ir vs raman spectroscopy - chem.fsu.edu

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Part 2.10: Vibrational Spectroscopy

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Single Atom

No RotationA point cannot rotate

3 Degrees of Freedom (DOF)0 Vibrations

Vibration- Atoms of a molecule changing their relative positions without changing the position of the molecular center of mass.

No Vibartion“It takes two to vibrate”

TranslationCan move in x, y, and/or z

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Diatomic Molecule

6 DOF- 3 Translation- 2 Rotation 1 Vibration

2 atoms x 3 DOF = 6 DOFTranslation

Rotation

For a Linear Molecule# of Vibrations = 3N-5

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Linear Triatomic Molecule

3 atoms x 3 DOF = 9 DOF

For a Linear Molecule# of Vibrations = 3N-5

O C O


Argon (1% of the atmosphere)-3 DOF, 0 Vibrations

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Nonlinear Triatomic Molecule


3 Translation3 Rotation

Linear non-linear

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For a nonlinear Molecule# of Vibrations = 3N-6

Rz

Rx

Ry

Transz

Transy

Transx

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For a nonlinear Molecule# of Vibrations = 3N-6

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Molecular VibrationsAtoms of a molecule changing their relative positions without changing the position of the molecular center of mass.

Even at Absolute Zero!

In terms of the molecular geometry these vibrations amount to continuously changing bond lengths and bond angles.

Center of Mass

Reduced Mass

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Molecular Vibrations

Hooke’s Law

Assumes-It takes the same energy to stretch the bond as to compress it.

The bond length can be infinite.

k = force constantx = distance

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Molecular VibrationsVibration Frequency (n)

Related to:Stiffness of the bond (k).

Atomic masses (reduced mass, m).

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Molecular Vibrations

Classical Spring

Quantum Behavior

Sometimes a classical description is good enough. Especially at low energies.

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6 Types of Vibrational ModesSymmetric Stretch

Twisting

Assymmetric Stretch Wagging

Scissoring Rocking

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What kind of information can be deduced about the internal motion of the molecule from its point-group symmetry?

Each normal mode of vibration forms a basis for an irreducible representation of the point group of the molecule.

1) Find number/symmetry of vibrational modes.

2) Assign the symmetry of known vibrations.

3) What does the vibration look like?

4) Find if a vibrational mode is IR or Raman Active.

Vibrations and Group Theory

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1) Finding Vibrational Modes1. Assign a point group2. Choose basis function (three Cartesian

coordinates or a specific bond)3. Apply operations

-if the basis stays the same = +1-if the basis is reversed = -1-if it is a more complicated change = 0

4. Generate a reducible representation5. Reduce to Irreducible Representation6. Subtract Translational and Rotational Motion

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Example: H2O

C2v point groupBasis: x1-3, y1-3 and z1-3

E: 3 + 3 + 3 = 9

1. Assign a point group2. Choose basis function3. Apply operations


HOH

E

Atom 1: x1 = 1 y1 = 1 z1 = 1

Atom 2: x2 = 1 y2 = 1 z2 = 1

Atom 3: x3 = 1 y3 = 1 z3 = 1

Atom: 1 2 3

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Example: H2O


E: 3 + 3 + 3 = 9

C2: 0 + -1 + 0 = -1



HOH

C2

Atom 1: x1 = 0 y1 = 0 z1 = 0

Atom 2: x2 = -1 y2 = -1 z2 = 1

Atom 3: x3 = 0 y3 = 0 z3 = 0

Atom: 1 2 3

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Example: H2O


E: 3 + 3 + 3 = 9

C2: 0 + -1 + 0 = -1

sxz: 0 + 1 + 0 = 1



HOH

sxz

Atom 1: x1 = 0 y1 = 0 z1 = 0

Atom 2: x2 = 1 y2 = -1 z2 = 1

Atom 3: x3 = 0 y3 = 0 z3 = 0

Atom: 1 2 3

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Example: H2O


E: 3 + 3 + 3 = 9

C2: 0 + -1 + 0 = -1

sxz: 0 + 1 + 0 = 1



HOH

syz: 1 + 1 + 1 = 3

syz

Atom 1: x1 = -1 y1 = 1 z1 = 1

Atom 2: x2 = -1 y2 = 1 z2 = 1

Atom 3: x3 = -1 y3 = 1 z3 = 1

Atom: 1 2 3

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Example: H2O1. Assign a point group2. Choose basis function3. Apply operations


4. Generate a reducible representation

G 9 3-1 1


E: 3 + 3 + 3 = 9

C2: 0 + -1 + 0 = -1

sxz: 0 + 1 + 0 = 1

HOH

syz: 1 + 1 + 1 = 3

Atom: 1 2 3

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4. Generate a reducible representation5. Reduce to Irreducible Representation

Reducible Rep. Irreducible Rep.


HOH

G 9 3-1 1

Example: H2O

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Decomposition/Reduction Formula

h = 1 + 1 + 1 + 1 = 4 order (h)

aA1 = + (1)(-1)(1) + (1)(1)(1) + (1)(3)(1) 14 [ ](1)(9)(1) = 3 = 12

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Example: H2O

G 9 3-1 1

G = 3A1 + A2 + 2B1 + 3B2

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4. Generate a reducible representation5. Reduce to Irreducible Representation6. Subtract Rot. and Trans.


HOH

Example: H2O

G = 3A1 + A2 + 2B1 + 3B2

3 atoms x 3 DOF = 9 DOF3N-6 = 3 Vibrations

Trans = A1 + B1 + B2

Rot = A2 + B1 + B2

Vib = 2A1 + B2

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4. Generate a reducible representation5. Reduce to Irreducible Representation6. Subtract Rot. and Trans.


HOH

Example: H2O

Vibration = 2A1 + B2

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B2

A1

A1

1. Start with a drawing of a molecule2. Draw arrows3. Use the Character Table4. Predict a physically observable phenomenon

Example: H2O


HOH

Vibrations = 2A1 + B2

All three are IR active but that is not always the case.

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2) Assign the Symmetry of a Known Vibrations

1. Assign a point group2. Choose basis function (stretch or bend)3. Apply operations



Vibrations = 2A1 + B2

Stretch Stretch Bend

HOH

Bend

HOH

Stretch

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-if the basis stays the same = +1-if the basis is reversed = -1 -if it is a more complicated change = 0

C2v point groupBasis: Bend angle

Example: H2O

HOH

sxz

E: 1

C2: 1

sxz: 1

syz: 1

HOH H

OH

EHOH H

OH

C2

HOH H

OH

syzHOH H

OH

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C2v point groupBasis: Bend angle

G 1 11 1

Example: H2O

HOH

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Vibrations = A1 + B2


A1

1. Assign a point group2. Choose basis function (stretch)3. Apply operations



HOH

Stretch

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C2v point groupBasis: OH stretch

Example: H2O

HOH

sxz

E: 2

C2: 0

sxz: 0

syz: 2

E

C2

syz

HOH H

OH

HOH

HOH

HOH H

OH

HOH

HOH

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G 2 20 0

Example: H2O

C2v point groupBasis: OH stretch

HOH

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Decomposition/Reduction Formula

h = 1 + 1 + 1 + 1 = 4 order (h)

aA1 = + (1)(0)(1) + (1)(0)(1) + (1)(2)(1) 14 [ ](1)(2)(1) = 1 = 4

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Example: H2O

G 2 20 0

G = A1 + B2

aB2 = + (1)(0)(-1) + (1)(0)(-1) + (1)(2)(1) 4 (1)(2)(1) = 1 =

4 1 [ ] 4

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Vibrations = A1 + B2


A1


By Inspection By Projection Operator

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G = A1 + B2

By Inspection

G 1 11 1 G 1 1-1 -1

A1 B2

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3) What does the vibration look like?Projection Operator

1. Assign a point group2. Choose non-symmetry basis (Dr1)3. Choose a irreducible representation (A1 or B2)4. Apply Equation

- Use operations to find new non-symmetry basis (Dr1)- Multiply by characters in the irreducible representation

5. Apply answer to structure

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3) What does the vibration look like?Projection Operator

1. Assign a point group2. Choose non-symmetry basis (Dr1)3. Choose a irreducible representation (A1)4. Apply Equation


C2v point groupBasis: Dr1

sxz

E

C2

syz

For A1

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1. Assign a point group2. Choose non-symmetry basis (Dr1)3. Choose a irreducible representation (A1)4. Apply Equation


sxz

E

C2

syz

Projection Operator


For A1

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1. Assign a point group2. Choose non-symmetry basis (Dr1)3. Choose a irreducible representation (B2)4. Apply Equation


sxz

E

C2

syz

Projection Operator


For B2

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1. Assign a point group2. Choose non-symmetry basis (Dr1)3. Choose a irreducible representation (B2)4. Apply Equation


5. Apply answer to structure

Projection Operator


B2A1

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Bend Symmetric Stretch Asymmetric Stretch

A1

B2

A1

A1

A1 B2

Molecular Structure+

Point Group=

Find/draw the vibrational modes of

the molecule

Does not tell us the energy!

Does not tell us IR or Raman active!

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Vibrations of C60

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Vibrations of C60

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Vibrations of C60

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Vibrations of C60

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Next ppt!

47Kincaid et al. J . Phys. Chem. 1988, 92, 5628.

2Cl

N

N

Ru

2

C2v: 20A1 + 19B2 + 9B1

2Cl

N

N

Ru

2

D

D

2Cl

N

N

Ru

2

D

D

2Cl

N

N

Ru

2

D

DDD

DD

D

Side note: A Heroic Feat in IR Spectroscopy

ir vs raman spectroscopy - chem.fsu.edu

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