We can keep track of the mixing of the 2s and 2p orbitals in beryllium as follows:

We can keep track of the mixing of the 2s and 2p orbitals in beryllium as follows: The beryllium sp orbitals overlap with hydrogen Is orbitals (the hydrogen's electrons are shown in the above orbital diagram 40 produce two 6 bonds and a resulting linear molecule, as is shown in Fig. 3-13. SP 2 Hybrid orbitals Other combinations of orbitals may be involved in hybridization. Boron (Z = 5) uses its 2s orbital and two of its 2p orbitajs to form a set of three equivalent sp 2 hybrid orbitals, as shown below: Each of die three sp 2 hybrids has much the same shape as an sp hybrid orbital, but the three are oriented at 120 from each other, as is shown in Fig. 3-14. If each of the sp 2 hybrid orbitals overlaps with a Is orbital of an H atom, the result is a boron hydride, or borane (BH), molecule. This molecule, shown in Fig. 3-15, is predicted to have a planar Chapter 3: Molecular structure Page 73

structure in which each H occupies the corner of an equilateral triangle. BH 3 is, however, an almost hypothetical molecule, having been observed only as a short-lived intermediate in certain rapid reaction. We have used it as an example because of the analogy with BeH 2 (just discussed) and with CH 4 (to be discussed next). Boron does form similar trigonal planar molecules of the type BX 2, where X is a halogen atom, F, Cl, Br. or I. sp 3 Hybrid orbitals Finally, we return to carbon and its hydrogen compound, methane (CH 4 ). Here the carbon atom uses its 2s and all three of its 2p orbitals to form four equivalent sp 3 hybrid orbitals: Chapter 3: Molecular structure Page 74

These orbitals look much like the sp and sp 2 hybrids but point toward the corners of a regular tetrahedron (Fig. 3-16). This accounts for the tetrahedral shape of the CH 4 molecule Chapter 3: Molecular structure Page 75

The ammonia molecule There are many small molecules in which the bonding is best described in terms of sp 3 hybrid orbitals. In ammonia, NH 3, the mixing of the s and p orbitals of N (Z = 7) takes place essentially as it does with C in this case, however, because N has one more electron than C, only three of the resulting sp 3 hybrid orbitals are available for forming bonds with H atoms. The fourth contains a lone pair. Therefore NH 3, has a geometrical shape like that of CH 4 except for Chapter 3: Molecular structure Page 76

the missing H atom. This is shown in Fig. 3-17 b which the location of the lone pair of electrons is shown as oval. In Fig. 3-17 the NH 3 is drawn so that you can compare it with the CI-Lj molecule. In Fig. 3-17 it has been flipped over so that it is sitting on its base of three H atoms, the lone pair pointing upward. The shape of the molecure is that of a trigonal pyramid with the three H's defining the base. In ammonia the H N H bond angles are 107.3, which is a little less than the tetrahedral angle 109.5, This is a result of repulsion between the lone pair of electrons and the three bonding pairs. The charge cloud of a lone pair of electrons is more diffuse, spread out over more space than that of a bonding pair, which is more tightly compressed into the region between the bonded atoms. The spreading out of the lone-pair charge cloud means that lone pairbonding pair repulsions (Fig. 3-18) are stronger than bonding pairbonding pair the bonding pairs, and so the H atoms adjust their positions for best overlap. Chapter 3: Molecular structure Page 77

The water molecule water is The bonding in H 2 O is similar to that in NH 3. The Lewis structure of The four orbitals in the valence shell of 0 (Z = 8) hybridize and the four sp 3 hybrid orbitals are occupied by two lone pairs and two bonding pairs of electrons. The resulting structure is described a bent, or angular (Fig.: 3-19), In H 2 O there is an even greater shrinking of the bond angle from the tetrahedral angle 109.5 than there is in NH 3, this being a result of the two lone pairs in H 2 O. The measured bond angle in H 2 O is only 104.5. Other hybrid orbital sets Other possibilities exist for the mixing of pure atomic orbitals to form sets of hybrid orbitals. The most important of these is the hybridization of one s, three p, and two d orbitals. If the d orbitals are from, the n -L shell of the atom, the hybrids are called d 2 sp 3. If they are from the valence shell, that is, if they have the same principal quantum number as the s and orbitals, then they are called sp 3 d 2 Chapter 3: Molecular structure Page 78

orbitals. In either case these orbitals have major lobes pointing out toward the corners of a regular octahedron, an eight-sided solid having faces that are identical equilateral triangles. It is evident that with such hybridization the valence shell of the central atom no longer contains just an octet but has been expanded to 12 electrons. Octahedral hybrid orbitals are used to ccount for the structure of sulfur hexafluoride, Table 3-3 shows a summary of the more important sets of hybrid orbitals, their geometries, and some examples. Table 3-3 hybrid Geometry Examples orbitals Sp Linear BeF 2, CdBr 2 Sp 2 Trigonal planar BF 3, B(CH 2 ) 3 Sp 3 Tetrahedral TiCl 4 CCl 4 SiF 4 dsp 3 or sp 3 d Trigonal bipyramidal PCl 3 MoCL 3 D 2 sp 3 or sp 3 d 2 Octahedral SF 8 Chapter 3: Molecular structure Page 79

The molecular orbital model Molecular-orbital (MO) theory provides an alternative perspective from which to view bonding. According to this approach all the valence electrons in a molecule have an influence on the Stability of the molecule. (Inner-shell electrons may also make a contribution to the bonding, but for many simple molecule the effect is small.) Furthermore, MO theory considers that valence-shell atomic orbitals (AOs) cease to exist when a molecule is formed. They arc replaced by a new set of energy levels with corresponding new charge-cloud (probability-density) distributions. These new energy levels are a property of the molecule as a whole, and are called, consequently, molecular orbitals. Calculating the properties of molecular orbitals is commonly done by assuming that AOs combine to form MOs. The wave functions of the AOs are combined mathematically to produce wave functions for the resulting MOs. The process is reminiscent of the mixing of pure atomic orbitals to form hybrids, except that in MO formation atomic orbitals of more than one atom are mixed. Nevertheless, just as in the case of hybridization, the number of new orbitals formed equals the number of original atomic orbitals combined. As with atomic orbitals, we are interested in two aspects of molecular orbitals (1) the shapes of the probability-density distributions in space and (2) the relative energies. First we consider their shapes. Chapter 3: Molecular structure Page 80

Spatial distributions of MOs We begin by looking at the MOs which are forme< when two atoms bond in a diatomic molecule. Using thi simplest approach we consider that one AO from on< atom combines with one AO from a second atom to form two MOs. In order for this process to be effective two conditions must be met: (1) the AOs must be of comparable energy, and (2) they must overlap significantly. The quantum-mechanical calculation for combining the original AOs consists of (l) an addition and (2) a subtraction of the AO wave functions. (If the two atoms are different, a factor is included which takes account of the fact that the two AOs will not contribute equally to the formation of the MOs.) The result, then, is two new MO wave functions, one from the addition and one from the subtraction. As always, squaring a wave function for an electron gives us information about the probability of finding that electron. When this is done for the new MOs, the result is probability-density information for electrons in a molecule, and from this information the corresponding boundary surfaces (and also energy levels) can be found. In Fig. 3-20 are shown the boundary surfaces of the two molecular orbitals which are formed by combining two 1s atomic orbitals. Shown at the left are the Chapter 3: Molecular structure Page 81

two overlapping Is AOs, and at the right, the resulting MOs The MO formed by subtracting the AO wave functions is labeled σ (read "sigma star"), while the one formed by adding them is labeled σ. The contrast between these two MOs is striking. There is an obvious increase in electronic charge density between the nuclei in the a, orbital but a decrease in the same region in the σ s orbital. For this reason the σ s orbital is called a bonding orbital and the σ s orbital, an antibonding orbital. The former tends to stabilize the bond, while the latter tends to destabilize it. Both of these orbitals are called σ orbitals because they are both centered on and symmetrical around the bone axis. A cross section of either orbital made perpendicular to the bond axis is circular. The combination of two p orbitals produces different results depending on which p orbitals are used. If the x axis is the bond axis, then two 2p x orbitals can overlap properly if they approach each other end-to-end, as is shown in Fig. 3-21. The resulting MOs are, as before, a bonding orbital, with electronic charge buildup between the nuclei, and an antibonding MO, with decreased charge Chapter 3: Molecular structure Page 82

between the nuclei. These orbitals are also σ orbitals, because they are symmetrical around the bond axis. They are designated σ x and σ x * to indicate that they have been derived, from p x atomic orbitals. When 2p v and 2p, orbitals overlap to form MOs, they do so side-to-side, In each case the result is a four-lobed antibonding orbital and a two-lobed bonding orbital. These orbitals are not symmetrical around the bond axis. Rather, there are two regions on opposite sides of the bond axis in which the charge-cloud density is high. This is characteristic of a Π orbital. Note that as before, the bonding orbital permits a high concentration of electronic charge in the region between the nuclei, while the antibonding orbital shows lowered charge density in this region. (Each antibonding orbital has a nodal plane between they, two nuclei.) Chapter 3: Molecular structure Page 83

Energies of MOs Whenever two atomic orbitals combine to form two molecular orbitals, the energy of the bonding MO is always lower than that of either AO, while the energy of The antibonding MO is higher. Figure 3-21 shows the energy relationships for the Is AO and σ S, MO orbitals for the case of a homonuclear diatomic molecule, one in which both atoms are the same. On the left and right are the 1, energy levels of two atoms of * element A (labeled A and A'). In the center are the σ s and σ s energy levels of molecule A-A'. The diagonally running broken lines point out that the MOs have been formed from the indicated AOs. Figure 3-22 could be used to show the formation of MOs from a pair of any s orbitals (2s, 3s, 4s, etc. case an antibonding orbital (of higher energy) bonding orbital (of lower energy) are formed. Chapter 3: Molecular structure Page 84

Consider next the formation of from a pair of 2p x, orbitals, orbitals With along the bonding axis (Fig. 3-23). Again we see the formation of a pair of MOs, one bonding (σ s.) and one antibonding (σ * x ) Next, look at the 2p y and 2p z AOs, which overlap side-to-side. The MOs ' formed from these are shown in Fig. 3-24. The p y, - p y, overlap is exactly like the p Z -p z overlap (except for orientation), and so the resulting MOs fall into sets of two orbitals of the same energy: the π y and π z (bonding) orbitals and the π * y and π * z (antibonding) orbitals. The filling of molecular orbitals : in order to build up the electronic configurations of atoms. We will now use a similar technique, but will add electrons to a filling diagram composed of MO energy levels. We wish to build up the Chapter 3: Molecular structure Page 85

ground-slate configurations of homonuclear diatomic molecules, and so we will add electrons starting at the bottom of the diagram and work upward toward higher-energy MOs. The MO filling diagram consists of Figs. 3-22 through 3-24. At the start, however, we need consider only the low-energy end of the diagram, that is, those MOs derived from the K. shells of the bonded atoms (Fig. 3-22). H 2. The simplest molecule is hydrogen. Figure 3-25 shows orbital populations for two unbonded ground-state H atoms at the left and right, together with that of the ground-state H; molecule, in rhe middle of the diagram. The two is electrons end up as a pair (antiparallel spins) in the bonding σ 2 orbital of H 2 and constitute a single bond. The electronic configuration of H 2 can be written H 2 : (o s ) 1 He 2. Next consider the molecule which might be formed from two atoms of helium, each of which furnishes two electrons to the molecule. This is two more than in H 2, so the MO population would look like that in Fig. 3-26. (But the (antibonding) σ s orbital is now filled, and its destabilizing effect cancels out the stabilizing effect of the two bonding electrons (in the σ s, orbital). The result is that there is no net attractive force between He atoms, and so He 2 does not exist. In molecular-orbital theory the bond order is defined as Bond order = bonding electrons - antibonding electrons 2 Thus the bond order in the H 2 molecules is 2-0 1 2 Chapter 3: Molecular structure Page 86

While in the He 2 is 2-2 2 0 EXAMPLE 3-1 Problem: Predict the stability of the hydrogen-molecule ion H 2 + Chapter 3: Molecular structure Page 87

+ Solution : The H 2 ion should have an orbital occupancy like that of H 2, but with one less electron. Therefore, its electronic configuration is H + 2 : (σ s ) 2 The bond order in H + 2 is 1/2(1 0), or 1/2. This means that the H + + 2 particle should exist, its atoms held together by a half bond. The H 2 ion does indeed exist; its bond energy is 255 kj mol- 1, a moderately high bond energy. (By comparison the bond energy in H 2 is 433 kjmol- 1.) Li 2. Now consider the Li 2 molecule. This molecule has a total of six electrons but four of these are in the (inner) K shells of the Li atoms, where they contribute little to the bonding. The valence elections of the two Li atoms are used to populate a new σ, MO as shown in Fig. 3-27. The Is atomic orbitals are essentially unperturbed. The configuration is much like that of H 2, and the bond order, which can be determined from the valence electrons only, is equal to 1/2(2 0), or 1. Representing each of the filled Is orbitals by K (for a K shell) the electronic configuration of Li 2 can be shown as Li 2 : KK.( σ S ) 2 With a bond order of 1 the Li 2 molecule is predicted to exist. Neither liquid nor solid Li consists of Li 2 molecules, but diatomic molecules are indeed found in gaseous lithium. The bond energy in Li 2 is 105 kj mol- 1. This is lower than that in H 2 ) (433 kj mol- 1 ) because of the shielding of the nucleus by the complete K shell in each atom. Chapter 3: Molecular structure Page 88

Be 2,. Moving on to the hypothetical Be;, molecule, we find a situation like that in He;. The atomic number of beryllium is 4, and the "seventh" and "eighth" electrons in the Be 2 molecule add to the σ s " orbital. The destabilizing effect of the filled σ s orbital cancels out the stabilizing effect of the filled σ, orbital, the bond order is zero, and therefore the Be; molecule should not be stable. Indeed, Be;, has not been observed. Next consider sequence B 2, C 2, N 2, O 2, F 2, and Ne 2, as we work across the rest of the second period constructing homonuclear diatomic molecules. But since we now need some more molecular orbitals, we go to the σ and π orbital. When we put these two diagrams together, however, we run into a small difficulty. The relative energy of the π y and π z orbitals is less than that of the σ orbital for B 2 through N 2, but greater for the remainder of the sequence. Thus the orbital energies for B 2, C 2, and N 2, are as shown in Fig. 3-28 a and for O 2. F 2 and Ne 2, as shown in Fig. 3-28b The main difference between Fig 3-28 a and b is the relative energy of the σ x, compared to the π y and π z orbitals. Chapter 3: Molecular structure Page 89

The change in sequence of MO energies between N 2 and O 2 occurs because the σ z and σ y MOs actually have some s character, a fact which we had to ignore, when we decided to use the "one AO plus one AO yields two MOs" simplification. (The amount of s character in these orbitals decreases as the nuclear charge increases across the period. Because of this the σ x, energy drops below the π y and π z energy at O 2 Chapter 3: Molecular structure Page 90