Capping [H<Subscript>8−n</Subscript>Ni<Subscript>42</Subscript>C<Subscript>8</Subscript>(CO)<Subscript>44</Subscript>]<Superscript>n−</Superscript> (n = 6, 7, 8) Octa-carbide Carbonyl Nanoclusters with [Ni(CO)] and [CuCl] Fragments

The reactions of [Ni₁₆(C₂)₂(CO)₂₃]^4? and [Ni₃₈C₆(CO)₄₂]^6? with CuCl afforded mixtures of the previously reported [HNi₄₂C₈(CO)₄₄(CuCl)]^7? bimetallic octa-carbide cluster and the new [HNi₄₃C₈(CO)₄₅]^7? and [HNi₄₄C₈(CO)₄₆]^7? homo-metallic octa-carbides. The three species have very similar properties resulting always in co-crystals such as [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·6.5MeCN (x = 0.14) (86% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 14%[HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?) and [NMe₄]₇[HNi_42+2xC₈(CO)_44+2x(CuCl)_1?x]·5.5MeCN (x = 0.30) (70% [HNi₄₂C₈(CO)₄₄(CuCl)]^7?, 30% [HNi₄₃C₈(CO)₄₅]^7?/[HNi₄₄C₈(CO)₄₆]^7?). The new homo-metallic octa-carbides can be obtained free from the Ni–Cu octa-carbido cluster by reacting [Ni₁₀(C₂)(CO)₁₆]^2? in thf with a stoichiometric amount of CuCl, and crystals of [NMe₄]₆[H₂Ni_43+xC₈(CO)_45+x]·6MeCN (x = 0.72), which contain [H₂Ni₄₄C₈(CO)₄₆]^6? (72%) and [H₂Ni₄₃C₈(CO)₄₅]^6? (28%), have been obtained. Despite the different charges and compositions, these anions display almost identical structures, which are also closely related to those previously reported for the bimetallic Ni–Cd octa-carbido clusters [Ni_42+xC₈(CO)_44+x(CdCl)]^7? and [HNi_42+xC₈(CO)_44+x(CdBr)]^6?. Indeed, all these clusters are based on the same Ni₄₂C₈ cage decorated by miscellaneous [CdX]⁺ (X = Cl, Br), [CuCl] and [Ni(CO)] fragments.     

Bacilli as Biological Nano-factories Intended for Synthesis of Silver Nanoparticles and Its Application in Human Welfare

The search of eco-friendly technologies for nano-synthesis is significant to expand their applications in human welfare. Nowadays, various inorganic nanoparticles with beneficial features have been synthesized via physical, chemical, and biological means. Significant biological applications of silver nanoparticles include on-infectious microbes, target drug delivery, cancer and vector-borne disease control. Their syntheses have been tested from plant fungi, bacteria, and viruses. The bacterial mediated synthesis of silver, gold, zinc and other metal leads to a milestone in nano-medicines. Thus, in this review, we focus on the contribution of Bacilli in the synthesis of silver nanoparticles, the mechanism of action and their potential application in the welfare of human beings.     

A New Trinuclear Zn(II) Complex {[Zn(μ-ONN)(μ<Subscript>2</Subscript>-O)(μ-OO)]<Subscript>2</Subscript>Zn}: Synthesis,Characterization, Thermal Decomposition and Antibacterial Activity

New centrosymmetric trinuclear zinc(II) complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} has been synthesized by the reaction of a potentially ONN tridentate Schiff base ligand, and N,N-dimethylethylendiamin, with Zn(OAc)₂·2H₂O in methanol, in the refluxed conditions and characterized by elemental analysis, FT-IR and UV–Vis spectroscopy. Single crystal X-ray structure analysis reveals a trinuclear complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} with zinc(II) ions connected by three different bridges, (μ-ONN) of the Schiff base ligand, μ₂-O and μ-OO of the acetate. The complex is centrosymmetric, with one of the Zn atoms located at the inversion center. While the central Zn(II) ion is six-coordinated, the coordination number of the other Zn(II) ions is five. Finally, the {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} complex was thermally decomposed in air at 700 °C resulted in ZnO nano crystalites with the average size of 42 nm. The antibacterial activity of ligand and its zinc(II) complex were tested against gram-positive and gram-negative bacteria. The ligand showed higher activity than its zinc(II) complex.     

Performance of a rigid rod statistical mechanical treatment to predict monolayer ordering: a study of chain interactions and comparison with molecular dynamics simulation

A statistical mechanical model that treats hydrocarbon self-assembled monolayer (SAM) chains as rigid rods is examined to interrogate the mechanisms involved in monolayer ordering. The statistical mechanical predictions are compared to fully atomistic molecular dynamics simulations of SAMs with different packing densities. The monolayer chain order is examined as a function of surface coverage, chain-surface interactions, and chain–chain interactions. Reasonable interaction potentials are deduced from ab initio electronic structure calculations of small model systems. It is found that the chain-surface interaction is the most important parameter in formation of flat-lying monolayer phases, while formation of standing phase monolayers is driven most importantly by increased density of molecules at the surface. A brief discussion of the utility and validity of the rigid rod treatment is given in light of the molecular dynamics results.     

New two stages high order symmetric six-step method with vanished phase–lag and its first,second and third derivatives for the numerical solution of the Schrödinger equation

In the present paper, we obtain and analyze, for the first time in the literature, a new two-stages high order symmetric six-step method. The specific characteristics of the new proposed method are the highest possible algebraic order, the elimination of the phase–lag and its first, second and third derivatives. Additionally, for the new method we give the analysis of the method (both error and stability and interval of periodicity analysis) and the comparison of the effectiveness of the new developed method with the effectiveness of well known methods and very recently produced methods in the literature. The comparison is based on the numerical solution of the Schrödinger equation. The theoretical achievements and the numerical results show the effectiveness of the new developed method in comparison with other well known or recently developed numerical methods.     

Lego-like spheres and tori

Given a connected surface \({\mathbb {F}}^2\) with Euler characteristic \(\chi \) and three integers \(b>a\ge 1<k\), an \((\{a,b\};k)\)-\({\mathbb {F}}^2\) is a \({\mathbb {F}}^2\)-embedded graph, having vertices of degree only k and only a- and b-gonal faces. The main case are (geometric) fullerenes (5, 6; 3)-\({\mathbb {S}}^2\). By \(p_a\), \(p_b\) we denote the number of a-gonal, b-gonal faces. Call an \((\{a,b\};k)\)-map lego-admissible if either \(\frac{p_b}{p_a}\), or \(\frac{p_a}{p_b}\) is integer. Call it lego-like if it is either \(ab^f\)-lego map, or \(a^fb\)-lego map, i.e., the face-set is partitioned into \(\min (p_a,p_b)\) isomorphic clusters, legos, consisting either one a-gon and \(f=\frac{p_b}{p_a}\,b\)-gons, or, respectively, \(f=\frac{p_a}{p_b}\,a\)-gons and one b-gon; the case \(f=1\) we denote also by ab. Call a \((\{a,b\};k)\)-map elliptic, parabolic or hyperbolic if the curvature \(\kappa _b=1+\frac{b}{k}-\frac{b}{2}\) of b-gons is positive, zero or negative, respectively. There are 14 lego-like elliptic \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,2)\). No \((\{1,3\};6)\)-\({\mathbb {S}}^2\) is lego-admissible. For other 7 families of parabolic \((\{a,b\};k)\)-\({\mathbb {S}}^2\), each lego-admissible sphere with \(p_a\le p_b\) is \(a^fb\) and an infinity (by Goldberg–Coxeter operation) of \(ab^f\)-spheres exist. The number of hyperbolic \(ab^f\,(\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,3)\) is finite. Such \(a^f b\)-spheres with \(a\ge 3\) have \((a,k)=(3,4),(3,5),(4,3),(5,3)\) or (3, 3); their number is finite for each b, but infinite for each of 5 cases (a, k). Any lego-admissible \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \(p_b=2\le a\) is \(a^f b\). We list, explicitly or by parameters, lego-admissible \((\{a,b\};k)\)-maps among: hyperbolic spheres, spheres with \(a\in \{1,2\}\), spheres with \(p_b\in \{2,\frac{p_a}{2}\}\), Goldberg–Coxeter’s spheres and \((\{a,b\};k)\)-tori. We present extensive computer search of lego-like spheres: 7 parabolic (\(p_b\)-dependent) families, basic examples of all 5 hyperbolic \(a^fb\) (b-dependent) families with \(a\ge 3\), and lego-like \((\{a,b\};3)\)-tori.     

Turing pattern formation in anisotropic medium

Diffusion of reacting species in chemical and biochemical systems in anisotropic medium is markedly different from those occurring in isotropic medium, therefore approximating diffusion coefficients as constants may not be desirable as this has dynamical consequences. This paper is devoted to the analytical and numerical investigation of the development of spatial patterns in such systems. To this end we consider a general reaction–diffusion system with concentration-dependent diffusion and formulate a scheme to derive the general form of envelope equation for such systems. The theory is applied to the chlorite–iodide–malonic acid system, a standard paradigm for activator–inhibitor mechanism, to derive the instability condition in terms of the anisotropy parameters (\(\kappa _{i}, i = u, v\) that impart concentration-dependence to the diffusion coefficients) and identify the supercritical and subcritical Turing regions in the bifurcation diagram. The theoretical predictions are in good agreement with the numerical simulations.     

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. Classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons. A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. In this paper we examine the existence of entire labeling, where face-weights of all 6-sided faces of disjoint union of toroidal fullerenes form an arithmetic progression with common difference \(\hbox {d}\in \{1,2,3\}\).     

Isochronicity and limit cycle oscillation in chemical systems

Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a limit cycle around an interior stationary point. In this context Lienard equation is specifically used in the study of nonlinear dynamical properties of an open system which can be utilized to obtain the condition of limit cycle. In conjunction with the property of limit cycle oscillation, here we have shown the condition for isochronicity for different chemical oscillators with the help of renormalisation group method with multiple time scale analysis from a Lienard system. When two variable open system of equations are transformed into a Lienard system of equation the condition for limit cycle and isochronicity can be stated in a unified way. For any such nonlinear oscillator we have shown the route of a dynamical transformation of a limit cycle oscillation to a periodic orbit of centre type depending on the parameters of the system.