Ch05 Molecular Structure and Orbitals.pdf - finedrafts

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E FIGURE 5.34 (a) The MO energy-level diagram for the H 2 molecule. (b) The shapes of the MOs are obtained by squaring the wave functions for MO 1 and MO 2. The positions of the nuclei are indicated by •. A Energy of an atomic orbital in a free atom Antibonding MO Bonding MO B Energy of an atomic orbital in a free atom FIGURE 5.35 Bonding and antibonding molecular orbitals (MOs). Bonding will result if the molecule has lower energy than the separated atoms. E H A 1s A (a) Energy diagram H 2 MO 2 MO 1 H B 1s B 5.3 The Molecular Orbital Model 219 3. MO 1 is lower in energy than the 1s orbitals of free hydrogen atoms, while MO 2 is higher in energy than the 1s orbitals. This fact has very important implications for the stability of the H 2 molecule, since if the two electrons (one from each hydrogen atom) occupy the lower-energy MO 1, they will have lower energy than they do in the two separate hydrogen atoms. This situation favors molecule formation, because nature tends to seek the lowest energy state. That is, the driving force for molecule formation is that the molecular orbital available to the two electrons has lower energy than the atomic orbitals these electrons occupy in the separated atoms. This situation is favorable to bonding, or probonding. On the other hand, if the two electrons were forced to occupy the higher-energy MO 2, they would be defi nitely antibonding. In this case, these electrons would have lower energy in the separated atoms than in the molecule, and the separated state would be favored. Of course, since the lower-energy MO 1 is available, the two electrons occupy that MO and the molecule is stable. We have seen that the molecular orbitals of the hydrogen molecule fall into two classes: bonding and antibonding. A bonding molecular orbital is lower in energy than the atomic orbitals of which it is composed. Electrons in this type of orbital will favor the molecule; that is, they will favor bonding. An antibonding molecular orbital is higher in energy than the atomic orbitals of which it is composed. Electrons in this type of orbital will favor the separated atoms (they are antibonding). Fig. 5.35 illustrates these ideas. 4. Fig. 5.34 shows that for the bonding molecular orbital in the H 2 molecule the electrons have the greatest probability of being between the nuclei. This is exactly what we would expect, since the electrons can lower their energies by being simultaneously attracted by both nuclei. On the other hand, the electron distribution for the antibonding molecular orbital is such that the electrons are mainly outside the space between the nuclei. This type of distribution is not expected to provide any bonding force. In fact, it causes the electrons to be higher in energy than in the separated atoms. Thus the molecular orbital model produces electron distributions and energies that agree with our basic ideas of bonding. This fact reassures us that the model is physically reasonable. 5. The labels on molecular orbitals indicate their symmetry (shape), the parent atomic orbitals, and whether they are bonding or antibonding. Antibonding character is indicated by an asterisk. For the H 2 molecule, both MOs have symmetry, and both are constructed from hydrogen 1s atomic orbitals. The molecular orbitals for H 2 are therefore labeled as follows: MO 1 5s 1s MO 2 5s 1s* 6. Molecular electron con gurations can be written in much the same way as atomic (electron) con gurations. Since the H 2 molecule has two electrons in the 1s molecular orbital, the electron con guration is 1s 2 . MO 2 MO 1 (b) Electron probability distribution Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
220 Chapter Five Molecular Structure and Orbitals E FIGURE 5.36 A molecular orbital energy-level diagram for the H 2 molecule. Although the model predicts that H 2 should be stable, this ion has never been observed, again emphasizing the perils of simple models. E FIGURE 5.37 The molecular orbital energy-level diagram for the H 2 ion. E H 1s H 1s He 1s Atomic orbitals in a free H atom σ 1s* σ 1s σ 1s* and σ 1s are molecular orbitals in the H 2 molecule σ 1s* σ 1s σ 1s* σ 1s FIGURE 5.38 The molecular orbital energy-level diagram for the He 2 molecule. H 1s H 1s He 1s 7. Each molecular orbital can hold two electrons, but the spins must be opposite. 8. Orbitals are conserved. The number of molecular orbitals will always be the same as the number of atomic orbitals used to construct them. Many of the above points are summarized in Fig. 5.36. Now suppose we could form the H 2 ion from a hydride ion (H ) and a hydrogen atom. Would this species be stable? Since the H ion has the con guration 1s 2 and the H atom has a 1s 1 con guration, we will use 1s atomic orbitals to construct the MO diagram for the H 2 ion, as shown in Fig. 5.37. The electron con guration for H2 is (1s) 2 ( 1s*) 1 . The key idea is that the H 2 ion will be stable if it has a lower energy than its separated parts. From Fig. 5.37 we see that in going from the separated H ion and H atom to the H 2 ion, the model predicts that two electrons are lowered in energy and one electron is raised in energy. In other words, two electrons are bonding and one electron is antibonding. Since more electrons favor bonding, H 2 is predicted to be a stable entity— a bond has formed. But how would we expect the bond strengths in the molecules of H 2 and H 2 to compare? In the formation of the H 2 molecule, two electrons are lowered in energy and no electrons are raised in energy compared with the parent atoms. When H 2 is formed, two electrons are lowered in energy and one is raised, producing a net lowering of the energy of only one electron. Thus the model predicts that H 2 is twice as stable as H 2 with respect to their separated components. In other words, the bond in the H 2 molecule is predicted to be about twice as strong as the bond in the H 2 ion. Bond Order To indicate bond strength, we use the concept of bond order. Bond order is the difference between the number of bonding electrons and the number of antibonding electrons divided by 2. Bond order 5 number of bonding electrons 2 number of antibonding electrons 2 We divide by 2 because, from the localized electron model, we are used to thinking of bonds in terms of pairs of electrons. Since the H 2 molecule has two bonding electrons and no antibonding electrons, the bond order is Bond order 5 2 2 0 2 The H 2 ion has two bonding electrons and one antibonding electron; the bond order is Bond order 5 2 2 1 2 5 1 5 1 2 Bond order is an indication of bond strength because it re ects the difference between the number of bonding electrons and the number of antibonding electrons. Larger bond order means greater bond strength. We will now apply the molecular orbital model to the helium molecule (He 2). Does this model predict that this molecule will be stable? Since the He atom has a 1s 2 con- guration, 1s orbitals are used to construct the molecular orbitals, and the molecule will have four electrons. From the diagram shown in Fig. 5.38 it is apparent that two electrons are raised in energy and two are lowered in energy. Thus the bond order is zero: 2 2 2 2 This implies that the He 2 molecule is not stable with respect to the two free He atoms, which agrees with the observation that helium gas consists of individual He atoms. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 5 0
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