Download - GROUP THEORY ( SYMMETRY)
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Done by Shobana.N.S
SymmetryBY
SHOBANA.N.SQUEEN MARY’S COLLEGE
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Symmetry is present in nature and in human culture
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Understand what orbitals are used in bonding.
Predict optical activity of a molecule.
Predict IR and Raman spectral activity
Using symmetry in Chemistry
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A molecule or object is said to possess a particular operation if that operation when applied leaves the molecule unchanged.
Symmetry operations
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There are 5 kinds of operations
1. Identity2. n-Fold Rotations3. Reflection4. Inversion5. Improper n-Fold Rotation
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IDENTITY
E (Identity Operation) = no change in the object.
Needed for mathematical completeness.
Every molecule has at least this symmetry operation.
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It is equal to rotation of the object 360/n degree about an axis .
The symmetry element is line.
Principle axis = axis with the largest possible n value.
Cnn Is equal to identity (E)
Cn Rotation (n-fold rotation)
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Symmetry element is plane.
Linear object has infinite σ.
σv- plane including principle axis
σh- plane perpendicular to principle axis.
σd- plane bisecting the dihedral angle between two σv plane.
REFLECTION OPERATION (σ)
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(x,y,z) --> (-x,-y,-z).
Symmetry element : point
Symmetry operation : inversion through a point.
i n is equal to identity (E)
INVERSION
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It is also known as ROTATION-REFLECTION AXIS.
Rotation followed by reflection.
Snn = E ( n= even number)
Sn2n = E ( n= odd number)
Improper axis of symmetry
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A symmetry element is a point of reference about which symmetry operations can take place
Symmetry elements can be 1. point 2. axis and 3. plane
Symmetry elements
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Symmetry element : point
Symmetry operation : inversion
Center of Symmetry
1,3-trans-disubstituted cyclobutane
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Symmetry element : plane
Symmetry operation : reflection
Plane of Symmetry
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Symmetry element : line
Symmetry operation : rotation
Axis of Symmetry
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element operation symbol
symmetry plane reflection through plane σ
inversion centerinversion: every point x,y,z translated to -x,-y,-z
i
proper axis rotation about axis by 360/n degrees Cn
improper axis
1. rotation by 360/n degrees2. reflection through plane perpendicular to rotation axis
Sn
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Point group
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The collection of symmetry elements present in a molecule forms a ‘group’, typically called a POINT GROUP.
The symmetry elements can combine only in a limited number of ways and these combinations are called the POINT GROUP.
WHY IS IT CALLED A “POINT GROUP”??
Because all the symmetry elements (points, lines, and planes) will intersect at a single point.
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Cyclic Symmetries
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Ci has 2 symmetry operations : E the identity operation
i point of inversion
Ci Group
C2H2F2Cl2
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It has two symmetry operations
E – identity operation
σ – reflection
Cs group
CH2BrCl
1- bromo, 2-chloro ethene
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Only one symmetry operation (E)
Molecules in this group have no symmetry
This means no symmetrical operations possible.
C1 axis of rotation
CHFBrClBromochlorofluoromethane
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C2 axis of rotationRotation of the molecule to 180 degree.
This point group contains only two symmetry operations:
E the identity operationC2 a twofold symmetry axis
Examples : water, chlorine trifluoride, hydrogen peroxide, formaldehyde
hydrazine
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24(2R,3R)-tartaric acid D-mannitol
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C3 axis of rotationRotation of the molecule to 120 degree.
This point group contains only two symmetry operations:
E the identity operationC3 a three fold symmetry axis
Examples: ammonia, boron trifluoride, triphenyl phosphine
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9b H-Phenalene 3,7,11-trimethyl cyclo dodeca 1,5,9-triene
2,6,7-trimethyl-1-aza-bicyclo [2.2.2]octane
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This point group contains the following symmetry operations
E the identity operation Cn n-fold symmetry axis.
nσv n reflection operation
Cnv Point Group
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This point group contains the following symmetry operations
E the identity operation
C2 2-fold symmetry axis.
2σv reflection operation
C2v Point Group
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Examples:
1. Ozone2. Thiophene3. Furan4. Pyridine
Sulphur dioxide
Formaldehyde(Z)-1,2-DICHLORO ETHENE
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30m-Xylene
Phenanthrene
O-dichloro benzenep-dichloro benzene
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Cyclohexane (boat) Water
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This point group contains the following symmetry operations
E the identity operation
C3 3-fold symmetry axis.
3σv reflection operation
C3v Point Group
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Examples:
Ammonia POCl3 Trichloro methane
Tert-butyl bromide
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This point group contains the following symmetry operations
E the identity operation
C4 n-fold symmetry axis.
4σv n reflection operation
C4v Point Group
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EXAMPLES
Xenon oxytetrafluoride
Sulfur chloride pentafluorideBromine pentafluoride
Fluorine pentafluoride
Calix[4]arene
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This point group contains the following symmetry operations
E the identity operation
C∞ ∞ -fold symmetry axis. ∞ σv n reflection operation
C∞v Point Group
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Linear Hetero nuclear Diatomic Molecule belongs to this category
These molecules don’t have centre of inversion.
Chloro ethyne
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This point group contains the following symmetry operations
E the identity operation
Cn n-fold symmetry axis. σh n reflection operation
NOTE : If n is even ‘i’ is present.
Cnh Point Group
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This point group contains the following symmetry operations
E the identity operation
C2 2-fold symmetry axis. σh reflection operation i inversion
C2h Point Group
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EXAMPLES
trans-1,2-dichloroethylene
Trans-1,3-butadiene
C2H2F2
N2F2
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1,4-dibromo-2,5-dichloro-benzene (E)-1,2-dichloro ethene
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This point group contains the following symmetry operations
E the identity operation
C3 3-fold symmetry axis. σh reflection operation
S3 improper axis of symmetry
C3h Point Group
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Benzene-1,3,5-triol
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DIHEDRAL GROUP
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This point group contains the following symmetry operations
E the identity operation
Cn n-fold symmetry axis.
nC2 2-fold symmetry axis. (perpendicular to Cn)
Dn Point Group
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This point group contains the following symmetry operations
E the identity operation
C2 n-fold symmetry axis.
2C2 2-fold symmetry axis.
D2 Point Group
twistane
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D3 Point Group This point group contains the following
symmetry operations
E the identity operation
C3 3-fold symmetry axis.
3C2 2-fold symmetry axis.
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Examples Ru(en)3
Perchlorotriphenylamine
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Tris(oxalato)iron111 Molecular knot
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This point group contains the following symmetry operations
E the identity operation
Cn n-fold symmetry axis.
nC2 2-fold symmetry axis.
nσd dihedral plane
Dnd Point Group
NOTE : ‘i’ is present when n is odd and S2n coincident to C2 axis
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This point group contains the following symmetry operations
E the identity operation
C2 n-fold symmetry axis.
2C2* 2-fold symmetry axis.
2σd dihedral plane
2S4 improper axis of symmetry
D2d Point Group
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allene (propa-1,2-diene) biphenyl
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COT1,3,5,7-
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This point group contains the following symmetry operations
E the identity operation
C3 n-fold symmetry axis.
2C2 2-fold symmetry axis.
3σd dihedral plane
2S6 improper axis of symmetry
D3d Point Group
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Cyclohexane chair form
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Ethane staggered form
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This point group contains the following symmetry operations
E the identity operation
2C4 n-fold symmetry axis.
4C2* 2-fold symmetry axis.
4σd dihedral plane
S8 improper axis of symmetry
C2 2-fold symmetry axis.
D4d Point Group
Mn2(CO)10
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This point group contains the following symmetry operations
E the identity operation
4C5 n-fold symmetry axis.
5C2* 2-fold symmetry axis.
5σd dihedral plane
S10 improper axis of symmetry
i inversion
D5d Point Group
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This point group contains the following symmetry operations
E the identity operation
Cn n-fold symmetry axis.
nC2 2-fold symmetry axis.
σh horizontal plane
nσv vertical plane
Sn improper axis of symmetry
Dnh Point Group
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D2h Point Group This point group contains the following symmetry operations
E the identity operation
C2 n-fold symmetry axis.
2C2 2-fold symmetry axis.
σh horizontal plane
2σv vertical plane
S2 improper axis of symmetry
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M2F6
ETHENE
DIBORANE
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1,4-DICHLOROBENZENE
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[2,2] PARACYCLOPHANE
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D3h Point Group This point group contains the following symmetry operations
E the identity operation
C3 3-fold symmetry axis.
3C2 2-fold symmetry axis.
σh horizontal plane
2σv vertical plane
2S3 improper axis of symmetry
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cyclopropane
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D4h Point Group This point group contains the following symmetry operations
E the identity operation
C4 4-fold symmetry axis.
4C2 2-fold symmetry axis.
σh horizontal plane
4σv vertical plane
S4 improper axis of symmetry
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Nickel tetracarbonyl
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[AlCl₄]− Xenon tetrafluoride
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D5h Point Group This point group contains the following symmetry operations
E the identity operation
C5 4-fold symmetry axis.
5C2 2-fold symmetry axis.
σh horizontal plane
5σv vertical plane
S5 improper axis of symmetry
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D6h Point Group This point group contains the following symmetry operations
E the identity operation
C6 6-fold symmetry axis.
6C2 2-fold symmetry axis.
σh horizontal plane
6σv vertical plane
S6 improper axis of symmetry
i inversion
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D∞h Point Group This point group contains the following symmetry operations
E the identity operation
C ∞ 4-fold symmetry axis.
∞ C2 2-fold symmetry axis. σh horizontal plane ∞ σv vertical plane
S ∞ improper axis of symmetry
i inversion
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LINEAR HOMONUCLEAR DIATOMIC MOLECULE
POSSESS CENTER OF SYMMETRY
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Cubic Point Group
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Tetrahedral Point Group
This point group contains the following symmetry operations
E the identity operation
4C3 3-fold symmetry axis.
3C2 2-fold symmetry axis.
6σd dihedral plane
3S4 improper axis of symmetry Total: 24 elements
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METHANE
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NEOPENTANE
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Octahedral Point Group
This point group contains the following symmetry operations
E the identity operation
3C4 4-fold symmetry axis.
3C2 2-fold symmetry axis.
3σh dihedral plane
3S4 improper axis of symmetry
i inversion
C3 3-fold symmetry axis
S6 improper axis of symmetry
6C2 2-fold symmetry axis.
6σd dihedral plane
TOTAL :48 elements
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Cr(CO)6[PtCl6]2-
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PF6- CUBANE
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SF6
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Icosohedral (Ih) This point group contains the following symmetry operations
E the identity operation
20C3 3-fold symmetry axis.
15C2 2-fold symmetry axis.
15σh horizontal plane
20S6 improper axis of symmetry
i inversion
20C3 3-fold symmetry axis
12S10 improper axis of symmetry
12C5 5-fold symmetry axis.
12S10* improper axis of symmetry
TOTAL : 120 elements
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dodecahedran fullerenes
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