Configurations, derivation from theory

The most convenient choice for Hq is the Fock operator since the Hartree-Fock wavefunction is an eigenfunction of the Fock operator, as are the excited configurations derived from it by replacing occupied orbitals by virtual orbitals. This choice of Hq yields Mpller-Plesset (MP) perturbation theory or many-body perturbation theory (MBPT)26,27 Through second order, the energy is ... 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

For the first time, DFT theory has been applied to a study of diastereofacial selectivity in 1,3-dipolar cycloadditions of nitrones to di-3,4-dimethylcyclobutene. ° The stereochemical outcome of the INAC reactions of nitrones (49) and (52) derived from 3-(9-allyl-D-hexoses is dependent only on the relative configuration at C(2,3), and thus 3-(9-allyl-D-glucose (48) and -o-altrose (threo configuration) afford oxepanes (50) selectively whereas 3-O-allyl-D-allose (51) and -D-mannose (erythro configuration) give tetrahydrofurans (53) and (54) selectively (Scheme 18). frani-2-Methylene-... 

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