Hybrid orbitals hybridization tetrahedron

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 ... 

The basic element of the silicon carbide structure is the tetrahedron [17] due to sp hybridization of the atomic orbitals. This tetrahedron consists of a silicon or a carbon atom at the spatial center, surrounded by four atoms of the other kind. The SiC- bond is 88% covalent. The tetrahedra are arranged in such a way that units of three silicon and three carbon atoms form angled hexagons which are arranged in parallel layers as shown in Fig. 4. 

The fixation of parameters d (those of the shape of the hybridization tetrahedron) can be considered as FO fixed orbitals) picture [93]. In this case only the resonance energy is the orientation dependent contribution. The angular dependence of the energy (bending) can be described by introducing small rotation vectors S(prm which after applying them to vectors CRmLm (distorted) coordination tetrahedron. The final result of... 

The axes of the sp orbitals point toward the corners of a tetrahedron Therefore sp hybridization of carbon is consistent with the tetrahedral structure of methane Each C—H bond is a ct bond m which a half filled Is orbital of hydrogen over laps with a half filled sp orbital of carbon along a line drawn between them... 

FIGURE 2 8 sp Hybridization (a) Electron configuration of carbon in its most stable state (b) Mixing the s orbital with the three p orbitals generates four sp hybrid orbitals The four sp hybrid orbitals are of equal energy therefore the four valence electrons are distributed evenly among them The axes of the four sp orbitals are directed toward the corners of a tetrahedron... 

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

FIGURE 3.13 These contours indicate the amplitude of the sp hybrid orbital wavefunction in a plane that bisects it and passes through the nucleus. Each sp hvbrid orbital points toward the corner of a tetrahedron. 

C atom has one unpaired electron in each of its four sp hybrid orbitals and can therefore form four cr-bonds that point toward the corners of a regular tetrahedron. The C—C bond is formed by spin-pairing of the electrons in one sp hybrid orbital of each C atom. We label this bond hybrid orbital composed of 2s- and 2/t-orbitals on a carbon atom, and the parentheses show which orbitals on each atom overlap (Fig. 3.15). Each C—H bond is formed by spin-pairing of an electron in one of the remaining sp hybrid orbitals with an electron in a 1 s-orbital of an H atom (denoted His). These bonds are denoted cr(C2s/ Hls). 

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

Let s look at an example. In ammonia (NH3), the nitrogen atom is sp hybridized, so all four orbitals arrange in a tetrahedral structure, just as we would expect. But only three of the orbitals in this arrangement are responsible for bonds. So, if we look just at the atoms that are connected, we do not see a tetrahedron. Rather, we see a trigonal pyramidal arrangement ... 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

The beautiful Bohr atomic model is, unfortunately, too simple. The electrons do not follow predetermined orbits. Only population probabilities can be given, which are categorized as shells and orbitals. The orbitals can only accommodate two electrons. Shells and orbitals can also merge ("hybridization"). In the case of carbon, the 2s orbital and the three 2p orbitals adopt a configuration in the shape of a tetrahedron. Each of these sp3 orbitals is occupied by one electron. This gives rise to the sterically directed four-bonding ability of carbon. 

Figure 3.17 Geometry of hybrid orbitals, (a) digonal sp hybrids oppositely directed along the same axis (b) trigonal sp2 hybrids pointing along three axes in a plane inclined at 120° (c) tetrahedral sp3 hybrids pointing towards the comers of a regular tetrahedron. (Reproduced with permission from R. McWeeny, Coulson s Valence, 1979, Oxford University Press, Oxford.)...

The four sp hybrid orbitals are degenerate and, as they are identical in shape, they will point towards the corners of a tetrahedron to minimise repulsion. 

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