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5. Why Inorganic Chemistry?
2008 Dodge Nitro Dodge Neon
2008 Chevrolet Cobalt Saturn Ion
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6. Lecture 6 Periodic properties of atoms Ionization energy
Electron affinity
Atom size
Electronegativity
Electronic structure of molecules
VSEPR
Molecular symmetry
Group theory
September 9, 2010
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7. Structures of Monocentric Molecules
Molecules of a given ABnEm
type are isostructural.
Terminal atoms are arranged around the central atom such that Coulomb repulsion between electron pairs on central atom are minimized.
Lone pairs tend to occupy more space around the central atom than bonding pairs.
Multiple bonds occupy more space around the central atom than single bonds.
Model applies to:
main group elements
transition metals with d0, d5, and d10 configuration
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X = Cl, Br, I; R = alkyl, aryl.

8. “Nature-made” Symmetry
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9. “Nature-made” Symmetry
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10. “Nature-made” Symmetry
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11. “Man-made” Symmetry
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12. “Man-made” Symmetry
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13. “Chemist-made” Symmetry
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14. From Molecular Formula to Properties
Molecule
Structure
Point Group
Orbital Symmetry
Bonding Description
Properties
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15. Symmetry Elements and Operations
Symmetry operation: reorientation of a body such that the initial and final orientations are indistinguishable.
Symmetry element: geometrical entity (line, point, or plane) with respect to which a symmetry operation is performed.
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16. Symmetry Elements and Operations
INVERSION
REFLECTION
ROTATION
IMPROPER ROTATION
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17. Case Study: IF5(AB5E) 4 1 2 3 5 C41, C43, C2 5 2 1 4 3 5 4 3 sV2 sd2
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18. Case Study: IF5(AB5E) (cont.)
C41, C43, C2 z
C41, C43, C2 5 4 3
sV2
sV2
sd1
sd1 1 x 2
sd2
sd2
sV1 y
sV1
E C41,C C sv1, sv sd1, sd2
The collection of all symmetry elements of a molecule form a Point Group.
C4v
E C4 C sv 2sd1
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19. Character Table of Point Groups (See also Table 4-7 of textbook)
h, Order of group =
# symmetry operations
= 8
Classes of operations
C4v 1E 2C4 1C sv sd A A B B E c,
Dimension of irreducible representations
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20. Character Tables of Point Groups
C2v
E C svxz svyz
A z, x2,y2, z2
A Rz, xy
B x, Ry, xz
B y, Rx, yz
x, y, z axes or p orbitals at the central atom of a molecule; z axis
coincides with highest order axis of the molecule
xy, xz, yz planes defined by the x and y, x and z, or y and z axes, respectively
Rx, Ry, Rz rotation around the x, y, and z axes, respectively
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21. Point Group Assignment
Does the molecule belong to a special group?
linear molecules D∞h (CO2) or C∞v (HCl, CO)
molecules with multiple high order axes:
Oh octahedral (SF6) or Td tetrahedral (CH4)
Molecule doesn’t have proper or improper rotation axes
C1, no symmetry element except identity, CHClBrF
Cs, molecule has only a symmetry plane, H2CCBrCl
Ci, molecule has only an inversion center
Molecule has only Sn axes, Sn
Decision tree for C and D groups
Identify Cn (highest order)
No C2 Cn nC2 Cn
There is sh no sh There is sh no sh
There is sv no sv There is sd no sd
Cnh Cnv Cn Dnh Dnd Dn
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22. Irreducible and Reducible Representations
C2v
E C svxz svyz G
A z, x2,y2, z2
A Rz, xy
B x, Ry, xz
B y, Rx, yz
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23. You should be able to:
Identify and show the symmetry operations of a molecule
Determine the point group of a molecule
Apply symmetry operations to atoms, orbitals or (x,y,z) axes centered at an atom in the molecule
Determine the irreducible representation(s) corresponding to the p orbitals of the central atom of a molecule or of axes centered at the central atom of the molecule
Determine if a group of 1 or more atoms, orbitals, or axes centered at atoms in a molecule are or are not a representation of the point group of a molecule
Calculate the total degrees of freedom for a given molecule
Determine the irreducible representations corresponding to translations and rotations of molecules
Calculate the number of vibrations of a linear or non-linear molecule
Decompose a reducible representation in irreducible representations
Determine the symmetry of vibrations
Determine which vibrations are IR and/or Raman active
Determine if a molecule can have a dipole moment based on its symmetry/point group
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24. Irreducible and Reducible Representations
C2v
E C svxz svyz G
A z, x2,y2, z2
A Rz, xy
B x, Ry, xz
B y, Rx, yz
# of classes of operations = # irreducible representations
h = sum(cE(j))2, j represents irreducible representations
Formula for reducing reducible representations:
# of operations
in class R
character of reducible
representation for class R
character of irreducible
representation for class R
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25. Molecular Vibrations for H2O
C2v
E C svxz svyz G
A z, x2,y2, z2
A Rz, xy
B x, Ry, xz
B y, Rx, yz
Translations along x, y, and z:
A1,B1,B2
Rotations around x, y, and z:
A2,B1,B2
Vibrations:
2A1+B1
# (A1) = (1x9-1x1+3x1+1x1)/4 = 3
# (A2) = (1x9-1x1-3x1-1x1)/4 = 1
# (B1) = (1x9+1x1+3x1-1x1)/4 = 3
# (B2) = (1x9+1x1-3x1+1x1)/4 = 2
G = 3A1 + 1A2 + 3B1 + 2B2
A molecular vibration is infrared active if it changes the molecule dipole moment. In group theory, this rule translates in the fact that a vibration is IR active if it corresponds to an irreducible representation with the same symmetry as the cartesian coordinates x, y, and/or z.
Polarizability is the relative tendency of a molecule’s charge to be distorted from its normal shape by an external electric field, such as an externally applied field or that caused by another molecule.
A molecular vibration is Raman active if it changes the polarizability of the molecule . In group theory, this rule translates in the fact that a vibration is Raman active if it corresponds to an irreducible representation with the same symmetry as a product of cartesian coordinates , ie x2, y2, z2, xy, xz, yz.
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26. Molecular Vibrations for H2O Table 4-11, p. 106
H H A1
Symmetric
stretch
IR active
3652 cm-1 B1
Antisymmetric
3756 cm-1
bend
1545 cm-1
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27. IR and Raman Spectroscopy
IR Spectroscopy
IR light source
IR light detector
Incident Light
Transmitted
Light
Sample cell
IR light detector
Scattered
Light
Sample cell
Incident Light
IR light source
Raman Spectroscopy
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28. Q charge on each of two atoms separated by distance r
Dipole Moment
= Qr
is the dipole moment
Q charge on each of two atoms separated by distance r
H - Br
r = Å
e- charge
= x (1.602 x C) x (1.415 x m) = x Cm = D
D = Debye = x Cm
H - Br
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29. Dipole Moment
Molecule types that may have dipole moment (Section 3-3):
molecules with no inversion center
molecules with coincident Cn axes
molecules with one mirror plane and no Cn axis
molecules with mirror planes that contain the coincident Cn axes
molecules with no symmetry
Only molecules of symmetry Cn, Cnv, and Cs, may have a dipole moment.
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