Partial structure expansion

Shelley, C.A., et al., An Approach to Automated Partial Structure Expansion, Anal. Chim. Acta, 103, 121, 1978. 

The results of partial structure factors analysis of reflectivity data relating to DPPC monolayers on a water subphase are shown in Tables 2 through 4. Table 2 summarizes the results gained from fitting experimental data to Eq. 10 pertaining to the DPPC alkyl-chain region of the monolayer. It is apparent that on expansion of the monolayer, both the expected reductions in thickness and the number density of the DPPC chains occur (Table 2). The decrease in thickness (from 20 A to 18 A) is explained by the increased number of gauche conformers introduced into the chains on expansion. The decrease in number density is a function of area per molecule and allows this quantity to be calculated (1/A, = njx). On comparison of these values in Table 2 it can... 

The partial structure factor allows the structure of water in the monolayer to be determined independent of the rest of the monolayer, and this reveals that the thickness of the water layer is approximately 16 A and does not alter significantly during expansion to higher molecular areas (Table 3). 

There are also excellent total syntheses of spirotryprostatins which do not apply intermolecular functionalisation of the indole 3-position with a C5 prenyl-type precursor and are, therefore, not discussed in detail. Carreira and co-workers started from 3-diazo-2-oxindole, which was used in a Rh(I)-catalysed cyclopropanation of 1,3-pentadiene. The resulting cyclopropane was subjected to Mgl2-catalysed ring expansion and added to an imine affording the spiro[5.5] partial structure [130, 131]. Overman and Rosen built up the indole system by intramolecular Heck reaction of a functionalised iodoaniline [132,133]. In a model study building up the indole system, Cacchi and co-workers synthesised 3-prenylindoles via Pd-catalysed cyclisation of orf/io-alkynyltrifluoroacetanilides with prenyl esters [134]. 

The asymptotic behavior of the second-order energy of the M0ller-Plesset perturbation theory, especially adapted to take advantage of the closed-shell atomic structure (MP2/CA), is studied. Special attention is paid to problems related to the derivation of formulae for the asymptotic expansion coefficients (AECs) for two-particle partial-wave expansions in powers... 

One of the most commonly used expansions in the theory of the electronic structure of atoms and molecules is the partial wave expansion, in which individual atomic orbitals are expressed as products of radial functions and spherical harmonics. Appropriately symmetrized sums of products of the spherical harmonics for the coordinates of each particle can be formed to yield eigenfunctions of total Lz, S, and Sz. To prevent lengthy expressions involving 3-j and 6-j symbols from obscuring the essential physics, I shall focus on the partial wave expansion for an 5-state of the helium atom ... 

Figure 1. 750 MHz ID NMR spectrum and the partial structure 1 (a) the expansion of alkoxy region, (b) the expansion of the aliphatic region, and (c) the full NMR spectrum.

The results of the present study have direct relevance to construction of approximate extrapolation schemes that aim at estimation of the CBS limits. Relying on the dominance of the leading large-/ asymptotic terms in the partial-wave expansions, these schemes are commonly employed in electronie structure calculations on systems with small to moderate electron correlation. As clearly demonstrated by the aforediscussed data, such extrapolations are bound to fail for strongly correlated species, especially when the nondynamical correlation effects are significant. 

Fuzzy 2D substructure searching is an extension of substructure searching to the minor extent that it permits the expansion of the query formulation vocabulary to include topological features and substructural wildcards described above. This involves the retrieval of all entities in a CIR system that contain the user-defined partial structure and that satisfy whatever wildcard specification pattern has been specified. The query identifies the partial structure and simple wildcard substitution patterns exactly. As with substructure searching, the use of query features on a partial structure will always identify structures which are equal in size or larger than the query. 

Partial confinement hampers expansion and allows the introduction of a combustion enhancing flow structure. 

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