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 Sept. 13, 2010 Seeing Bonds by Electron Difference Density For copyright notice see final page of this file

2. Smoothly Modulated Scattering from a Pair. (Slight change in deflection changes phase difference only slightly)

3. Long-Range Regular Repetition “Focuses” the Scattered Intensity.

4. Repetition of Pairs “Focuses” their Smoothly-Varying Intensity.

5. Understanding Crystal X-Ray Diffraction as a “Convolution” of Pattern and Lattice

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

7. Benzene Snowflake Isolated “Benzene” Look for e-density on evenly spaced planes. (or near) Greater spacing gives smaller angles.

8. Benzene Snowflake Isolated “Benzene” Greater spacing gives smaller angles. Look for e-density on (or near) evenly spaced planes. High-angle reflections are weak, because finite size of scatters gives substantial electron density between closely-spaced planes

9. Benzene Snowflake Slide with regular lattice of “benzenes" Lattice repeat concentrates the benzene snowflake scattering into tightly-focussed spots Molecule (row) Two rows (cosine) consider vertical scattering only Lattice (precise angles)

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

11. “Direct” or “Real” Space “Unit Cell” Structure Fuzzy Pattern Crystal Lattice Viewing Holes Decreasing Spacing Increasing Spacing Crystal “Diffraction” or “Reciprocal” Space Diffraction Photo (intensity) (location)

12. Filament Light Bulb Filament (helix)

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

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

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

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

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

18. Using pretty heavy-duty math, (that earned a Nobel Prize, but is now a canned program) one can go the other way. Knowing the molecule’s electron density, it is straightforward to calculate a crystal’s diffraction pattern.

19. 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 this Carbon Nucleus This Carbon Nucleus lies out of this plane Stout & Jensen X-Ray Structure Determination (1968)

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

21. 1 e/Å 3 contours Rubofusarin (planar) No H? High e-Density Stout & Jensen "X-Ray Structure Determination (1968) 5 e/Å 3 7 e/Å 3 long short intermediate No : Bonds! Spherical Atoms No : on O!

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

23. 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)

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

25. 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)

26. 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) more ^

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

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

29. 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

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

31. The Second Key Question

32. See web page for video The Beiderbeck Affair (1985) ©1984 Granada Television

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

34. TFDCB Where is the C-F Bond? To avoid “Pauli” problems we need to subtract not “unbiased” spherical C CC C F N C which would start with 2.75 electrons in the bonding quadrants (1 from C, 1.75 from F) but rather “valence prepared” “Pauli Principle” No more than two electrons in an “orbital”.

35. Dunitz et al. (1981)

36. End of Lecture 6 Sept 13, 2010 Copyright © J. M. McBride 2009-2010. 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