Methane orbital overlapping

Section 2 6 Bonding m methane is most often described by an orbital hybridization model which is a modified form of valence bond theory Four equiva lent sp hybrid orbitals of carbon are generated by mixing the 2s 2p 2py and 2p orbitals Overlap of each half filled sp hybrid orbital with a half filled hydrogen Is orbital gives a ct bond... 

A complete orbital overlap view of methane appears in Figure 10-10. Hybridization gives each carbon orbital a strongly favored direction for overlap with an atomic 1. S orbital from an approaching hydrogen atom. Four such interactions generate four localized bonds that use all the valence electrons of the five atoms involved. 

Methane forms from orbital overlap between the hydrogen 1 S orbitals and the s hybrid orbitals of the carbon atom. 

We generate hybrid orbitals on inner atoms whose bond angles are not readily reproduced using direct orbital overlap with standard atomic orbitals. Consequently, each of the electron group geometries described in Chapter 9 is associated with its own specific set of hybrid orbitals. Each type of hybrid orbital scheme shares the characteristics described in our discussion of methane ... 

Now let us return to our discussion of the conical intersection structure for the [2+2] photochemical cycloaddition of two ethylenes and photochemical di-Jt-methane rearrangement. They are both similar to the 4 orbital 4 electron model just discussed, except that we have p and p overlaps rather than Is orbital overlaps. In Figure 9.5 it is clear that the conical intersection geometry is associated with T = 0 in Eq. 9.2b. Thus (inspecting Figure 9.5) we can deduce that... 

Now we can consider the bonding in methane. Using orbital overlap as in the hydrogen molecule as a model, each sp orbital of carbon can now overlap with a 1 orbital of a hydrogen atom, generating a bonding molecular orbital, i.e. a ct bond. Four such... 

Figure 6.3 The MO diagram of tetrahedral (7"d) methane, and overlap diagrams for the 1 a1 and 1t2 orbitals. The 1s orbital of the carbon atom is not shown, but would be labelled 1a1...

This overlap is what allows the hydrogen atoms to form a single bond. The first bond that forms between two atoms is called a sigma bond (a). The sigma bond arises from the overlap of two s orbitals or from the overlap of one s and one p orbital, or from the overlap of two p orbitals. The bonds in a molecule of methane (Figure 5.14) are an example of a situation in which hybridized p orbitals overlap with an s orbital. 

Figure 1.21 depicts some of the spatial aspects of orbital hybridization. Each sp hybrid orbital has two lobes of unequal size, making the electron density greater on one side of the nucleus than the other. In a bond to hydrogen, it is the larger lobe of a carbon sp orbital that overlaps with a hydrogen Is orbital. The orbital overlaps corresponding to the four C—H bonds of methane are portrayed in Figure 1.22. Orbital overlap along the intemuclear axis generates a bond with rotational symmetry—in this case a C(2sp )—H(l.y) CT bond. A tetrahedral arrangement of four a bonds is characteristic of sp -hybridized carbon.

For the di-7t-methane reactions of the (S)-(-)-proline tert-butyl ester salt and the (S,S)-(+)-pseudoephedrine salt in Scheme 36, absolute configuration correlations between reactant and photoproduct could be elucidated by X-ray crystallography. The correct absolute configurations of the reactants and the products are as shown in the scheme. The observed selective benzo-vinyl bridging to one direction is ascribed both to reduced steric repulsion between the vinyl substituents and to better orbital overlap in the transition state [65]. It is concluded for the 11,12-dicarboxydibenzobarrelene derivatives that initial benzo-vinyl bridging is favored at the carboxylate salt-bearing vinyl carbon atom both in the solid state and in solution [66]. 

Consider a methane molecule, CH4. It has four H atoms bonded to a central C atom. An isolated ground-state C atom ([He] 2s 2p ) has four valence electrons two in the 2s orbital and one each in two of the three 2p orbitals. We might easily see how the two half-filled p orbitals of C could overlap with the ]s orbitals of two H atoms to form two C—H bonds with a 90° H—C—H bond angle. But methane is not CH2 and doesn t have a bond angle of 90°. It s not as easy to see how the orbitals overlap to form the four C—H bonds with the 109.5° bond angle that occurs in methane. 

Qualitative application of VB theory to molecules containing second-row elements such as carbon, nitrogen, and oxygen involves the concept of hybridization, which was deveioped by Linus Pauling. The atomic orbitals of the second-row elements include the spherically symmetric 2s and the three 2p orbitals, which are oriented perpendicularly to one another. The sum of these atomic orbitals is equivalent to four sp orbitals directed toward the corners of a tetrahedron. These are called sp hybrid orbitals. In methane, for example, these orbitals overlap with hydrogen Is orbitals to form CT bonds. 

In ammonia, nitrogen resembles the carbon of methane. Nitrogen is sp -hybridized, but (Table 1.1) has only three unpaired electrons they occupy three of the sp orbitals. Overlap of each of these orbitals with the s orbital of a hydrogen atom results in ammonia (Fig. 1.12). The fourth sp orbital of nitrogen contains a pair of electrons. 

The four sp orbitals point to the corners of a tetrahedron and we build up a molecule of methane by overlapping the large lobe of each sp orbital with the Is orbital of a hydrogen atom, as shown in the margin. Each overlap forms an MO (2sp + Is) and we can put two electrons in each to form a C—H a bond. There will of course also be an antibonding MO, a (2sp - Is) in each case, but these orbitals are empty. Overall, the electrons are spatially distributed exactly as they were in our previous model, but now we can think of them as being located in four bonds. 

Orbital overlap models of methane, ammonia, and water. 

Hybridization of atomic orbitals. To account for the bonding in diatomic molecules like HF or F2, we picture direct overlap of s and/or p orbitals of isolated atoms. But how can we account for the shape of a molecule like methane from the shapes and orientations of C and H atomic orbitals A C atom ([He] 2f2p ) has two valence electrons in the spherical 2s orbital and one each in two of the three mutually perpendicular 2p orbitals. If the half-filled p orbitals overlap the Is orbitals of two H atoms, two C— H bonds would form with a 90° H—C—H bond angle. But methane has the formula CH4, not CH2, and its bond angles are 109.5°. 

An alternative but equivalent model for describing benzene (and other resonance-stabilized structures) is molecular orbital theory. We have already seen how this theory can explain the formation of molecular structures such as methane, ethene and others. In localized molecules like ethene, C2H4, two unhybridized p orbitals overlap to form a Jt molecular orbital in which a pair of electrons is shared between tbe nuclei of two carbon atoms. In molecular orbital theory, resonance-stabilized structures are described in terms of delocalized Jt orbitals where the Jt electron clouds extend over three or more atoms. 

We know from experiments that a methane molecule has tetrahedral geometry. How does carbon form four equivalent, tetrahedrally arranged covalent bonds by orbital overlap with four other atoms ... 

The simplest hydrocarbon observed imder normal laboratory conditions is methane, CH4. This is a stable, unreactive molecule with a molecular formula consistent with the octet rule of the Lewis theory. To obtain this molecular formula by the valence bond method, we need an orbital diagram for carbon in which there are four unpaired electrons so that orbital overlap leads to four C—H bonds. To get such a diagram, imagine that one of the 2s electrons in a ground-state C atom absorbs energy and is promoted to the empty 2p orbital. The resulting electron configuration is that of an excited state. 

Hybrid orbitals are atomic orbitals formed by combinations of s, p, and d atomic orbitals, and are useful in describing the bonding in compounds. There are various types. In carbon, for instance, the electron configuration is ls 2s 2p. Carbon, in its outer (valence) shell, has one filled s orbital, two filled p orbitals, and one empty p orbital. These four orbitals may hybridize (sp hybridization) to act as four equal orbitals arranged tetrahedrally, each with one electron. In methane, each hybrid orbital overlaps with a hydrogen s orbital to form a sigma bond. Alternatively, the s and two of the p orbitals may hybridize (sp hybridization) and act as three orbitals in a plane at 120°. The re-... 

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

---