1. Chem 125 Lecture 7 9/14/05 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. Rubofusarin No H? long short High e-Density No : ! Stout & Jensen "X-Ray Structure Determination (1968) 5 e/Å 3 7 e/Å 3 No : Bonds! Spherical Atoms

3. Visualizing Bonds with Difference Density Maps Observed e-Density - Atomic e-Density (experimental) (calculated) sometimes called Deformation Density Maps

4. Spherical Carbon Atoms Subtracted from Experimental Electron Density (H not subtracted) Triene 7 65 4 ~0.2 e ~0.1 e H ~1 e

5. Triene plane of page cross section partial double bond

6. Leiserowitz ~0.1 e ~0.3 e ~0.2 e C C C C Why not? Bent bonds from tetrahedral C ?

7. Lewis Bookkeeping 4 2 6 Integrated Difference Density (e) How many electrons are there in a bond? Bond Distance (Å) 1.21.41.6 0.2 0.1 0.3 Berkovitch-Yellin & Leiserowitz (1977)

8. Bonding Density is about 1/20 th of a “Lewis”

9. Tetrafluorodicyanobenzene CC C C F N CC C C F N F F Dunitz, Schweitzer, & Seiler (1983) unique

10. TFDCB C CC C F N is round not clover-leaf nor diamond! C N Triple Bond

11. TFDCB Where is the C-F Bond? C CC C F N Unshared Pair!

12. The Second Great Question

13. Compared to what? What d'you think of him? Exactly! Compared with what, sir? 1) RESONANCE STABILIZATION 2) DIFFERENCE DENSITY

14. TFDCB Where is the C-F Bond? C CC C F N Unshared Pair! Need to subtract F instead of “unbiased ” spherical F

15. Dunitz et al. (1981) Pathological Bonding  0.002 Å ! for average positions Typically vibrating by ±0.050 Å in the crystal

16. Dunitz et al. (1981) Pathological Bonding Surprising only for its beauty

17. Lone "Pair" of N atom Dunitz et al. (1981) Pathological Bonding Bond Cross Sections Missing Bond? H H H H H H

18. Dunitz et al. (1981) Pathological Bonding Missing Bond ! Bent Bonds !

19. Lewis Pairs/Octets provide a pretty good bookkeeping device for keeping track of valence but they are hopelessly crude when it comes to describing actual electron distribution. There is electron sharing (~5% of Lewis's prediction). There are unshared "pairs" (<5% of Lewis's prediction).

20. Is there a Better Bond Theory, maybe even a Quantitative one? YES! Chemical Quantum Mechanics

21. Erwin Schrödinger (Zurich,1925) www.zbp.univie.ac.at/schrodinger

22. www.uni-leipzig.de/ ~gasse/gesch1.html "So in one of the next colloquia, Schrödinger gave a beautifully clear account of how de Broglie associated a wave with a particle…When he had finished, Debye casually remarked the he thought this way of talking was rather childish… he had learned that, to deal pro- perly with waves, one had to have a wave equation. It sounded rather trivial and did not seem to make a great impression, but Schrödinger evidently thought a bit more about the idea afterwards." Felix Bloch, Physics Today (1976) "Once at the end of a colloquium I heard Debye saying something like: Schrödinger, you are not working right now on very important problems anyway. Why don't you tell us sometime about that thesis of de Broglie?

23. Well, I have found one." "Just a few weeks later he gave another talk in the colloquium, which he started by saying: My colleague Debye suggested that one should have a wave equation: H  = E 

24. Stockholm (1933) www.th.physik.uni-frankfurt.de/~jr Paul Dirac Werner Heisenberg Erwin Schrödinger

25. Schrödinger Equation H  = E 

26. Leipzig (1931) American Institute of Physics Werner Heisenberg Felix Bloch Victor Weisskopf

27. Felix Bloch & Erich Hückel on  Gar Manches rechnet Erwin schon Mit seiner Wellenfunktion. Nur wissen möcht man gerne wohl, Was man sich dabei vorstell'n soll. Erwin with his Psi can do calculations, quite a few. We only wish that we could glean an inkling of what Psi could mean. (1926)

28.  Function of What? Named by "quantum numbers" (e.g. n,l,m ; 1s ; 3d xy ;  Function of Particle Position(s) [and time and "spin"] We focus first on one dimension, then three dimensions (one e), then many e atoms, then many atoms. N particles  3N arguments! [sometimes 4N+1]

29. Solving a Quantum Problem Given : a set of particles their masses & their potential energy law [ e.g. 1 Particle/1 Dimension : 1 amu & Hooke's Law ] To Find :  a Function of the position(s) of the particle(s) Such that H  /  is the same (E) everywhere Reward : Knowledge of Everything At least everything knowable to experiment Allowed Es, Structure (probability of) All Chemical & Physical Properties

30. = H  = E  Kinetic Energy + Potential Energy = Total Energy Given - Nothing to do with  Hold your breath! H  = E 

31. Kinetic Energy! 22 xi2xi2  22 yi2yi2  22 zi2zi2  ++ 1 mimi  i h2h2 8282  d2d2 dx2dx2  1 m C  C  Curvature of  m One particle;One dimension: