# X-Ray Diffraction. wavelength Electric field of light

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1 Light is composed of electromagnetic radiation with an electric component that modulates versus time perpendicular to the direction it is travelling (the magnetic component is also perpendicular to the electric, but it is not causing diffraction) Force wavelength Electric field of light Time The electric component will interact with charged species (causing the modulating force) In an atom, because the electrons are ~2000 times lighter than a proton the electrons will be displaced by interaction with light, therefore an X-ray diffraction is caused by diffraction of electrons in the sample Ultimately, X-ray diffraction will indicate the position of electrons (not nuclei) (Because diffraction will only be resolved if the wavelength of light used is smaller than the distance between objects, X-ray diffraction can indicate position of electrons) [C-C bond for example is 1.54 Å, visible light is ~4000 Å, X-ray light used is ~0.7 Å] 56

2 Consider electrons at spots A and B in parallel planes separated by a distance d θ A θ d B When a X-ray beam of light hits the plane at an angle θ, the electrons will vibrate due to interaction with the electric field, and as vibrating charges will radiate light at the same reflected path θ A parallel beam of light can be diffracted by electron B in the other plane The two diffracted beams will be in phase only if the correct relationship between the wavelength of light used (λ) and the distance between the spots (d) is an integer number 2d sin θ = nλ Bragg s law 57

3 Instead of the distance between two electrons (or two molecules), a single crystal is used in order to have a regular array of the diffracting units to allow the diffracted light to be bright enough enough to measure Incoming X-ray Single crystal Diffraction lines detector Rotate 90 Second unit cell axis One axis in unit cell The regular array of the crystalline lattice will cause diffraction peaks on the detector when the regular array diffracts in a reinforcing manner, depending upon the wavelength of light used, the distance between the sample and the detector and the repeat size of the regular array The distance between the peaks will therefore be related to the unit cell dimension (the regular array within the crystal) By rotating the crystal in the X-ray beam, different planes of diffraction can be detected in three dimensions 58

4 The regular pattern of the diffraction peaks therefore is an indication of the dimension of the repeat unit in the crystal (the unit cell) The spacing of the rows and columns indicates the unit cell The electron distribution within a unit cell however is related to the relative intensity of individual spots Due to how the electrons are distributed within the unit cell, the diffracted lines can have either constructive or destructive interference All spots would only have the ~ the same intensity if the electrons are equally distributed within the unit cell, how they reinforce however indicates the unequal distribution Symmetrical distribution of electrons within unit cell Unsymmetrical distribution of electrons within unit cell With computer programs, it is possible to determine the electron density within a unit cell (and hence where are electrons in a bond) by measuring the relative intensity of a large number of diffraction peaks 59

5 When a single crystal structure is determined what is actually obtained is the relative placement of electron density in a unit cell Consider the molecule Celebixanthone O O OC 3 O O O *observe electron distribution (nuclei position is assumed) Oxygen atoms can be distinguished from carbon due to extra electron density *electrons appear as spherical balls surrounding each atom (electrons are NOT between atoms) Stout, et. al., Tetrahedron, 1963, 19, Contour interval: 1 e / A 3 60

6 Does this mean Lewis and Valence Bond Theory is wrong? What is a bond and why do the atoms remain attached if no electron density is between the atoms? Need to consider Electron Deformation Density (sometimes called electron difference density ) Consider how much the spherical atoms are distorted when forming a bond by subtracting the electron density from a pure symmetrically oriented sphere F F N C C N F F Still seems like spherical balls for atoms Contour interval: 0.1 e / A 3 Appears differently with electron deformation density Can now see electrons between bonds (and lone pairs on nitrogen) irshfeld, Acta. Cryst., 1984, B40, Dunitz, et. al., elv. Chim. Acta, 1983, 66,

7 While we can now be comfortable with our Valence Bond Theory (and Lewis can sleep comfortably!) it still seems like this is a small effect and 2 electrons are not held between bonds as Lewis proposed but are mainly near each atom of a bond Consider tetraphenylbutatriene to see some issues C C C C Make slice and rotate Deformation density for each phenyl looks promising Density is not symmetrical, looks like a π bond from overlapping p orbitals! C1-C2 C2-C3 L. Leiserowitz, et. al., J. Am. Chem. Soc., 1975, 97, Adjacent π bonds are orthogonal to each other! Problem is that the electron density in bond can be integrated 62

8 There are many gratifying results from electron deformation density maps for a qualitative verification of Lewis dot structures (and Valence Bond Theory in general): electrons are located between bonded atoms, when π bonds are formed between atoms the electron density is not symmetric about the internuclear axis and lone pairs of electrons can be detected A problem however is the amount of electron density between bonded atoms Valence Bond Theory would predict there are 2 electrons involved in a single bond, 4 electrons in a double bond and 6 electrons in a triple bond (and 3 electrons in a bond that resonates between a single and double bond) The electron density in the bonding region can be quantified by integrating the deformation map Electron density C1-C2 C2-C3 Ph-Ph C1-Ph The amount of electron density in a bonding region is significantly less than predicted by Lewis L. Leiserowitz, et. al., J. Am. Chem. Soc., 1975, 97,

9 The amount of electron density in a bond was determined from a number of high quality electron deformation density maps 0.3 Charge (electrons) Actual density in a bond determined by experiment is ~ 5% of predicted Lewis dot structures 0.2 Tetraphenylbutatriene Other structures 0.1 C C C C C C C C Bond Length (Å) Density determined from electron deformation density maps is ~0.1 electrons for a single bond (not 2!), 0.2 electrons for a double bond and 0.3 electrons for a triple bond L. Leiserowitz, et. al., J. Am. Chem. Soc., 1977, 99,

10 What can electron deformation maps indicate about strained compounds? Where is the electron density located in a strained system? Consider the highly strained cyclopropane The electron density truly does form bent bonds, bonding electron density is not along internuclear axis Valence Bond Theory therefore does do a very good qualitative job describing bonding, it lacks in providing some quantitative ability for both bonding and also reactivity For a better quantitative job, Molecular Orbital Theory is useful D. Nijveldt and A. Vos, Acta Cryst., 1988, B44,

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