title
DESCRIPTION
How to read. Title. and understand…. Page. Left system. crystal system. Left point group. point group symbol. Left space group1. space group symbol international (Hermann-Mauguin) notation. Left space group2. space group symbol - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/1.jpg)
Title
How to read
and understand…
![Page 2: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/2.jpg)
Page
![Page 3: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/3.jpg)
Left system
crystal system
![Page 4: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/4.jpg)
Left point group
point group symbol
![Page 5: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/5.jpg)
Left space group1
space group symbol
international(Hermann-Mauguin) notation
![Page 6: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/6.jpg)
Left space group2
space group symbol
Schönflies notation
![Page 7: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/7.jpg)
Left symmetry diagram
diagram of symmetry operations
positions of symmetry operations
![Page 8: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/8.jpg)
Left positions diagram
diagram of equivalent positions
![Page 9: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/9.jpg)
Left origin
origin position vs. symmetry elements
![Page 10: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/10.jpg)
Left asymmetric
unit
definition of asymmetric unit (not unique)
![Page 11: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/11.jpg)
Left Patterson
Patterson symmetry
Patterson symmetry group is always primitive centrosymmetric without translational symmetry operations
![Page 12: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/12.jpg)
Right positions
equivalent positions
![Page 13: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/13.jpg)
Right special positions
special positions
![Page 14: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/14.jpg)
Right subgroups
subgroups
![Page 15: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/15.jpg)
Right absences
systematic absences
systematic absences result from translational symmetry elements
![Page 16: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/16.jpg)
Right generators
group generators
![Page 17: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/17.jpg)
Individual items
Interpretation of
individual items
![Page 18: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/18.jpg)
Left system
crystal system
![Page 19: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/19.jpg)
Systems
7 (6) Crystal systems
Triclinic a b c , , 90º
Monoclinic a b c 90º, 90º
Orthorhombic a b c 90º
Tetragonal a b c 90º
Rhombohedral a b c
Hexagonal a b c 90º , 120º
Cubic a b c 90º
![Page 20: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/20.jpg)
Left point group
point group symbol
![Page 21: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/21.jpg)
Point groups
Point groups describe symmetry of finite objects (at least one point invariant)
Set of symmetry operations:
rotations and rotoinversions
(or proper and improper rotations)
mirror = 2-fold rotation + inversion
Combination of two symmetry operations
gives another operation of the point group
(principle of group theory)
![Page 22: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/22.jpg)
Point groups general
Point groups describe symmetry of finite objects (at least one point invariant)
Schönflies International Examples
Cn N 1, 2, 4, 6
Cnv Nmm mm2, 4mm
Cnh N/m m, 2/m, 6/m
Cni , S2n N 1, 3, 4, 6
Dn N22 222, 622
Dnh N/mmm mmm, 4/mmm
Dnd N2m, Nm 3m, 42m, 62m
T , Th , Td 23, m3, 43m
O , Oh 432, m3m
Y , Yh 532, 53m
_ _ _ _ _
_ _ _ _ _
_
__
![Page 23: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/23.jpg)
Point groups crystallographi
c
32 crystallographic point groups (crystal classes) 11 noncentrosymmetric
Triclinic 1 1
Monoclinic 2 m, 2/m
Orthorhombic 222 mm2, mmm
Tetragonal 4, 422 4, 4/m, 4mm, 42m, 4/mmm
Trigonal 3, 32 3, 3m, 3m
Hexagonal 6, 622 6, 6/m, 6mm, 62m, 6/mmm
Cubic 23, 432 m3, 43m, m3m
_
_ _
_ _
_ _
_
![Page 24: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/24.jpg)
Trp
Trp RNA-binding protein 1QAW
11-foldNCS axis (C11)
![Page 25: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/25.jpg)
Xyl
Xylose isomerase 1BXB
![Page 26: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/26.jpg)
Xyl 222
Xylose isomerase 1BXB
Tetramer222 NCSsymmetry (D2)
![Page 27: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/27.jpg)
Left space group
space group symbols
![Page 28: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/28.jpg)
Space groups
Combination of point group symmetry with translations
- Bravais lattices
- translational symmetry elements
Space groups describe symmetry of infinite objects (3-D lattices, crystals)
![Page 29: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/29.jpg)
Bravais lattices
but the symmetry of the crystal is defined by its content, not by the lattice metric
![Page 30: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/30.jpg)
Choice of cell
Selection of unit cell
- smallest
- simplest
- highest symmetry
![Page 31: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/31.jpg)
Space group symbols
![Page 32: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/32.jpg)
321 vs. 312
![Page 33: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/33.jpg)
Left symmetry diagram
diagram of symmetry operations
positions of symmetry operations
![Page 34: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/34.jpg)
Symmetry operators symbols
![Page 35: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/35.jpg)
Left origin
origin position vs. symmetry elements
![Page 36: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/36.jpg)
Origin P212121
![Page 37: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/37.jpg)
Origin P212121b
![Page 38: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/38.jpg)
Origin C2
![Page 39: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/39.jpg)
Origin C2b
![Page 40: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/40.jpg)
Left asymmetric
unit
definition of asymmetric unit (not unique)
Va.u. = Vcell/N rotation axes cannot pass through the asymm. unit
![Page 41: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/41.jpg)
Asymmetric unit P21
![Page 42: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/42.jpg)
Left positions diagram
diagram of equivalent positions
![Page 43: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/43.jpg)
Right positions
equivalent positions
these are fractional positions
(fractions of unit cell dimensions)
![Page 44: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/44.jpg)
2-fold axes
![Page 45: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/45.jpg)
P43212 symmetry
![Page 46: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/46.jpg)
P43212 symmetry 1
![Page 47: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/47.jpg)
P43212 symmetry 2
![Page 48: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/48.jpg)
P43212 symmetry 2b
![Page 49: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/49.jpg)
Multiple symmetry axes
Higher symmetry axes include lower symmetry ones
4 includes 2 6 “ 3 and 2 41 and 43 “ 21 42 “ 2 61 “ 31 and 21 65 “ 32 and 21 62 “ 32 and 2 64 “ 31 and 2 63 “ 3 and 21
![Page 50: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/50.jpg)
P43212 symmetry 3
![Page 51: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/51.jpg)
P43212 symmetry 4
![Page 52: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/52.jpg)
P43212 symmetry 4b
![Page 53: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/53.jpg)
P43212 symmetry 5
![Page 54: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/54.jpg)
P43212 symmetry 6
![Page 55: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/55.jpg)
P43212 symmetry 7
![Page 56: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/56.jpg)
P43212 symmetry 8
![Page 57: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/57.jpg)
P43212 symmetry 8b
![Page 58: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/58.jpg)
Right special positions
special positions
![Page 59: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/59.jpg)
Special positions 0
![Page 60: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/60.jpg)
Special positions 1
![Page 61: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/61.jpg)
Special positions 2
![Page 62: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/62.jpg)
Special positions 3
![Page 63: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/63.jpg)
Special positions 3b
![Page 64: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/64.jpg)
Special positions
Special positions
on non-translational symmetry elements (axes, mirrors or inversion centers)
degenerate positions (reduced number of sites)
sites have their own symmetry (same as the symmetry element)
![Page 65: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/65.jpg)
Right subgroups
subgroups
![Page 66: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/66.jpg)
Subgroups
Subgroups
reduced number of symmetry elements
cell dimensions may be special
cell may change
![Page 67: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/67.jpg)
Subgroups 0
![Page 68: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/68.jpg)
Subgroups 1a
![Page 69: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/69.jpg)
Subgroups 1b
![Page 70: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/70.jpg)
Subgroups PSCP
Dauter, Z., Li M. & Wlodawer, A. (2001). Acta Cryst. D57, 239-249.
After soaking in NaBr cell changed, half of reflections disappeared
![Page 71: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/71.jpg)
Right generators
group generators
![Page 72: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/72.jpg)
Right absences
systematic presences (not absences)
systematic absences result from translational symmetry elements
![Page 73: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/73.jpg)
Absences 1
![Page 74: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/74.jpg)
Absences 2
![Page 75: Title](https://reader036.vdocument.in/reader036/viewer/2022062518/56814446550346895db0e561/html5/thumbnails/75.jpg)
Personal remark
My personal remark:
I hate when people quote space groups
by numbers instead of name.
For me the orthorhombic space group
without any special positions is
P212121, not 19