Zero-sum problems with subgroup weights

In this note, we generalize some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider ℤ _p ^d for a general d and subgroups of Z* _p as weights.     

Structural asymmetry in liquid Fe–Si alloys

The thermodynamic properties and microscopic structure of liquid Fe–Si alloys at 1873 K were studied by using the regular associated solution model. The model was utilized to determine the complex concentration in a regular associated solution of Fe, Si and Fe₂Si. The complex concentration was then used to calculate the integral excess free energy of mixing, activity, concentration fluctuations in the long-wavelength limit, S_CC (0), and the Warren–Cowley short-range parameter α ₁. The analysis suggests that heterocoordination leading to the formation of complex Fe₂Si is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the alloy is more ordered towards the Fe-rich region. The observed asymmetry in the properties of mixing of Fe–Si alloys in the molten state is successfully explained on the basis of the regular associated solution model.     

Topological studies related to molecular systems formed during the Big Bang: H3+ as an example

In the present article are analyzed the non-adiabatic coupling terms (NACT) for two molecular systems, namely H₃⁺ and H₃. In contrast to previous occasions in which the NACTs are studied along (closed) circular contours usually surrounding conical intersections (ci), in the present article are studied distribution of the NACTs in (planar) configuration spaces (CS). The motivation for this study has to do with a novel idea being mentioned earlier (Molec. Phys., 116, 2435 [2018]; ArXiv:1801.00103) that NACTs are like a Glue (eventually) associated with the ability of creating molecules and/or protecting them from breaking up. It was found that the distributions of the NACTs due to the two molecules are similar as long as the attention is given to regions close to their equilateral cis, but then they behave significantly different in other regions. In case of H₃⁺, the NACTs are distributed rather uniformly whereas, in case of H₃ they become spiky the closer they approach the diatom axis. The main conclusion of this study is that the glue which has its origin in the NACTs is most likely to be effective in case of H₃⁺ that explains the creation and later survival of this molecule.     

Determination of thiocarbamyl sulphenamides, thiuram disulphides and dibenzothiazyl disulphide by amperometric titration

An amperometric method for the determination of thiocarbamyl sulphonamides has been developed, based on the cleavage of the S-N bond by hydriodic acid. The method can also be applied for the cleavage of the S-S bond in thiuram disulphides and dibenzothiazyl disulphide, and thus provides a useful means for the estimation of these compounds as well.     

Synthesis and properties of mononuclear and binuclear molybdenum complexes derived from bis(2-hydroxy-1-naphthaldehyde)oxaloyldihydrazone

The monomer molybdenum(VI) complex [MoO(2)(napoxlhH(2))].2H(2)O (1) has been synthesized from the reaction of MoO(2)(acac)(2) with bis(2-hydroxy-1-naphthaldehyde)oxaloyldihydrazone (napoxlhH(4)) in 1:1 molar ratio in ethanol under reflux. This complex on reaction with pyridine/3-picoline/4-picoline yielded the dimer molybdenum(VI) complexes [Mo(2)O(4)(napoxlhH(2))(2)(A)(2)].2H(2)O (A=py (2), 3-pic (3), 4-pic (4)), whereas reaction with isonicotinoylhydrazine (inhH(3)) and salicyloylhydrazine (sylshH(3)) lead to the reduction of the metal centre yielding monomeric molybdenum(V) complexes [Mo(napoxlhH(2))(hzid)].2H(2)O (where hzidH(3)=inhH(3) (5) and sylshH(3) (6)). The complexes have been characterized by elemental analyses, molecular weight determinations, molar conductance data, magnetic moment data, electronic, IR, ESR and (1)H NMR spectroscopic studies. The complexes (5) and (6) are paramagnetic to the extent of one unpaired electron. The electronic spectra of the complexes are dominated by strong charge transfer bands. In all of the complexes, the principal dihydrazone ligand has been suggested to coordinate to the metal centres in the anti-cis-configuration. The complexes (1), (5) and (6) are suggested to have six-coordinate octahedral stereochemistry around molybdenum(VI) and molybdenum(V) metal centres, respectively, while the complexes (2)-(4) are suggested to have eight coordinate dodecahedral stereochemistry around molybdenum(VI) metal centre.     

Curl condition for a four-state Born-Oppenheimer system employing the Mathieu equation

When a group of four states forms a subspace of the Hilbert space, i.e., appears to be strongly coupled with each other but very weakly interacts with all other states of the entire space, it is possible to express the nonadiabatic coupling (NAC) elements either in terms of s or in terms of electronic basis function angles, namely, mixing angles presumably representing the same sub-Hilbert space. We demonstrate that those explicit forms of the NAC terms satisfy the curl conditions--the necessary requirements to ensure the adiabatic-diabatic transformation in order to remove the NAC terms (could be often singular also at specific point(s) or along a seam in the configuration space) in the adiabatic representation of nuclear SE and to obtain the diabatic one with smooth functional form of coupling terms among the electronic states. In order to formulate extended Born-Oppenheimer (EBO) equations [J. Chem. Phys. 2006, 124, 074101] for a group of four states, we show that there should exist a coordinate independent ratio of the gradients for each pair of ADT/mixing angles leading to zero curls and, thereafter, provide a brief discussion on its analytical validity. As a numerical justification, we consider the first four eigenfunctions of the Mathieu equation to demonstrate the interesting features of nonadiabatic coupling (NAC) elements, namely, the validity of curl conditions and the nature of curl equations around CIs.     

A dinuclear Ni(I) system having a diradical Ni2N2 diamond core resting state: synthetic, structural, spectroscopic elucidation, and reductive bond splitting reactions

One-electron reduction of the square-planar nickel precursor (PNP)NiCl ( 1) (PNP (-) = N[2-P(CHMe 2) 2-4-methylphenyl] 2) with KC 8 effects ligand reorganization of the pincer ligand to assemble a Ni(I) dimer, [Ni(mu 2-PNP)] 2 ( 2), containing a Ni 2N 2 core structure, as inferred by its solid-state X-ray structure. Solution magnetization measurements are consistent with a paramagnetic Ni(I) system likely undergoing a monomer <--> dimer equilibrium. The room-temperature and 4 K solid-state X-band electron paramagnetic resonance (EPR) spectra display anisotropic signals. Low-temperature solid-state X-band EPR data at 4 K reveal rhombic values g z = 1.980(4), g x = 2. 380(4), and g y = 2.225(4), as well as a forbidden signal at g = 4.24 for the Delta M S = 2 half field transition, in accord with 2 having two weakly interacting metal centers. Utilizing an S = 1 model, full spin Hamiltonian simulation of the low-temperature EPR spectrum on the solid sample was achieved by applying a nonzero zero-field-splitting parameter ( D = 0.001 cm (-1)), which is consistent with an S = 0 ground state with a very closely lying S = 1 state. Solid-state magnetization data also corroborate well with our solid-state EPR data and reveal weak antiferromagnetic behavior ( J = -1.52(5) cm (-1)) over a 2-300 K temperature range at a field of 1 Tesla. Evidence for 2 being a masked "(PNP)Ni" scaffold originates from its reaction with N 2CPh 2, which traps the Ni(I) monomer in the form of a T-shaped species, Ni(PNPNNCPh 2), a system that has been structurally characterized. The radical nature of complex 2, or its monomer component, is well manifested through the plethora of cooperative H-X-type bond cleavage reactions, providing the nickel(II) hydride (PNP)NiH and the corresponding rare functionalities -OH, -OCH 3, -PHPh, and -B(catechol) integrated into the (PNP)Ni moiety in equal molar amounts. In addition to splitting H 2, compound 2 can also engage in homolytic X-X bond cleavage reactions of PhXXPh to form (PNP)Ni(XPh) (X = S or Se).     

Structure and Properties of Nanocomposites Based on SBS Block Copolymer and Alumina

The addition of inorganic filler into commodity plastics has a long history. Today, polymer composites based on nanosized filler are popular among polymer scientists from academia and industries due to their ability to enhance a number of physical properties. In this work, we investigate the dispersion and reinforcing effect of alumina nanoparticles using a polystyrene-polybutadiene based block copolymer (SBS) and organically modified alumina nanofiller. With the aid of solution casting procedures, polymer composites with good dispersion of nanoparticles could be produced. It has been demonstrated that with suitably coated nanoparticles, polymer composites with optimum dispersion of nanofiller ensuring marked reinforcement effect can be achieved.     

Chemical ordering and thermodynamic properties of HgNa liquid alloys

We have studied the thermodynamic properties and microscopic structures of HgNa liquid alloy at 673 K on the basis of regular associated solution model. The concentrations of ApB type complex in a regular associated solution of Hg and Na have been determined. We have then used the concentration of complex to calculate the free energy of mixing, enthalpy of mixing, entropy of mixing, activity, concentration fluctuations in long wavelength limit S_CC(0) and the Warren-Cowley short-range parameter α₁. The analysis suggests that heterocoordination leading to the formation of complex Hg₄Na is likely to exist in the liquid and is of a strongly interacting nature. The theoretical analysis reveals that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Hg-rich region.     

Reactions of halogenated organic peroxyl radicals with some biologically important compounds in a quaternary microemulsion

Reactions of various halogenated peroxyl radicals with guanine, uric acid, xanthine, hypoxanthine and ascorbic acid in a quaternary microemulsion consisting of sodium lauryl sulfate/water/1-pentanol/cyclohexane have been studied using the technique of pulse radiolysis. For all purine derivatives and ascorbic acid, formation of the respective radical cations have been observed. Variation in biomolecular rate constant values for the reactions of peroxyl radicals with the above-mentioned compounds has been discussed in terms of diffusion of radicals.