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