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. 14, 2009 Seeing Bonds by Electron Difference Density Preliminary For copyright notice see final page of this file

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

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

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

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

Benzene Snowflake Slide with regular lattice of “benzenes" Lattice repeat concentrates the benzene snowflake scattering into tightly-focussed spots molecule lattice consider vertical scattering only

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

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

Filament Light Bulb Filament (helix)

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)

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

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

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

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

Using pretty heavy-duty math, that earned a Nobel Prize (but by 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.

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 Nucleus Nucleus out of plane Stout & Jensen X-Ray Structure Determination (1968)

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

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

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

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

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

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)

Lewis Bookkeeping electrons Integrated Difference Density (e) How many electrons are there in a bond? Bond Distance (Å) Berkovitch-Yellin & Leiserowitz (1977) more ^

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

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

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

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

The Second Key Question

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

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

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”

Dunitz et al. (1981) Pathological Bonding  Å ! for average positions Typically vibrating by ±0.050 Å in the crystal (measured at 95K)

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

End of Lecture 6 Sept 14, 2009 Copyright © J. M. McBride 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