Power geminal

Bis-ylides (Scheme 31) may function as four-electron donors and become geminally diaurated. The donor capacity of ylides is generally higher than that of most other ligands, and even powerful donors like tertiary phosphines can thus be readily replaced by non-stabilized ylides. Ylides may therefore be used as auxiliary ligands which are retained, while other components of the coordination sphere are subject to substitution. 

A. J. Coleman, Structure of fermionic density matrices.2. anti symmetrized geminal powers. J. Math. Phys. 6, 1425 (1965). 

In contrast, geminate recombination, caused, for example, by proximal trapping of the injected electron, would yield power-independent recovery times see Scheme 2. (Of course, if the trapped electrons were not immobilized, but instead were able to migrate rapidly from surface state to surface state, overall second-order behavior would be recovered [37].)... 

The ground state wavefunction is given by the geminal power... 

Progress in Heterocyclic Chemistry (PHC) Volume 8 reviews critically the heterocyclic literature published mainly in 1995. The first two chapters are review articles. Chapter 1 by T. Kappe deals with Geminal Diazides of Heterocycles, and Chapter 2 by M. Sibi and J. Ji provides extensive coverage of the important emerging area of Radical Methods in the Synthesis of Heterocyclic Compounds. The unusual length of the latter contribution attests to the rising power of this methodology in heterocycle construction. 

Neither the maximum nor the descending branches of the upper curves, representing geminate recombination, are reproduced in the Markovian theory. It predicts the monotonous ion accumulation and still further decrease in the ionization quantum yield /. This is because the Markovian theory does not account for either static or subsequent nonstationary electron transfer. When ionization is under diffusional control, both these are faster than the final (Markovian) transfer. EM is a bit better in this respect. As a non-Markovian theory, it accounts at least for static ionization and qualitatively reproduces the maximum in the charge accumulation kinetics. However, the subsequent geminate recombination develops exponentially in EM because the kinematics of ion separation is oversimplified in this model. It roughly contradicts an actual diffusional separation of ions, characterized by numerous recontacts and the power dependence of long-time separation kinetics studied in a number of works [20,21,187],... 

The one-center energy components have no clear correspondence in the standard MM setting. In our approach the one-center contributions E- arise due to deviations of the geminal amplitude related ES Vs (7>P and 41 ) from their transferable values. These deviations interfere with hybridization. The derivatives of E f s with respect to the angles Land uji, taken at the values characteristic for the stable hybridization tetrahedra shapes which appear in the FATO model, yield quasi- and pseudotorques acting upon the hybridization tetrahedron. In evaluating these quantities we notice that all the hybridization dependence which appears in the one-center terms is that of the matrix elements of eq. (2.71). In the latter, the only source of the hybridization dependence is that of the second and fourth powers of the coefficients of the s-orbital in the HOs. Since they do not depend on the orientation of the hybridization tetrahedra, we immediately arrive at the conclusion that no quasitorques caused by the variation of electron densities appear in the TATO setting ... 

Some interconnections can be mentioned here. The first concerns Coleman s so-called extreme state (17) (cf. the theories superconductivity and superfluidity). If h is a set of two particle determinants and the wave function is constructed from an antisymmetric geminal power, based on gi, then the reduced density matrix can be expressed as... 

Blatt [36], Coleman [37, 38], then Bratoz and Durand [39] investigated a special N-electron wave function in which all geminals were constrained to have the same form, and established the relationship between this function and that used by Bardeen, Cooper and Shieffer (BCS) [40] to describe superconducting systems with electron pairs. The underlying wave function was termed as the antisymmetrized geminal power (AGP) function. 

AGPTDA antisyrametrized geminal power Tamm-Dancoff approximation (Section VII. C),... 

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