Chemistry-140 Lecture 26

1. Chemistry-140 Lecture 26 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals • Chapter Highlights • intro to VB & MO theory • orbital overlap • orbital hybridization • multiple bonding (p bonds) • bond order • MO theory

2. Chemistry-140 Lecture 26 • Valence Bond (VB) Theory: (Linus Pauling, 1954) assumes covalent bonding is due to overlap of atomic orbitals which create a region of shared electron density between the nuclei • Molecular Orbital (MO) Theory: (Robert Mulliken, 1966) assumes valence electrons are in molecular orbitals which extend over several atoms Two Approaches to Chemical Bonding

3. Chemistry-140 Lecture 26 • Orbital overlap: If two H-atoms approach each other closely enough their 1s orbitals can partially occupy the same region of space…. Valence Bond Theory: Orbital Overlap

4. H-atoms HB:1sB HA:1sA H2 molecule 1sB 1sA Overlap Region Chemistry-140 Lecture 26 VB Theory: Orbital Overlap

5. Chemistry-140 Lecture 23 Energy Profile of a Covalent Bond

6. Chemistry-140 Lecture 26 • The valence bond orbital between two atoms is a region of high probability of finding the electron. • There is an optimum distance between the two nuclei, called the bond length: the distance of separation at which the total energy is minimized. • The imaginary line that passes through both nuclei is called the internuclear axis Orbital Overlap

7. Chemistry-140 Lecture 26 • Sigma (s) bond: • A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis. Sigma (s) Bonds

8. Chemistry-140 Lecture 26 What Orbitals Do We Use to Make the Tetrahedral Molecule CH4 ? C: [He]2s22p2 H: 1s1

9. Chemistry-140 Lecture 26 • Hybridization: The process of mathematically mixing two or more atomic orbitals, on a single atom. • Hybrid orbital: The result of this blending of orbitals. The number of hybrid orbitals formed is always the same as the number of atomic orbitals used Hybrid Orbitals

10. 2p 2s 1s Chemistry-140 Lecture 26 • CH4 has four equivalent C-H bonds sp3 Hybridization ground state promoted state

11. 2sp3 1s Chemistry-140 Lecture 26 • sp3 hybrid orbitals: are formed from the mixing of ones-orbital and threep-orbitals. The arrangement of the foursp3 hybrid orbitals is tetrahedral, with a 109.5° angle between the hybrid orbitals sp3 Hybridization

12. Chemistry-140 Lecture 26 sp3 Hybridization

13. 2p 2s 1s Chemistry-140 Lecture 26 • BF3 has three equivalent B-F bonds sp2 Hybridization ground state promoted state

14. 1s 2sp2 2p Chemistry-140 Lecture 26 • sp2 hybrid orbitals: are formed from the mixing of ones-orbital and twop-orbitals. The arrangement of the threesp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals sp2 Hybridization

15. Chemistry-140 Lecture 26 November 8th, 1996 Chemistry-140 Lecture 26 sp2 Hybridization

16. 2p 2s 1s Chemistry-140 Lecture 26 sp Hybridization • BeF2 has two equivalent Be-F bonds ground state promoted state

17. 1s 2sp 2p Chemistry-140 Lecture 26 • sp hybrid orbitals: are formed from the mixing of ones-orbital and one p-orbital. The arrangement of the twosp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals sp Hybridization

18. Chemistry-140 Lecture 26 sp Hybridization

19. Chemistry-140 Lecture 26

20. Chemistry-140 Lecture 28 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals • Chapter Highlights • intro to VB & MO theory • orbital overlap • orbital hybridization • multiple bonding (p bonds) • bond order • MO theory

21. 2p 2s 1s Chemistry-140 Lecture 28 • BF3 has three equivalent B-F bonds sp2 Hybridization ground state promoted state

22. 1s 2sp2 2p Chemistry-140 Lecture 28 • sp2 hybrid orbitals: are formed from the mixing of ones-orbital and twop-orbitals. The arrangement of the threesp2 hybrid orbitals is trigonal planar, with a 120° angle between the hybrid orbitals sp2 Hybridization

23. Chemistry-140 Lecture 28 Chemistry-140 Lecture 26 November 8th, 1996 sp2 Hybridization

24. 2p 2s 1s Chemistry-140 Lecture 28 sp Hybridization • BeF2 has two equivalent Be-F bonds ground state promoted state

25. 1s 2sp 2p Chemistry-140 Lecture 28 • sp hybrid orbitals: are formed from the mixing of ones-orbital and one p-orbital. The arrangement of the twosp hybrid orbitals is linear, with a 180° angle between the hybrid orbitals sp Hybridization

26. Chemistry-140 Lecture 28 sp Hybridization

27. Chemistry-140 Lecture 28

28. Chemistry-140 Lecture 28

29. Chemistry-140 Lecture 28 • Sigma (s) bond: • A bond in which the electron density is circularly symmetrical about the internuclear axis. The orbital overlap is along the internuclear axis. Sigma (s) Bonds

30. Chemistry-140 Lecture 28 • In almost all cases, single bonds are s-bonds • BUT: To explain double and triple bonds we need another kind of bond. Multiple Bonds C2H2 acetylene C2H4 ethylene

31. Chemistry-140 Lecture 28 • p-bonds: those in which the electron density is above and below the internuclear axis. The internuclear axis is a region of zero electron density. p-Orbital Overlap

32. 2p 2s 1s 1s 2sp2 2p Chemistry-140 Lecture 28 • 10 of 12 valence electrons are used to form the C-H (four) and C-C (one) s-bonds. The extra p-orbitals are perpendicular to the plane of the molecule and contain a single electron Ethylene (sp2 hybridization) ground state promoted state sp2 hybridization

33. Chemistry-140 Lecture 28 Ethylene (sp2 hybridization)

34. Chemistry-140 Lecture 28 Ethylene (sp2 hybridization)

35. C(sp2) H(1s) s-bonds C(p) p-bond Chemistry-140 Lecture 28 Ethylene (sp2 hybridization)

36. 2p 2s 1s 1s 2p 2sp Chemistry-140 Lecture 28 • 6 of 10 valence electrons are used to form the C-H (two) and C-C (one) s-bonds. The TWO extra p-orbitals are perpendicular to the axis of the molecule and contain a single electron each Acetylene (sp hybridization) ground state promoted state sp hybridization

37. Chemistry-140 Lecture 28 Acetylene (sp hybridization)

38. Chemistry-140 Lecture 28 Acetylene (sp hybridization)

39. Cl C H Chemistry-140 Lecture 28 Consequences of Multiple Bonding Free rotation occurs around the axis of a single s-bond This cannot occur for a multiple p-bond system and isomers may result trans cis

40. Chemistry-140 Lecture 28 Bond Order and Hybridization in Resonance Structures TWO p-electrons over THREE atoms. O-O bond order is 1.5!! O-O distance & energy an average of a single & a double bond

41. Chemistry-140 Lecture 28 Question Complete this Lewis structure and assign hybridization schemes to all the non-hydrogen atoms. How many electrons are there in p-orbitals in this compound? Identifying Orbital Hybridization Schemes

42. sp2 sp3 sp2 sp3 Chemistry-140 Lecture 28 Answer Identifying Orbital Hybridization Schemes Since there is only ONE p-bond, the number of electrons in p-bonds is TWO!

43. Chemistry-140 Lecture 29 Chapter 10: Bonding & Molecular Structure: Orbital Hybridization, Molecular Orbitals • Chapter Highlights • intro to VB & MO theory • orbital overlap • orbital hybridization • multiple bonding (p bonds) • bond order • MO theory

44. O O = Chemistry-140 Lecture 29 • Molecular Orbitals: Valence electrons are in molecular orbitals, MO’s extending over the whole molecule. • Emphasizes the uniqueness of each molecule rather than being the sum of its atoms (VB theory) • Why Bother!!! • O2 is paramagnetic!! That's a good reason!! An Introduction to Molecular Orbitals

45. Chemistry-140 Lecture 29 • TWO atomic orbitals HA(1s) and HB(1s) combine mathematically (a linear combination) to produce TWO molecular orbitals H2 (s1s)andH2(s1s*). Molecular Orbitals From Atomic Orbitals s1s = Bonding MO s1s* = Antibonding MO

46. Chemistry-140 Lecture 29 • Bonding MO (s1s): From addition of the two atomic orbitals. Leads to an increased probability that the electrons are found in this region. Electrons and orbital are concentrated between the nuclei. • Antibonding MO (s1s*): From subtraction of the two atomic orbitals. Leads to a reduced probability that the electrons are found in this region. Without significant electron density between the nuclei, they are repelled. Molecular Orbitals From Atomic Orbitals

47. HA(1s) HB(1s) sigma* antibonding MO with node HB(1s) HA(1s) sigma bonding MO Molecular Orbital Description of H2 Chemistry-140 Lecture 29

48. Chemistry-140 Lecture 29 A Molecular Orbital Diagram for H2

49. Chemistry-140 Lecture 29 • A first principle: The number of molecular orbitals (MO) produced is always equal to the number of atomic orbitals (AO) used in the combination. • A second principle:Bonding MO’s are always lower in energy and antibonding MO’s higher in energy than their parent AO’s. • A third principle: Electrons are assigned to MO’s with successively higher energies; obeying the Pauli exclusion principle and Hund’s rule. Some Basic Principles of MO Theory

50. Chemistry-140 Lecture 29 Recall:Bond order was defined as the number of bonding electron pairs linking two atoms. In MO Theory: Bond Order in MO Theory Bond order = 1/2 [(number of electrons in bonding MO’s) - (number of electrons in antibonding MO’s)]