Carbon charge density

In general, the total carbon charge densities alternate their signs along the chain in antiplanar D2d cumulenes, whereas in planar Dih systems there seems to be no corresponding alternation. 

H), 5(C), J(C,H), and J(H,H) have been considered in relation to proton and carbon charge densities (from parametric LCAO-MO calculations) in Ge(CH3)4, Si(CH3)4, and various organic compounds [62]. 

Figure Al.3.22. Spatial distributions or charge densities for carbon and silicon crystals in the diamond structure. The density is only for the valence electrons the core electrons are omitted. This charge density is from an ab initio pseudopotential calculation [27].

To obtaiti the total charge density r, at atom C we must sum over all occupied or partially occupied orbitals and subtract the I esult from 1,0. the n charge density of the carbon atom alone... 

Its charge density distribution is like that of the cation (with sign reversal) because the added electron goes into the nonbonded orbital with a node at the central carbon atom. The probability of finding that electron precisely at the central carbon atom is zero. 

Summing over the squares of the coefficients of the lower two orbitals (the upper orbital is unoccupied), we get electron densities of 1.502 at the terminal carbon atoms and 0.997 at the central atom. The charge densities on this iteration are... 

Note that agreement with Pariser and Parr s empirical value is better for Y13 than for Yn ) Use Salem s values to calculate election densities on the three carbon atoms of the allyl anion for one iteration beyond the initial Huckel values, as was done in Exercise 8.9.1. Comment on the results you get, as to the qualitative picture of the anion, the influence of election repulsion on the charge densities, and agreement or lack of agreement with the results already obtained with the Pariser and Parr parameters. 

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

Several calculations of the electronic structure of isoindoles have Ijeen published, and the distribution of charge density around the isoindole nucleus calculated by these methods is summarized in X able I. A common prediction of the calculations, which are based on tlie LCAO-MO method or the frontier electron concept, is the relatively high electron density to bo found at position 1, and the expectation, thei efore, i.s that electrophilic substitution on carbon... 

Y is a strongly pi electron donor group. As previously noted in the results section, examples of Y from Table VI include centers of high pi electron charge density at carbon, sulfur, nitrogen, and oxygen. Also included in Table VI are examples of nucleophilic substitution transition states (cf. reactions 21 and 22) of the type... 

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