1. 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. 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. 3. GEOMETRICAL OBJECTS SOURABH MUKTIBODH
4. 4. AND THE MONUMENTS SOURABH MUKTIBODH
5. 5. THE EIFFIL TOWER SOURABH MUKTIBODH
6. 6. BEAUTIFUL COLLOIDAL NANO-PARTICES - LOOK HOW BEAUTIFUL THEY ARE. SOURABH MUKTIBODH
7. 7. THE QUESTION IS- How to quantify this beauty aspect ? and The answer is. SOURABH MUKTIBODH
8. 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. 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. 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. 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. 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. 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. 14. FIND THE HIGHEST ORDER AXIS IN THE FOLLOWING MOLECULES- Choloromethane ferrocynide ion H ClH Cl SOURABH MUKTIBODH
15. 15. Cl B Cl Cl Cl O O O O O O biphenyl 18-crown-6 SOURABH MUKTIBODH
16. 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. 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. 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. 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. 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. 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. 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. 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. 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. 25. IDENTIFY THE MOLECULES WHICH CONTAIN POINT OF INVERSION H ClH Cl B Cl Cl Cl Cl ClCl SOURABH MUKTIBODH
26. 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. 27. IMPROPER ROTATION The staggered conformation of ethane has an S6 axis that goes through both carbon atoms. SOURABH MUKTIBODH
28. 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. 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. 30. IMPROPER ROTATION Likewise, an S2 axis is a center of inversion. S 2= i SOURABH MUKTIBODH
31. 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. 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. 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. 34. REFERENCES A.F.Cotton Chemical Applications of Group Theory ISBN 0471510947 Next- Molecular point group SOURABH MUKTIBODH