Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

Doubly excited states of highly stripped ions: a time dependent perturbation approach

Doubly excited singlet states have been calculated for the astrophysically important highly stripped He like ions Al^{11 +}, Si^{12 +}, P^{13 +}, S^{14 +} and Cl^{15 +} for the transitions 2s ²: ¹ S ^e, 2p ²: ¹ D ^e, 2snp: ¹ P ⁰, 2snd: ¹ D ^e and 2pnd: ¹F⁰ for n45. The transition energies are obtained from the position of resonances in the oscillations of the two electron charge cloud under an external harmonic perturbation. Linearised version of a suitably constructed variational functional is used for obtaining the response properties of the system. Most of the results are new. Agreement with the only few existing experimental data along this line is very reasonable. Analytic representations of the doubly excited states are obtained and the Coulomb repulsion integral in these states are estimated for checking the consistency of the wavefunctions. The doubly excited state wavefunctions so obtained may be used for evaluating other physical properties connected with transitions.     

NS and NSO-Donor ligands and their metal complexes. Synthesis and characterisation of a new low-spin iron(III) complex with 1,2-di(o-aminophenylthio)ethane and iron(III), cobalt(III) and manganese(III) complexes of 1,2-di(o-salicylaldiminophenylthio)ethane

Summary Iron(III) complexes of a quadridentate N₂S₂ donor ligand, 1,2-di(o-aminophenylthio)ethane (DAPTE) and its Schiff Base with salicylaldehyde, a hexadentate N₂S₂O₂ donor ligand,viz. 1,2-di(o-salicylaldiminophenylthio)ethane (H₂DSALPTE) have been synthesised and characterised.The Schiff base ligand (1 mol) gave a dark green tri-iron(III) [Fe₃(DSALPTE)(HDSALPTE)Cl₃]Cl₂ complex when reacted with anhydrous iron(III) chloride (1 mol). The Mössbauer data of this complex suggest the presence of three iron sites, one of which is octahedral and the other two tetrahedral. On the other hand, Fe(ClO₄)₃ reacted smoothly with H₂DSALPTE in ethanol to give a mononuclear pseudo-octahedral complex in which the ligand functions in a dibasic hexadentate fashion. Mössbauer data suggest the presence of a low-spin-high-spin equilibrium in the solid state. The manganese(III) and cobalt(III) complexes of the Schiff base, H₂DSALPTE, are also studied for the sake of comparison with the corresponding iron(III) complex. The N₂S₂ ligand, however, formed a low-spin pseudo-octahedral iron(III) complex. The complexes have been characterised by elemental analysis, molar conductance values, cryomagnetic data and i.r., electronic and Mössbauer spectral data.     

On a new partitioning of the Hamiltonian in many-body calculation of pair-correlation energies in closed-shell systems

We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle–hole (p–h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle–particle (p–p) and hole–hole ladders exactly to all orders. The effect of the off-diagonal p–p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p–h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.     

Synthesis of thio- and selenoglycosides by cleavage of dichalconides in the presence of zinc/zinc chloride and reaction with glycosyl bromides

A convenient odorless methodology has been devised for the preparation of 1,2-trans-thio- and selenoglycosides through zinc-mediated cleavage of disulfides and diselenides and reaction of the thiolate and selenides formed in situ with glycosyl bromides. The yields were excellent in all cases.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

Synthesis, X-ray structure and properties of a new nitrite-bound copper(II) complex with 2-(3,5- dimethylpyrazol-1-ylmethyl)pyridine in a CuN4(O) coordination

Synthesis and characterization of a nitrite-bound copper(II) compound [CuL⁴)₂(ONO)]ClO₄ have been achieved (L⁴ = 2-(3,5-dimethylpyrazol-1-ylmethyl)pyridine]. The bidentate ligand L⁴ provides a pyridine and a pyrazole donor site; however, they are separated by a methylene spacer. The complex has been structurally characterized and it belongs to only a handful of complexes having nitrito-bound mononuclear copper(II) centre. The metal atom has a distorted square pyramidal geometry with the copper atom displaced from the equatorial plane by 0.25 Å. In MeCN solution the green complex exhibits a broad ligand-field transition at 655 nm with a shoulder at 675 nm and in dichloromethane-toluene glass (80 K) it exhibits an EPR spectral feature characteristic of the unpaired electron in the d_x²−y² orbital. Variable-temperature (80–300 K) magnetic susceptibility measurements in the solid state as well as room temperature measurement in MeCN solution reveal mononuclear magnetically dilute copper(II) centre. When examined by cyclic voltammetry (MeCN solution) it displays electrochemically irreversible Cu^II---Cu^I response [cathodic peak potential, E_pc (V vs saturated calomel electrode (SCE)): −0.32]. An oxidative response is observed at 1.14 V, probably due to bound-nitrite oxidation and is partially removed to generate a solvated complex at the electrode surface. The latter species gives rise to reversible Cu^II---Cu^I redox response [ ].