1. Chem 125 Lecture 15 10/8/08 This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed further. It is not readily understood without reference to notes from the lecture.

2. Perspectives: Molecule (Reality) Computer (Approximate Schroedinger) Chemist (Understand Bonds)

3. Missing Bond ? (e.g. 32 nd of 33 occupied MOs) Cf. Lecture 7 - Dunitz et al. (1981) Experiment: Pathological Bonding Bent Bonds ? Would a Computer’s MOs Provide Understanding? No! Far too complicated to answer “Why?”

4. But analysis in terms of pairwise bonding overlap of hybrid AOs provides clear explanations. Experiment: Pathological Bonding Missing Bond ? Bent Bonds ? Best Overlap Possible for 60° C-C-C  Very Poor Overlap >90°? p sp 4.1 sp 1.4 Because sp 4.1 extends to give best overlap Why not p orbitals (90°) ? Rehybridizing to strengthen this bond would weaken six others.

5. Three Views of BH 3 2) Molecular Orbitals 1) Total Electron Density 3) Bonds from Hybrid AOs (Nature) (Computer) (Student)

6. B H H H Electron Cloud of by "Spartan"

7. BH 3 Total e-Density 0.30 e/Å 3 Mostly 1s Core of Boron B H H H

8. BH 3 Total e-Density 0.15 e/Å 3

9. BH 3 Total e-Density (0.05 e/Å 3 ) Dimple H atoms take e-density from valence orbitals of B B H + H B

10. BH 3 Total e-Density 0.02 e/Å 3

11. BH 3 Total e-Density 0.002 e/Å 3 van der Waals surface (definition)

12. BH 3 Total e-Density 0.002 e/Å 3 Electrostatic Potential Energy of a + probe on the surface low (-) high (+) H  

13. Computer Partitions Total e-Density into Symmetrical MOs (à la Chladni)

14. BH 3 8 low-energy AOs  8 low-energy MOs B : 1s, 2s, 2p x, 2p y, 2p z 3  H : 1s AO “basis” set MOLECULAR ORBITALS

15. noccupiednoccupied BH 3 8 electrons / 4 pairs B : 5 electrons 3  H : 3  1 electron OMO s UMO s LUMOHOMO( s) ccupiedccupied ighestighest owestowest MOLECULAR ORBITALS

16. 1s 1s Boron Core MOLECULAR ORBITALS

17. 2s Radial Node MOLECULAR ORBITALS

18. 2p x MOLECULAR ORBITALS

19. 2p y MOLECULAR ORBITALS

20. 2p z MOLECULAR ORBITALS

21. 3s MOLECULAR ORBITALS

22. 3d x 2 - y 2 MOLECULAR ORBITALS

23. 3d xy MOLECULAR ORBITALS

24. We Partition Total e-Density into Atom-Pair Bonds (and anti-bonds) & Lone Pairs (and vacant atomic orbitals) (à la Lewis) usually  When this doesn't work, and we must use more sophisticated orbitals, we say there is RESONANCE

25. 2p z   B H H B Same Total e-Density! Same Total Energy!    B H H B For Many Purposes Localized Bond Orbitals are Not Bad Boron Core And they are easy to think about; but beware of resonance.

26. The Localized Bond Orbital Picture (Pairwise MOs and Isolated AOs) is our intermediate between H-like AOs and Computer MOs When must we think more deeply? When mixing of localized orbitals causes Reactivity or Resonance

27. Where are We? Molecules Plum-Pudding Molecules ("United Atom" Limit) Understanding Bonds (Pairwise LCAO) "Energy-Match & Overlap" Structure (and Dynamics) of XH 3 Molecules Parsing Electron Density Atoms 3-Dimensional Reality (H-like Atoms) Hybridization Orbitals for Many-Electron Atoms (Wrong!) Recovering from the Orbital Approximation Recognizing Functional Groups Payoff for Organic Chemistry! Reactivity SOMOs, high HOMOs, and low LUMOs

28. Which MO Mixings Matter for Reactivity? etc. etc. UMOs OMOs B A UMOs Myriad Possible Pairwise Mixings  molecule

29. Which MO Mixings Matter for Reactivity? etc. etc. UMOs OMOs SOMO B A SOMO-SOMO (when they exist) UMOs many atoms "free radicals" e.g. H Cl CH 3  not so common inglyingly molecule

30. Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Nothing Weak Net Repulsion Negligible Mixing because of Bad E-match molecule

31. Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Bonding! Unusually High HOMO with Unusually Low LUMO molecule Negligible Mixing because of Bad E-match

32. Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Bonding! Unusually High HOMO with Unusually Low LUMO BASE ACID molecule

33. Most mixing of MOs affects neither overall energy nor overall electron distribution for one (or more) of these reasons: 1) Electron occupancy 4 or 0 2) Poor energy match 3) Poor overlap BUT

34. High HOMO- Low LUMO mixing constitutes Reactivity

35. Acid-Base Theories THEORYACIDBASE Lavoisier (1789) Oxidized Substance Substance to be Oxidized Arrhenius (1887) H + SourceOH - Source Increasing Generality Brønsted/Lowry (1923) H + DonorH + Acceptor Lewis (1923) e-Pair Acceptor "Electrophile" e-Pair Donor "Nucleophile" HOMO/LUMO (1960s) unusually High HOMO unusually Low LUMO

36. sp 3 C 1s H Unusual: Compared to What?  * CH  CH "usual" LUMO "usual" HOMO (or  * CC ) (or  CC ) I. Unmixed Valence-Shell AOs III. Unusual AO Energy in MO Sources of weirdness: IV. Electrical Charge II. Poor Overlap of AOs

37. I. Unmixed Valence-Shell Atomic Orbitals  * CH  CH sp 3 C 1s H BH 3 low LUMO CH 3 high HOMO NH 3 high HOMO "usual" LUMO "usual" HOMO OH 2 high HOMO OH high HOMO (or  * CC ) (or  CC ) H + low “LUMO” (energies qualitative only) (Also IV: Electrical Charge)

38. End of Lecture 15 Oct. 18, 2008