1. MOLECULAR STRUCTURE CHAPTER 14 Experiments show O 2 is paramagnetic

2. Objectives: Extend atomic concepts to electronic structures of molecules Utilize two quantum mechanical theories of molecular electronic structure Valence bond theory Bonding as a result of a shared electron pair between two atoms Molecular orbital theory Concept of atomic orbital extended to molecular orbital Molecular orbital is a wavefunction spread over entire molecule

3. Hybridization – mixing of two or more atomic orbitals to form a new set of hybrid orbitals. 1.Mix at least 2 nonequivalent atomic orbitals (e.g. s and p). Hybrid orbitals have very different shape from original atomic orbitals. 2.Number of hybrid orbitals is equal to number of pure atomic orbitals used in the hybridization process. 3.Covalent bonds are formed by: a.Overlap of hybrid orbitals with atomic orbitals or b.Overlap of hybrid orbitals with other hybrid orbitals

4. Fig 11.7 An sp 3 orbital formed from superposition of s and three p orbitals on same atom Four LCAOs give four equivalent hybrid MOs: h 1 = s + p x + p y + p z h 2 = s - p x - p y + p z h 3 = s - p x + p y - p z h 4 = s + p x - p y - p z

5. Fig 11.8 Each sp 3 hybrid orbital forms a σ bond by overlap with an H 1s orbital 109.5° e.g., wavefunction for overlap of hybrid h 1 and H 1s: Ψ = h 1 (1)A(2)+ h 1 (2)A(1)

6. Fig 11.9 More detailed representation of formation of an sp 3 hybrid orbital

7. Fig 11.10 An sp 2 orbital formed from superposition of s and two p orbitals on same atom Three LCAOs give three equivalent hybrid MOs: h 1 = s + √ 1/2 p y h 2 = s + √ 3/2 p x - √ 1/2 p y h 3 = s - √ 3/2 p x - √ 1/2 p y Remaining unhybridized p orbital

8. Fig 11.11 Representation of double bond in C 2 H 4

9. Fig 11.12 Representation of triple bond in C 2 H 2

10. # of Lone Pairs + # of Bonded Atoms HybridizationExamples 2 3 4 5 6 sp sp 2 sp 3 sp 3 d sp 3 d 2 BeCl 2 BF 3 CH 4, NH 3, H 2 O PCl 5 SF 6 How do I predict the hybridization of the central atom? Count the number of lone pairs AND the number of atoms bonded to the central atom

12. Summary of Valence Bond Theory Developed substantially by Linus Pauling (1935) Bonding pair of electrons localized between two atoms Includes concepts of σ and π bonds and hybridization Discrepancies between theoretical and observed bond angles (e.g., H 2 O and NH 3 ) Does not address magnetic properties of molecules

13. Molecular Orbital Theory Developed much more fully than VB theory Concept of atomic orbital extended to molecular orbital Molecular orbital is a wavefunction spread over entire molecule Bonding pair of electrons delocalized over entire molecule Includes concepts of σ and π bonds, bond order, anti-bonding orbitals, and resonance Allows prediction of magnetic properties of molecules

14. Born-Oppenheimer approximation The nuclei are relatively massive and may be treated as stationary while the electrons move in their field.

15. The hydrogen molecule-ion, H 2 + where:

16. Fig 11.13 (a) Amplitude of bonding MO in H 2 + A B Fig 11.13 (b) Contour rep of the amplitude Ψ ± = N(A ± B) Electron may be found in AO on atom A and in AO atom B, then overall Ψ ± is a superposition of both AOs:

17. Fig 11.14 General shape of the boundary surface of a σ orbital

18. Fig 11.15 General shape of the boundary surface of a σ orbital Probability density: Ψ 2 + = N 2 (A 2 + 2AB + B 2 ) Constructive: Ψ + = N(A + B) Overlap density

19. Fig 11.16 Calculated and experimental molecular potential energy curves for H 2 +

20. Fig 11.17 Constructive interference when two H1s orbitals overlap to form a σ orbital Superposition: Ψ ± = N(A ± B) Constructive: Ψ + = N(A + B)

21. Fig 11.18 Destructive interference when two H1s orbitals overlap to form a σ * orbital Superposition: Ψ ± = N(A ± B) Destructive: Ψ - = N(A - B) Probability density: Ψ 2 - = N 2 (A 2 - 2AB + B 2 ) node

22. Fig 11.19 (a) Amplitude of antibonding MO in H 2 + Fig 11.19 (b) Contour rep of the amplitude

23. Fig 11.20 General shape of the boundary surface of a σ * orbital Destructive: Ψ - = N(A - B) Probability density: Ψ 2 - = N 2 (A 2 - 2AB + B 2 )

24. Fig 11.21 Partial explanation of the origin of bonding and antibonding effects σ σ*σ*

25. Fig 11.23 MO energy level diagram for H 2 constructed from overlap of H1s orbitals D o = 7.18 x 10 -19 J = 36,130 cm -1

26. Fig 11.24 MO energy level diagram for He 2 constructed from overlap of H1s orbitals Bond order: b = ½(n – n*)