1. Molecular Orbital Theory Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

2. A Little Review What is an orbital? What is the maximum number of electrons that can be in one orbital? What is the name of the mathematical function that determines the shape of an orbital? Give an example of an atomic orbital?

3. 7/13/2015 Molecular Orbitals When two atoms come close to each other, what happens to the orbitals of each atom? a bond forms 1s atomic orbital 1s atomic orbital  s b molecular orbital sigma s bonding molecular orbital

4. 7/13/2015 Molecular Orbitals Orbital wave functions can add & subtract to give new wave functions and corresponding molecular orbitals (mo). Atoms bond together when the wave functions constructively overlap.

5. 7/13/2015 SIGMA BOND (  ) A bond between two atoms in which the electron density of the molecular orbital is between the two nuclei is called a sigma bond. (  s b ) 2 molecular orbital nuclei

6. 7/13/2015 Molecular Orbital Theory Atomic orbitals can mix together to give a new set of molecular orbitals. Similarities of atomic & molecular orbitals 2 electrons max/orbital occupy specific regions of space One molecular orbital is formed for each atomic orbital used

7. 7/13/2015 Orbitals Are Wave Functions Wave functions contain mathematical terms that can have positive and negative values. An s orbital value can either be less than zero or greater than zero. The two lobes of a p orbital are separated by a node and have opposite signs.

8. 7/13/2015 Orbitals Are Wave Functions Different colors represent opposite mathematical signs.

9. 7/13/2015 Sigma Bond Formation z p z - p z Orbital Overlap

10. 7/13/2015 Sigma Bonds z p z - p z Orbital OverlapResulting Molecular Orbital (zb)(zb)

11. 7/13/2015 Sigma Antibond Formation z p z - p z Orbital Overlap

12. 7/13/2015 z Sigma Antibond Formation p z - p z Orbital Overlap (z*)(z*) Resulting Antibonding Molecular Orbital

13. 7/13/2015 Sigma Bonds  indicates the most probable electron position is on the internuclear axis (zb)(zb) (z*)(z*) b indicates a bonding molecular orbital z indicates the molecular orbital involves two p z atomic orbitals * indicates an antibonding molecular orbital Electrons in this orbital will weaken the bonds between these atoms.

14. 7/13/2015 Sigma Bonds z s indicates the molecular orbital involves at least one s atomic orbital. (sb)(sb) (s*)(s*)

15. 7/13/2015 Pi Bond Formation z y p y - p y Orbital Overlap A pi bond (  ) occurs when two lobes of each atomic orbital overlap.

16. 7/13/2015 Pi Bond Formation z y z y p y - p y Orbital Overlap Resulting Bonding Molecular Orbital y The molecular orbital does not lie directly on the internuclear axis.

17.  Antibond Formation What is the symbol of a  antibond? What does a  antibond look like? How is a  antibond formed?

18. 7/13/2015 Pi Antibond Formation z y p y - p y Antibond Orbital Overlap Resulting Antibonding Molecular Orbital z y

19. 7/13/2015 Pi Bonds ybyb  y b bonding orbital has two lobes and holds a maximum of two electrons. y*y*  y * bonding orbital has four lobes and holds a maximum of two electrons.

20. 7/13/2015 Pi Bonding Involving P x Orbitals x x p x - p x Orbital Overlap Resulting Bonding Molecular Orbital xbxb

21. 7/13/2015 Pi Bonding Involving P x Orbitals p x - p x Antibonding Orbital Overlap Resulting Antibonding Molecular Orbital xx x*x*

22. 7/13/2015 Pi Bonding Involving p Orbitals 2p p x -p x overlap gives  x b and  x * p y -p y overlap gives  y b and  y * From the mo diagram, how can you determine that  x b and  y b are equally stable? x z yy Why are  x b and  y b equally stable?

23. 7/13/2015 Molecular Orbital Diagrams Involving s and p Orbitals energy 2s 1s 2p overlap direction energy The molecular orbitals formed depend on the atomic orbitals’

24. 7/13/2015 Molecular Orbital Diagrams Involving s and p Orbitals 2s 1s 2p Bonding molecular orbitals Antibonding molecular orbitals Nonbonding molecular orbitals Sigma bonds and antibonds Pi bonds and antibonds Identify the orbitals that represent the following Weak p z -s mo interaction Homonuclear examples: O 2, F 2

25. 7/13/2015 Diatomic Molecular Orbital Diagram Strong p z -s interaction energy 2s 1s 2p Homonuclear Examples: Li 2, B 2, C 2, N 2 Heteronuclear Examples: NO, BO, BO +, CO, CO +, CN, CN –

26. 7/13/2015 Homonuclear Diatomic Molecules  Determine is the sequence of molecular orbitals based on the strong p z -s interaction diagram.  Determine the bond order and magnetic properties for homodiatomic molecules of the first nine elements.  Show the bond lengths are consistent with these diagrams.

27. 7/13/2015 Orbital Sequence energy 2s 1s 2p snsn sbsb s*s*  x,y b zbzb x,y*x,y* z*z* (sn)(sn) (sb)(sb)(s*)(s*)(  x,y b )(zb)(zb)(x,y*)(x,y*)(z*)(z*)

28. 7/13/2015 Complete the mo diagram for Li 2, Be 2, B 2, C 2 or N 2 Dilithium (6 total e – ) Bond Order and Magnetic Properties? Diberyllium (8 total e – ) Bond Order and Magnetic Properties? Diboron (10 total e – ) Bond Order and Magnetic Properties? Dicarbon (12 total e – ) Bond Order and Magnetic Properties? Dinitrogen (14 total e – ) energy 2s 1s 2p snsn sbsb s*s*  x,y b zbzb x,y*x,y* z*z* Bond Order and Magnetic Properties? First, fill in the valence electrons. Then, fill in the mo diagram

29. 7/13/2015 Compare the bond order, bond length and magnetic properties of O 2, O 2 +, O 2 – and O 2 2– energy 2s 1s 2p snsn sbsb s*s*  x,y b x,y*x,y* z*z* zbzb O2O2 O2+O2+ O2–O2– O 2 2– 1.207 Å properties? 1.123 Å properties? 1.26 Å properties? 1.49 Å properties?

30. Dioxygen What are the advantages and disadvantages of this description of dioxygen? O O

31. 7/13/2015 Compare the physical properties predicted for Dioxygen by the Lewis Dot Diagram and MO Theory Bond OrderMagnetic Properties Lewis Dot Structure Molecular Orbital Theory 2? (diamagnetic) 2 paramagnetic 2 unpaired electrons O O Liquid dioxygen will cling to the pole of a magnet.

32. 7/13/2015 Compare the physical properties for the Dioxygenyl(I) Ion, Dioxygen, Superoxide Ion and Peroxide Ion Bond Length Bond Order O2+O2+ O2O2 O2–O2– O22–O22– 1.123 Å 1.207 1.26 1.49 2.5 2 1.5 1 Magnetic Properties paramagnetic (1) paramagnetic (2) paramagnetic (1) diamagnetic

33. Oxygen-Oxygen Bonds Which oxygen-oxygen bond is easier to break? O O H O HO

34. 7/13/2015 Difluorine (18 total e – ) Bond Order and Magnetic Properties? Dineon (20 total e – ) energy 2s 1s 2p snsn sbsb s*s*  x,y b x,y*x,y* z*z* zbzb Bond Order and Magnetic Properties?

35. 7/13/2015 Homodiatomic Molecules Electronic Configuration H2H2 He 2 Li 2 Be 2 B2B2 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x b ) 1 (  y b ) 1 (   s n ) 4 (  s b ) 2 (  s *) 2 (   s n ) 4 (  s b ) 2 (  s b ) 2 (  s *) 2 (sb)2(sb)2 bond length (Å) magnetic properties 0.74 2.67 1.59 diamagnetic paramagnetic bond order 1 0 1 0 1

36. 7/13/2015 Homodiatomic Molecules Electronic Configuration C2C2 N2N2 O2O2 F2F2 Ne 2 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x,y b ) 4 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x,y b ) 4 (  z b ) 2 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x,y b ) 4 (  z b ) 2 (  x *) 1 (  y *) 1 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x,y b ) 4 (  z b ) 2 (  x,y *) 4 (   s n ) 4 (  s b ) 2 (  s *) 2 (  x,y b ) 4 (  z b ) 2 (  x,y *) 4 (  z *) 2

37. 7/13/2015 Homodiatomic Molecules C2C2 N2N2 O2O2 F2F2 Ne 2 bond length (Å) magnetic properties 1.31 1.207 diamagnetic paramagnetic bond order 2 3 2 1 0 diamagnetic 1.10 1.42

38. 7/13/2015 Skeleton Diagram Failures Carbon Monoxide C O C O or How would the hybridization of the atoms in carbon monoxide be described?

39. 7/13/2015 energy CO C O

40. 7/13/2015 Carbon Monoxide Sigma orbital overlaps of CO. + -+-+ + ++++ + -+-+ - ++-- - -++- - -++- - -++- + -+-+

41. Is the HOMO of carbon monoxide bonding, nonbonding or antibonding? CO1.1282 Å CO + 1.1151 Å

42. 7/13/2015 energy CO C O Where on carbon monoxide is the HOMO located?

43. Species containing three or more atoms

44. 7/13/2015 Beryllium Hydride Draw the orbital overlaps of BeH 2. Rank the orbitals in terms of energy. + + + + + - - - + + - + + - Draw a molecular orbital diagram of BeH 2. (draw the nodes in each diagram)

45. 7/13/2015 energy BeH 2 Be 2 H Sigma (  ) bonds form orbitals are conserved two bonds are formed all e - are paired

46. 7/13/2015 Draw the molecular orbital diagram for the nitrate ion. What is the hybridization of nitrogen? How many atomic orbitals are there? How many p-  orbitals are there? How are the energies of the p-  orbitals going to split? How many nonbonding orbitals are expected?

47. 7/13/2015 Nitrate Ion N O O O N O O O N O O O The double bond is delocalized over the three nitrogen-oxygen bonds. Bond order = 1.33 +++

48. 7/13/2015 Nitrate Ion The nitrogen-oxygen bond length is intermediate between N-O and N=O. typical N-O bond length: 1.40 Å typical N=O bond length: 1.21 Å - N O O O 1.22 Å What is the hybridization of nitrogen? How do the orbitals of the atoms in nitrate overlap?

49. 7/13/2015 Nitrate Ion Top down view (xz plane) The nitrogen atom in nitrate ion is sp 2 hybridized and overlaps a p z orbital on each oxygen. three N - O sigma bonds N O O O +

50. 7/13/2015 Nitrate Ion Top down view (xz plane) If you don’t believe in hybridization. three N - O sigma bonds N O O O + How does the double bond form?

51. 7/13/2015 Nitrate Ion Edge on view N O O O pi overlap involves the nitrogen p y orbital with all three oxygen p y orbitals to form one pi bond the oxygen orbitals with single electrons change from one oxygen atom to another + y

52. 7/13/2015 Nitrate Ion Edge on view one N - O pi bond delocalized over three oxygen atoms this hybridization requires that the nitrate ion is planar What would the p y -orbitals look like if all four atoms in this ion were not planar? y

53. 7/13/2015 Nitrate Ion Edge on view one N - O pi bond delocalized over three oxygen atoms if nitrate ion wasn’t planar What would the p y -orbitals look like if all four atoms in this ion were not planar? y

54. energy 3 ONNO 3 -

55. Sigma Bonding Patterns Nitrogen s, p x and p y orbitals overlap with oxygen.

56. energy 3 ONNO 3 -

57. How are the energies of the p-  orbitals going to split?

58. energy 3 ONNO 3 -

59. 7/13/2015

61. energy CO C O

62. energy OOON