Geminal relationship

Another route to construction of the approximate 1-RDM functional involves employment of expressions for E and D afforded by some size-consistent formalism of electronic structure theory. Mazziotti [42] proposed a geminal functional theory (GET) where an antisymmetric two-particle function (geminal) serves as the fundamental parameter. The one-matrix-geminal relationship allowed him to define a D-based theory from GET [43]. He generalized Levy s constrained search to optimize the universal functionals with respect to 2-RDMs rather than wavefunctions. 

When two atoms or groups are attached to the same carbon, those groups or atoms are said to hegeminal or to have a geminal relationship. The term comes from the Latin word gemini (twin). This relationship is seen in 40 (2,2-dichlorobutane). 

Do the chlorine atoms in 2,3-dichlorohexane have a geminal relationship ... 

Geminal to each other (a 1-3 angle bending relationship)... 

The relative configuration is derived from the NOE difference spectra. Significant NOEs are detected owing to cis relationships within the neighbourhood of non-geminal protons ... 

FIGURE 8.3 Geometric and energetic relationship for electron thermalization by random walk in liquid hexane in the presence of the geminate positive ion. Here = fid). Reproduced from Mozumder and Magee (1967), with the permission of Am. Inst. Phys. . 

Methyl deoxypodocarpate 127 (Scheme 1) 129) represents a simple problem since the ketone 132 is well-known and readily available from Hagemann s ester in three steps. The problem of geminal alkylation of this ketone stems from its existence as an EjZ mixture of ring fusion isomers. Recognizing that decarbonylation of aldehydes occurs readily with Wilkinson s catalyst creates a structural equivalence of an acetaldehyde chain and a methyl group as in 128. This simple relationship immediately establishes several options, a simple one uses a thioacetal such as 129 as a synthon for the aldehyde. The presence of a carbonyl group three carbons away... 

The kinetics data of the geminate ion recombination in irradiated liquid hydrocarbons obtained by the subpicosecond pulse radiolysis was analyzed by Monte Carlo simulation based on the diffusion in an electric field [77,81,82], The simulation data were convoluted by the response function and fitted to the experimental data. By transforming the time-dependent behavior of cation radicals to the distribution function of cation radical-electron distance, the time-dependent distribution was obtained. Subsequently, the relationship between the space resolution and the space distribution of ionic species was discussed. The space distribution of reactive intermediates produced by radiation is very important for advanced science and technology using ionizing radiation such as nanolithography and nanotechnology [77,82]. 

The recombination of ions formed from the same solvent or solute molecule by ionisation (geminate ion-pair recombination) is considered in Chap. 7. In the following, only reactions of one ion with homogeneous distributions of the other reactant ion are discussed. Chapter 7 discusses the relationship between these two types of reaction. 

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