1. 1 Advanced Theories of Chemical Bonding Chapter 10 Atomic Orbitals Molecules

2. 2 MOLECULAR ORBITAL THEORY — Robert Mullikan (1896- 1986)MOLECULAR ORBITAL THEORY — Robert Mullikan (1896- 1986) valence electrons are delocalizedvalence electrons are delocalized valence electrons are in orbitals (called molecular orbitals) spread over entire molecule.valence electrons are in orbitals (called molecular orbitals) spread over entire molecule. Two Theories of Bonding

3. 3 VALENCE BOND THEORY — Linus PaulingVALENCE BOND THEORY — Linus Pauling valence electrons are localized between atoms (or are lone pairs).valence electrons are localized between atoms (or are lone pairs). half-filled atomic orbitals overlap to form bonds.half-filled atomic orbitals overlap to form bonds. See Screen 10.3 and Figures 10.1 and 10.2.See Screen 10.3 and Figures 10.1 and 10.2.

4. 4 Sigma Bond Formation by Orbital Overlap Two s orbitals overlap

5. 5 Sigma Bond Formation Two s orbitals overlap Two p orbitals overlap

6. 6 Using VB Theory Bonding in BF 3 planar triangle angle = 120 o

7. 7 Bonding in BF 3 How to account for 3 bonds 120 o apart using a spherical s orbital and p orbitals that are 90 o apart?How to account for 3 bonds 120 o apart using a spherical s orbital and p orbitals that are 90 o apart? Pauling said to modify VB approach with ORBITAL HYBRIDIZATIONPauling said to modify VB approach with ORBITAL HYBRIDIZATION — mix available orbitals to form a new set of orbitals — HYBRID ORBITALS — that will give the maximum overlap in the correct geometry. (See Screen 10.6)— mix available orbitals to form a new set of orbitals — HYBRID ORBITALS — that will give the maximum overlap in the correct geometry. (See Screen 10.6)

8. 8 Bonding in BF 3 See Figure 10.9 and Screen 10.6 rearrange electronshydridize orbs. unused p orbital three sp 2 hybrid orbitals 2p 2s

9. 9 The three hybrid orbitals are made from 1 s orbital and 2 p orbitals  3 sp 2 hybrids. The three hybrid orbitals are made from 1 s orbital and 2 p orbitals  3 sp 2 hybrids. Bonding in BF 3 Now we have 3, half-filled HYBRID orbitals that can be used to form B-F sigma bonds.Now we have 3, half-filled HYBRID orbitals that can be used to form B-F sigma bonds.

10. 10 An orbital from each F overlaps one of the sp 2 hybrids to form a B-F  bond. Bonding in BF 3

11. 11 Bonding in CH 4 How do we account for 4 C—H sigma bonds 109 o apart? Need to use 4 atomic orbitals — s, p x, p y, and p z — to form 4 new hybrid orbitals pointing in the correct direction.

12. 12 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals. Bonding in a Tetrahedron — Formation of Hybrid Atomic Orbitals

13. 13 4 C atom orbitals hybridize to form four equivalent sp 3 hybrid atomic orbitals.

14. 14 Bonding in CH 4 Figure 10.6

15. 15 Orbital Hybridization Figure 10.5 BONDSSHAPEHYBRID REMAIN 2linear sp2 p’s 3trigonal sp 2 1 p planar 4tetrahedral sp 3 none

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17. 17 Bonding in Glycine

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22. 22 Multiple Bonds Consider ethylene, C 2 H 4

23. 23 Sigma Bonds in C 2 H 4

24. 24 π Bonding in C 2 H 4 The unused p orbital on each C atom contains an electron and this p orbital overlaps the p orbital on the neighboring atom to form the π bond. (See Fig. 10.9)

25. 25 π Bonding in C 2 H 4 The unused p orbital on each C atom contains an electron and this p orbital overlaps the p orbital on the neighboring atom to form the π bond. (See Fig. 10.9)

26. 26 Multiple Bonding in C 2 H 4

27. 27  and π Bonding in C 2 H 4 Figure 10.11

28. 28  and π Bonding in CH 2 O Figure 10.12

29. 29  and π Bonding in C 2 H 2 Figure 10.13

30. 30 Consequences of Multiple Bonding Figure 10.14 There is restricted rotation around C=C bond.

31. 31 Consequences of Multiple Bonding See Butene.Map in ENER_MAP in CAChe models. Restricted rotation around C=C bond.

32. 32 Double Bonds and Vision See Screen 10.13, Molecular Orbitals and Vision See also Chapter Focus 10, page 380

33. 33 Valence electrons are delocalizedValence electrons are delocalized Valence electrons are in orbitals (called molecular orbitals) spread over entire molecule.Valence electrons are in orbitals (called molecular orbitals) spread over entire molecule. Molecular Orbital Theory

34. 34 The Paramagnetism of O 2

35. 35 Molecular Orbital Theory Bonding and antibonding sigma MO’s are formed from 1s orbitals on adjacent orbitals.Bonding and antibonding sigma MO’s are formed from 1s orbitals on adjacent orbitals.

36. 36 Molecular Orbital Theory Figure 10.17 1. No. of MO’s = no. of atomic orbitals used. 2. Bonding MO is lower in energy than atomic orbitals. Antibonding MO is higher. 3. Electrons assigned to MO’s of higher and higher energy.

37. 37 Dihelium Molecule Bond order = 1/2 [# e- in bonding MOs - # e- in antibonding MOs]

38. 38 Sigma Bonding from p Orbitals

39. 39 π Bonding from p Orbitals Sideways overlap of atomic 2p orbitals that lie in the same direction in space give π bonding and antibonding MOs.

40. 40  & π Bonding from p Orbitals

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42. 42 MO Theory of Metals & Semiconductors Can explainCan explain –Luster –Electrical and thermal conductivity –Malleability All explanations come down to electron mobilityAll explanations come down to electron mobility

43. 43 MO Theory of Metals & Semiconductors Electrical conductivityElectrical conductivity –Metals — conductivity decreases with temperature –Semiconductors — increases with T –Insulator — very low conductivity

44. 44 MO Theory of Metals & Semiconductors Band theory-The central idea underlying the description of the electronic structure of solids is that valence electrons donated by atoms are spread over the entire structure.

45. 45 MO Theory of Metals & Semiconductors

46. 46 Only 1/2 of the levels are filled. 1/2 bond per atom.

47. 47 Be Metal and MOs This gives 1 bond per Be atom

48. 48 Al Metal and MOs This gives 3/2 bond per Al atom Use 1000 Al atoms and get 4000 MOs Have 3000 e- or 1500 pairs This fills the bottom levels 3/4 of the way. 1.5 pairs per Al atom

49. 49 Silicon and MOs This gives 2 bond per Si atom Have 1000 Si atoms 4000 e- or 2000 pairs 2 pairs per Si atom Band is completely filled

50. 50 Heat of Atomization ∆H of vaporization (or atomization) is a good measure of bonding in solids. M(s) ---> M(g) Energy change = ∆H vap High ∆H values for transition metals indicate d orbital participation.

51. 51 Heat of Vaporization

52. 52 Fermi Level The HOMO at T = 0 is the Fermi level. At temp > 0, electrons near Fermi level can be promoted to nearby empty levels. These promoted e- are mobile and move under electric field. Promotion gives e- in higher levels and “hole” in lower levels. Therefore, 2 mobile e-.

53. 53 Electrical Conductivity Conduction band Valence band

54. 54 Electrical Conductivity Metal conductivity DECREASES with increase in T.Metal conductivity DECREASES with increase in T. Contrary to expectation. Would expect increased electron promotion.Contrary to expectation. Would expect increased electron promotion. Ability of e- to travel smoothly thru the solid in a conduction band depends on uniformity of atom arrangement.Ability of e- to travel smoothly thru the solid in a conduction band depends on uniformity of atom arrangement. An atom vibrating vigorously at a site is equivalent to an impurity that disrupts the orbitals.An atom vibrating vigorously at a site is equivalent to an impurity that disrupts the orbitals. Thus, higher T means lower conductivity.Thus, higher T means lower conductivity.

55. 55 Insulators Very few e- from the valence band have sufficient energy to move to the conduction band. Valence band is full 6 eV in diamond

56. 56 Semiconductors Group 4A elementsGroup 4A elements –C (diamond) is an insulator –Si, Ge, and gray Sn are semiconductors »all of the above have the diamond structure, which appears especially favorable to semiconductor behavior –White Sn and Pb are metals

57. 57 Semiconductors Many inorganic compounds are semiconductors. Best known are “III-V” compounds GaAs = “Ge” InSb = “Sn” Have ZnS or zinc blende structure.

58. 58 Band Theory & Semiconductors Semiconductors have a band structure similar to insulators but band gap is smallSemiconductors have a band structure similar to insulators but band gap is small Band gap = 0.5 to 3.0 eVBand gap = 0.5 to 3.0 eV At least a few electrons have sufficient thermal energy to be promoted to an empty band.At least a few electrons have sufficient thermal energy to be promoted to an empty band.

59. 59 Band Theory & Semiconductors Semiconductors have a band structure similar to insulators but have a small band gap Electrons can be promoted thermally. The higher the temperature the more electrons are promoted. Valence band Conduction band e-e-e- +++ Small band gap

60. 60 Intrinsic Semiconductors Group 4A Band gap (eV) C6.0 Si1.1 Ge0.7 Gray Sn (>13 ˚C)0.1 White Sn (<13 ˚C)0 Lead0 Valence band Conduction band e-e-e- +++ Small band gap These are called INTRINSIC semiconductors

61. 61 Extrinsic Semiconductors traceConductivity controlled by a trace of dopant such as Ga (or Al) or As The dopant atom takes the place of a Si atom. Dopant atom has one fewer electrons than Si (= Ga or Al) or one more electron than Si (= As).

62. 62 Add Group 3A Atom --> p-type Semiconductor If Ga conc. is small, acceptor levels are “discrete” — not extended over the lattice. Positive holes left in valence band can move. p- type semiconductorSi + Ga (or Al) is a positive hole or p- type semiconductor.

63. 63 p-Type Semiconductor Acceptor level is slightly higher in energy than Fermi level. Electrons readily promoted into acceptor level. Valence band Conduction band e-e-e- +++ 1.1 eV Acceptor level

64. 64 n-Type Semiconductor Add As — has 5e- and so adds extra e-. Donor level has electrons. Electrons promoted from donor level to conduction band. Negative electrons are charge carriers and so called n-type. Valence band Conduction band e-e-e- 1.1 eV Donor level

65. 65 Summary Conductivity of extrinsic >> intrinsic semiconductors.Conductivity of extrinsic >> intrinsic semiconductors. Conductivity of extrinsic semiconductors can be accurately controlled.Conductivity of extrinsic semiconductors can be accurately controlled. Intrinsic semiconductors are very dependent on T and on stray impurities.Intrinsic semiconductors are very dependent on T and on stray impurities.