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Lecture 8Lecture 8

Symmetry II: Vibrational Spectroscopy

Reading: Shriver and Atkins 6.4-6.5, 8.4g ,

Recall from last class…

Character tables identify the properties of a moleculeCharacter tables identify the properties of a molecule• columns correspond to classes of group elements (i.e., symmetry

operations).

• rows correspond to irreducible group representations: they describe the allowed transformations of an object in the group

• The entries consist of characters, related to the trace of the matrices representing the group elements.

+

px ‐ +

‐ +

+ ‐dxy

x xxy>0

y

xy<0x

x=0 x>0x<0x

xy>0 xy<0

Vibrational Spectroscopy

• Used to characterize a molecule’s strength, stiffness, and number of bonds

Al d d f k d i h i •Also used to detect presence of known compounds, monitor changes in concentration of a species during a reaction, determine components of an

unknown compound, and determine the likely structure

•A molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and

rotational motion.

•Typical frequencies: <1012-1014 Hzyp q

)1( E k)

2( nEn

Normal Modes

• Different, independent vibrations of a molecule

•A molecule consisting of N atoms has 3N‐6 normal

modes if it is non-linear and 3N‐5 normal modes if it is

linear

•Example: CO 4 normal •Example: CO2 4 normal modes

• Only normal modes ycorresponding to a changing electric dipole moment can

absorb radiation

Infrared Spectroscopy

• An IR vibrational spectrum is obtained by exposing the sample to y p g p

IR radiation and recording the variation of the absorbance with

frequencyfrequency

•Wavelengths of ~2000-16000nm (~2x1013-1.2x1014 Hz)

•Glass and water cannot be used, unless the spectral bands of

interest occur at frequencies not

OH stretch (3600)

C=O stretch interest occur at frequencies not absorbed by either (typically use

CsI optical windows)

d

(1700)

•Depends on a molecule’s electric dipole moment

General Trends in Infrared Spectroscopy

1 Stretching frequencies are higher than corresponding bending frequencies (It 1. Stretching frequencies are higher than corresponding bending frequencies. (It is easier to bend a bond than to stretch or compress it.)

2 Bonds to H have higher stretching frequencies than those to heavier atoms2. Bonds to H have higher stretching frequencies than those to heavier atoms.

3. Triple bonds have higher stretching frequencies than corresponding double bonds, which in turn have higher frequencies than single bonds (Except for , g q g ( pbonds to hydrogen).

2 5 3 4 5 6 7 8 9 10 11 12 14

Wavelength (microns)

2.5 3 4 5 6 7 8 9 10 11 12

Stretching vibrations

14

Bending vibrations

5000 4000 3000 2000 1000 800 700Frequency (cm-1)

Raman Spectroscopy

I R h • In Raman spectroscopy, the sample is exposed to visible light

• Most photons are elastically Most photons are elastically scattered (with no change of

frequency)

l ll d• Some are inelastically scattered, with frequency differences from

the incident radiation equivalent to the vibrational frequencies of the

molecule

• Aqueous solutions can be used Aqueous solutions can be used, but linewidths are usually larger

than with IR

• depends on a molecule’s polarizability

IR versus Raman

• IR: depends on electric dipole moment of molecule: p=qd (d=z,y,z)

•Raman: depends on polarizability: =p/E ([E]=V/m, [p]=Cm, []=Cm2/V)

IR versus Raman

• IR: The symmetry of the vibration must be the same as that of x, y, z in the ch r cter t blez in the character table

• Raman: the symmetry must be a quadratic function (i.e, xy or x2)

I h i i diffi l j d h h i l i bili f In cases where it is difficult to judge the change in polarizability of a normal mode, can use the exclusion rule:

If a molecule has a center of inversion none of its modes can be If a molecule has a center of inversion, none of its modes can be both IR and Raman active

Example: CO2

Which modes are IR or Raman Active?

Example: CO2

Which modes are IR or Raman Active?

IR inactive IR active

IR active IR active

Example: CO2

Which modes are IR or Raman Active?

IR inactive IR activeld b ( ) bCould be Raman active (it is) cannot be Raman active

IR active IR activecannot be Raman activecannot be Raman active

Raman activity from symmetries of normal modes

Consider a square planar Pd complex

Cl Cl

Cis (C2v symmetry) E, C2, σv, σv’

Trans (D2h symmetry) E, 2C3, 3C2, σh, 3σv’, 2S3

H3N

Cl

ClPd H3N NH3

Cl

Pd

NH3 Cl

• IR x, y, z in the character table

• Raman quadratic function Raman quadratic function

Cis isomer: Cis (C2v symmetry) C E C σ σ ’ h=4

Cl

Cis (C2v symmetry) E, C2, σv, σv’

C2v E C2 σv σv h=4

A1 1 1 1 1 z x2, y2, z2

A 1 1` 1 1 R

H3N ClPd

A2 1 1` ‐1 ‐1 Rz xy

B1 1 ‐1 1 ‐1 x, Ry xz

NH3B2 1 ‐1 ‐1 1 y, Rx yz

BA1B2

Both are IR active (A1z, B2y). Also, both are Raman active

Trans isomer: Cl

H3N NH3

Cl

PdTrans (D2h symmetry) E, 2C3, 3C2, σh, 3σv’, 2S3

Cl

D2h E C2 (z) C2 (y) C2 (x) i σ (xy) σ (xz) σ (yz)

Ag 1 1 1 1 1 1 1 1 x2, y2, z2

B1g 1 1 ‐1 ‐1 1 1 ‐1 ‐1 Rz xyB2 1 ‐1 1 ‐1 1 ‐1 1 ‐1 R xzB2g 1 1 1 1 1 1 1 1 Ry xzB3g 1 ‐1 ‐1 1 1 ‐1 ‐1 1 Rx yzAu 1 1 1 1 ‐1 ‐1 ‐1 ‐1B 1 1 1 1 1 1 1 1 zB1u 1 1 ‐1 ‐1 ‐1 ‐1 1 1 zB2u 1 ‐1 1 ‐1 ‐1 1 ‐1 1 yB3u 1 ‐1 ‐1 1 ‐1 1 1 ‐1 x

g (gerade): symmetric to inversionu (ungerade): antisymmetric to inversion

Trans isomer: Cl

H3N NH3

Cl

PdTrans (D2h symmetry) E, 2C3, 3C2, σh, 3σv’, 2S3

Cl

IR active Raman active (B2uy)(Agx2)

A 1 1 1 1 1 1 1 1 x2 y2 z2

D2h E C2 (z) C2 (y) C2 (x) i σ (xy) σ (xz) σ (yz)

Ag 1 1 1 1 1 1 1 1 x2, y2, z2

B2u 1 ‐1 1 ‐1 ‐1 1 ‐1 1 y

Spectra for these Pd complexes

• In Pd-Cl stretching region, the cis isomer has

b d i b h IR d two bands in both IR and Raman spectra (since both modes are IR and

)Raman active)

Th i h l•The trans isomer has only one band at a different

frequency in each spectra (since only the symmetric mode IR active, and only

the antisymm mode is Raman active)

Tetrahedral Ni(CO)4

Ni(CO)4 is characterized by four CO displacements. How many IR and p y

Raman bands are expected?

All 4 displacements away from Ni

2 in, 2 out

Tetrahedral Ni(CO)4

Td E 8C3 3C2 6S4 6σd h=24

4 1 0 0 2

All four displacement

t i

Only one remains the

Two remain the same

vectors remain unchanged

same None remain the same

Tetrahedral Ni(CO)4

Raman active

IR & Raman active

This set of characters corresponds to the sum of characters of A1 and T2

Td E 8C3 8C2 6S4 6σd h=24

4 1 0 0 2

All four displacement

t i

Only one remains the

Two remain the same

vectors remain unchanged

same None remain the same

Therefore, one IR band and two Raman bands in CO stretching region