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.     

Energy expressions for atomic configurations in the L–S coupling scheme

The matrix elements of the spin-free Hamiltonian between two atomic configuration state functions (CSF 'S ) in the L–S coupling scheme are expressed in terms of the atomic integrals F^k's and G^k's. Using these general expressions, the matrix elements have been obtained for all the atomic configurations with three valence electrons that have not been solved so far by earlier methods. The scope for applying this new approach to obtain the Auger line energies and the promotion energies of metals that involve more than two partially filled shells is indicated. The energy expressions for some of the relevant configurations are tabulated.     

Oligosaccharides through reactivity tuning: convergent synthesis of the trisaccharides of the steroid glycoside Sokodoside B isolated from marine sponge Erylus placenta

Chemical synthesis of the trisaccharide of the steroid glycoside Sokodoside B isolated from Erylus placenta is reported. Stereoselective, high-yielding glycosylation strategies through thioglycoside activation using H₂SO₄ immobilized on silica in conjunction with N-iodosuccinimide are used for better results. A late stage TEMPO-mediated oxidation was performed for the formation of required uronic acid moiety. An analog of the target trisaccharide is also prepared by using a bis-glycosylation approach.     

Synthesis of mixed acid anhydrides from methane and carbon dioxide in acid solvents

[reaction: see text] The reaction of CH(4) with CO(2) has been performed in anhydrous acids using VO(acac)(2) and K(2)S(2)O(8) as promoters. NMR analysis establishes that the primary product is a mixed anhydride of acetic acid and the acid solvent. In sulfuric acid, the overall reaction is CH(4) + CO(2) + SO(3) --> CH(3)C(O)-O-SO(3)H. Hydrolysis of the mixed anhydride produces acetic acid and the solvent acid. When trifluoroacetic acid is the solvent, acetic acid is primarily formed via the reaction CH(4) + CF(3)COOH --> CH(3)COOH + CHF(3).     

Van der Waals interaction between spherical voids

The problem of calculating the non-retarded Van der Waals type of interaction between two spherical voids in an electron gas is presented from a new approach. The formulation is based on an integral equation for the self-induced density oscillations derived from a semi-classical treatment of the density-density response theory for inhomogeneous electron systems. The interaction energy between two identical voids is found to obey d^-6 law for large separation d between the voids, the law being determined by the dipolar plasma oscillations alone.     

Dual solutions in boundary layer flow of a moving fluid over a moving permeable surface in presence of prescribed surface temperature and thermal radiation

An analysis of the heat transfer for a boundary layer forced convective flow past a moving permeable flat surface parallel to a moving fluid is presented. Prescribed surface temperature at the boundary is considered. A thermal radiation term in the energy equation is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with the available results for some particular cases of this study. Dual solutions exist when the surface and the fluid move in the opposite directions.