Nucleophilic ligand displacement in dichloro[2-(arylazo)heterocycle]palladium(II) complexes by benzimidazole – a kinetic and mechanistic study

The reactions of benzimidazole (Bimz) with dichloro{2-(arylazo)pyridine}palladium(II), [Pd(aap)Cl₂ (3), aap = RC₆H₄N= N-2-C₅H₄N; R = H(a), o-Me(b), m-Me(c), p-Me(d), p-Cl(e)] and dichloro{2-(arylazo)pyrimidine}palladium(II), [Pd(aapm)Cl₂ (4), aapm = RC₆H₄N=N-2-C₆H₃N₂; R = H(a), o-Me(b), m-Me(c), p-Me(d), p-Cl(e)] were followed separately. The kinetics were examined under pseudo-first order conditions with reference to Bimz in MeCN at 385 and 390 nm, respectively and at 298 K using a u.v.–vis. spectrophotometer. The product was isolated and characterised as trans-Pd(Bimz)₂Cl₂. The reaction between Pd(aap)Cl₂ and Bimz follows the rate law, rate = K[Bimz]²[Pd(aap)Cl₂], a single step process, whereas biphasic behaviour is observed for the reaction between Pd(aapm)Cl₂ and Bimz; each step is first order with respect to the concentration of complex and to Bimz. The rate data support a nucleophilic association path and the rate decreases upon addition of Cl^–(LiCl). The aryl ring substituent of the arylazoheterocycle influences the substitution rate as follows: k(e) > k(a) > k(d) > k(c) > k(b). The k-values are linearly correlated with Hammett constants with usual deviations for the m-Me and o-Me substituents because of their steric crowding. The rate follows the order: k(aap) > k(aapm). This is unusual with reference to the -acidity order of the heterocycles, pyridine < pyrimidine, as the increased -acidity will enhance the nucleophilic association. The charge density calculation by MNDO method shows that in the pyrimidine ring of arylazopyrimidine, the peripheral m-N(uncoordinated) carries a high negative charge which may retard the nucleophilic association rate. This effect is absent in the pyridine ring of arylazopyridine and may be the reason for the faster single step nucleophilic substitution in Pd(aap)Cl₂.     

Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry

Threefold rotational symmetry has been used to develop an algorithm for the construction of planar graphs of IPR fullerenes and to factorize their characteristic polynomials. Two series of fullerenes of the formula C_60+12n and C_60+18n have thus been obtained. The algorithm has been shown to be useful for predicting the nature of variation of the point groups of the fullerenes with increased n, for counting the number of ¹³C nuclear magnetic resonance (NMR) signals (along with their relative intensities), and also for obtaining a large part of their eigenspectra. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Inter-string arrays of bimetallic assemblies with alternative Cu2+-Cl-Cu2+ and Cu-NC-M (M = Co3+, Fe+3, Cr+3) bridges: syntheses, crystal structure, and magnetic properties

Three bimetallic assemblies with alternate homometallic bridges through chloride ligands and heterometallic bridges through cyanide ligands of formula [(323)(2)Cu(2)(Cl)M(CN)(6)](n).2n(H(2)O), where 323 = N,N'-bis(3-aminopropyl)ethylenediamine and M = Co(3+) for 1, Fe(3+) for 2, and Cr(3+) for 3, were synthesized. They have been characterized structurally, analytically, spectroscopically, and magnetically. All three assemblies crystallize in the monoclinic system in the same space group P2(1)/n, with a = 11.642(2) A, b = 10.285(3) A, c = 13.622(2) A, beta = 95.69(3) degrees, V = 1623.1(6) A(3), and Z = 4 for 1; a = 11.681(4) A, b = 10.315(3) A, c = 13.567(5) A, beta = 95.62(3) degrees, V = 1626.8(9) A(3), Z = 4 for 2, and a = 11.782(4) A, b = 10.386(2) A, c = 13.755(4) A, beta = 95.51(3) degrees, V = 1657.4(8) A(3), Z = 4 for 3. Crystal structure analyses reveal that one-dimensional zigzag chains propagate in two different crystallographic directions (a and b) which are held together during the course of their propagation. All three assemblies have a homometallic Cu-Cl-Cu core in common. Assembly 1 exhibits metamagnetic behavior and shows weak antiferromagnetic interactions between Cu(2+) paramagnetic centers, through the chloride bridges. The Neel temperature, T(N), is 3.5 K, and the critical field is 4 T. In the presence of a magnetic field larger than 4 T, the local spin doublets of Cu(2+) in the assembly 1 remain in parallel arrangements. Assemblies 2 and 3 may be described as an alternative repetition of the antiferromagnetically coupled Cu-Cl-Cu fragment and ferromagnetically coupled Cu-CN-Fe(3+)/Cr(3+)fragment. The overall magnetic character of the strings in assemblies 2 and 3 are antiferromagnetic. Ferromagnetic interaction evidenced by the (Cu-CN-Fe(3+)/Cr(3+)) fragment was masked by the antiferromagnetic interaction between the Cu(2+) centers through the chloride bridge. The magnetic properties agree well with those expected for two [323 Cu(2+)] and a [Fe(CN)](3+) unit with spin-orbit coupling effect of the low-spin iron(III) ions for 2 and for two [323 Cu(2+)] and a [Cr(CN)](3+) unit for 3. In aqueous solution, trinuclear [(323)(2)Cu(2)M(CN)(6)](+) and dinuclear [(323)CuM(CN)(6)](-) species were observed.     

A DFT‐based exploration augmented by X‐ray and NMR of the stereoselectivity in the 1,3‐dipolar cycloaddition of 1‐pyrroline‐1‐oxide to methyl cinnamate and benzylidene acetophenone

A B3LYP/6–31G* study was carried out for the reactions of 1‐pyrroline‐1‐oxide (N1) with methyl cinnamate (E1) and benzylidene acetophenone (E2) for getting a quantitative rationalization of the experimental findings. The product ratios were determined by NMR studies of the crude reaction mixtures. The conformation and stereochemistry of the isolated cycloadducts were finally confirmed by 2D NMR and X‐ray diffraction. The endo/exo‐selectivities were predicted through the computation of activation parameters on the basis of assumed concerted mechanism. The regioselectivity and reactivity were amply predicted by local and global electrophilicity indices and were found to be in good agreement with the experimental findings which were supportive of polar character and of the direction of charge transfer (CT) accompanying the cycloaddition. It was found that the cycloaddition involving methyl cinnamate was endo‐selective, while that with benzylidene acetophenone produced the exo‐isomer as the major adduct. Copyright © 2010 John Wiley & Sons, Ltd.     

Optically-driven red blood cell rotor in linearly polarized laser tweezers

We have constructed a dual trap optical tweezers set-up around an inverted microscope where both the traps can be independently controlled and manipulated in all the three dimensions. Here we report our observations on rotation of red blood cells (RBCs) in a linearly polarized optical trap. Red blood cells deform and become twisted in hypertonic phosphate buffer saline and when trapped, experience an unbalanced radiation pressure force. The torque generated from the unbalanced force causes the trapped RBC to rotate. Addition of Ca⁺⁺ ions in the solution, keeping the osmolarity same, makes the cell membranes stiffer and the cells deform less. Thus the speed of rotation of the red blood cells can be controlled, as less deformation and in turn less asymmetry in shape produces less torque under the radiation pressure resulting in slower rotation at the same laser power     

Fuzzy inventory model with two warehouses under possibility measure on fuzzy goal

Multi-item inventory model with stock-dependent demand and two-storage facilities is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise) under inflation and time value of money. Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) function as well as some constraints are imprecise in nature. Model is formulated as to optimize the possibility/necessity measure of the fuzzy goal of the objective function and constraints are satisfied with some pre-defined necessity. A genetic algorithm (GA) is developed with roulette wheel selection, binary crossover and mutation and is used to solve the model when the equivalent crisp form of the model is available. In other cases fuzzy simulation process is proposed to measure possibility/necessity of the fuzzy goal as well as to check the constraints of the problem and finally the model is solved using fuzzy simulation based genetic algorithm (FSGA). The models are illustrated with some numerical examples and some sensitivity analyses have been done.     

Note On a Comparative Evaluation of Nine Well-Known Algorithms for Solving the Cell Formation Problem in Group Technology

Over the last three decades, numerous algorithms have been proposed to solve the work-cell formation problem. For practicing manufacturing managers it would be nice to know as to which algorithm would be most effective and efficient for their specific situation. While several studies have attempted to fulfill this need, most have not resulted in any definitive recommendations and a better methodology of evaluation of cell formation algorithms is urgently needed. Prima facie, the methodology underlying Miltenburg and Zhang's (M&Z) (1991) evaluation of nine well-known cell formation algorithms seems very promising. The primary performance measure proposed by M&Z effectively captures the objectives of a good solution to a cell formation problem and is worthy of use in future studies. Unfortunately, a critical review of M&Z's methodology also reveals certain important flaws in M&Z's methodology. For example, M&Z may not have duplicated each algorithm precisely as the developer(s) of that algorithm intended. Second, M&Z's misrepresent Chandrasekharan and Rajagopalan's [C&R's] (1986) grouping efficiency measure. Third, M&Z's secondary performance measures lead them to unnecessarily ambivalent results. Fourth, several of M&Z's empirical conclusions can be theoretically deduced. It is hoped that future evaluations of cell formation algorithms will benefit from both the strengths and weaknesses of M&Z's work.     

Dynamics of 2-D one electron quantum dots in periodically fluctuating confinement potential: Influence of size and anharmonicity

We explore the dynamics of harmonically confined single electron quantum dots as a function of dot size under periodically fluctuating confinement potential. The system of interest is a 2-D system in the presence of a perpendicular magnetic field. We show that for given strengths of the magnetic field and effective mass, a periodic variation in the strength of the confinement potential could invite interesting features in the dynamics of the system. Also, the pattern of time evolution of eigenstates of the unperturbed system reveals significant size-dependence. The fluctuation in the confinement potential from its initial value is found to modulate the dynamical aspects in a prominent way. The presence of cubic anharmonicity in the confining field brings in new features in the dot dynamics.     

Dynamics of 2-D one electron quantum dots in pulsed field: Influence of size

We explore the dynamics of harmonically confined single electron quantum dots as a function of dot size when an external time varying pulsed electric field is switched on. The system of interest is a 2-D system in the presence of a perpendicular magnetic field. We show that for given strengths of the confining potentials, the pattern of time evolution of eigenstates of the unperturbed system reveals significant size-dependence. The pulse duration time is also found to modulate the dynamical aspects in a prominent way.