Orbitals of carbon atom

For a homonuclear diatomic system in the Hilrikel approximation the integrals given by Eqs. (128)—(131) take the simple forms Haa = Hyy = or, Hab = Hta = P and 5 = 0. The atomic orbitals involved, Xa and xtb are of coarse the px orbitals of carbon atoms a and b, respectively. The resulting secular determinant is then simply... 

Thus we calculated the value E based on equation (10) for several compounds and radicals during photosynthesis - tables 4 and 5. For radical - C =0 the calculations were made in two possible variants of activity of valence orbitals of carbon atoms. The compliance of calculated E values with reference data [12,13] was in the range of 5% for all bonds of covalence type without introducing the coefficient 0.83. 

Cyclic organic compounds as a basic variant of carbon nanostructures. Apparently, not only inner-atom hybridization of valence orbitals of carbon atom takes place in cyclic structures, but also total hybridization of all cycle atoms. 

Various atomic orbitals of carbon atom are not of equal energy. The Is orbital has the lowest energy. The 2s orbital is next in energy and the 2p orbitals have the highest energies. The three 2p orbitals have the same energy, i.e. they are degenerate. 

A similar approach can be applied for the Y atom insertion into the C-H bond of alkenes and other alkanes. Our calculation by the Cl method in a 6-311-H-G(2d,2p) basis set with a complete active space for 8 electrons in 8 orbitals (Is orbital of carbon atom is frozen) predicts that the vertical S-T excitation energy in methane is around 11 eV (11.37 eV or 262 kcal/mol). Following the above approximation it is equal -2 Jch- From Eq. (9) the activation energy for the yttrium atom insertion reaction, Eq. (1) M=Y, should be 17.6 kcal/mol. This simple estimation is in a good agreement with very accurate ab initio calculations, Ea = 20.7 kcal/mol [15]. 

To investigate this interaction it is necessary to examine the symmetry of the molecular orbitals that contain substantial contributions from these atomic orbitals. The bond lengths in the carbanions in the structures examined are close to those expected from simple Hiickel bond orders for the isolated carbanion. As noted, the carbanion 7r-orbital contribution to the HOMO of the complex is probably very similar to the HOMO of the free carbanions. The symmetries of the HOMO s of the free benzyl and fluorenyl carbanions and the orientation of the N—Li—N groups with respect to the carbanions are shown in Figures 25 and 26. The N—Li—N group is positioned to permit the appropriate symmetry overlap of the lithium p orbital, which is parallel to the carbanion plane and the appropriate pz orbitals of carbon atoms in the plane. 

As the electronic structure of the frontier orbitals in the sp -hybridized polythiophene chain is due to the overlap of the p -orbitals of carbon atoms in the chain, leading to the bonding n and anti-bonding n bands, any disturbance to this overlap will lead to changes of the electronic structure. The dimerization of the carbon chain—the modulation of the carbon-carbon distance—is already there in polythiophene, and this dimerization contributes to the band-gap [26]. Small... 

The particular hybridisation of the orbitals of carbon atoms in ethene, are called spl hybrids... 

Various atomic orbitals of carbon atom are not of equal... 

Considering again the case of benzene, we note that in the 1,3,5-cyclohexatriene molecule the single bonds are formed by overlap of sjP —orbitals of carbon atoms. In the cyclohexene molecule, which is taken as a standard for the heat of hj drogenation, the single bonds adjacent to the double bonds are formed by —sp ... 

The first two strucmres are famous Kekule structures, the next three are Dewar strucmres, and the sixth is an example of the possible mixed covalent-ionic structures. From these graphs, we may deduce which atomic orbitals (out of the 2p. orbital of carbon atoms, z is perpendicular to the plane of the benzene ring) take part in the covalent bond (of the tt type). As far as the mathematical form of the [Pg.613]

Values of the preexponential multipliers A in Arrhenius equation differ slightly in different objects if one type of TS is considered, so the influence lies in electronic effects conjugation p-orbitals of carbon atoms and chlorine atoms, which causes... 

Within the molecular orbital theory presented earlier in this book, aromatic stabilization is described by ju-orbitals, constructed by combining six 2p atomic orbitals of carbon atoms which are perpendicular to the molecular plane. 

In the case of covalent functionalization, the local stresses due to misalignment of 31 orbitals of carbon atoms with sp hybridization make the carbon nanotubes more reactive than a graphene sheet, facilitating covalent bonding of chemical species. However, even when extensive damage to the carbon nanotubes structure are avoided, a notable disadvantage of this process of functionalization is the breakdown of the conjunction of the carbon nanotubes in with the conversion of carbon with hybridization sp -sp (Han and Fina 2011). 

The frontier orbitals of PPYV are shown in Fig. 6b. The first electronic transition corresponds to a 7t - n transition, for which the ti orbital has a large contribution from the p orbitals of carbon atoms from the vinylene linkage. The band just below the highest occupied one is the nitrogen lone-pair band and it gives rise to a low-energy n-n transition. 

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