Molecular Orbital Theory

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

2. Bonding Theories • Ionic Model • Skeleton Diagrams • Lewis Dot Diagrams • Formal Charge, Resonance • Molecular Orbital Theory • Extends atomic orbitals concepts to molecules

3. • • • • • • • • • • • A+ B C D • • • • • • • • • • • Ionic bonding Covalent bonding Bonding in Diatomic Molecules Diatomic: molecule contains two atoms large difference in electronegativity small difference in electronegativity Give an example of a compound with ionic bonding.

4. • • • • • • • A A • • • • • • • Homodiatomic Molecules The best example of covalent bonding involves homodiatomic molecules. Contains two of the same type of atom. e.g., H2, O2, F2, N2 Why are these molecules the best examples of covalent bonding?

5. positive end negative end Heterodiatomic Molecules HF, BN and CO are heterodiatomic molecules. Contain two different atoms. H - F These molecules are polar covalent. What factors might help predict the positive and negative ends of the molecule?

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

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

8. 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.

9. nuclei SIGMA BOND (s) A bond between two atoms in which the electron density of the molecular orbital is between the two nuclei is called a sigma bond. (ssb)2 molecular orbital

10. Molecular Orbitals (mo) • Obey many of the same rules as atomic orbitals (ao). • two electrons per molecular orbital. • specific regions of space. • one molecular orbital formed for each atomic orbital used.

11. Wave Functions The amplitude (height) of each wavefunction can either be positive or negative.

12. WavefunctionsBonding & Antibonding Orbitals sb Constructively interfere in certain regions of space. s* Destructively interfere in certain regions of space.

13. ssb H H ss* Bonding & Antibonding Orbitals When a bonding molecular orbital forms, an antibonding molecular orbital also forms. Bonds form where orbitals overlap and electrons are.

14. z y x Atomic and Molecular Orbitals Atomic orbitals include 3dz2 2py 1s

15. y x px* Atomic and Molecular Orbitals Molecular orbitals include z ssb sz*

16. Atomic and Molecular Orbitals This represents an orbital

17. energy Atomic and Molecular Orbitals carbon: 1s2 2s2 2p2 An orbital can be empty or can contain 1 or 2 electrons. Orbitals can have different energies

18. Molecular Orbital Diagrams • Examples • dihydrogen • dihelium • dihelium(I) ion

19. H H energy H H Dihydrogen, H2 ss* ssb The branch lines indicate which atomic orbitals are involved in generating the molecular orbitals. Two 1s1hydrogen orbitals overlap to form assb bonding molecular orbital 1s1 hydrogen orbital of two hydrogen atoms

20. ss* H H energy Dihydrogen is diamagnetic and contains onebond (one pair of bonding electrons). ssb ao mo ao (ssb)2 electronic configuration of the hydrogen molecule. Dihydrogen, H2 What advantage can an orbital gain in forming a molecular orbital from an atomic orbital? Why is dihydrogen diamagnetic?

21. energy atomic orbital of one He atom atomic orbital of the other He atom Dihelium, He2 Two electrons occupy the highest molecular orbital forming a ss* ss* Each helium atom has the electronic configuration 1s2 (eachcontributes 2 electrons to the helium molecular orbitals) Two electrons occupy the lowest molecular orbital forming a ssb ssb

22. ss* energy ssb Dihelium, He2 Why doesn’t He2 exist as a stable molecule? The electronic configuration of the dihelium molecule is (ssb)2 (ss*)2

23. He He He energy He+ Dihelium(I) Ion, He2+ ss* ssb How many valence electrons must be considered in the dihelium(I) ion? Complete the molecular orbital diagram using the available electrons.

24. He energy He+ Dihelium(I) Ion, He2+ These represent the atomic orbitals. ss* ssb Shaded means 2 electrons Lined means 1

25. He energy He+ Dihelium(I) Ion, He2+ ss* ssb Draw an outline of the molecular orbitals. Fill-in the molecular orbitals, shaded for 2 electrons, lined for 1.

26. ss* energy ssb Dihelium(I) Ion, He2+ What physical properties are predicted for the dihelium(I) ion? (magnetic and bond order)

27. 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.

28. Orbitals Are Wave Functions Different colors represent opposite mathematical signs.

29. Pi Bond Formation y A pi bond (p) occurs when two lobes of each atomic orbital overlap. z py- py Orbital Overlap

30. y z Pi Bond Formation The molecular orbital does not lie directly on the internuclear axis. y y z Resulting Bonding Molecular Orbital py- py Orbital Overlap

31. p Antibond Formation • What is the symbol of a p antibond? • How is a p antibond formed? • What does a p antibond look like?

32. y z Resulting Antibonding Molecular Orbital Pi Antibond Formation y z py- py Antibond Orbital Overlap

33. py* pyb Pi Bonds py* bonding orbital has four lobes and holds a maximum of two electrons. pyb bonding orbital has two lobes and holds a maximum of two electrons.

34. x Pi Bonding Involving Px Orbitals x pxb Resulting Bonding Molecular Orbital px- px Orbital Overlap

35. x x Pi Bonding Involving Px Orbitals px* Resulting Antibonding Molecular Orbital px- px Antibonding Orbital Overlap

36. y y 2p x z Pi Bonding Involving p Orbitals px-px overlap gives pxband px* py-py overlap gives pyband py* From the mo diagram, how can you determine that pxband pyb are equally stable? Why are pxband pybequally stable?

37. 2p energy 2s 1s Molecular Orbital DiagramsInvolving s and p Orbitals The molecular orbitals formed depend on the atomic orbitals’ overlap direction energy

38. 2p 2s 1s Molecular Orbital DiagramsInvolving s and p Orbitals Identify the orbitals that represent the following Nonbonding molecular orbitals Antibonding molecular orbitals Pi bonds and antibonds Bonding molecular orbitals Sigma bonds and antibonds Weak pz-s mo interaction Homonuclear examples: O2, F2

39. 2p energy 2s 1s Diatomic Molecular Orbital DiagramStrong pz-s interaction Homonuclear Examples: Li2, B2, C2, N2 Heteronuclear Examples: NO, BO, BO+, CO, CO+, CN, CN–

40. Homonuclear Diatomic Molecules • Determine is the sequence of molecular orbitals based on the strong pz-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.

41. 2p energy 2s 1s Orbital Sequence (ssn) (ssb) (ss*) (px,yb) (szb) (px,y*) (sz*) sz* px,y* szb px,yb ss* ssb ssn

42. Dinitrogen (14 total e–) Diboron (10 total e–) Dicarbon (12 total e–) Diberyllium (8 total e–) Dilithium (6 total e–) sz* px,y* energy 2p szb px,yb ss* ssb 2s ssn 1s Complete the mo diagram for Li2, Be2, B2, C2 or N2 Bond Order and Magnetic Properties? Bond Order and Magnetic Properties? Bond Order and Magnetic Properties? Bond Order and Magnetic Properties? Bond Order and Magnetic Properties? First, fill in the valence electrons. Then, fill in the mo diagram

43. sz* px,y* energy 2p px,yb szb ss* 1.123 Å 1.207 Å 1.26 Å 1.49 Å 2s properties? properties? properties? properties? ssb ssn 1s Compare the bond order, bond length and magnetic properties of O2, O2+, O2–and O22– O2 O2– O2+ O22–

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

45. • • • • • • O O • • Lewis Dot • • • • Structure Molecular paramagnetic Orbital 2 unpaired electrons Theory Compare the physical properties predicted for Dioxygen by the Lewis Dot Diagram and MO Theory Bond Order Magnetic Properties 2 ? (diamagnetic) 2 Liquid dioxygen will cling to the pole of a magnet.

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

47. H O H O O O • • • • • • • • • • • • • • • • Oxygen-Oxygen Bonds Which oxygen-oxygen bond is easier to break?

48. Difluorine (18 total e–) Dineon (20 total e–) sz* px,y* energy 2p px,yb szb ss* 2s ssb ssn 1s Bond Order and Magnetic Properties? Bond Order and Magnetic Properties?

49. 1 diamagnetic 0 1 diamagnetic 0 1 paramagnetic Homodiatomic Molecules bond length (Å) magnetic properties bond order Electronic Configuration H2 (ssb)2 0.74 He2 (ssb)2 (ss*)2 Li2 (s1sn)4 (ssb)2 2.67 Be2 (s1sn)4 (ssb)2 (ss*)2 B2 (s1sn)4 (ssb)2 (ss*)2 (pxb)1 (pyb)1 1.59

50. Homodiatomic Molecules Electronic Configuration (s1sn)4(ssb)2(ss*)2(px,yb)4 C2 N2 (s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 O2 (s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px*)1 (py*)1 F2 (s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px,y*)4 Ne2 (s1sn)4 (ssb)2 (ss*)2 (px,yb)4 (szb)2 (px,y*)4 (sz*)2