2. Molecular Geometry and Bonding Theories Brown, LeMay Ch 9 AP Chemistry

3. 2 9.1 – 9.2: V.S.E.P.R. Valence-shell electron-pair repulsion theory Because e - pairs repel, molecular shape adjusts so the valence e - pairs are as far apart as possible around the central atom. Electron domains: areas of valence e - density around the central atom; result in different molecular shapes Includes bonding e - pairs and nonbonding e - pairs A single, double, or triple bond counts as one domain Summary of L m AB n (Tables 9.1 - 9.3): L = lone or non-bonding pairs A = central atom B = bonded atoms Bond angles notation used here: < xº means ~2-3º less than predicted << xº means ~4-6º less than predicted

4. 3 Tables 9.1 - 9.3 # of e - domains & # and type of hybrid orbitals e - domain geometry Formula & Molecular geometry Predicted bond angle(s) Example (Lewis structure with molecular shape) 2 Two sp hybrid orbitals Linear AB 2 Linear 180º BeF 2 CO 2 A |X|X X A |B|B B

5. 3 Three sp 2 hybrid orbitals Trigonal planar AB 3 Trigonal planar 120º BF 3 Cl-C-Cl < 120º Cl 2 CO LAB 2 Bent < 120º NO 2 1- A |X|X XX A |B|B BB A |B|B :B

6. 5 Example: CH 4 Molecular shape = tetrahedral Bond angle = 109.5º H | H—C—H | H 109.5º

7. 4 Four sp 3 hybrid orbitals or Tetrahedral AB 4 Tetrahedral 109.5º CH 4 LAB 3 Trigonal pyramidal < 109.5º Ex: NH 3 = 107º NH 3 L 2 AB 2 Bent <<109.5º Ex: H 2 O = 104.5º H2OH2O X A X X X X A X XX B A B BB : A B BB : A B B:

8. 7 PCl 5 Molecular shape = trigonal bipyramidal Bond angles equatorial = 120º axial = 90º :Cl: \ / :Cl—P—Cl: | :Cl: : : :: : : : 120º 90º

9. 5 Five sp 3 d hybrid orbitals Trigonal bipyramidal AB 5 Trigonal bipyramidal Equatorial = 120º Axial = 90º PCl 5 LAB 4 Seesaw Equatorial < 120º Axial < 90º SF 4 X X X A X |X|X B B B A B |B|B : B - A - B B B

10. 5 Five sp 3 d hybrid orbitals Trigonal bipyramidal L 2 AB 2 T-shaped Axial << 90º ClF 3 L 3 AB 2 Linear Axial = 180º XeF 2 X X X A X |X|X B : : A B |B|B : : : A B |B|B

11. 6 Six sp 3 d 2 hybrid orbitals Octahedral AB 6 Octahedral 90º SF 6 LAB 5 Square pyramidal < 90º BrF 5

12. 6 Six sp 3 d 2 hybrid orbitals Octahedral L 2 AB 4 Square planar 90º XeF 4 L 3 AB 3 T-shaped <90º KrCl 3 1-

13. 12 9.3: Molecular Polarity A molecule is polar if its centers of (+) and (-) charge do not coincide. A bond’s polarity is determined by the difference of EN between atoms in bond. Partial (+) and partial (-) on atoms in a polar bond can be represented as  + and  -. H-Cl: : : : :  +  - Bond polarity is most often represented by an arrow that points toward the  - (most EN atom), showing the shift in e - density.

14. 13 The dipole moment (  ) is a vector (i.e., has a specific direction) measuring the polarity of a bond which contains partial charges (Q) that are separated by a distance (r). The sum of the bond dipole moments in a molecule determines the overall polarity of the molecule. 1.Draw the true molecular geometry. 2.Draw each bond dipole. 3.Add the vectors, and draw the overall dipole moment. If none, then  = 0.  = Q r

15. Ex: Draw Lewis structures, bond dipole moments, and overall dipole moments. Also, name the e - domain geometry and the molecular geometry. CO 2 BF 3 H 2 O CCl 4 NH 3 PH 3

16. 15 9.4: Covalent Bonding and Orbital Overlap Valence-bond theory: overlap of orbitals between atoms results in a shared valence e - pair (i.e., bonding pair) Energy (kJ/mol) 0 -436 0.74 Å H-H distance Figure 9.13: Formation of bond in H 2 a.As 2 H atoms approach, the 2 valence e- in the 1s orbitals begin to overlap, becoming more stable. b.As H-H distance approaches 0.74 Å, energy lowers b/c of electrostatic attraction between the nuclei & the incoming e-. c.When H-H distance = 0.74 Å, energy is at its lowest because electrostatic attractions & repulsions are balanced. (This is the actual H-H bond distance. d.When H-H distance < 0.74 Å, energy increases b/c of electrostatic repulsion between 2 nuclei & between the 2 e-. a b c d

17. 16 9.5: Hybrid Orbital Theory Explains the relationship between overlapping orbitals (valence bond theory) and observed molecular geometries (VSEPR theory).

18. 17 “sp” hybrid orbitals BeF 2 (g): observed as a linear molecule with 2 equal-length Be-F bonds. Valence bond theory predicts that each bond is an overlap of one Be 2s e - and one 2p e - of F. However, Be’s 2s e - are already paired. So… To form 2 equal bonds with 2 F atoms: 1.In Be, one 2s e - is promoted to an empty 2p orbital. 2.The occupied s and p orbitals are hybridized (“mixed”), producing two equivalent “sp” orbitals. 3.As the two “sp” hybrid orbitals of Be overlap with two p orbitals of F, stronger bonds result than would be expected from a normal Be s and F p overlap. (This makes up for energy needed to promote the Be e - originally.)

19. Be (ground state) → Be (promoted) → Be (sp hybrid) 2p 2s Energy → Orbital “shapes” One s + one p→ Two sp orbitals (to bond with 2 F’s) A central atom in a Lewis structure with exactly 2 e - domains has sp hybrid orbitals. F

20. 19 “sp 2 ” hybrid orbitals BF 3 (g): observed as trigonal planar molecule with 3 equal- length B-F bonds. However, 2 valence e- in B are paired, and the s and p e - can’t make the observed 120 º angle. 2p 2s One s + two p→ Three sp 2 orbitals (to bond with 3 F’s) A central atom with exactly 3 e- domains has sp 2 hybrid orbitals. B (ground) → B (promoted) → B (sp 2 hybrid) F F F

21. 20 “sp 3 ” hybrid orbitals CH 4 (g): observed as tetrahedral 2p 2s One s + three p→ Four sp 3 orbitals (to bond with 4 H’s) A central atom with exactly 4 e- domains has sp 3 hybrid orbitals. C (ground) → C (promoted) → C (sp 3 hybrid) H H

22. 21 “sp 3 d” hybrid orbitals (or dsp 3 ) PCl 5 (g): observed as trigonal bipyramidal; forms 5 bonds of equal energy (* but not equal length: equatorial are slightly longer) 3d 3p 3s One s + three p + one d → Five sp 3 d orbitals (to bond with 5 Cl’s) A central atom with exactly 5 e- domains has sp 3 d hybrid orbitals. P (ground) → P (promoted) → P (sp 3 d hybrid) Cl Cl Cl Cl Cl

23. 22 “sp 3 d 2 ” hybrid orbitals (or d 2 sp 3 ) SF 6 (g): observed as octahedral; forms 6 equal-length bonds One s + three p + two d → Six sp 3 d 2 orbitals A central atom with exactly 6 e- domains has sp 3 d 2 hybrids.

24. 23 Non-bonding e- pairs Lone pairs occupy hybrid orbitals, too Ex: H 2 O (g): observed as bent; but e- domain is tetrahedral 2p 2s Four sp 3 orbitals (2 bonding, 2 non-bonding) O (ground) →O (sp 3 hybrid) 2 non-bonding pairs (lone pairs) 2 bonding pairs H

25. 24 9.6: Multiple Bonds Draw Lewis structures. For C’s: label hybridization, molecular geometry, and unique bond angles C 2 H 6 C 2 H 4 C 2 H 2 C 6 H 6

26. 25 Sigma and Pi bonds Sigma (  ) bond: Covalent bond that results from axial overlap of orbitals between atoms in a molecule Lie directly on internuclear axis “Single” bonds Ex: F 2 Pi (  ) bond: Covalent bond that results from side-by-side overlap of orbitals between atoms in a molecule. Are “above & below” and “left & right” of the internuclear axis and therefore have less total orbital overlap, so they are weaker than  bonds Make up the 2 nd and 3 rd bonds in double & triple bonds. Ex: O 2 N 2

27. 26 Sigma (  ) bonds in C 2 H 4 Ex: ethene; C-C and C-H  -bonds result from axial overlap of H s-orbitals and C sp 2 -orbitals

28. 27 Pi (  ) bonds in C 2 H 4 Each C has 4 valence e - : 3 e - for 3  bonds 1 e - for 1  bond, which results from side-by-side overlap of one non-hybridized p-orbital from each C 2p C 2s sp 2 hybrids bond axially =  bonds p orbital bonds side- by-side =  bond

29. 28 Sigma (  ) bonds in C 2 H 2 Ex: ethyne (a.k.a. acetylene) C-C and C-H  -bonds result from axial overlap of H s-orbitals and C sp-orbital

30. 29 Pi (  ) bonds in C 2 H 2 Each C has 4 valence e - : 2 e - for 2  bonds 2 e - for 2  bonds, which result from side-by-side overlap of two non-hybridized p-orbitals from each carbon sp hybrids bond axially =  bonds 2p C 2s p orbital bonds side- by-side =  bonds 

31. 30 Sigma (  ) bonds in C 6 H 6 Ex: benzene; C-C and C-H  -bonds result from axial overlap of H s-orbitals and C sp 2 -orbitals

32. 31 Localized vs. Delocalized  Bonds (localized)(delocalized)

33. 32 Delocalized  bonds in C 6 H 6 C-C  -bonds result from overlap of one non-hybridized p-orbitals from each C Delocalization of e - in  -bonds results in a “double-donut” shaped e - cloud above and below the molecular carbon plane.

34. 33 9.7: Molecular Orbital (MO) theory So far we have used valence-bond theory (covalent bonds form from overlapping orbitals between atoms) with hybrid orbital theory and VSEPR theory to connect Lewis structures to observed molecular geometries. MO theory is similar to atomic orbital (AO) theory (s, p, d, f orbitals) and helps to further explain some observed phenomena, like unpredicted magnetic properties in molecules like those in O 2. AO are associated with the individual atoms, but MO are associated with the whole molecule.

35. Combination of two 1s AO from each H forms two MO in H 2 molecule. Bonding MO: form between nuclei and are stable Antibonding MO: marked with *; form “behind” nuclei and are less stable. 1s Molecular orbitals E  1s  * 1s *AO & MO in H 2 Atomic orbitals Bonding orbital Anti-bonding orbital

36. 35 *Types of MO Sigma (  ) MO: form from combinations of: Two 1s or 2s orbitals from different atoms; written as  1s or  2s. Two 2p z orbitals from different atoms (axial overlap); written as  2p z. Pi (  ) MO: form from combinations of: Two 2p x or 2p y orbitals from different atoms; written as  2p x or  2p y. Do not appear until B 2 molecule

37. 36 *MO diagrams for “< O 2 ” Bond order = ½ (# bonding e - - # antibonding e - ) B.O. (N 2 ) = ½ (10 – 4) = 6 / 2 = 3 (triple bond) N 2 has no unpaired electrons which makes it diamagnetic. Resulting MO for diatomic molecules with < 16 e- (B 2, C 2, N 2, etc.) N atom

38. 37 *MO diagrams for “≥ O 2 ” Resulting MO for diatomic molecules with ≥ 16 e- (like O 2, F 2, Ne 2, etc.) O atom Bond order = ½ (# bonding e - - # antibonding e - ) B.O. (O 2 ) = ½ (10 – 6) = = 2 (double bond) O 2 has unpaired electrons which makes it paramagnetic.

39. 38 Liquid N 2 and liquid O 2 From U. Illinois: http://www.chem.uiuc.edu/clcwebsite/liquido2.html N2N2 O2O2

40. 39 Magnetism In an element or compound: Diamagnetism: all e - paired; no magnetic properties Paramagnetism: at least 1 unpaired e - * Drawn into exterior magnetic field since spins of atoms become aligned; unlikely to retain alignment when field is removed Ex:NO ScMn O 2 * Ferromagnetism: occurs primarily in Fe, Co, Ni Drawn into exterior magnetic field since spins of atoms become aligned; very likely to retain alignment when field is removed (i.e., “a permanent magnet”) Nd 2 Fe 14 B is very ferromagnetic