Sp3 hybrid atomic orbitals

A carbon atom combining with four other atoms clearly does not use the one 2s and the three 2p atomic orbitals that would now be available, for this would lead to the formation of three directed bonds, mutually at right angles (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C—H bonds in, for example, methane are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109° 28 to each other. This may be accounted for on the basis of redeploying the 2s and the three 2p atomic orbitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds (cf. p. 5). These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are obtained as hybridisation ... 

If the spin density not contributing to the muon hyperfine parameter were assumed to be equally divided among the ten closest silicons around the tetrahedral interstice and if at these silicon sites the unpaired spin were assumed to be in sp3 hybridized atomic orbitals, then the isotropic hyperfine parameter for a 29Si on any of these 10 sites would be about - 60 MHz. 

Dimethylberyllium, Be(CH3)2, is a polymeric white solid containing infinite chains, as shown in Fig. 12.7.1(a). Each Be center is tetrahedrally coordinated and can be considered to be sp3 hybridized. As the CH3 group only contributes one orbital and one electron to the bonding, there are insufficient electrons to form normal 2c-2e bonds between the Be and C atoms. In this electron-deficient system, the BeCBe bridges are 3c-2e bonds involving sp3 hybrid atomic orbitals from two Be atoms and one C atom, as shown in Fig. 12.7.1(b). 

Carbon occurs in the allotropes (different forms) diamond, graphite, and the fullerenes. The fullerenes are molecular solids (see Section 16.6), but diamond and graphite are typically network solids. In diamond, the hardest naturally occurring substance, each carbon atom is surrounded by a tetrahedral arrangement of other carbon atoms, as shown in Fig. 16.26(a). This structure is stabilized by covalent bonds, which, in terms of the localized electron model, are formed by the overlap of sp3 hybridized atomic orbitals on each carbon atom. 

Carbon is able to form sp, sp2, and sp3 hybridized atomic orbitals and a and n molecular orbitals (see Skill 1.3c). For example, in CH4, the electron density of the four sp3 orbitals of C each overlap with an s orbital of H to form four a bonds. In C2H4 (an alkene), two sp2 orbitals on each C overlap with H, the remaining sp2 orbitals overlap with each other in a crbond, and the p orbitals (drawn as shaded shapes) overlap with each other above and beneath the carbons in a n bond (also drawn as shaded shapes). In CO2, the C atom has two sp hybrid orbitals and two p orbitals. These form one crbond and one n bond with the two unfilled p orbitals on each 0 atom. In C2H2 (an alkyne), a triple bond forms with one crand two n. 

Although we have described the structures of several molecules in terms of hybrid orbitals and VSEPR, not all structures are this simple. The structures of H20 (bond angle 104.4°) and NH3 (bond angles 107.1°) were described in terms of sp3 hybridization of orbitals on the central atom and comparatively small deviations from the ideal bond angle of 109° 28 caused by the effects of unshared pairs of electrons. If we consider the structures of H2S and PH3 in those terms, we have a problem. The reason is that the bond angle for H2S is 92.3°, and the bond angles in PH3 are 93.7°. Clearly, there is more than a minor deviation from the expected tetrahedral bond angle of 109° 28 caused by the effect of unshared pairs of electrons ... 

Carbon atoms (1) and (2) undergo sp2 hybridization, while carbon atoms (3), (4) and (5) undergo sp3 hybridization. The orbital overlaps are similar to those in 2-butene except carbon atoms (1) and (2) are involved in the double bond and carbon atom (2) is bonded to carbon atom (3) by sp2-sp3 overlap. The overlap of the hybrid orbitals with the Is orbitals of H atoms gives the C-H bonds. 

Pauling showed that the quantum mechanical wave functions for s and p atomic orbitals derived from the Schrodinger wave equation (Section 5.7) can be mathematically combined to form a new set of equivalent wave functions called hybrid atomic orbitals. When one s orbital combines with three p orbitals, as occurs in an excited-state carbon atom, four equivalent hybrid orbitals, called sp3 hybrids, result. (The superscript 3 in the name sp3 tells how many p atomic orbitals are combined to construct the hybrid orbitals, not how many electrons occupy each orbital.)... 

Carbon uses hybrid atomic orbitals for bonding (Sections 7.11 and 7.12). A carbon that bonds to four atoms uses sp3 orbitals, formed by the combination of an atomic s orbital with three atomic p orbitals. These sp3 orbitals point toward the corners of a tetrahedron, accounting for the observed geometry of carbon. 

To truly understand the geometry of bonds, we need to understand the geometry of these three different hybridization states. The hybridization state of an atom describes the type of hybridized atomic orbitals (sp3, sp2, or sp) that contain the valence electrons. Each hybridized orbital can be used either to form a bond w ith another atom or to hold a lone pair. 

Similarly, in H20. the oxygen is sp3 hybridized. So all four orbitals are in a tetrahedral arrangement, just as we would expect for an sp3 hybridized atom. But only two of the orbitals are being used for bonds. So if we look just at the atoms that are connected, we do not see a tetrahedron. Rather, we see a bent arrangement ... 

For a given atom A, acidity increases with increased s character of the A-H bond that is, A(sp)-H is more acidic than A(sp2)-H, which is more acidic than A(sp3)-H (cf. pyrH+ with R3NH+, and HC=CH, benzene, and alkanes). The lone pair of the conjugate base of an sp-hybridized atom is in a lower energy orbital than that of an sp3-hybridized atom. 

An answer was provided in 1931 by Linus Pauling, who showed how an s orbital and three p orbitals on an atom can combine mathematically, or hybridize, to form four equivalent atomic orbitals with tetrahedral orientation. Shown in Figure 1.10, these tetrahedrally oriented orbitals are called sp3 hybrids. Note that the superscript 3 in the name sp3 tells how many of each type of atomic orbital combine to form the hybrid, not how many electrons occupy it. 

When we discussed sp3 hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent sp3 hybrids. Imagine instead that the 2s orbital combines with only two of the three available 2p orbitals. Three sp2 hybrid orbitals result, and one 2p orbital remains unchanged- The three sp2 orbitals lie in a plane at angles of 120° to one another, with the remaining p orbital perpendicular to the sp2 plane, as shown in Figure 1.13. 

Hybrid orbital (Section 1.6) An orbital derived from a combination of atomic orbitals. Hybrid orbitals, such as the sp3, s/J2, and sp hybrids of carbon, are strongly directed and form stronger bonds than atomic orbitals do. 

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. 

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