Symmetry &
Teory Group
OlehYateman Arryanto
The concept of symmetry is exist in an everyday sense.
If we say something is ‘symmetrical’, we usually mean it has mirror symmetry, or ‘left-right’ symmetry, and would look the same if viewed in a mirror.
Symmetry is also very important in chemistry.
Some molecules are clearly ‘more symmetrical’ than others, but what consequences does this have, if any?
Symmetry & Teory Group
The aim of this course is to provide a systematic treatment of symmetry in chemical systems within the mathematical framework known as group theory
Symmetry & Teory Group
The aim of applications of group theory are : Predicting whether a given molecule will
be chiral, or polar. Examining chemical bonding and
visualising molecular orbitals Chemical Properties
Predicting whether a molecule may absorb light, and which spectroscopic transitions occurs.
Investigating the vibrational motions of the molecule.
Symmetry, Art & Science
often used as an implied symbol
of the essential symmetry of the human body, and by
extension, to the universe as a whole
Symmetry & Nature
Symmetry & Nature
Symmetry & Nature
Apex episcopus Nautilus pompilus
Symmetry & Nature
Spiral Symmetry
Symmetry & Nature
Architecture (Spiral Symmetry)
Symmetry & Nature
(Bilateral / Mirror Sym)
Symmetry & Architecture
Taj Mahal (Agra, India) Giza Pyramid Field (Cairo, Egypt)
Symmetry & Architecture
Eiffel Tower (Paris)325 m, 10.1 tons)
Symmetry & Landscaping
Toukouji (Japan) Trocadero Palace (Paris) from Eiffel tower
Symmetry & Nature
Symmetry & Nature
Super-High Symmetry in Super-Low “Life Forms”
Super-High Symmetry in Super-Low “Life Forms”
Symmetry & Nature
Symmetry & Nature
Symmetry & Nature
Wallpaper pattern for Ontmoeting. From: M.C.Escher, 1944
A frieze pattern
Symmetry is BeautifulSymmetry is Living
Symmetry is chemistrySymmetry is Beautiful
Living
Be Symmetric and be best chemist
To make a beautiful life
The Icosahedron
The Icosahedron
The Dodecahedron
The Cube (Hexahedron)
The Oktahedron
The Tetrahedron
The Platonic Solids
The Cube The Methane Molecule
The Structure of Crystal
The Oktahedron
Simetri adalah PolaSimetri adalah KeteraturanSimetri adalah Keindahan
Belajar Simetri berarti belajar tentang pola, keteraturan,
keindahan sehingga dengan belajar simetri kita menjadi simetri dan mampu berperanan menciptakan
dunia yang teratur, simetri dan indah
(mamahayu ning bawono lan angkoso )
P. H. Walton “Beginning Group Theory for Chemistry”Oxford University Press Inc., New York, 1998ISBN 019855964
A.F.Cotton “ Chemical Applications of Group Theory”ISBN 0471510947
S.F.A Kettle “ Symmetry and Structure, Readable Group Theory for Chemist “, 2nd Edition, John Wiley & SonsISBN 0 471 9554 7
TEXT BOOKS
Symmetry Symmetry is the notion that
an object of study may look the same from different points of view.
Figure 1 : Bilateral and rotational symmetry. From: [8].
What is symmetry? An object displays symmetry if
you can “do something to it” (rotate it, reflect it, invert it etc.) without changing its appearance
The process of doing the rotation, reflection etc. Is referred to as a SYMMETRY OPERATION if it does not
change the appearance of the molecule
Symmetry elements
Symmetry element is the line about which a rotation occurs or the plane through which a reflection takes place etc,
Symmetry elements are labeled based on : Rotation axis, Cn ( The n indicates the
angle through which the rotation takes place. (Angle = 360/n )
Mirror plane, σh, σv, σd ( h=horizontal, v=vertical or d=dihedral mirror indicate orientation of plane with respect to any rotation axes )
Symmetry elements
Inversion center, i
Improper rotation axis, Sn (This involves a combination of rotation and reflection. The n indicates the angle through which the rotation takes place. Angle = 360/n
Identity, E (E is always a symmetry element as doing nothing to an object, always the same
Mirror planes
σv includes the principle rotation axis
σvσv
v = vertical
σh is perpendicular to the principle rotation axis
Mirror planes
σh
h = horizontal
σd includes the principle rotation axis, but lies between C2 axes that are perpendicular to the principle axis
Mirror planes
Mirror planes
Symmetry elements of benzene ringThere is one horizontal reflection plane σh and two sets of vertical reflection plane (σd) and (σh )
Mirror planes
Borazine
B B
Rotate 120O
F1 F1
F2F3
F3F2
Operation rotation by 360/3 around C3 axis (element)
Rotations 360/n where n is an integer
BF3
B B
Rotate 120O
F1 F1
F2F3
F3F2
Operation rotation by 360/3 around C3 axis (element)
Rotations 360/n where n is an integer
BF3
A threefold rotation and the corresponding C3 in NH3There are two rotation assosiated with this axis, one through 120o [ C3
+ ] and the other -120o [ C3
- ]
C3+ C3
+
C3-
Rotation axesRotasi positif
Rotasi negatif
An H2O molecule may be rotated through any angle about the bisector of the HOH bond angle, but only a rotation of 180o, C2 leaves it apparently unchanged
Rotation axes
Rotation axes examples 1
The two fold rotational axis in cis-dinitrogen di florida
Molecule having n fold axis(a) Amonia (b) penta carbonil iron, (c) hexa carbonil iron
(a) (b) (c)
C2 C2 C2
C2
C2
C2C2
C2
C2
C2, C3, C6
Symmetry of hexagonal planar
Rotation axes examples 1
Rotation axes examples 2
Molecules containing five-fold rotational axes(a)Eclipsed ferrocene side and top view
(b) Staggered ferrocene
Inversion center
The invertion operation and invertion center of SF6
Note inversion (i) and C2 are not equivalent
Inversion operation
Two fold rotation
Inversion center examples
The center of symmetry of 1,2-dimethyl-1,2 –diphenyldiphospine disulfide
(a) (b) (c)
(a) and (b) do not have inversion center
Improper rotation axes An improper rotation involves a combination of
rotation and reflection The rotation and the reflection do not have
to besymmetry operations of the molecule in their
own right
A fourfold axis of improper rotation S4 in the CH4 molecule