slides2014 hoa tinh the prof van luc

Crystallography - Molecular architecture
• Symmetry (molecule, stacking objects)
point groups, plane groups, space groups

• Crystal structure determination using X-ray diffraction
• Cambridge Structural Database


What is: crystallography – crystal ?
• Krústallos (Gr. Frozen water)
• solid state of matter
• regular external faces
geometrical law - Steno (1669)
angle between two corresponding
faces is constant
• regular internal structure
Keppler (New year’s day 1611)
• Hauy (1784): identical building blocks


What is: crystallography – crystal ?
• originaly part of geology - mineralogy
• discovery X-rays
(Röntgen, 1895, NP 1901)
• diffraction experiment crystal
(von Laue, 1912, NP 1914)
• structure determination simple salts
(Bragg, 1913, NP 1915)
• since then more and more
complex structures

Crystallography evoluates from description of external
structure to internal structure!


Relation to other sciences…
Structure and properties of…
• minerals
• metals, alloys
• (in)organic compounds
• polymers
• biomolecules

mineralogy
material science
chemistry, pharmacy
solid-state physics
polymer science
biochemistry, molecular
biology, medecine

With the help of…
mathematics
informatics


Relation to other sciences…
Some examples…

CHEMISTRY

C60, fullerene
Proven by X-ray
(derivative)


Relation to other sciences…
Some examples…

BIOCHEMISTRY

NP Chemistry 2003 – structure determination water- ion channels


Relation to other sciences…
Some examples…

PHARMACY


Relation to other sciences…
Some examples… POLYMER SCIENCES

Polyethylene

Importance crystallinity


Importance symmetry

External order of a crystal reflects

an internal submicroscopic order.

Symmetry is important in almost all
disciplines of science, art and
society.


Some important realisations crystallography
• theory electrostatic bond in inorganic ion structures
• proof tetrahedral carbon atom
• structure elucidation benzene ring
• proof existence H-bond
• -helix, -plate in proteins
• DNA-model
• determination absolute configuration


Crystallisation techniques
•

Principle: bring the system slowly toward a state of
minimum solubility (supersaturation)

•
•

Driving force ?
Large number of variables (purity, concentration, pH,
temperature, buffer, additives, precipitants…)

•

Some methods
-

Cooling

-

Concentration
(evaporation volatile solvent, NMR tube)

-

Solvent diffusion
solvent

Anti-solvent


-

Vapour diffusion

-

Reactant diffusion (gel)
Seed crystals
Sublimation

•

Sparse matrix screen
- samples a finite number of variables, e.g. pH and [(NH4)2SO4]
- uses very small samples
- usually gives preliminary conditions (to be optimised)
Grease

Precipitant
in reservoir

1-5 L sample
1-5 L precipitant
Mix

Invert, seal


•

Crystallisation robot
liquid handling arm with tips (0.25-250 µl)

Mosquito


XtalScreens
Database of crystallisation screens

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Part 1. Symmetry - Introduction
(a) Description of symmetry
• symmetry element
symmetry operation

rotate 90°
• symmetry figure

• equivalent positions


• symmetry matrix
(2 x rotation)

• mathematical group – multiplication table (Caley) - order
product - Abels
E
X-1
associative

A = 90
B = 180
C = 270
E = 360/0

• Schoenflies and Hermann-Mauguin notation
C4
4

cyclic (A=generating element)


(b) What is a crystal ?
Precisely ordered three dimensional array of ions, atoms or
molecules

(1)

(2)

(3)

(1) Asymmetric unit (building block)
(2) Build unit cell by symmetry operations
(inversion, rotation axis, mirror plane)
(3) Lattice translation symmetry


Chapter 1. Point symmetry
•

Symmetry elements

Inversion centre 1

Ci

Mirror plane m

σ
Cn

n-fold rotation axis n
Rotation inversion axis -n
Rotation reflection axis Sn

(n=2, 3, 4 or 6)
Rotation of (360/n)°
Proper rotation
Point symmetry

Chirality!

Hermann-Mauguin or International Tables
Schoenflies


•

Point groups (32)
 set of symmetry operations that leave a point fixed and form
a mathematical group
 describe the symmetry of an object (e.g. a molecule!)

Point group 4/mmm
(porphyrazin)


 Multiplication table for NH3

 Overview 32 point groups


 Some examples

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