1. Chem 125 Lecture 14 10/9/2006 Projected material 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. Orbital Paradise  (3N e variables) =  1 (x 1,y 1,z 1 )   2 (x 2,y 2,z 2 )  … Total e-density (x,y,z) =  1 2 (x,y,z) +  2 2 (x,y,z) + … Total e-Energy =  1 + E 2 + … e.g. Ne (1s) 2 (2s) 2 (2p x ) 2 (2p y ) 2 (2p z ) 2

3. "Correlation Energy" Error after full SCF calculation to “Hartree-Fock” limit: Get correct energy / total electron density by experiment or by a whopping calculation: e.g. “Configuration Interaction” (CI) or “Density Functional Theory” (DFT)

4. If we’re really lucky, "Correlation Energy" might be Negligible.

5. + + + + + + C +6 - -- - - Energy Magnitudes Should Chemists care about the error in Orbital Theory? 8 0 6 2 4 -2 log (Energy) kcal / mole C Atom (2  10 4 ) 1/2  4 C-C Bonds (2  10 2 ) "Non-bonded" Contact (1-10) HeHe 52Å! (2  10 -6 ) Changes in "correlation energy" are ~10-15% of Bond Energy. Orbital Theory is fine for Qualitative Understanding of Bonding. C "Correlation Energy" (10 2 ) - C C 12 C Nucleus (2  10 9 ) Nuclear energy totally unchanged by chemistry! Loses 0.1 amu (E = mc 2 )

6. Orbitals can't be “true” (for >1 electron) but we'll use them to understand bonding, structure, energy, and reactivity

7. What gives Atomic Orbitals their Shape? Potential Energy scales r Kinetic Energy creates nodes 4d 2s double nuclear charge

8. If we use orbitals, how should we reckon total electron density? Density of electron 1 =  1 2 (x 1,y 1,z 1 ) Density of electron 2 =  2 2 (x 2,y 2,z 2 ) Total density (x,y,z) =  1 2 (x,y,z) +  2 2 (x,y,z) (Sum, not Product. Not a question of joint probability)

9. How Lumpy is the N Atom? spherical“dumb-bells” Total = K(r 2 ) e -  (2p x ) 2 = K x 2 e -  (2p y ) 2 = K y 2 e -  (2p z ) 2 = K z 2 e -  Total = K(x 2 + y 2 + z 2 ) e -  Spherical !

10. TFDCB C CC C F N is round not clover-leaf nor diamond! C N Triple Bond 2p x 2 + 2p y 2 depends on (x 2 +y 2 ) It is thus symmetrical upon any rotation about the z axis

11. What's Coming for Next Exam? Molecules Plum-Pudding Molecules ("United Atom" Limit) Understanding Bonds (Pairwise LCAO) "Energy-Match & Overlap" Structure (and Dynamics) of XH 3 Molecules Atoms 3-Dimensional Reality (H-like Atoms) Hybridization Orbitals for Many-Electron Atoms (Wrong!) Recovering from the Orbital Approximation Payoff for Organic Chemistry! Reactivity HOMOs and LUMOs Recognizing Functional Groups

12. Ways of Looking at an Elephant

13. Set of atoms Atoms with weak bonding Single “United Atom” distorted by a fragmented nucleus Ways of Looking at a Molecule (or a Molecular Orbital) e-density contours of H 2 Which contour should we use? Molecule from atoms Molecule as one atom Nuclei embedded in a cloud of electrons dispersed and “noded” by kinetic energy J. J. Thomson's Plum Pudding! Molecule as atoms

14. How the Plums Distort Electronic Puddings

15. Methane & Ammonia Spartan 6-31G* calculates good SCF MOs (on my laptop!) We want to understand them visually.

16. 4 Pairs of Valence Electrons H CHH H NHH H Compare MOs to AOs of Ne (4 electron pairs n=2)

17. 1s CH 4 NH 3 "Core" Orbitals Like 1s of C/N Tightly Held Little Distortion Contour Level 0.001 e/Å 3 We'll focus on Valence Orbitals Boring!.. 8 valence e -  4 MOs 8 valence e -  4 MOs

18. 1s..

19. 1s.. But we'll neglect the tiny spherical node for this discussion. Actually 2s

20. 2p x.. CH 4 NH 3..

21. CH 4 NH 3 2p y.. CH 4 NH 3..

22. CH 4 NH 3 2p y.. CH 4 NH 3..

23. CH 4 NH 3 2p z HOMO Lewis's "unshared pair".. CH 4 NH 3.. +Unoccupied Orbitals

24. End