Spin density, relationship

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

Spin densities help to predict the observed coupling constants in electron spin resonance (ESR) spectroscopy. From spin density plots you can predict a direct relationship between the spin density on a carbon atom and the coupling constant associated with an adjacent hydrogen. 

Display spin density surfaces for all radicals. For which radical is the unpaired electron least delocalized from the radical center For which is it the most delocalized Is there any relationship between degree of puckering of the radical center and extent of spin delocalization ... 

The relationship between iV-particle states, in which we include mixed states, represented by A -particle operators as defined in Eq. (2.1), and the space-spin density p(y) is not 1-1. Here and throughout the following development, y... 

TABLE 2. Relationship between calculated spin densities and the g and an values of Ar3Ge radicals... 

Of course, any correlation between and the direction of, say, substitution does not prove that the reaction necessarily takes the ion-radical pathway. This means that the correlation may represent the relationship, for example, between the orientation and tendency of a substrate to locate a charge or between the electronic structure of the transition state and distribution of the spin density in the substrate ion-radical. Nevertheless, such correlation deserves to be considered it can serve as one, but not single and self-sufficient, proof in favor of the ion-radical pathway. 

The r-space and p-space representations of the ( th-order density matrices, whether spin-traced or not, are related [127] by a fif -dimensional Fourier transform because the parent wavefunctions are related by a 3A -dimensional Fourier transform. Substitution of Eq. (5.1) in Eq. (5.8), and integration over the momentum variables, leads to the following explicit spin-traced relationship ... 

McConnell (74) has shown that for the case of aromatic radical species where the interaction is between a spin density localized on a ptr orbital of a carbon atom and the proton bonded to that carbon atom a relationship exists between an observed proton contact interaction constant a, and the spin density p, on the adjacent carbon atom. This relationship is... 

An experimental determination of the spin density distribution in the allyl radical recently has become available (30) and is in fair agreement with the results of the valence bond calculation and in somewhat better agreement with an extended Hartree-Foek calculation to be described below. It is seen that although the allyl radical possesses only a single unpaired electron, the total calculated ir-electron spin density on the molecule is % to % units depending on the approximation employed. However, the relationship (75)... 

The structure-transport relationship characteristic of the catalyst pellet is shown by comparison of Figs 20a-c the spatial heterogeneity in the values of the molecular diffusion coefficient is much more consistent with the heterogeneity in the intensity shown in the Ti map than that of the spin-density map. Thus, we conclude that it is the spatial variation of local pore size that has the dominant influence on molecular transport within the pellet. 

In an investigation of the spin-density (voidage) and spin-lattice relaxation time maps of many pellets, it was found that it was the heterogeneity in pore size, as characterized by the fractal dimension of the Ti map, that was consistent between images of pellets drawn from the same batch 58). The fractal dimensional of these images identifies a constant perimeter-area relationship for clusters of pixels of... 

The contact hyperfine shift contains information on conformational arrangements because it is somehow related to chemical bonds. The information, however, is generally hidden, with the exception of few cases. For example, if we have a CH moiety of an sp3 carbon bound to an sp2 carbon which bears spin density in the pz orbital, we have already seen that a spin density of the same sign is transferred to the methyl protons (Section 2.3.2). A mechanism to originate spin density at the methyl proton is the direct overlap between the sp2 carbon pz and the Is hydrogen orbital [51-54] (Fig. 2.14). Such overlap depends on the dihedral angle between the pz(axis)-C-C plane and the C-C-H plane (Fig. 2.14). The relationship is described by the general Karplus equation [55]... 

It is important to note that the proportional relationship between Amax, Amid, and Amin for these couplings is the same for 100% spin density, and for the present case with approximately 50% spin density. When this is so it indicates that there is no rocking motion at the radical site. This is good evidence therefore that the radical site is essentially planar. The best evidence for radical planarity comes from the analysis of the direction cosines associated with each principal values of the hyperfine coupling tensor. The direction of Amin (Table 18-2) is known to be associated with the direction of the >C-H bond, while the direction associated with the Amid indicates the direction of the n-clcctron orbital. These directions are easily calculated from the crystal structure, and are included in Table 18-2. One sees that the direction associated with Amid deviates only 2.0° from the computed perpendicular to the ring plane, while the direction of Amin, deviates only 2.8° from the computed direction of the C6-H bond. The errors listed on these values are at the 95% confidence level. This is very clear evidence that the radical shown here is planar in the solid-state. Any torsional motion of the C6-H would lead to asymmetries of the hyperfine coupling tensor, and would not produce the observed agreement between the direction cosines and the known directions obtained from the crystal structure. 

Some methylbenz[c]acridines are strongly carcinogenic, whereas their derivatives are inactive [18-22]. Previously, we reported on the relationship between the carcinogenic activity of benz[a]acridines [30-40] and the zr-spin density [25] and the relationship between the carcinogenic activity of benz[a]acridines [30-41] and the values of the resonance energy per. v-elecIron (REPE) [26,27]. Consequently, by clockwise rotation on an angular ring or naphthalene moiety, the distribution of the zr-spin dens-... 

The spin density (pi) at the unsubstituted end of the radical can be calculated directly from the proton hyperfine coupling constants, using the relationship, A = 2i-lp (McConnell and Chesnut, 1958 Fessenden and Schuler, 1963). The spin density (ps) at the substituted end of the radicals can be calculated if it is assumed that the total spin density in the conjugated 77-electron system of the radical is unaffected by substitution. Then ... 

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