Relativistic quantum mechanics of spin-0 and spin-1 bosons

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) ispossible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrainedto be positive definite for allsolutions. Consequently, the antiparticles must be interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by second quantization and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics.on sabbatical leave from S. N. Bose National Centre for Basic-Sciences. Block JD. Sector III. Salt Lake. Calcutta 700 091. India.     

Spectrophotometric determination of osmium with 2R-acid in the presence of other platinum metals

Osmium(VIII) produces two coloured species with lambda(max) 680 nm (green) and 530 nm (red) with excess of 2-amino-8-naphthol-3,6-disulphonic acid in aqueous solution. The green complex is stable between pH 2.5 and 8.0 and the red complex between pH 11.0 and 12.0. The effects of temperature and time, reagent concentration, optimum conditions for the spectrophotometric determination of trace amounts of osmium, and other variables, have been studied at pH 11.5. At this pH, other platinum metals do not interfere. The sensitivity of the colour reaction is 0.2 microg/cm(2) and the system conforms to Beer's law over a concentration range of 1.5-10 microg of osmium.     

Thermal effects on cation distribution of CuCr2O4

Thermal studies on CuCr₂O₄ spinel indicated the phase present above 870 K to be cubic CuCr₂O₄. However, when the substance was quenched from 1023 K, 1173 K, 1273 K and 1473 K, only the tetragonal phase of CuCr₂O₄ was obtained. This is because the first-order, diffusionless, tetragonal to cubic phase transition at 865 K occurs reversibly at a very fast rate. Thec/a ratio for CuCr₂O₄ present in the various quenched samples did not change when the quenching temperature was raised. A strong preference of the Cr³⁺ ion for the B site prevents it from interchanging sites with Cu²⁺ ions, thus keeping the lattice parametersc anda unchanged.

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Zusammenfassung Thermische Untersuchungen am CuCr₂O₄ Spinell zeigten, daß die Phase oberhalb von 870 K aus kubischem CuCr₂O₄ besteht. Wenn jedoch von 1023 K, 1173 K, 1273 KL und 1473 K schnell abgekühlt wurde, entsteht nur die tetragonale Phase von CuCr₂O₄. Der Grund hierfür ist, daß der diffusionsfreie Übergang erster Ordnung von der tetragonalen zur kubischen Phase bei 865 K reversibel mit sehr großer Geschwindigkeit vor sich geht. Das Verhältnisc/a von CuCr₂O₄ in den verschiedenen schnell abgekühlten Phasen verändert sich durch das Erhöhen der Ausgangstemperatur der Abkühlung nicht. Ein starker Vorrang des Cr³⁺-Ions für die B Plätze verhindert den Austausch von Plätzen mit Cu²⁺-Ionen, wodurch die Gitterparameter c und a unverändert bleiben.

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Résumé L'étude des propriétés terhmiques du spinelle CuCr₂O₄ indique que la phase présente au-dessus de 870 K consiste en CuCr₂O₄ cubique. Cependant, en refroidissant très rapidement à partir de 1023, 1173, 1273 et 1473 K on n'a obtenu que la phase tétragonale de CuCr₂O₄. Ce résultat est dû au fait que la transition sans diffusion du premier ordre de la phase tétragonale en la phase cubique s'effectue réversiblement, à une vitesse très élevée, à 865 K. Le rapportc/a de CuCr₂O₄ présent dans les divers prélèvements refroidis rapidement, n'a pas été modifié en augmentant la température de départ du refroidissement rapide. Une forte préférence de l'ion Cr³⁺ pour les sites B empêche celui-ci d'échanger ses sites avec les ions Cu²⁺, maintenant ainsi les paramètres du réseau c et a inchangés.

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CuCr₂O₄ , 870 . , 1023 , 1173 , 1273 1473 . , 865 . / . Cr³⁺ , Cu²⁺, «c» «a».

     

Ring electrographic analysis of some ancient punch-marked silver coins from Soron, Allahabad, India

The chemical analysis of a number of punch-marked silver coins of the period 400-300 B.C., obtained from the archaeological site at Soron, Phoolpur Sub Division, Allahabad District, India, has been carried out nondestructively by a modified ring colorimetric method. On the basis of the compositions the order of their age has been suggested.     

Molecular orbital study of the ring nitrogen basicity of various dihydrofolate reductase inhibitors

We present molecular orbital (CNDO /2) calculations on the key fragments of different dihydrofolate reductase inhibitors. Distance geometry analysis, physicochemical parameter dependent QSAR , and molecular shape analysis raised some questions regarding the basicity of the ring nitrogen (N1) in these inhibitors and the effect of the various substituents on the basicity. We show that the ring nitrogen N1 of methotrexate has a considerably higher tendency to be protonated compared to that of folic acid. However, not all 2,4-diamino inhibitors are equally basic. Even 2-amino-4-hydroxyquinazoline is sufficiently basic to be protonated, but not the 2,4-diamino-5-sulfonyl derivatives. The pyrimidinium ion seems to be highly solvated, since in spite of its high protonation energy it is strongly basic. Triazines were found to be the most basic of all the classes studied.     

Structure of 4-amino-3-butyl-1,2,4-triazole-5-thione: Relation to derivatives with H, Me, Et, and Pr in the 3-position

The compound 4-amino-3-butyl-1,2,4-triazole-5-thione [crystal data: C₆H₁₂N₄S, triclinic, P , Z = 2, a = 7.546(2), b = 11.217(3), c = 5.681(1) ?, α = 103.12(2), β = 91.33(2), γ = 72.41(2)°, V = 445.9(2) ?³] contains an essentially planar triazole ring with the butyl group rotated out of the plane by approximately 104°. The molecules form hydrogen-bonded dimers through intermolecular N–HS interactions involving the thione sulfur atom and the protonated nitrogen atom on the ring. These units are then linked into columns through N–HN hydrogen bonds between the amine group and the unsubstituted ring N atom of adjacent molecules. The structural features of this compound are compared with those of the corresponding triazoles with H, methyl, ethyl and propyl groups on the 3-carbon.     

Density functional studies of LiN and LiN+ (N = 2–30) clusters: Structure,binding and charge distribution

Density functional calculations using B3LYP/6‐311G method have been carried out for small to medium‐sized lithium clusters (Li_N, N = 2–30). The optimized geometries of neutral and singly charged clusters, their binding energies, ionization potential, electron affinity, chemical potential, softness, hardness, highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gap, and static dipole polarizability have been investigated systematically. In addition, we study the distribution of partial charges in detail using natural population analysis (NPA) in small‐sized clusters (Li_N, N = 2–10), both neutral and cationic, and demonstrate the correlation between symmetry and charge. Uniform distribution of charges in cationic clusters confirms them to be energetically more favorable than the neutral counterparts. Whenever possible, results have been compared with available data. An excellent agreement in every case supports new results as reliable predictions. A careful study of optimized geometries shows that Li₉ is derivable from bulk Li structure, i.e., body centered cubic cell, and higher clusters have optimized shapes derived from this. Further, the turnover form two to three dimensional structure occurs at cluster size N = 6. The quantity α^1/3 (α = polarizability) per atom is found to be broadly proportional to softness (per atom) as well as inverse ionization potential (per atom). The present work forms a sound basis for further study of large‐sized clusters as well as other atomic clusters. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Controlling the density and site of attachment of gold nanoparticles onto the surface of carbon nanotubes

A facile method for controlling the density and site of attachment of gold nanoparticles onto the surface of carbon nanotubes is demonstrated. Nitric acid based oxidation was carried out to create carboxylic groups exclusively at the ends of carbon nanotubes, whereas oxidation using a mixture of nitric and sulfuric acid with varied reaction time was carried out to control the population of carboxylic groups on the side walls of nanotubes. In turn, 4-aminothiophenol modified gold nanoparticles were covalently interfaced to these carboxylated multi-walled carbon nanotubes in the presence of a zero length cross-linker, 1-ethylene-3-(3-dimethylaminopropyl) carbodiimide. Raman spectroscopic results showed increase in height of disorder band with each of these successive steps, indicating the increase in degree of functionalization of the carbon nanotubes. Fourier transformed infrared spectroscopic analysis affirmed the functionalization of nanostructures and the formation of nanohybrid. Transmission electron and field emission scanning electron microscopic analysis ascertained the attachment of gold nanoparticles to the ends and side walls of the multi-walled carbon nanotubes. The new hybrid nanostructures may find applications in electronic, optoelectronic, and sensing devices.