Theoretical studies on tautomerism of imidazole-2-selenone

The tautomerism of all possible forms of imidazole selenone (ISe1–ISe6), induced by proton transfer was studied theoretically in different environments including gas phase, continuum solvent, and microhydrated environment with one explicit water molecule. The calculations were performed at the MP2 and CAM-B3LYP levels of theory, separately. It was found that the imidazole selenone, in the form of ISe3, is the most stable isomer in both gas phase and solvent. The activation energy for conversion of ISe3 to imidazole selenol (ISe6), as the second stable form, is 41.72 and 43.0 kcal/mol in the gas phase and water, respectively. The infrared spectral frequencies as well as the vibrational frequency shifts were reported and assigned to their corresponding vibrational modes. In addition, the variation of dipole moments and charges on the atoms with change of solvent was studied. The energies of HOMO, LUMO, and HOMO–LUMO gap were calculated in both gas phase and solvent. Specific solvent effects with addition of water molecule near the electrophilic centers of tautomers and the transition states of proton transfer, assisted by water molecule, were investigated. It was found that the water molecule can form different hydrogen bonds with the molecule. Aggregation of the isomers with water molecule does not change the order of stability of isomers, but proton transfer reaction assisted by a water molecule needs less energy than when the proton shifts through the intramolecular process.     

Single-molecule magnet behavior for an antiferromagnetically superexchange-coupled dinuclear dysprosium(III) complex

A family of five dinuclear lanthanide complexes has been synthesized with general formula [Ln(III)(2)(valdien)(2)(NO(3))(2)] where (H(2)valdien = N1,N3-bis(3-methoxysalicylidene)diethylenetriamine) and Ln(III) = Eu(III)1, Gd(III)2, Tb(III)3, Dy(III)4, and Ho(III)5. The magnetic investigations reveal that 4 exhibits single-molecule magnet (SMM) behavior with an anisotropic barrier U(eff) = 76 K. The step-like features in the hysteresis loops observed for 4 reveal an antiferromagnetic exchange coupling between the two dysprosium ions. Ab initio calculations confirm the weak antiferromagnetic interaction with an exchange constant J(Dy-Dy) = -0.21 cm(-1). The observed steps in the hysteresis loops correspond to a weakly coupled system similar to exchange-biased SMMs. The Dy(2) complex is an ideal candidate for the elucidation of slow relaxation of the magnetization mechanism seen in lanthanide systems.     

An Analytical Technique,Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.     

Lanthanide complexes of tritopic bis(hydrazone) ligands: single-molecule magnet behavior in a linear Dy(III)3 complex

Tritopic pyridinebis(hydrazone)-based ligands typically produce square M(9) [3 × 3] grid complexes with first-row transition-metal ions (e.g., M = Mn, Fe, Co, Cu, Zn), but with larger lanthanide ions, such coordination motifs are not produced, and instead linear trinuclear complexes appear to be a preferred option. The reaction of 2pomp [derived from pyridine-2,6-bis(hydrazone) and 2-acetylpyridine] with La(III), Gd(III), and Dy(III) salts produces helical linear trinuclear [Ln(3)(2pomp)(2)]-based complexes, where each metal ion occupies one of the three tridentate ligand pockets. Two ligands encompass the three metal ions, and internal connections between metal ions occur through μ-O(hydrazone) bridges. Coligands include benzoate, nitrate, and N,N-dimethylformamide. The linear Dy(III)(3) complex exhibits single-molecule magnet behavior, demonstrated through alternating-current susceptibility measurements. Slow thermal magnetic relaxation was detected in an external field of 1800 Oe, where quantum-tunneling effects were suppressed (U(eff) = 14 K).     

A novel high-spin tridecanuclear Ni(II) cluster with an azido-bridged core exhibiting disk-like topology

A high-spin tridecanuclear Ni(II) cluster, [Ni(II)(13)(N(3))(18)(dpo)(4)(Hdpo)(2)(H(2)hpo)(4)(H(2)O)(MeOH)] [Ni(II)(13)(N(3))(18)(dpo)(4)(Hdpo)(2)(H(2)hpo)(4)(H(2)O)(2)] (1) (Hdpo = 1-(dimethylamino)propan-2-one oxime and H(2)hpo = 1-(hydroxyamino)propan-2-one oxime) with a purely azido-bridged core, is reported with dominant ferromagnetic coupling between Ni(II) ions. The latter molecule exhibits a unique planar core topology with the largest N(3)(-):Ni(II) ratio reported to date.     

Predictable self-assembled [2×2] Ln(III)4 square grids (Ln = Dy,Tb)-SMM behaviour in a new lanthanide cluster motif

The ditopic carbohydrazone ligand (L1) produces the square, self-assembled [2×2] grids [Dy(4)(L1)(4)(OH)(4)]Cl(2) (1) and [Ln(4)(L1)(4)(μ(4)-O)(μ(2)-1,1-N(3))(4)] (Ln = Dy (2), Tb (3)), with 2 exhibiting SMM behaviour. Two relaxation processes occur with U(eff) = 51 K, 91 K in the absence of an external field, and one with U(eff) = 270 K in the presence of a 1600 Oe optimum field.     

THz wave sensing for petroleum industrial applications

We present the results of terahertz (THz) sensing of gasoline products. The frequency-dependent absorption coefficients, refractive indices, and complex dielectric constants of gasoline and xylene isomers were extracted in the spectral range from 0.5–3.0 THz. The THz spectra of gasoline (#87, #89, #93) and related BTEX (benzene, toluene, ethylbenzene, and xylene) compounds were studied by using Fourier transform infrared spectroscopy (FTIR) in the 1.5–20 THz (50–660 cm⁻¹). The xylene isomers, which are used as antiknock agent in gasoline were determined quantitatively in gasoline in the THz range. Our investigations show the potential of THz technology for the petroleum industrial applications.     

Planar tetranuclear Dy(III) single-molecule magnet and its Sm(III), Gd(III), and Tb(III) analogues encapsulated by salen-type and β-diketonate ligands

The syntheses, structures, and magnetic properties are reported for four new lanthanide clusters [Sm(4)(μ(3)-OH)(2)L(2)(acac)(6)]·4H(2)O (1), [Gd(4)(μ(3)-OH)(2)L(2)(acac)(6)]·4CH(3)CN (2), and [Ln(4)(μ(3)-OH)(2)L(2)(acac)(6)]·2H(2)L·2CH(3)CN (3, Ln = Tb; 4, Ln = Dy) supported by salen-type (H(2)L = N,N'-bis(salicylidene)-1,2-cyclohexanediamine) and β-diketonate (acac = acetylacetonate) ligands. The four clusters were confirmed to be essentially isomorphous by infrared spectroscopy and single-crystal X-ray diffraction. Their crystal structures reveal that the salen-type ligand provides a suitable tetradentate coordination pocket (N(2)O(2)) to encapsulate lanthanide(III) ions. Moreover, the planar Ln(4) core is bridged by two μ(3)-hydroxide, four phenoxide, and two ketonate oxygen atoms. Magnetic properties of all four compounds have been investigated using dc and ac susceptibility measurements. For 4, the static and dynamic data indicate that the Dy(4) complex exhibits slow relaxation of the magnetization below 5 K associated with single-molecule magnet behavior.     

On Proximal Relations in Transformation Semigroups Arising from Generalized Shifts

For a finite discrete topological space $X$ with at least two elements, a nonempty set $\Gamma$, and a map $\varphi:\Gamma \to \Gamma$, $\sigma_{\varphi}:X^{\Gamma} \to X^{\Gamma}$with $\sigma_{\varphi}((x_{\alpha})_{\alpha \in \Gamma})=(x_{\varphi(\alpha)})_{\alpha \in \Gamma}$ (for $(x_{\alpha})_{\alpha \in \Gamma} \in X^{\Gamma}$) is a generalized shift. In this text for $\mathcal{S} = \{\sigma_{\varphi}:\varphi \in \Gamma^{\Gamma}\}$ and $\mathcal{H}=\{\sigma_{\varphi}:\Gamma \xrightarrow{\varphi} \Gamma$ is bijective$\}$ we study proximal relations of transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$. Regarding proximal relation we prove: $$P(\mathcal{S}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \exists \beta \in \Gamma (x_{\beta} = y_{\beta})\}$$and $P(\mathcal{H}, X^{\Gamma} ) \subseteq \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\beta \in \Gamma : x_{\beta} = y_{\beta}\}$ is infinite$\}$ $\cup\{($ $x,x) : x \in \mathcal{X}\}$. Moreover, for infinite $\Gamma$, both transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$ are regionally proximal, i.e., $Q(\mathcal{S}, X^{\Gamma}) = Q(\mathcal{H}, X^{\Gamma} ) = X^{\Gamma} \times X^{\Gamma}$, also for sydetically proximal relation we have $L(\mathcal{H}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\gamma ∈ \Gamma :$ $x_{\gamma} \neq y_{\gamma}\}$ is finite$\}$.