Search Results (73)

Molybdenum lithium compounds and materials are being researched and applied in cutting-edge industries; however, their bonding has not been explored in a systematic way. The present study investigates the MoLi molecule, to shed light on its bonding. Specifically, the electronic structure and bonding of the ground and 40 low-lying states of the MoLi molecule are explored, employing multireference methodologies, i.e., CASSCF and MRCISD(+Q) in conjunction with the aug-cc-pV5z(-PP) basis set. Bond distances, dissociation energies, dipole moments as well as common spectroscopic constants are given, while the potential energy curves are plotted. For the ground state, X${}^6\Sigma _{+}$, it is found that $R_{\mathrm{e}}$ = 2.708 Å, $D_{\mathrm{e}}$ = 24.1 kcal/mol, ${\omega }_{\mathrm{e}}$ = 316.8 ${\mathrm{cm}}^{-1}$, ${\omega }_{\mathrm{e}}{x}_{\mathrm{e}}$ = 2.11 ${\mathrm{cm}}^{-1}$, and μ = 3.63 D. Overall, the calculated states present a variety of bonds, from weak van der Waals up to the formation of 2.5 bonds. The dissociation energies of the calculated states range from 2.3 kcal/mol ($\mathrm{a}{}^8{\Sigma }^{+}$) to 34.7 ($\mathrm{c}{}^4\Pi$), while the bond distances range from 2.513 Å to 3.354 Å. Finally, dipole moment values up to 3.72 D are calculated. In most states, a 2s${2\mathrm{p}}_{\mathrm{z}}$ hybridization on Li and a ${4\mathrm{d}}_{{\mathrm{z}}^2}$5s${5\mathrm{p}}_{\mathrm{z}}$ or 5s${5\mathrm{p}}_{\mathrm{z}}$ hybridization on Mo are found. Moreover, it is observed that the excited Li(${}^2\mathrm{P}$) atom forms the shortest bonds because its empty ${2\mathrm{s}}^0$ orbital can easily accept electrons, resulting in a strong σ dative bond. Finally, the present work highlights the exceptional ability of lithium atoms to participate in a variety of bonding schemes, and it could provide the opening gate for further investigation of this species or associated material and complexes. Full article

In this paper, the fixed points of involutions on the moduli space of principal $E_6$-bundles over a compact Riemann surface X are investigated. In particular, it is proved that the combined action of a representative $\sigma$ of the outer involution of $E_6$ with the pull-back action of a surface involution $\tau$ admits fixed points if and only if a specific topological obstruction in $H^2\left(X/\tau ,{\pi }_0\left(E_6^{\sigma }\right)\right)$ vanishes. For an involution $\tau$ with $2k$ fixed points, it is proved that the fixed point set is isomorphic to the moduli space of principal H-bundles over the quotient curve $X/\tau$, where H is either $F_4$ or $PSp(8,\mathbb{C})$ and it consists of $2^{g-k+1}$ components. The complex dimensions of these components are computed, and their singular loci are determined as corresponding to H-bundles admitting non-trivial automorphisms. Furthermore, it is checked that the stability of fixed $E_6$-bundles implies the stability of their corresponding H-bundles over $X/\tau$, and the behavior of characteristic classes is discussed under this correspondence. Finally, as an application of the above results, it is proved that the fixed points correspond to octonionic structures on $X/\tau$, and an explicit construction of these octonionic structures is provided. Full article

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involution $\tau$ on X and a Cartan involution $\theta$ of G, producing an involution $\sigma ={\theta }_{\ast }\circ {\tau }_{\ast }$. These fixed points are shown to correspond to stable $G_{\mathbb{R}}$-bundles over the real curve $(X_{\tau },\tau )$, where $G_{\mathbb{R}}$ is the real form associated with $\theta$. The fixed point set ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ consists of exactly $2^r$ connected components, each a smooth complex manifold of dimension ${\displaystyle \frac{(g-1)\dim G}{2}}$, where r is the rank of the fundamental group of the compact form of G. A cohomological obstruction in $H^2(X_{\tau },{\pi }_1\left(G_{\mathbb{R}}\right))$ characterizes which bundles are fixed. A key result establishes a derived equivalence between coherent sheaves on ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ and on the fixed point set of the dual involution on the moduli space of $G^{\vee }$-local systems, where $G^{\vee }$ denotes the Langlands dual of G. This provides an extension of the Geometric Langlands Correspondence to settings with involutions. An application to the Chern–Simons theory on real curves interprets ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ as a $(B,B,B)$-brane, mirror to an $(A,A,A)$-brane in the Hitchin system, revealing new links between real structures, quantization, and mirror symmetry. Full article

In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control inputs and attainable outputs (either measured or estimated), which accordingly proposes a model-free (MF) nonsingular terminal sliding mode control (MFTSMC) for higher-order dynamic systems to reduce the tedious modelling work and the design complexity associated with the model-based control approaches. The total model-free controllers, derived from the Lyapunov differential inequality, obviously provide conciseness and robustness in analysis/design/tuning and implementation while keeping the essence of the TSMC. Three simulated bench test examples, in which two of them have representatively numerical challenges and the other is a two-link rigid robotic manipulator with two input and two output (TITO) operational mode as a typical multi-degree interconnected nonlinear dynamics tool, are studied to demonstrate the effectiveness of the MFTSMC and employed to show the user-transparent procedure to facilitate the potential applications. The major MFTSMC performance includes (1) finite time ($2.5\pm 0.05$ s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error $0\pm 0.002$, (3) robustness (zero sensitivity at state output against the unknown bounded internal uncertainty and external disturbance), (4) no singularity issue in the neighborhood of TSM $\sigma =0$, (5) stable chattering with low amplitude ($\pm 0.01$) at frequency 50 mHz due to high gain used against disturbance $d(t)=100+30\sin (2\pi t)$). The simulation results are similar to those from well-known nominal model-based approaches. Full article

The aromatic boron cluster B₈^2– (D_7h) has similar π bonding to C₆H₆, which is named “borozene”. The B₈^2– ligand has been observed to stabilize monovalent Ln(+I) in C_7v-LnB₈⁻ (Ln = La, Pr, Tb, Tm, and Yb) borozene complexes. Low-valency actinide complexes have been reported more rarely, and B₈^2– may be one of the potential ligands. Here, we report a theoretical study on a series of actinide metal-doping octa-boron clusters AnB₈ (An = Pa, U, Np, and Pu). It was found that each species has both half-sandwich and chair-like structures. Except for PaB₈, the half-sandwich structures of UB₈, NpB₈, and PuB₈ are more energetically stable than the chair-like structures, and the half-sandwich clusters of AnB₈ are found to be actinide(II) borozene complexes with the M^II[B₈²⁻] type. For each of the half-sandwich clusters, the B₈²⁻ ligand has σ and π double aromaticity. Various bonding analyses of AnB₈ confirm the covalent interactions between the doped actinide metals and the octa-boron clusters, which further stabilize the complexes and determine the relative stability of AnB₈. As expected, these complexes show high bond dissociation energies, especially PaB₈ with stronger Pa-B covalent bonds. These results demonstrate that the B₈²⁻ doubly aromatic ligand is able to stabilize divalent actinides. Full article

This paper studies the computational complexity of subclasses of semiperfect rings from the perspective of computability theory. A ring is semiperfect if the identity can be expressed as a sum of mutually orthogonal local idempotents. Semisimple rings and local rings are typical subclasses of semiperfect rings that play important roles in noncommutative algebra. First, we define a ring to be semisimple if the left regular module can be decomposed as a finite direct sum of simple submodules and prove that the index set of computable semisimple rings is ${\mathsf{\Sigma }}_2^0$-hard within the index set of computable rings. Second, we define local rings by using equivalent properties of non-left invertible elements of rings and show that the index set of computable local rings is ${\mathsf{\Pi }}_2^0$-hard within the index set of computable rings. Finally, based on the ${\mathsf{\Pi }}_2^0$ definition of local rings, computable semiperfect rings can be described by ${\mathsf{\Sigma }}_3^0$ formulas. As a corollary, we find that the index set of computable semiperfect rings can be both ${\mathsf{\Sigma }}_2^0$-hard and ${\mathsf{\Pi }}_2^0$-hard within the index set of computable rings. Full article

In our recent work, we revisited C–H and C–C bond activation in rhodium (I) complexes of pincer ligands PCP, PCN, PCO, POCOP, and SCS. Our findings indicated that an η³-C_sp2C_sp3H agostic intermediate acts as a common precursor to both C–C and C–H bond activation in these systems. We explore the electronic structure and bonding nature of these precleavage complexes using electron density and molecular orbital analyses. Using NBO, IBO, and ESI-3D methods, the bonding in the η³-CCH agostic moiety is depicted by two three-center agostic bonds: Rh–C_sp2–C_sp3 and Rh–C_sp3–H, with all three atoms datively bound to Rh(I). IBO analysis specifically highlights the involvement of three orbitals (CC→Rh and CH→Rh σ donation, plus Rh→CCH π backdonation) in both C–C and C–H bond cleavages. NCIPLOT and QTAIM analyses highlight anagostic (Rh–H) or β-agostic (Rh–C_sp2–H) interactions and the absence of Rh–C_sp³ interactions. QTAIM molecular graphs suggest bond path instability under dynamic conditions due to the nearness of line and ring critical points. Several low-frequency and low-force vibrational modes interconvert various bonding patterns, reinforcing the dynamic η³-CCH agostic nature. The kinetic preference for C–H bond breaking is attributed to the smaller reduced mass of C–H vibrations compared to C–C vibrations. Full article

The decomposition mechanisms of Fe(EDTA)⁻ and Fe(EDTMP)⁻ complexes, widely used in various industrial applications, were investigated through a theoretical approach. Despite their structural similarities, the phosphonic acid and carboxylic acid groups in these complexes lead to vastly different decomposition behaviors. Fe(EDTA)⁻, stabilized by delocalized π bonds in carboxylic acid groups, exhibited higher stability than that of Fe(EDTMP)⁻, which has only σ bonds in phosphonic acid groups. Interaction Region Indicator (IRI) analysis revealed that the steric hindrance of Fe(EDTMP)⁻ was stronger than that of Fe(EDTA)⁻. Ab initio molecular dynamics simulations revealed that Fe(EDTMP)⁻ undergoes rapid decomposition due to the ease of breaking P-C bonds and the repulsion between phosphonic acid groups. In contrast, Fe(EDTA)⁻ decomposes more slowly. These findings suggest the incorporation of phosphonic acid groups for easier degradation pathways when designing organic acid molecules. Understanding these mechanisms provides a basis for developing strategies for wastewater treatment in industrial settings. Full article

The noncovalent chalcogen interaction between SO₂/SO₃ and diazines was studied through a dispersion-corrected DFT Kohn–Sham molecular orbital together with quantitative energy decomposition analyses. For this, supramolecular circular chains of up to 12 molecules were built with the aim of checking the capability of diazine molecules to detect SO₂/SO₃ compounds within the atmosphere. Trends in the interaction energies with the increasing number of molecules are mainly determined by the Pauli steric repulsion involved in these σ-hole/π-hole interactions. But more importantly, despite the assumed electrostatic nature of the involved interactions, the covalent component also plays a determinant role in its strength in the involved chalcogen bonds. Noticeably, π-hole interactions are supported by the charge transfer from diazines to SO₂/SO₃ molecules. Interaction energies in these supramolecular complexes are not only determined by the S···N bond lengths but attractive electrostatic and orbital interactions also determine the trends. These results should allow us to establish the fundamental characteristics of chalcogen bonding based on its strength and nature, which is of relevance for the capture of sulfur oxides. Full article

This study aimed to investigate the insertion reaction of the polar monomers mediated by the cationic rare earth metal complex [(C₅H₅)Sc(NMe₂CH₂C₆H₄-o)]⁺ utilizing a combination of density functional theory (DFT) calculations and multivariate linear regression (MLR) methods. The chain initiation step of the insertion reaction could be described by the poisoning effect and the ease of monomer insertion, which could be represented via the DFT-calculated energy difference between σ- and π-coordination complexes (ΔΔE) and insertion energy barrier (ΔG^≠), respectively. The results indicate that ΔΔE and ΔG^≠ can be predicted by only several descriptors using multiple linear regression methods, with a root mean squared error (RMSE) of less than 2.5 kcal/mol. Furthermore, the qualitative analysis of the MLR models provided effective information on the key factors governing the insertion reaction chain initiation. Full article

Introduction: N-heterocyclic carbenes (NHCs) are considered important preferred auxiliary ligands for transition metals due to their strong σ-donor and weak π-acceptor properties and ease of structural modification in catalyst design. The functionalization of NHC by adding different substituent groups is an effective strategy for designing complexes with desired electronic and steric properties. NHC–Pd complexes are of particular importance due to their resistance to air, moisture and heat and their strong stability under catalytic and biological conditions. It is known that NHC–Pd complexes show excellent performance in the Suzuki–Miyaura cross-coupling reaction. The traditional Suzuki–Miyaura reaction involves the cross-coupling reaction of alkyl and arylboronic acids with aryl halides. This reaction has some advantages over other C-C coupling reactions. The use of water as a suitable and reliable solvent in the reaction, the fact that the reaction products are generally poorly soluble in water and can be easily separated from the reaction mixture, the use of non-toxic chemicals, the moderation of reaction conditions, and good functional group compatibility make it useful and worth studying. There are many examples of studies on the application of NHC–Pd complexes in the Suzuki–Miyaura reaction in aqueous media, and the highly effective catalytic activities and versatility of these reactions have been proven. Methods: In this study, a series of benzimidazole-based Pd–NHC complexes were synthesized. The synthesized complexes were characterized by spectroscopic methods. All complexes were tested as catalysts in the Suzuki–Miyaura cross-coupling reaction. Results: According to the obtained results, the synthesized benzimidazole-based Pd–NHC complexes were found to have high catalytic activity in the Suzuki–Miyaura cross-coupling reaction. Conclusions: The synthesized NHC-Pd complexes can be used as potential catalysts due to their high catalytic activity. It is thought that these catalysts can be used in different biochemical studies in the future. Full article

This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which can be tempered to display the aptness to form a π-hole halogen bond with a series of electron density-rich sites (Lewis bases) hosted individually by 32 other partner molecules. The [MP2/aug-cc-pVTZ] level characteristics of the π-hole halogen bonds in 33 binary complexes obtained from the charge density approaches (quantum theory of intramolecular atoms, molecular electrostatic surface potential, independent gradient model (IGM-δg^inter)), intermolecular geometries and energies, and second-order hyperconjugative charge transfer analyses are discussed, which are similar to other non-covalent interactions. That a π-hole can be observed on halogen in halogenated molecules is substantiated by experimentally reported crystals documented in the Cambridge Crystal Structure Database. The importance of the π-hole halogen bond in the design and growth of chemical systems in synthetic chemistry, crystallography, and crystal engineering is yet to be fully explicated. Full article

A systematic theoretical study was conducted on the triel bonds (TrB) within the BH₃∙∙∙M(MDA)₂ and C₅H₄BX∙∙∙M(MDA)₂ (M = Ni, Pd, Pt, X = H, CN, F, CH₃, NH₂, MDA = enolated malondialdehyde) complexes, with BH₃ and C₅H₄BX acting as the electron acceptors and the square-coordinated M(MDA)₂ acting as the electron donor. The interaction energies of these systems range between −4.71 and −33.18 kcal/mol. The larger the transition metal center M, the greater the enhancement of the TrB, with σ–hole TrBs found to be stronger than π–hole TrBs. In the σ–hole TrB complex, an electron-withdrawing substituent on the C opposite to the B atom enhances the TrB, while an electron-donating substituent has little effect on the strength of TrB in the Pd and Pt complexes but enhances the TrB in the Ni-containing complexes. The van der Waals interaction plays an important role in stabilizing these binary systems, and its contribution diminishes with increasing M size. The orbital effect within these systems is largely due to charge transfer from the d_z² orbital of M into the empty p_z orbital of B. Full article

Metal complexes of mesoionic carbenes (MICs) of the triazolylidene type and their derivatives have gained increasing attention in the fields of electrocatalysis and photochemistry. The redox activity of these metal complexes is critical for their applications in both the aforementioned fields. Easy accessibility and modular synthesis open a wide field for the design of ligands, such as bidentate ligands. The combination of an MIC with a pyridyl unit in a bidentate ligand setup increases the $\pi$ acceptor properties of the ligands while retaining their strong $\sigma$ donor properties. The analogy with the well-established 2,2′-bipyridine ligand allows conclusions to be drawn about the influence of the mesoionic carbene (MIC) moiety in tetracarbonyl group 6 complexes in cyclic voltammetry and (spectro)electrochemistry (SEC). However, the effects of the different connectivity in pyridyl-MIC ligands remain underexplored. Based on our previous studies, we present a thorough investigation of the influence of the two different pyridyl-MIC constitutional isomers on the electrochemical and the UV-vis-NIR/IR/EPR spectroelectrochemical properties of group 6 carbonyl complexes. Moreover, the presented complexes were investigated for the electrochemical conversion of CO₂ using two different working electrodes, providing a fundamental understanding of the influence of the electrode material in the precatalytic activation. Full article

Two ferrocenecarboxylate (fca)-bridged dirhodium (Rh₂) complexes, [Rh₂(fca)₄] (1) and [Rh₂(fca)(piv)₃] (2; piv = pivalate), were prepared through the carboxylate-exchange reactions of [Rh₂(O₂CCH₃)₄(H₂O)₂] and [Rh₂(piv)₄], respectively, with fcaH and characterized by ¹H NMR, ESI-TOF-MS, and elemental analyses. Single-crystal X-ray diffraction analyses of [Rh₂(fca)₄(MeOH)₂] (1(MeOH)₂) and [Rh₂(fca)(piv)₃(MeOH)₂] (2(MeOH)₂), which are recrystallized from MeOH-containing solutions of 1 and 2, revealed that (1) 1(MeOH)₂ and 2(MeOH)₂ possess homoleptic and heteroleptic paddlewheel-type dinuclear structures, respectively; (2) both complexes have a single Rh–Rh bond (2.3771(3) Å for 1(MeOH)₂, 2.3712(3) Å for 2(MeOH)₂); and (3) the cyclopentadienyl rings of the fca ligands in 1(MeOH)₂ adopt an eclipsed conformation, whereas those in 2(MeOH)₂ are approximately 12–14° rotated from the staggered conformation. Density functional theory (DFT) calculations revealed that (1) the electronic configurations of the Rh₂ core in 1(MeOH)₂ and 2(MeOH)₂ are π⁴σ²δ²π*²δ*²π*² and π⁴σ²δ²δ*²π*⁴, respectively; and (2) the occupied molecular orbitals (MOs) localized on the fca ligands are energetically degenerate and relatively more unstable than those on the Rh₂ cores. Absorption features and electrochemical properties of 1 and 2 were investigated in a 9:1 CHCl₃-MeOH solution and compared with those of fcaH and [Rh₂(piv)₄]. Through examining the obtained results in detail using time-dependent DFT (TDDFT) and unrestricted DFT, we found that 1 and 2 exhibit charge transfer excitations between the fca ligands and Rh₂ cores, and 1 shows electronic interactions between ferrocene units through the Rh₂ core in the electrochemical oxidation process. Full article