Molecular orbital theory describes how atomic orbitals combine to form molecular orbitals in molecules. When atoms bond, their atomic orbitals overlap and interact to form new molecular orbitals that are shared between the bonded atoms. Electrons occupy these molecular orbitals rather than the individual atomic orbitals. Molecular orbital diagrams illustrate the relative energies of the molecular orbitals and how electrons fill them according to certain rules. Molecular orbital theory can be used to explain bonding properties in diatomic and more complex polyatomic molecules.

1. Molecular Orbital Theory

8. Energy Diagram of Sigma Bond Formation by Orbital Overlap

9. sp 3 Hybrid atomic orbitals

10. sp 2 Hybrid atomic orbitals

11. sp Hybrid atomic orbitals

12. Multiple bonds with VB

13. Multiple bonds with VB

18. The He “dimer”

19. Examples of Sigma Bond Formation

20. Molecular Orbital Diagram (H 2 ) http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

21. Molecular Orbitals from p A.O.s NOTE: Symmetry is important in forming M.O. from A.O.s (LCAO)

22. Molecular Orbitals from p A.O.s

23. MO Diagram for O 2 http://www.chem.uncc.edu/faculty/murphy/1251/slides/C19b/sld027.htm

24. M.O.s from O 2  1s   1s  2s   2s  2p  2p   2p

25. Electron configurations for diatoms

26. Molecular Orbital Diagram (HF) http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

27. Valence MOs  1s F H HF          2s 2p Energy Levels in HF This diagram shows the allowed energy levels of Isolated H (1s 1 ) and F (1s 2 2s 2 2p 5 ) atoms and, between them, the HF molecule. Note: 1. F 1s is at much lower energy than H 1s (because of the higher nuclear charge) 2. F 1s 2 electrons are core electrons. Their energy does not change when HF is formed. 3. H 1s and F 2p valence electrons go into molecular orbitals with new energies. 

28.  1s F H HF          2s 2p  Molecular Orbitals in HF This core orbital is almost unchanged from the F 1s orbital. The electrons are bound tightly to the F nucleus. This non-bonding molecular orbital ( n ) has an almost spherical lobe showing only slight delocalisation between the two nuclei. Non-bonding orbitals look only slightly different to atomic orbitals, and have almost the same energy. H F n n

29. Molecular Orbitals in HF These two degenerate (filled) HOMO’s are centred on the F atom, like 2p x and 2p y orbitals. This MO, which is is like a 2p z orbital, is lower in energy in the molecule (a bonding orbital), and one lobe is delocalised around the H atom. This ( empty ) LUMO is an antibonding orbital with a node on the interatomic axis between H and F. Electrons in these two orbitals are not shared (much) by the fluorine nucleus. They behave like the 2p orbitals and are also non-bonding (n) .  1s F H HF         2p   n n   n n

31. Molecular Orbital Diagram (H 2 O)

32. The second set of combinations with  symmetry (orthogonal to the first set): This produces an MO over the molecule with a node on the bond between the F atoms. This is thus a bonding MO of  u symmetry. Molecular Orbital Theory Diatomic molecules: The bonding in F 2 2p xA + This produces an MO around both F atoms that has two nodes: one on the bond axis and one perpendicular to the bond. This is thus an antibonding MO of  g symmetry.  u =  0.5 (2p xA + 2p xB ) 2p xB -  g * =  0.5 (2p xA - 2p xB ) 2p xA 2p xB  

33. F Energy F F 2 2s 2s 2  g 2  u * 2p 2p 3  g 3  u * 1  u 1  g * Molecular Orbital Theory MO diagram for F 2 (p x ,p y ) p z You will typically see the diagrams drawn in this way. The diagram is only showing the MO’s derived from the valence electrons because the pair of MO’s from the 1s orbitals are much lower in energy and can be ignored. Although the atomic 2p orbitals are drawn like this: they are actually all the same energy and could be drawn like this: at least for two non-interacting F atoms. Notice that there is no mixing of AO’s of the same symmetry from a single F atom because there is a sufficient difference in energy between the 2s and 2p orbitals in F. Also notice that the more nodes an orbital of a given symmetry has, the higher the energy. Note: The the sake of simplicity, electrons are not shown in the atomic orbitals.

34. F Energy F F 2 2s 2s 2  g 2  u * 2p 2p 3  g 3  u * 1  u 1  g * Molecular Orbital Theory MO diagram for F 2 (p x ,p y ) p z Another key feature of such diagrams is that the  -type MO’s formed by the combinations of the p x and p y orbitals make degenerate sets (i.e. they are identical in energy). The highest occupied molecular orbitals (HOMOs) are the 1  g * pair - these correspond to some of the “lone pair” orbitals in the molecule and this is where F 2 will react as an electron donor. The lowest unoccupied molecular orbital (LUMO) is the 3  u * orbital - this is where F 2 will react as an electron acceptor. HOMO LUMO

35. B Energy B B 2 2s 2s 2  g 2  u * 2p 2p 3  g 3  u * 1  u 1  g * Molecular Orbital Theory MO diagram for B 2 ( p x ,p y ) p z In the MO diagram for B 2 , there several differences from that of F 2 . Most importantly, the ordering of the orbitals is changed because of mixing between the 2s and 2p z orbitals. From Quantum mechanics: the closer in energy a given set of orbitals of the same symmetry, the larger the amount of mixing that will happen between them. This mixing changes the energies of the MO’s that are produced. The highest occupied molecular orbitals (HOMOs) are the 1  u pair. Because the pair of orbitals is degenerate and there are only two electrons to fill, them, each MO is filled by only one electron - remember Hund’s rule. Sometimes orbitals that are only half-filled are called “singly-occupied molecular orbtials” (SOMOs). Since there are two unpaired electrons, B 2 is a paramagnetic (triplet) molecule. HOMO LUMO

36. Remember that the separation between the n s and n p orbitals increases with increasing atomic number. This means that as we go across the 2nd row of the periodic table, the amount of mixing decreases until there is no longer enough mixing to affect the ordering; this happens at O 2 . At O 2 the ordering of the 3  g and the 1  u MO’s changes. As we go to increasing atomic number, the effective nuclear charge (and electronegativity) of the atoms increases. This is why the energies of the analogous orbitals decrease from Li 2 to F 2 . The trends in bond lengths and energies can be understood from the size of each atom, the bond order and by examining the orbitals that are filled. Diatomic molecules: MO diagrams for Li 2 to F 2 Molecular Orbital Theory In this diagram, the labels are for the valence shell only - they ignore the 1s shell. They should really start at 2  g and 2  u *. 2s-2p z mixing Molecule Li 2 Be 2 B 2 C 2 N 2 O 2 F 2 Ne 2 Bond Order 1 0 1 2 3 2 1 0 Bond Length (Å) 2.67 n/a 1.59 1.24 1.01 1.21 1.42 n/a Bond Energy (kJ/mol) 105 n/a 289 609 941 494 155 n/a Diamagnetic (d)/ Paramagnetic (p) d n/a p d d p d n/a

37. More complicated molecules

38. Modern MO calculations W. Kohn (1923-) J. A. Pople (1925-2004) Nobel prize in Chemistry 1998