Molecular Geometry and Bonding Theories

1. Molecular Geometry andBonding Theories Brown, LeMay Ch 9 AP Chemistry

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 LmABn (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

3. X B |X |B Tables 9.1 - 9.3 A A

4. X B B X B : |X |B |B A A A

5. 109.5º 109.5º 109.5º 109.5º Example: CH4 Molecular shape = tetrahedral Bond angle = 109.5º H | H—C—H | H

6. B B X B X : : B X A A A A X B X B : B B B X X A X

7. : : :Cl: :Cl: \ / :Cl—P—Cl: | :Cl: : : : : : 90º 90º 120º 90º 120º PCl5 Molecular shape = trigonal bipyramidal Bond angles equatorial = 120º axial = 90º

8. X B X B A A X B | X | B : X B B - A - B B B

9. X B B X : : A A A X B : | B | X | B X : :

12. : : H-Cl: H-Cl: : : 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 d+ and d-. d+d- • Bond polarity is most often represented by an arrow that points toward the d- (most EN atom), showing the shift in e- density.

13. The dipole moment (m) 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. • Draw the true molecular geometry. • Draw each bond dipole. • Add the vectors, and draw the overall dipole moment. If none, then m = 0. m = Q r

14. Ex: Draw Lewis structures, bond dipole moments, and overall dipole moments. Also, name the e- domain geometry and the molecular geometry. CO2 BF3 H2O CCl4 NH3 PH3

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) • As 2 H atoms approach, the 2 valence e- in the 1s orbitals begin to overlap, becoming more stable. • As H-H distance approaches 0.74 Å, energy lowers b/c of electrostatic attraction between the nuclei & the incoming e-. • 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. • When H-H distance < 0.74 Å, energy increases b/c of electrostatic repulsion between 2 nuclei & between the 2 e-. Figure 9.13: Formation of bond in H2 Energy (kJ/mol) 0  -436 d a b c 0.74 Å H-H distance

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

17. “sp” hybrid orbitals • BeF2 (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: • In Be, one 2s e- is promoted to an empty 2p orbital. • The occupied s and p orbitals are hybridized (“mixed”), producing two equivalent “sp” orbitals. • 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.)

18. F F 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.

19. F F F “sp2” hybrid orbitals • BF3 (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 120º angle. B (ground) → B (promoted) → B (sp2 hybrid) 2p 2s • One s + two p → Three sp2 orbitals(to bond with 3 F’s) • A central atom with exactly 3 e- domains has sp2 hybrid orbitals.

20. H H H H “sp3” hybrid orbitals • CH4 (g): observed as tetrahedral C (ground) → C (promoted) → C (sp3 hybrid) 2p 2s • One s + three p → Four sp3 orbitals(to bond with 4 H’s) • A central atom with exactly 4 e- domains has sp3 hybrid orbitals.

21. Cl Cl Cl Cl Cl “sp3d” hybrid orbitals (or dsp3) • PCl5 (g): observed as trigonal bipyramidal; forms 5 bonds of equal energy (* but not equal length: equatorial are slightly longer) P (ground) → P (promoted) → P (sp3d hybrid) 3d 3p 3s • One s + three p + one d → Five sp3d orbitals(to bond with 5 Cl’s) • A central atom with exactly 5 e- domains has sp3d hybrid orbitals.

22. “sp3d2” hybrid orbitals (or d2sp3) • SF6 (g): observed as octahedral; forms 6 equal-length bonds • One s + three p + two d → Six sp3d2 orbitals • A central atom with exactly 6 e- domains has sp3d2 hybrids.

23. 2 bonding pairs 2 non-bonding pairs(lone pairs) H H Non-bonding e- pairs • Lone pairs occupy hybrid orbitals, too Ex: H2O (g): observed as bent; but e- domain is tetrahedral O (ground) → O (sp3 hybrid) 2p 2s • Four sp3 orbitals (2 bonding, 2 non-bonding)

24. 9.6: Multiple Bonds Draw Lewis structures. For C’s: label hybridization, molecular geometry, and unique bond angles C2H6 C2H4 C2H2 C6H6

25. Sigma and Pi bonds Sigma (s) bond: • Covalent bond that results from axial overlap of orbitals between atoms in a molecule • Lie directly on internuclear axis • “Single” bonds Ex: F2 Pi (p) 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 s bonds • Make up the 2nd and 3rd bonds in double & triple bonds. Ex: O2 N2

26. Sigma (s) bonds in C2H4 Ex: ethene; C-C and C-H s-bonds result from axial overlap of H s-orbitals and C sp2-orbitals

27. Pi (p) bonds in C2H4 • Each C has 4 valence e-: • 3 e- for 3 s-bonds • 1 e- for 1 p-bond, which results from side-by-side overlap of one non-hybridized p-orbital from each C p orbital bonds side-by-side = p bond 2p C 2s sp2 hybrids bond axially = s bonds

28. Sigma (s) bonds in C2H2 Ex: ethyne (a.k.a. acetylene) C-C and C-H s-bonds result from axial overlap of H s-orbitals and C sp-orbital

29. Pi (p) bonds in C2H2 p orbital bonds side-by-side = p bonds • Each C has 4 valence e-: • 2 e- for 2 s-bonds • 2 e- for 2 p-bonds, which result from side-by-side overlap of two non-hybridized p-orbitals from each carbon 2p C 2s sp hybrids bond axially = s bonds p

30. Sigma (s) bonds in C6H6 Ex: benzene; C-C and C-H s-bonds result from axial overlap of H s-orbitals and C sp2-orbitals

31. Localized vs. Delocalized p Bonds (localized) (delocalized)

32. Delocalized p bonds in C6H6 • C-C p-bonds result from overlap of one non-hybridized p-orbitals from each C • Delocalization of e- in p-bonds results in a “double-donut” shaped e- cloud above and below the molecular carbon plane.

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 O2. • AO are associated with the individual atoms, but MO are associated with the whole molecule.

34. *AO & MO in H2 Atomic orbitals • Combination of two 1s AO from each H forms two MO in H2 molecule. • Bonding MO: form between nuclei and are stable • Antibonding MO: marked with *; form “behind” nuclei and are less stable. Anti-bonding orbital s*1s Molecular orbitals E 1s 1s Bonding orbital s1s

35. *Types of MO • Sigma (s) MO: form from combinations of: • Two 1s or 2s orbitals from different atoms; written as s1s or s2s. • Two 2pz orbitals from different atoms (axial overlap); written as s2pz. • Pi (p) MO: form from combinations of: • Two 2px or 2py orbitals from different atoms; written as p2px or s2py. • Do not appear until B2 molecule

36. *MO diagrams for “< O2” • Resulting MO for diatomic molecules with < 16 e- (B2, C2, N2, etc.) • Bond order = ½ (# bonding e- - # antibonding e-) B.O. (N2) = ½ (10 – 4) =6 / 2 = 3 (triple bond) • N2 has no unpaired electrons which makes it diamagnetic. N atom N atom

37. *MO diagrams for “≥ O2” • Resulting MO for diatomic molecules with ≥ 16 e- (like O2, F2, Ne2, etc.) • Bond order = ½ (# bonding e- - # antibonding e-) B.O. (O2) = ½ (10 – 6) == 2 (double bond) • O2 has unpaired electrons which makes it paramagnetic. O atom O atom

38. Liquid N2 and liquid O2 • From U. Illinois: http://www.chem.uiuc.edu/clcwebsite/liquido2.html N2 O2

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: N O Sc Mn O2 • * 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”) • Nd2Fe14B is very ferromagnetic