Atomic orbitals, combining

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

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. 

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. 

The atomic orbitals of atoms are combined to give a new set of molecular orbitals characteristic of the molecule as a whole. The number of molecular orbitals formed is equal to the number of atomic orbitals combined. When two H atoms combine to form H two s orbitals, one from each atom, yield two molecular orbitals. In another case, six p orbitals, three from each atom, give a total of six molecular orbitals. 

For purposes of illustration, consider a lithium crystal weighing one gram, which contains roughly 1023 atoms. Each Li atom has a half-filled 2s atomic orbital (elect conf. Li = ls22s1). When these atomic orbitals combine, they form an equal number, 1023, of molecular orbitals. These orbitals are spread over an energy band covering about 100 kJ/moL It follows that the spacing between adjacent MOs is of the order of... 

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. 

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. 

Molecular orbitals are generated by combining atomic orbitals. The number of molecular orbitals formed is always equal to the number of atomic orbitals that combine. So, if two atomic orbitals combine, then two molecular orbitals will be formed. This is the case when two hydrogen Is atomic orbitals combine to produce two molecular orbitals in a hydrogen molecule (H ). 

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. 

Molecular orbitals are formed by combining atomic orbitals on different atoms. The number of molecular orbitals formed is the same as the number of atomic orbitals combined. 

Now consider what happens if we bring together an increasingly larger number of Na atoms to build up a crystal of sodium metal. The key idea to remember from Section 7.13 is that the number of molecular orbitals formed is the same as the number of atomic orbitals combined. Thus, there will be three MOs for a triatomic Na3 molecule, four MOs for Na4, and so on. A cubic crystal of sodium metal, 1.5 mm on an edge, contains about 1020 Na atoms and therefore has about 1020 MOs, each of which is delocalized over all the atoms in the crystal. As shown in Figure 21.7, the difference in energy between successive MOs in an Na molecule decreases as the... 

Recall from Section 3.6 that molecules such as benzene that have a series of conjugated p orbitals cannot be described very well by localized molecular orbitals that extend over only two atoms at a time. Instead, delocalized pi MOs that extend over the entire group of conjugated p orbitals must be employed. For benzene, all six of the p atomic orbitals combine to form six delocalized MOs. The number of MOs equals the number of AOs that overlap to form them. 

The number of hybrid orbitals obtained equals the number of atomic orbitals combined. 

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. 

Now, how can the carbon s 2s and 2p atomic orbitals combine with the four hydrogen Is atomic orbitals The carbon s 2s orbital can overlap with all four hydrogen Is orbitals at once with all the orbitals in the same phase. In more complicated systems like this, it is clearer to use a diagram of the AOs to see what the MO will be like. 

Like an atomic orbital, a molecular orbital has a specific site, shape, and energy. In the Hj molecule, for example, two singly occupied Is atomic orbitals combine. There are two ways for the orbital oomWnaiion to occur— an additive way and a subtractive way. The additive combination Wads to formation of a molecular orbital that is rot hly egg Shaped. while- the sub tractiw combiaatioi) leads to formation of a molecular orbital that has a node between nudei (Figure 1.10). Note that the additive combination is a... 

An answer waa provided in 1931 by Linus Pauling, who showed mathematically how an a orbital and three p orbitala on an atom can combine, or hybridiva, to form four e<]uival [ic atomic orbitals with tetrahedral ori-ematlon. Shown In Figure l.ll. these Tcimhcdrally oncmed orbitals are called sp hybrids. (The superscript 3 in the nmne indicates that threep atomic orbitals combine to form the hybrid, not that 3 electrons occupy it>... 

Since the boron atom has a ls22s22p configuration, we describe the B2 > molecule by considering how p atomic orbitals combine to form MOs. Recall that p orbitals have two lobes and that they occur in sets of three mutually j perpendicular orbitals [Fig. 14.35(a)]. When two B atoms approach each other, two pairs of p orbitals can overlap in a parallel manner [Figs. 14.35(b) and (c)] and one pair can overlap head-on [Fig. 14.35(d)],... 

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 ... 

---