# Biopolymer Spectroscopy

```Biopolymer Spectroscopy
Introduction to Spectroscopy I
Vibrational &amp; Rotational Spectroscopy
Figure 19.1
Table 19.1
Infrared region of the electromagnetic spectrum
Gunzler and Gremlich, IR Spectroscopy, p. 1
Infrared Regions
The infrared region may be divided into three sections; near-, midand far-infrared:
Region
Wavelength range
(mm)
Wavenumber range
(cm-1)
Near
0.78 - 2.5
12800 - 4000
Middle
2.5 - 50
4000 - 200
Far
50 -1000
200 - 10
The most useful IR region lies between 4000 – 670 cm-1.
Figure 19.4
B12    N1  B21   N2  A21 N2
Spontaneous emission is a
completely random process, the
emitted photons are incoherent
In simple diatomic molecules, such as BrCl or CO, there is a
certain distance between the atoms at which the attractive
bonding forces and repulsive interactions between electrons
balance each other. This distance is referred to as the
equilibrium bond distance, req, and it can be changed by
applying energy
bond strength
 k
mass
 is the frequency of vibration
k is the force constant of the bond
(the resistance of the bond to
vibration and a measure of its
strength)
Vibrational frequencies
Reduced mass (m) = (m1 x m2)/(m1 + m2)
The frequency of the vibrational transition is dependent on
the nature of the atoms (reduced mass) and the strength
(force constant) of the bonds between them.
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/infrared.htm#ir3
Molecular vibrations
Morse potential, V(x) (red curve), as a function of the bond length, x, for HCl The
zero of energy is chosen to be the bottom of the potential. The yellow curve
shows a harmonic potential, which is a good approximation to the Morse potential
near the bottom of the well. The horizontal lines indicate allowed energy levels in
the Morse potential. De and Do represent the bond energies defined with respect
to the bottom of the potential and the lowest state, respectively,and xe is the
equilibrium bond length.
Harmonic/Anharmonic energy levels
The total vibrational energy of a molecule is quantized, such that the
vibrational quantum number, , can take on values V = 0, +1, +2, +3,
+4, ... Vibrational selection rule D V = +1 (0  1)
For a harmonic oscillator, the energy (Joules) of a particular energy
level is given by:

1 h
Evib = h(V + &frac12;)vib=  V  
2  2

k
m
For an anharmonic oscillator, the expression is:
Evib = h[(V + &frac12;)vib + (V + &frac12;)Xcvib]
where Xc is an anharmonicity constant
1 h

En   V  
2  2

k
m
1   h  
1

En  h  v   
v  
2  4 De 
2

2
Harmonic/Anharmonic energy levels
Selection rule
DV  1
DV  1; 2; 3...
Hendra, Jones &amp; Warnes, Fourier Transform Raman Spectroscopy, p. 21
Energy difference between any pairs of
m
h
DE  hvm 
2
k
h
h  hvm 
2
1
v  frequency  
2
k
m
k
m
or   wave number  
1
k
2 c
m
Rotational Selection Rules
Rotational Selection Rules:
Dipole Moment Change is parallel
to principal rotational axis of
symmetry
DJ = &plusmn; 1 (no Q fine structure)
Dipole Moment Change is
perpendicular
to
principal
rotational axis of symmetry
DJ = &plusmn; 1 (Q fine structure)
Brisdon, p. 23
Vibrational energy levels – rotational energy
levels
DJ = +1 (R)
DJ = -1 (P)
http://www.chemistry.nmsu.edu/studntres/chem435/Lab9/intro.html
P, Q, and R Branches (NO gas)
http://faculty.augie.edu/~kjbetsch/exp5.html
IR Spectrum
1
Baseline
2
Background
absorption
3
Absorption
maximum
4
Shoulder; two nonseparable bands
5
Disturbances by absorption of
CO2 and H2O in the air
Gunzler and Gremlich, IR Spectroscopy, p. 1
Vibrational excitations
• The main types of bond excitation are stretching (XY) and bending
(dYXY) and often the absorption of certain wavelengths of infrared
radiation may be correlated with the stretching or bending of certain
types of bonds within a molecule.
• Infrared spectra of compounds are complicated by bond oscillations
in the whole molecule, giving rise to overtone and harmonic
absorptions.
Stretching and Bending Vibrations
http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/irspec1.htm
Infrared Active and Inactive Modes
For a vibration mode to be infrared (IR) active, it must be
accompanied by a change in the molecular electric dipole
moment
eg. linear CO2
No change in dipole moment
Change in dipole moment
Housecroft and Sharpe, p. 84
Infrared active stretches and bend
Symmetric stretch
Asymmetric stretch
Bend
http://sis.bris.ac.uk/~sd9319/spec/IR.htm
Active, inactive, and weakly active -C≡Cstretches
CH3-C≡C-H
infrared active, significant
dipole moment
CH3-C≡C-CH3
infrared inactive, no
dipole moment
CH3-C≡C-CH2CH3
weakly infrared active,
small dipole moment
Vibrational Degrees of Freedom
A molecule containing n atoms has 3n degrees of
freedom, which describe the translational, rotational, and
vibrational motions of the molecule:
translational: 3 degrees of freedom (x, y, and z
Cartesian axes)
rotational: a non-linear molecule has 3 degrees
of rotational freedom, while a linear
molecule has 2 degrees of freedom
vibrational: a non-linear molecule has 3n - 6
degrees of vibrational freedom, while
a linear molecule has 3n - 5 degrees
of freedom
Vibrational modes for linear CO2
Linear CO2 – number of modes = 3(3) – 5 = 4
Housecroft and Sharpe, p. 84
Infrared Spectrum of CO2 gas
dOCO
CO
http://chemistry.beloit.edu/Warming/moviepages/greenIR.htm
Vibrational modes for bent SO2
Bent SO2 - number of modes = 3(3) – 6 = 3
Housecroft and Sharpe, p. 84
Infrared Spectrum of H2O
Infrared Spectrum of H2O vapour
http://chemistry.beloit.edu/Warming/moviepages/greenIR.htm
IR absorbance for common functional groups
The infrared spectrum of benzyl alcohol displays a broad, hydrogenbonded -OH stretching band in the region
3400 cm-1, a sharp
unsaturated (sp2) CH stretch at about 3010 cm-1 and a saturated (sp3)
CH stretch at about 2900 cm-1; these bands are typical for alcohols and
for aromatic compounds containing some saturated carbon. Acetylene
(ethyne) displays a typical terminal alkyne C-H stretch, as shown in the
second panel.
Saturated and unsaturated CH bands also are shown clearly in the
spectrum of vinyl acetate (ethenyl ethanoate). This compound also shows
a typical ester carbonyl at 1700 cm-1 and a nice example of a carboncarbon double bond stretch at about 1500 cm-1. Both of these bands are
shifted to slightly lower wave numbers than are typically observed (by
about 50 cm-1) by conjugation involving the vinyl ester group.
Amide vibrations
The peptide group, the structural repeat unit of proteins, gives up to 9
characteristic bands named amide A, B, I, II ... VII.
•The amide A band (about 3500 cm-1) and amide B (about 3100 cm-1)
originate from a Fermi resonance between the first overtone of amide
II and and the N-H stretching vibration.
•Amide I and amide II bands are two major bands of the protein
infrared spectrum.
The amide I band (between 1600 and 1700 cm-1) is mainly associated with the C=O
stretching vibration(70-85%)and is directly related to the backbone conformation.
Amide II results from the N-H bending vibration (40-60%) and from the C-N
stretching vibration (18-40%). This band is conformational sensitive.
Amide III and IV are very complex bands resulting from a mixture of several
coordinated is placements. The out-of-plane motions are found in amide V, VI and
VIII.
Amide A is with more than 95% due to the the N-H stretching vibration.
This mode of vibration is not depend on the backbone conformation but
is very sensitive to the strength of a hydrogen bond (between 3225 and
3280 cm-1 for hydrogen bond length from 2.69 to 2.85 angstrom,
(Krimm &amp; Bandekar Adv Protein Chem 1986;38:181-364).
Amide I is the most intense absorption band in proteins. It is
primilary goverend by the stretching vibration of the C=O (70-85%)
and C-N groups (10-20%). Its frequency is found in the range
between 1600 and 1700 cm-1. The exact band position is determined
by the backbone conformation and the hydrogen bonding pattern.
Amide II is found in the 1510 and 1580 cm-1 region and it is more
complex than amide I. Amide II derives mainly from in-plane N-H
bending (40-60% of the potential energy). The rest of the potential
energy arises from the C-N (18-40%) and the C-C (about 10%)
stretching vibrations.
frequency,
absorbance at
the maximum
(Ao), full width
at half height
(FWHH),
surface of
Gaussian band
st=stretching
vibration
bd=bending
s=symetrical
as=asymetrical
```