1. Hexagonal “benzene” masks and Franklin’s X-ray pattern of DNA explain how a diffraction pattern in “reciprocal space” relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. Electron difference density maps reveal bonds, and unshared electron pairs, and show that they are only 1/20 th as dense as would be expected for Lewis shared pairs. Anomalous difference density in the carbon-fluorine bond raises the course’s second key question, “Compared to what?” Chemistry 125: Lecture 6 Seeing Bonds by Electron Difference Density Synchronize when the speaker finishes saying, “It’s clear that there’s some relationship...” Synchrony can be adjusted by using the pause(||) and run(>) controls. For copyright notice see final page of this file

2. Understanding Diffraction Patterns

3. Benzene Snowflake Slide with Randomly positioned but Oriented "Benzenes" (Random position- ing generates the same diffraction as a single pattern, but more intense.)

4. Benzene Snowflake Isolated “Benzenes” Look for e-density on evenly spaced planes. (or near)

5. Benzene Snowflake Isolated “Benzenes” Closer-spaced planes give higher angles. Look for e-density on (or near) evenly spaced planes.

6. Benzene Snowflake Slide with regular lattice of “benzenes" Lattice repeat concentrates the benzene snowflake scattering into tightly-focussed spots

7. Diffraction from 2D Lattice of “Benzenes” Molecular snowflake pattern viewed through lattice “pegboard” and amplified to give same total intensity

8. “Direct” or “Diffraction” or “Real” Space “Reciprocal” Space Crystal Diffraction Photo “Unit Cell” Structure Fuzzy Pattern Crystal Lattice Viewing Holes Decreasing Spacing Increasing Spacing

9. Filament Light Bulb Filament (helix)

10. Filament Light Bulb Filament (helix) X angle tells helix pitch Spot spacing tells scale Spot spacing tells scale Spots weaken successively (from wire thickness) (given & slide-screen distance)

11. HELIX w S S vw S Curious Intensity Sequence B-DNA R. Franklin (1952)

12. Even Double Helix would cancel every other “reflection” (planes twice as close)

13. Offset Double Helix repeated pair pattern Much more electron density near planes than in between.

14. BASE STACKING B-DNA R. Franklin (1952) w S S vw S MAJOR & MINOR GROOVES HELIX DIAMETER

15. Using pretty heavy duty math (or a canned program) one can go the other way. Knowing the molecule’s electron density, it is easy to calculate a crystal’s diffraction pattern.

16. X-Ray Diffraction Old-Style Electron Density Map (one slice) Contours drawn by hand to connect points of equivalent electron density on computer printout. Cuts near Nucleus Nucleus out of plane Stout & Jensen X-Ray Structure Determination (1968)

17. K Penicillin K + Penicillin - 3-D map on plastic sheets ( 1949) K

18. 1 e/Å 3 contours Rubofusarin (planar) No H? High e-Density No : on O! Stout & Jensen "X-Ray Structure Determination (1968) 5 e/Å 3 7 e/Å 3 long short intermediate No : Bonds! Spherical Atoms

19. “Seeing” Bonds with Difference Density Maps Observed e-Density - Atomic e-Density (experimental) (calculated) sometimes called Deformation Density Maps

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

21. Triene plane of page C cross section (round) C cross section (oval)

22. Leiserowitz ~0.1 e ~0.3 e ~0.2 e Why so little build-up here? C C C C as if there are bent bonds from tetrahedral C atoms Be patient (Quantum Mechanics)

23. Lewis Bookkeeping electrons 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)

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

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

26. TFDCB C CC C F N is round not clover-leaf nor diamond! C N Triple Bond ? C C “Aromatic” Bond C C Single Bond

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

28. The Second Great Question

29. The Beiderbeck Affair (1985) ©1984 Granada Television See following slide for summary of missing film clip

30. Compared to what? What d'you think of him? Exactly! Compared with what, sir? 1) SPECIAL “RESONANCE” STABILIZATION / 2) DIFFERENCE ELECTRON DENSITY Compared observed (or calculated) energy to energy expected for a single Lewis structure See webpage for dialogue and context Compared observed (or calculated) total e-density to the sum of e-densities for a set of undistorted atoms

31. TFDCB Where is the C-F Bond? To avoid “Pauli” problems we need to subtract not “unbiased” spherical which would start with 2.75 electrons in the bonding quadrant (1 from C, 1.75 from F) C CC C F N but rather “valence prepared”

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

33. End of Lecture 6 Sept 15, 2008 Copyright © J. M. McBride 2009. Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0