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What is Symmetry ? Symmetry Operations and Symmetry Elements: Identity, E C3H6O3 DNA CHClBrF
Symmetry Operations and Symmetry Elements: Cn Ammonia
Water
Symmetry Operations and Symmetry Elements:
n­fold Rotation, Cn C2
Symmetry Operations and Symmetry Elements:
n­fold Rotation, Cn C3
Ammonia NH3
Symmetry Operations and Symmetry Elements:
n­fold Rotation, Cn C6
Benzene: one C6 axis and six C2 axes
Symmetry Operations and Symmetry Elements:
n­fold Rotation, C HCN
Symmetry Operations and Symmetry Elements:
Reflection, v H2O
BF3
Symmetry Operations and Symmetry Elements:
Reflection, h Symmetry Operations and Symmetry Elements:
Inversion, i SF4
PF5
SF6
Symmetry Operations and Symmetry Elements:
n­fold Improper Rotation, Sn Methane CH4
Ethane C2H6
Molecular symmetry groups Group Ci
Molecular symmetry groups Group C2
Molecular symmetry groups: Cnv NH_3: Group C3v
H2O: Group C2v
Molecular symmetry groups: Cnh Butadiene C4H6: C2h group
C3h group
Relation Between C2+ h and the Inversion C2 h = i
Molecular symmetry groups: Dn D6 group
Molecular symmetry groups: Dnd Molecular symmetry groups: Dnh Benzene C6H6: D6h group BF3: D3h group Molecular symmetry groups: Sn The cubic groups: Td and Oh Tetrahedral molecule
CH4: Td group
Octahedral molecule
SF6: Oh group
The cubic groups: T and O Tetrahedral molecule
Octahedral molecule
Group Multiplication Table: NH3 molecule E, C3+, C3­, v, v’, v’’ va
C3 = vb
C3 va = vc
Determining the Point Group of a Molecule
A Fow Dyagram
Molecular Vibrations: Normal Modes of an Elastic Bar
x
/ y = 2.4461…
x
/ y = 5/3
x
= y Normal Vibrational Modes: Thriatomics H2O
CO2
Effect of the C∞ on degenerate vibration
Normal Vibrational Modes: H2CO (formaldehyde) Model
xy
Symmetry of Vibrational Wavefunctions:
Non­degenerate Vibration Symmetric Vibration
A∙Qi = Qi
v = 2 1 0
A∙ vi(Qi) = vi(Qi)
1
Antisymmetric Vibration
0.75
0.5
A∙Qi = – Qi
0.25
­4
­2
2
­0.25
­0.5
­0.75
4
A∙ vi(Qi) = (­1)vi vi(Qi)
Symmetry of Electronic Orbitals Symmetry of two p orbitals under reflection through the mirror plane
Symmetry of Electronic Orbitals: H2O O2px = b1
O2py = b2
O2pz = a1
Molecular plane is YZ
Classes of Symmetry Operations: C3v group Linear Combinations of Atomic Orbitals: C2v group NO2: = Op1x – Op 2x χ(E) = 1
χ(C2) = 1
χ( v) = –1
χ( v') = –1
Linear Combinations of Atomic Orbitals: C3v group NH3: = sa + sb + sc
NH3: 1 = – sa + ½(sb + sc)
a
b
c
NH3: 2 = sb – sc
H3C – CCl3: = pa + pb + pc
Vanishing Integrals I = f1f2 d Building of Bonding and Antibonding Orbitals a1 molecular orbital s1 = Ha(1s) + Hb(1s) + Hc(1s)
N(2s) + s1
Building of Bonding and Antibonding Orbitals e molecular orbitals
s2 = – Ha(1s) + ½Hb(1s) + ½Hc(1s)
N(2px) + s2
s3 = Hb(1s) – Hc(1s)
N(2py) + s3
Selection Rules for Electronic Transitions
C2v symmetry