Evaluation of mean and variance integrals without integration

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential calculus. The general nature of the technique has potential for wider applications.     

Kinetic Studies on Interaction of Platinum(II) Complexes with an ‘S’ Containing Ligand in Aqueous Medium

The kinetics of the substitution reactions of [Pt(dach)(H₂O)₂]²⁺ and [Pt(en)(H₂O)₂]²⁺ (where ‘dach’ and ‘en’ are cis-1,2-diaminocyclohexane and ethylenediamine, respectively) with excess N,N′-diethylthiourea have been studied in aqueous solution by UV–Vis spectrophotometry. The effect of different N–N spectator ligands on the reactivity of platinum(II) complexes was investigated by studying the water lability of the reactant complexes. The kinetic study has been substantiated by product isolation, IR, NMR and ESI-MS spectral analysis and DFT calculations. The reactions follow normal square-planar substitution mainly in an associative way. Rate parameters have been evaluated under different conditions. The substitution rates of the complexes studied can be tuned through the nature of the N–N chelates, which is important in the development of new active compounds for cancer therapy.     

Kinetic study of the interaction of three glycine‐containing dipeptides with diaquaethylenediamineplatinum(II) in aqueous medium

The kinetics of the interaction of three glycine‐containing dipeptides, namely, glycine‐L‐leucine (Gly‐Leu), glycine‐L‐isoleucine (Gly‐Ile), and glycine‐valine (Gly‐Val) with [Pt(en)(H₂O)₂](ClO₄)₂ has been studied spectrophotometrically as a function of [substrate complex], [dipeptides] and temperature at a particular pH(4.0), where the substrate complex exists predominantly as the diaqua species and the dipeptides as a zwitterion. The substitution reaction shows two consecutive steps; the first is the ligand‐assisted anation and the second is the chelation step. The activation parameters for both the steps were evaluated using Eyring's equation. The low ΔH₁^≠ and large negative value of ΔS₁^≠ as well as ΔH₂^≠ and ΔS₂^≠ indicate an associative mode of activation for both the aqua ligand substitution processes. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 498–506, 2011     

Concentration fluctuations in binary mixtures of model polar fluids

We present calculations of the mean square concentration fluctuations, S_α(0), for binary mixtures of model polar fluids. The assumed pair interactions are taken to be of the forms of a hard core plus either dipole-dipole, quadrupole-quadrupole or dipole- quadrupole terms. The calculations are carried out within a mean field approximation. We have considered in some detail the interplay between size differences and the difference in the strength and range of the potentials in deciding how S_α(0) deviates from the ideal behaviour.     

Magnetism in FeNiW disordered alloys: Experiment and theory

We report here an experimental study of magnetization of FeNiW alloys at different compositions. We have studied variation of magnetization with temperature (at low external fields) and magnetic field (at low temperatures). The alloy shows para to ferromagnetic transitions across the composition range. We do not find any indication of the spin-glass phase. We have supplemented the experimental work with theoretical analysis using the first-principles tight-binding linear muffin-tin orbitals based augmented space recursion method. Our theoretical estimates of magnetic moment and Curie temperatures agree well with experiment. Our mean-field phase analysis also does not indicate the possibility of a spin-glass phase.     

Cascade synthesis of selective dihydro pyridazino fused acridinone derivatives via MCM-41 catalyzed ring-opening/ring-closure reaction

An enhanced one-pot synthesis of new functionalized 5,6-dihydro-5,5-dimethyl-2-phenyl-2H-pyridazino[3,4,5-kl]acridin-1(4H)-one derivatives with different substituted patterns by using mesoporous MCM-41 catalyst via a ring opening/ring closure reaction process has been established. This MCM-41 silica catalyst has been synthesized and characterized using an array of sophisticated analytical techniques like BET, XRD, UHRTEM, etc. This reaction could be conducted from inexpensive substrates within short period under neat reflux conditions. Compared with the usual methods, the remarkable advantages of this method are milder reaction conditions, operational simplicity, higher yields, short reaction times and an environmentally friendly procedure.     

Graphene as a reversible spin manipulator of molecular magnets

One of the primary objectives in molecular nanospintronics is to manipulate the spin states of organic molecules with a d-electron center, by suitable external means. In this Letter, we demonstrate by first principles density functional calculations, as well as second order perturbation theory, that a strain induced change of the spin state, from S=1→S=2, takes place for an iron porphyrin (FeP) molecule deposited at a divacancy site in a graphene lattice. The process is reversible in the sense that the application of tensile or compressive strains in the graphene lattice can stabilize FeP in different spin states, each with a unique saturation moment and easy axis orientation. The effect is brought about by a change in Fe-N bond length in FeP, which influences the molecular level diagram as well as the interaction between the C atoms of the graphene layer and the molecular orbitals of FeP.