Atomic orbitals, combining bonding

Fig. 1.20. Atomic orbital combinations giving rise to bonding molecular orbitals for methane.

Having just seen a resonance description of benzene, let s now look at the alternative molecular orbital description. We can construct -tt molecular orbitals for benzene just as we did for 1,3-butadiene in Section 14.1. If six p atomic orbitals combine in a cyclic manner, six benzene molecular orbitals result, as shown in Figure 15.3. The three low-energy molecular orbitals, denoted bonding combinations, and the three high-energy orbitals are antibonding. 

Molecular orbitals are formed by combining atomic orbitals when atomic orbitals interfere constructively, they give rise to bonding orbitals when they interfere destructively, they give rise to antibonding orbitals. N atomic orbitals combine to give N molecular orbitals. 

Consider first the ethylene molecule. Its geometrical structure is shown in Fig. 5. The s, py and pz atomic orbitals of the carbon atoms are assumed to be hybridized. This sp2 hybridization implies H-C-H bond angles of 120°, approximately in agreement with experimental results. The remaining two px orbitals are thus available to contribute to a -electron system in the molecule. Here again, the two linear combinations of atomic orbitals yield bonding and... 

We know that atomic orbitals combine to form a molecular orbital. When two atomic orbitals of comparable energy combine, they form two molecular orbitals, one of which is called the bonding molecular orbital and is of lower energy than each of the combining atomic orbitals and the other is of higher energy called the antibonding molecular orbital. 

When two atomic orbitals combine, two molecular orbitals (one bonding and the other antibonding) are formed. 

In conclusion, the energies E that sahsfy Eq. (1.19) are associated to molecular electronic states. Since Eq. (1.19) is an equation of Nat order, we obtain Nat energy values E/ (/ = 1,. .., Nat), that is, as many molecular levels as atomic orbitals. In the simple example of H2 discussed in Sechon 1.1, Aat = 2 and both I5 atomic orbitals combine to form bonding ag and antibonding a MOs. In the case of N2 (see Fig. 1.1), neglechng I5 core electrons, the combinahon of two sp and one pz atomic orbitals per N atom leads to six MOs. 

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. 

But how do we account for the bond angles in water (104°) and ammonia (107°) when the only atomic orbitals are at 90° to each other All the covalent compounds of elements in the row Li to Ne raise this difficulty. Water (H2O) and ammonia (NH3) have angles between their bonds that are roughly tetrahedral and methane (CH4) is exactly tetrahedral but how can the atomic orbitals combine to rationalize this shape The carbon atom has electrons only in the first and second shells, and the Is orbital is too low in energy to contribute to any molecular orbitals, which leaves only the 2s and 2p orbitals. The problem is that the 2p orbitals are at right angles to each other and methane does not have any 90° bonds. (So don t draw any either Remember Chapter 2.). Let us consider exactly where the atoms are in methane and see if we can combine the AOs in such a way as to make satisfactory molecular orbitals. 

If two atomic orbitals combine, two molecular orbitals are formed. This is fundamentally different than valence bond theory. Because aromaticity is based on p orbital overlap, what does MO theory predict will happen when two p (atomic) orbitals combine ... 

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