Chapter 12: Molecular Structure By Diffraction Experiments

Question 1

Describe the structure of a protein crystal

Answer 1

• Contain 10^13 - 10^15 individual molecules
• Weak hydrogen bonds maintain the structure (hence are fragile)
• Formation is a random process as each protein behaves differently

Question 2

What does successful crystal formation depend on?

Answer 2

• The precipitant used
• The pH
• The concentration of ions
• The temperature

Question 3

Outline the general process of crystal formation

Answer 3

Crystals are formed by placing the protein in a solution and slowly adding precipitant to reduce the mobile water concentration. Precipitants are generally salts, polymers, or organic solvents.

Question 4

Define vapour diffusion

Answer 4

A common technique used in protein crystal formation.

Question 5

Outline the process of vapour diffusion for crystal formation

Answer 5

A drop containing the protein in solution is placed inside a container alongside a larger reservoir of water with polymers. The concentration of polymers in the reservoir is increased so the vapour pressure inside the container is reduced and water is slowly extracted from the drop via controlled evaporation. Eventually, enough water is extracted from the drop for crystallisation to take place.

Question 6

The vapour diffusion technique is ______ driven and occurs between the macromolecules in the container (the proteins).

Answer 6

Entropy

Question 7

What are the requirements for a successful diffraction experiment?

Answer 7

• Similar or smaller wavelength to the structural scale
• Absorption shouldn’t be too strong (to prevent radiation damage)
• Appropriate properties of interaction with matter

Question 8

What are the two main types of diffraction?

Answer 8

Neutron diffraction
X-ray diffraction

Question 9

Compare the energy of neutron and X-ray diffraction

Answer 9

Neutron: 0.005eV
Electron: 3keV

Question 10

Compare the scatterers in neutron and X-ray diffraction

Answer 10

Neutron: atomic nuclei (point scatters)
X-ray: electrons (not point scatters)

Question 11

Compare the scattered wave in neutron and X-ray diffraction

Answer 11

Neutron: wave is isotropical (uniform in all orientations)
X-ray: scattering decreases with increasing angle

Question 12

Compare the dominant elements in neutron and X-ray diffraction

Answer 12

Neutron: there are no dominant elements
X-ray: heavier elements dominate the diffraction process as scattering power increases with more electrons

Question 13

What is the spin of a neutron?

Answer 13

1/2

Question 14

What does scattering power depend on for neutron diffraction?

Answer 14

Relative orientation of neutron spin

Question 15

Compare the visibility of hydrogen atoms in neutron and X-ray diffraction

Answer 15

Neutron: hydrogen atoms can be seen readily
X-ray: hydrogen atoms are difficult to see

Question 16

Compare the absorption in neutron and X-ray diffraction

Answer 16

Neutron: low neutron absorption
X-ray: absorption increases with wavelength (but so does radiation damage)

Question 17

Compare the sources of neutron and X-ray diffraction

Answer 17

Neutron: deuterium or tritium fusion
X-ray: synchotron radiation

Question 18

Define crystal unit cells

Answer 18

The basic element on the structure of a crystal, due to its periodic structure. They are characterised by three vectors, a, b, c, and three angles, α, β, γ.

Question 19

Describe a simple model for a unit cell (cubic and orthorhombic)

Answer 19

a = b = c (cubic)
a ≠ b ≠ c (orthorhombic)

Orthogonal axis: α = β = γ = π/2

Question 20

Define Bragg’s law

Answer 20

A specific case of diffraction that gives the angles for coherent scattering waves from a crystal lattice.

Question 21

Derive Bragg’s law

Answer 21

d = distance between two electrons

Question 22

Give the equation for Bragg’s law

Answer 22

d = distance between two electrons

Question 23

Give the scattering vector for x-ray diffraction

Answer 23

S = scattering vector
k = wave vector
u_0 = incident wave direction
u_1 = scattered wave direction

Question 24

How is the scattering vector related to the distance between two electrons? (EXTRA: how is this concluded?)

Answer 24

S = scattering vector
d = distance between two electrons

EXTRA: the equations for the scattering vector and
Bragg’s law are combined.

Question 25

What are the two ways that the distance between two electrons can be changed in X-ray diffraction?

Answer 25

• Decreasing the wavelength (smaller distance)
• Changing the angle of incident waves

Question 26

Why does the atom an x-ray hits impact the scattering amplitude? (EXTRA: what factor describes this dependence?)

Answer 26

Because each atom have a unique number of electrons and electron distribution.

EXTRA: the scattering factor

Question 27

Give the equation for the structure factor of a unit cell by considering the equation for a scattered wave

Answer 27

F(S) = structure factor
g_j = scattered wave
f_j = scattering factor
r_j = position
n = number of atoms

Question 28

How can scattering event calculations in a unit cell be adapted for a whole crystal?

Answer 28

-The calculations are expanded for n unit cells in the a, b and c directions and are defined by t, u and v steps in each direction.
-The structure factor for all unit cells, K(S), is found where r = ta, ub, or vc and the product of three separate exponential is taken for all values of n.

Question 29

Give the equation for the structure factor for all unit cells for X-ray diffraction

Answer 29

K(S) = structure factor for all unit cells
n = number of unit cells

Question 30

What are the Laue conditions for scattering?

Answer 30

h, k, l = integers

Question 31

How are K(S) and F(S) related?

Answer 31

The amplitude of K(S) is proportional to F(S) x n where n = n1 x n2 x n3 (the total number of unit cells)

Question 32

Define the Miller indices

Answer 32

The three parameters, h, k, l, which represent the sets of planes in which the scatterers must be located so that the scattered waves all have the same phase (so generate constructive interference pattern known as reflections in X-ray diffraction terminology). They indicate how many times each axis should be divided into equal section, which is how these planes are drawn.

Question 33

What does the intensity of X-ray diffraction reflections depend on?

Answer 33

• How many atoms there are (greater number means higher intensity)
• The location of the respective electrons of each atom in the set of planes.
• The intensity of reflection is proportional to the square of the structure factor.

Question 34

The intensity of reflections from a unit cell is impacted by the _________ _________ of the atoms in the cell.

Answer 34

Geometric arrangement

Question 35

Give the equation for the structure factor when the Laue conditions are met

Answer 35

h, k, l = Laue conditions

Question 36

Describe a primitive unit cell

Answer 36

8 atoms, one in each corner. As these atoms are all shared by 8 other unit cells, primitive unit cells are considered to have one atom each.

Question 37

Describe a body centred unit cell

Answer 37

8 atoms, one in each corner and one atom at the centre of the cell giving a total of 2 cells following the same logic as or a primitive unit cell.

Question 38

Describe a face centred unit cell

Answer 38

8 atoms, one in each corner (resulting in 1 overall atom per unit cell). There are also 6 additional atoms, one at the centre of each face which are all shared with the adjacent face so are considered to be 3 per unit cell. This leaves a total of 4 atoms per unit cell.

Question 39

How can the electron density of a crystal be derived?

Answer 39

The structure factor is a Fourier Transform of the electron density when it is written in integral form.

Question 40

What is the equation for the electron density?

Answer 40

Question 41

What is the equation for the electron density in one dimension?

Answer 41

Question 42

What are the uses of finding the electron density of a unit cell?

Answer 42

The molecular structure of the crystal molecule can be found.