SYMMETRY ELEMENTS AND OPERATIONS PROF. SOURABH MUKTIBODH OLD GDC, INDORE The symmetry properties of molecules can be used to predict vibrational spectra, hybridization, optical activity, simplifying calculations in quantum mechanics etc. SOURABH MUKTIBODH
1. SYMMETRY ELEMENTS AND OPERATIONS PROF. SOURABH MUKTIBODH OLD
GDC, INDORE The symmetry properties of molecules can be used to
predict vibrational spectra, hybridization, optical activity,
simplifying calculations in quantum mechanics etc. SOURABH
MUKTIBODH
2. THE TERM SYMMETRY IS ASSOCIATED WITH- 1. Beauty 2.
Regularity 3. Periodicity 4. Harmonicity and 5. Systemization In
geometrical objects. (molecules for chemist) SOURABH MUKTIBODH
3. GEOMETRICAL OBJECTS SOURABH MUKTIBODH
4. AND THE MONUMENTS SOURABH MUKTIBODH
5. THE EIFFIL TOWER SOURABH MUKTIBODH
6. BEAUTIFUL COLLOIDAL NANO-PARTICES - LOOK HOW BEAUTIFUL THEY
ARE. SOURABH MUKTIBODH
7. THE QUESTION IS- How to quantify this beauty aspect ? and
The answer is. SOURABH MUKTIBODH
8. SYMMETRY ELEMENTS AND OPERATIONS Symmetry elements are
geometrical entities such as a plane, an axis (of rotation),
centers (of inversion), etc., through which a symmetry operation
can be performed. A molecule has a given symmetry element if the
operation leaves the molecule looks as if nothing has changed (even
though atoms and bonds may have been moved). A symmetry operation
produces a superimposable configuration. (equivalent or identical
configuration.) SOURABH MUKTIBODH
9. SYMMETRY ELEMENTS Element Symmetry Operation Symbol Identity
E n-fold axis Rotation by 2/n Cn Mirror plane Reflection Center of
in- Inversion i version n-fold axis of Rotation by 2/n Sn improper
rotation followed by reflection perpendicular to the axis of
rotation
10. IDENTITY, E All molecules have Identity. This operation
leaves the entire molecule unchanged. A highly asymmetric molecule
such as a tetrahedral carbon with 4 different groups attached has
only identity, and no other symmetry elements. It also signifies
operation of doing nothing. It is there for mathematical reasons.,
such as in Group theory. Note- some chemists do not consider this
as an operation. SOURABH MUKTIBODH
11. N-FOLD AXIS OF ROTATION Ammonia has a C3 axis. Note that
there are two operations associated with the C3 axis. Rotation by
120o in a clockwise or a counterclockwise direction provide two
different orientations of the molecule. SOURABH MUKTIBODH
12. LET US ROTATE BENZENE MOLECULE BY 60 DEGREE, PERPENDICULAR
TO THE MOLECULAR PLANE C6 1 = C6 1 C6 2 = C3 1 C6 3 = C2 1 C6 4 =
C3 2 C6 5 = C6 5 C6 6 = E Thus a C6 axis generates only two genuine
C6 operations. Others can be seen as lower order operations. A C6
thus generates- 2 C6 ,2 C3 , 1C2 1 2 6 3 5 4 6 1 5 2 4 3 5 6 4 1 3
2 4 5 3 6 2 1 3 4 2 5 1 6 2 3 1 4 5 SOURABH MUKTIBODH
13. A MOLECULE MAY CONTAIN SEVERAL AXES ( HIGHEST ORDER AXIS IS
KNOWN AS PRINCIPAL AXIS), SAY FOR EXAMPLE IN BORON TRIFLUORIDE
MOLECULE- C3 1 , C3 2 ,3 C2 B F 2 F 1 F 3 SOURABH MUKTIBODH
14. FIND THE HIGHEST ORDER AXIS IN THE FOLLOWING MOLECULES-
Choloromethane ferrocynide ion H ClH Cl SOURABH MUKTIBODH
15. Cl B Cl Cl Cl O O O O O O biphenyl 18-crown-6 SOURABH
MUKTIBODH
16. MIRROR PLANES/ SYMMETRY The reflection of the water
molecule in either of its two mirror planes results in a molecule
that looks unchanged. A plane of reflection bisects the molecule
into equal halves. This operation is denoted by . SOURABH
MUKTIBODH
17. REFLECTING TWICE BY THE SAME PLANE OF COURSE GIVES ORIGINAL
CONFIGURATION - Plane of symmetry or mirror plane does not generate
number of symmetry operations. As it is obvious that- 1 = 2 = E 3 =
4 = E Thus n = if n= odd and n = E if n = even SOURABH
MUKTIBODH
18. TYPES OF MIRROR PLANES- THEY HAVE BEEN CLASSIFIED AS OF
THREE TYPES- 1. vertical plane of reflection- denoted by v 2.
Horizontal plane of of reflection - denoted by h 3. Dihedral plane
of reflection - denoted by d SOURABH MUKTIBODH
19. MIRROR PLANES / SYMMETRY The subscript v in v, indicates a
vertical plane of symmetry. This indicates that the mirror plane
includes the principal axis of rotation (C2). SOURABH
MUKTIBODH
20. MIRROR PLANES- HORIZONTAL PLANE The benzene ring has a C6
axis as its principal axis of rotation. The molecular plane is
perpendicular to the C6 axis, and is designated as a horizontal
plane, h. All planar molecules have horizontal plane of reflection.
C6 . SOURABH MUKTIBODH
21. MIRROR PLANES- DIHEDRAL PLANE The vertical planes, v, go
through the carbon atoms, and include the C6 axis. The planes that
bisect the bonds are called dihedral planes, d. A dihedral plane
passes between two mutually perpendicular C2 C6 . SOURABH
MUKTIBODH
22. XENON TETRAFLUORIDE MOLECULE CONTAINS ALL THREE TYPES OF
PLANES- Xe F F F F Xe F F F F Xe F F F F SOURABH MUKTIBODH
23. CENTRE OF INVERSION/ CENTER OF SYMMETRY The inversion
operation projects each atom through the center of inversion, and
across to the other side of the molecule. This operation is
symbolized by i . SOURABH MUKTIBODH
24. INVERSION CENTRE We proceed to identify centre of symmetry
as following- 1. choose a centre within the molecule. 2. draw lines
in the direction where the atoms are located. 3. if the same atom
in equal and opposite direction is seen, true for every situation,
than the molecule possesses a centre of symmetry. SOURABH
MUKTIBODH
25. IDENTIFY THE MOLECULES WHICH CONTAIN POINT OF INVERSION H
ClH Cl B Cl Cl Cl Cl ClCl SOURABH MUKTIBODH
26. IMPROPER ROTATION An improper rotation is rotation,
followed by reflection in the plane perpendicular to the axis of
rotation. Thus Sn = Cn * i = i * Cn both independent symmetry
operations commute. Essentially Cn SOURABH MUKTIBODH
27. IMPROPER ROTATION The staggered conformation of ethane has
an S6 axis that goes through both carbon atoms. SOURABH
MUKTIBODH
28. IMPROPER ROTATION Note that an S1 axis doesnt exist; it is
same as a mirror plane. S1 = C1 1 * 1 = E * 1 = SOURABH
MUKTIBODH
29. NOTE THAT SIMILAR TO PROPER ROTATION, IMPROPER ROTATION
ALSO GENERATES N-1 OPERATIONS, N BEING THE ORDER OF AXIS-S4 1 = C4
1 * 1 = S4 1 S4 2 = C4 2 * 2 = C2 * E = C2 1 S4 3 = C4 3 * 3 = S4 3
S4 4 = C4 4 * 4 = E * E = E Out of four such combinations, only two
are true S4 representations. Thus a S4 axis generates only two
genuine symmetry operations. SOURABH MUKTIBODH
30. IMPROPER ROTATION Likewise, an S2 axis is a center of
inversion. S 2= i SOURABH MUKTIBODH
31. EX. IDENTIFY ALL SYMMETRY ELEMENTS AND OPERATIONS OF THE
FOLLOWING MOLECULES- O HH N H H H E C2 v v` E C3 3v SOURABH
MUKTIBODH
32. SIMILARLY IDENTIFY ALL ELEMENTS AND OPERATIONS FOR
SYMMETRIC BF3 MOLECULE E C3 1 and C3 2 C2 (Along BF1 bond) C2
(Along BF2 bond) C2 (Along BF3 bond) v (Along BF1 bond) v ` (Along
BF2 bond) v (Along BF3 bond) h ( molecular plane) S3 1 and S3 2 B F
2 F 1 F 3 SOURABH MUKTIBODH
33. SUMMARY 1. Symmetry elements and operations are though, two
slightly different terms, but are often treated collectively. 2. A
symmetry operation produces superimposable configuration. 3. There
are five fundamental symmetry elements and operations. They are 1.
identity (E) 2. proper rotation ( Cn) 3. mirror symmetry or
reflection () 4. centre of symmetry or inversion centre (i) and 5.
improper rotation.(Sn) 4. A molecule may or may not contain all
symmetry elements and operations. More operations present assures
more symmetric nature. 5. Symmetry elements and operations allow us
to identify point group of the molecule and then detailed
applications of group theory can be explored. SOURABH
MUKTIBODH
34. REFERENCES A.F.Cotton Chemical Applications of Group Theory
ISBN 0471510947 Next- Molecular point group SOURABH MUKTIBODH