Lucas Paquin
CHEM 166A
April 30
th
, 2018
High Resolution Fourier Transform-Infrared Spectroscopy
Introduction
Spectroscopy probes transitions between different energy levels, or states, using light.
Light in the infrared region of the EM spectrum can be used to probe vibrational and rotational
transitions. The specific rotational and vibrational states are a result of the interactions between
the different atoms in the molecule and, since each molecule has a unique arrangement of atoms,
it has a unique IR spectrum almost like a fingerprint.
In this lab, the spectra of HCl and DCl were obtained and analyzed. More specifically, the
energy levels that are involved in the transitions that lead to each line of the spectrum were
evaluated.
The simplest model that considers rotational states is the rigid rotor (RR). This model
considers two atoms at a fixed distance that rotate as a unit. The quantized energy levels of the
rigid rotor are given in the following equation:
h
¯
¿
2
2
I
J
(
J
+
1
)
E
J
=
¿
(1)
where J is the rotational quantum number that spans integers from 0 to ∞. The degeneracy of the
J
th
quantum level is 2J+1. I is the moment of inertia, which is given by:
I
=
μr
2
(2)
where r is the distance between two atoms, and μ is the reduced mass, which is given by:
μ
=
m
a
m
b
m
a
+
m
b
(3)
The simplest model for vibrations is the harmonic oscillator (HO). The vibrational levels
for the harmonic oscillator are given by the following equation:
E
v
=
(
υ
+
1
2
)
hv
(4)
where υ spans integers from 0 to ∞ and ν is the frequency of vibration.
Transitions where Δυ=+1 and ΔJ=+1 are called the “R branch”, those where Δυ=+1 and
ΔJ=−1 are called the “P branch”, and those where Δυ=+1 and ΔJ=0 are the “Q branch”. For

diatomic molecules the Q branch is a forbidden transition (rotation about the bond axis has no
effect on the dipole moment) and is not observed in a spectrum
(1)
.
As you count away from the center of the spectrum the intensity of individual lines
increases, goes through a maximum and then falls off in the wings. This pattern arises from a
combination of two effects, the population of molecules in a quantum state and the number of
quantum states at a particular energy. The population in state J is given by the following
equation:
N
(
J
)
=
N
0
(
2
J
+
1
)
e
−
B
0
J
(
J
+
1
)
kT
(5)

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- Atom, Infrared Spectroscopy, DCL