1. 11-1 Chapter 11 Theories of Covalent Bonding

2. 11-2 Theories of Covalent Bonding 11.1 Valence bond (VB) theory and orbital hybridization 11.2 The mode of orbital overlap and types of covalent bonds 11.3 Molecular orbital (MO) theory and electron delocalization

3. 11-3 Figure 9.2 The three models of chemical bonding

4. 11-4 Figure 9.11 Covalent bond formation in H 2

5. 11-5 Structure dictates shape Shape dictates function Key Principles shape = conformation Molecules can assume more than one shape (conformation) in solution!

6. 11-6 The Complementary Shapes of an Enzyme and Its Substrate

7. 11-7 Valence-shell Electron-Pair Repulsion (VSEPR) Theory A method to predict the shapes of molecules from their electronic structures (Lewis structures do not depict shape) Basic principle: each group of valence electrons around a central atom is located as far away as possible from the others in order to minimize repulsions Both bonding and non-bonding valence electrons around the central atom are considered. AX m E n symbolism: A = central atom, X = surrounding atoms, E = non-bonding electrons (usually a lone pair)

8. 11-8 Figure 8.12 A periodic table of partial ground-state electron configurations

9. 11-9 Figure 10.12 The steps in determining a molecular shape molecular formula Lewis structure electron-group arrangement bond angles molecular shape (AX m E n ) Count all e - groups around the central atom A Note lone pairs and double bonds Count bonding and non-bonding e - groups separately. Step 1 Step 2 Step 3 Step 4

10. 11-10 Figure 10.1 Steps to convert a molecular formula into a Lewis structure molecular formula atom placement sum of valence e - remaining valence e - Lewis structure Place the atom with the lowest EN in the center Add A-group numbers Draw single bonds and subtract 2e - for each bond Give each atom 8e - (2e - for H) Step 1 Step 2 Step 3 Step 4

11. 11-11 Figure 10.5 Electron-group repulsions and the five basic molecular shapes Ideal bond angles are shown for each shape.

12. 11-12 Figure 10.8 The three molecular shapes of the tetrahedral electron-group arrangement Examples: CH 4, SiCl 4, SO 4 2 -, ClO 4 - Examples: NH 3 PF 3 ClO 3 H 3 O + Examples: H 2 O OF 2 SCl 2

13. 11-13 Figure 10.10 The four molecular shapes of the trigonal bipyramidal electron-group arrangement Examples: SF 4 XeO 2 F 2 IF 4 + IO 2 F 2 - Examples: ClF 3 BrF 3 Examples: XeF 2 I 3 - IF 2 - Examples: PF 5 AsF 5 SOF 4

14. 11-14 VSEPR (Valence Shell Electron Pair RepulsionTheory) Accounts for molecular shapes by assuming that electron groups tend to minimize their repulsions Does not show how shapes can be explained from the interactions of atomic orbitals

15. 11-15 The Central Themes of Valence Bond (VB) Theory Basic Principle A covalent bond forms when the orbitals of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei. Three Central Themes A set of overlapping orbitals has a maximum of two electrons that must have opposite spins. The greater the orbital overlap, the stronger (more stable) the bond. The valence atomic orbitals in a molecule are different from those in isolated atoms (hybridization).

16. 11-16 Figure 11.1 Orbital overlap and spin pairing in three diatomic molecules hydrogen, H 2 hydrogen fluoride, HF fluorine, F 2

17. 11-17 Linus Pauling Proposed that valence atomic orbitals in the molecule are different from those in the isolated atoms Mixing of certain combinations of atomic orbitals generates new atomic orbitals Process of orbital mixing = hybridization; generates hybrid orbitals

18. 11-18 Hybrid Orbitals The number of hybrid orbitals obtained equals the number of atomic orbitals mixed. The type of hybrid orbitals obtained varies with the types of atomic orbitals mixed. Key Points spsp 2 sp 3 sp 3 dsp 3 d 2 Types of Hybrid Orbitals

19. 11-19 Figure 11.2 The sp hybrid orbitals in gaseous BeCl 2 atomic orbitals hybrid orbitals orbital box diagrams VSEPR predicts a linear shape

20. 11-20 Figure 11.2 The sp hybrid orbitals in gaseous BeCl 2 (continued) orbital box diagrams with orbital contours

21. 11-21 Figure 11.3 The sp 2 hybrid orbitals in BF 3 VSEPR predicts a trigonal planar shape

22. 11-22 Figure 11.4 The sp 3 hybrid orbitals in CH 4 VSEPR predicts a tetrahedral shape

23. 11-23 Figure 11.5 The sp 3 hybrid orbitals in NH 3 VSEPR predicts a trigonal pyramidal shape

24. 11-24 Figure 11.5 The sp 3 hybrid orbitals in H 2 O VSEPR predicts a bent (V) shape

25. 11-25 Figure 11.6 The sp 3 d hybrid orbitals in PCl 5 VSEPR predicts a trigonal bipyramidal shape

26. 11-26 Figure 11.7 The sp 3 d 2 hybrid orbitals in SF 6 VSEPR predicts an octahedral shape

27. 11-27

28. 11-28 Figure 11.8 Conceptual steps from molecular formula to the hybrid orbitals used in bonding molecular formula Lewis structure molecular shape and e - group arrangement hybrid orbitals Figure 10.1 Step 1 Figure 10.12 Step 2Step 3 Table 11.1

29. 11-29 SAMPLE PROBLEM 11.1Postulating Hybrid Orbitals in a Molecule SOLUTION: PROBLEM:Use partial orbital diagrams to describe how the mixing of atomic orbitals on the central atoms leads to hybrid orbitals in each of the following molecules. PLAN:Use Lewis structures to establish the arrangement of groups and the shape of each molecule. Postulate the hybrid orbitals. Use partial orbital box diagrams to indicate the hybrid for the central atoms. (a) methanol, CH 3 OH (b) sulfur tetrafluoride, SF 4 (a) (a) CH 3 OHThe groups around C are arranged as a tetrahedron. O has a tetrahedral arrangement with two non-bonding e - pairs.

30. 11-30 SAMPLE PROBLEM 11.1(continued) (b) SF 4 has a seesaw shape with four bonding and one non-bonding e - pairs. S atom hybridized S atom single C atomsingle O atom hybridized O atomhybridized C atom distorted trigonal bipyramidal

31. 11-31 Figure 11.9  bonds in ethane, CH 3 -CH 3 both carbons are sp 3 hybridized s-sp 3 overlaps to  bonds sp 3 -sp 3 overlap to form a  bond relatively even distribution of electron density over all  bonds Covalent Bonds Between Carbon Atoms - Single Bonds free rotation ~109.5 o

32. 11-32 Figure 11.10  and  bonds in ethylene, C 2 H 4 overlap in one position -  p overlap -  electron density Covalent Bonds Between Carbon Atoms - Double Bonds hindered rotation ~120 o

33. 11-33 Figure 11.11  and  bonds in acetylene, C 2 H 2 overlap in one position -  p overlap -  Covalent Bonds Between Carbon Atoms - Triple Bonds hindered rotation 180 o

34. 11-34 Video: Hybridization

35. 11-35 SAMPLE PROBLEM 11.2 Describing bonding in molecules with multiple bonds SOLUTION: PROBLEM:Describe the types of bonds and orbitals in acetone, (CH 3 ) 2 CO. PLAN:Use the Lewis structure to determine the arrangement of groups and the shape at each central atom. Postulate the hybrid orbitals, taking note of multiple bonds and their orbital overlaps. sp 3 hybridized sp 2 hybridized  bonds  bond

36. 11-36 Figure 11.12 Restricted rotation in  -bonded molecules cistrans No spontaneous interconversion between cis and trans forms (isomers) in solution at room temperature!

37. 11-37 Limitations of VB Theory Inadequately explains magnetic/spectral properties Inadequately treats electron delocalization VB theory assumes a localized bonding model

38. 11-38 Molecular Orbital (MO) Theory A delocalized bonding model A quantum-mechanical treatment of molecules similar to that used for isolated atoms Invokes the concept of molecular orbitals (MOs) (extension of atomic orbitals) Exploits the wave-like properties of matter (electrons)

39. 11-39 Central themes of molecular orbital (MO) theory A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals. Atomic wave functions are summed to obtain molecular wave functions. If wave functions reinforce each other, a bonding MO is formed (region of high electron density exists between the nuclei). If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the nuclei).

40. 11-40 Amplitudes of wave functions are added Figure 11.13 An analogy between light waves and atomic wave functions Amplitudes of wave functions are subtracted

41. 11-41 Figure 11.14 Contours and energies of the bonding and antibonding molecular orbitals in H 2

42. 11-42 Bonding MO: lower in energy than isolated atoms Antibonding MO: higher in energy than isolated atoms number of AOs combined = number of MOs produced To form MOs, AOs must have similar energy and orientation Sigma (  ) and pi (  ) bonds are denoted as before; a star (asterick) is used to denote antibonding MOs.

43. 11-43 Figure 11.15 Molecular orbital diagram for the H 2 molecule MOs are filled in the same sequence as for AOs (aufbau and exclusion principles, Hund’s rule)

44. 11-44 The MO bond order [1/2 (no. of e - in bonding MOs) - (no. of e - in antibonding MOs)] higher bond order = stronger bond Has predictive power!

45. 11-45 Figure 11.16 MO diagrams for He 2 + and He 2 Energy MO of He +  * 1s  1s AO of He + 1s MO of He 2 AO of He 1s AO of He 1s  * 1s  1s Energy He 2 + bond order = 1/2He 2 bond order = 0 AO of He 1s can exist!cannot exist!

46. 11-46 SAMPLE PROBLEM 11.3Predicting species stability using MO diagrams SOLUTION: PROBLEM:Use MO diagrams to predict whether H 2 + and H 2 - can exist. Determine their bond orders and electron configurations. PLAN:Use H 2 as a model and accommodate the number of electrons in bonding and antibonding orbitals. Calculate the bond order.   1s AO of H 1s MO of H 2 + bond order = 1/2(1-0) = 1/2 H 2 + does exist!   MO of H 2 - bond order = 1/2(2-1) = 1/2 H 2 - does exist! 1s1s AO of H AO of H - configuration is (  1s ) 2 (   1s ) 1 AO of H AO of H + configuration is (  1s ) 1

47. 11-47 *2s*2s 2s2s 2s2s 2s2s 1s1s *1s*1s 1s1s 1s1s Figure 11.17 1s1s *1s*1s 1s1s 1s1s 2s2s 2s2s *2s*2s 2s2s Li 2 bond order = 1Be 2 bond order = 0 Bonding in s-block homonuclear diatomic molecules Energy Li 2 Be 2

48. 11-48 Bonding and antibonding MOs for core electrons cancel = no net contribution to bonding Only MO diagrams showing MOs created by combining valence-electron AOs are important.

49. 11-49 Figure 11.18 Contours and energies of  and  MOs through combinations of 2p atomic orbitals end-to-end overlap side-to-side overlap

50. 11-50 Relative energies  2p <  2p <  * 2p <  * 2p More effective end-to-end interaction relative to side-to-side in bonding MOs

51. 11-51 Figure 11.19 Relative MO energy levels for Period 2 homonuclear diatomic molecules MO energy levels for O 2, F 2 and Ne 2 MO energy levels for B 2, C 2 and N 2 without 2s-2p mixing with 2s-2p mixing

52. 11-52 Figure 11.20 MO occupancy and molecular properties for B 2 through Ne 2

53. 11-53 Figure 11.21 The paramagnetic properties of O 2 Explained by MO diagram

54. 11-54 SAMPLE PROBLEM 11.4Using MO theory to explain bond properties SOLUTION: PROBLEM:As the following data show, removing an electron from N 2 forms an ion with a weaker, longer bond than in the parent molecule, whereas the ion formed from O 2 has a stronger, shorter bond. PLAN:Find the number of valence electrons for each species, draw the MO diagrams, calculate bond orders, and compare the results. Explain these facts with diagrams showing the sequence and occupancy of MOs. bond energy (kJ/mol) bond length (pm) N2N2 N2+N2+ O2O2 O2+O2+945 110 498841623 112121112 N 2 has 10 valence electrons, so N 2 + has 9. O 2 has 12 valence electrons, so O 2 + has 11.

55. 11-55 SAMPLE PROBLEM 11.4(continued) 2s2s  2s 2p2p 2p2p  2p  2p N2N2 N2+N2+ O2O2 O2+O2+ bond orders 1/2(8-2) = 31/2(7-2) = 2.51/2(8-4) = 21/2(8-3) = 2.5 2s2s  2s 2p2p 2p2p  2p  2p bonding e - lost antibonding e - lost (weaker)

56. 11-56 Energy MO of HF AO of H 1s1s  2px2px 2py2py  AO of F 2p2p Figure 11.22 The MO diagram for HF Heteronuclear Diatomic Molecules lower in energy than 1s of H! nonbonding MOs

57. 11-57 In polar covalent compounds, bonding MOs are closer in energy to the AOs of the more electronegative atom.

58. 11-58 Energy Figure 11.23 The MO diagram for NO MO of NO 2s AO of N 2p2p *2s*2s 2s2s 2s AO of O 2p2p 2p2p 2p2p *2p*2p *2s*2s possible Lewis structures bond order = 2.5

59. 11-59 Figure 11.24 The lowest energy  -bonding MOs in benzene and ozone resonance hybrid