizes their potential significance in efficient ammonia production. [ABSTRACT FROM AUTHOR]

LixMoS2 is not only a lithium battery material, but is also an important precursor for the synthesis of MoS2 nanomaterials. Current syntheses of MoS2, such as in n‐butyllithium/LiBH4 or electrochemically, are not satisfying in terms of defined stoichiometry and crystallinity, so an accurate experimental crystal structure determination of this important and widely used material has been long awaited. A high‐pressure/high‐temperature synthesis yielded highly crystalline 1T′′‐LixMoS2 (x=1, 1.333). 1T′′‐LiMoS2 crystallizes in the space group P1‾ $\bar 1$ with a=6.2482(3) Å, b=6.6336(3) Å, c=6.7480(3) Å, α=119.321(2)°, β=90.010(2)° and γ=90.077(2)°. The arrangement of Mo atoms within the b‐c‐plane confirmed a predicted Peierls distortion. A similar atom distribution pattern to that of Mo is also observed for the lithium atoms. Calculation of bond valence site energies gave an activation barrier of 1.244 eV for 2D lithium‐ion migration. For x=1.333, a phase‐pure synthesis was achieved. [ABSTRACT FROM AUTHOR]