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Infrared Spectroscopy
The Interaction of Light with Matter
Electric fields apply forces to charges, according to
F = qE
In an electric field, a positive charge will experience a force, but
a negative charge will experience the opposite force (as q → −q).
A magnetic field is similar, except that it only affects charged
particles that are moving, according to
F = q (v × B)
Again, typical magnetic fields you’d apply to neutral matter would
do something (the electrons are moving inside an atom), but the
effects are very small compared to the intraatomic charge interactions.
Light, from radio waves through X-rays, is an electromagnetic
wave; that is, it consists of electric and magnetic fields that are
oscillating with time. At any given point in space, you’d experience
electric and magnetic fields changing at a frequency ν:
E(t)
= E0 cos 2πt
B(t)
= B0 sin 2πt
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Polar Covalent Bonds
There is a continuum between perfect, symmetric electron sharing
in covalent bonds and complete electron transfer in ionic bonds:
with intermediate bonds referred to as polar covalent bonds:
Electronegativity provides a useful handle for estimating the nature
of a bond:
1. If there is no difference in electronegativity, the bond is covalent; this is the case for all symmetric diatomics: H2 , Cl2 ,
O2 , etc.
2. If there is a very large difference in electronegativity (∆χ >
1.5), the bond is ionic. Practically, this means O (χ = 3.44)
or a halogen (χ > 2.66) with alkali, alkali earths, and some
transition metals, or alkali metals with nonmetals, etc.
3. Intermediate electronegativity differences give polar covalent
bonds.
We draw polar covalent bonds with partial charges—Unlike formal
charges and oxidation states, these are real charges.
The dipole moment
µ = Qr
depends on the separation of two charges (r) and their magnitude
(Q). A big dipole moment means
1. large charges separated, or
2. charges separated over a long distance.
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Dipole Moments of Polyatomics
When complex molecules contain polar bonds, the dipole resulting
from each bond adds together to make a molecular dipole moment.
Dipole moments can be very small in some molecules, but there
will always be a dipole moment unless
1. bonds are composed of the same element (having two atoms
with similar electronegativity is not similar enough), or
2. polar covalent bonds are arranged symmetrically.
Note that you need to consider all resonance structures when evaluating symmetry.
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Light and Dipoles
Put a dipole in an oscillating electric (and magnetic) field:
Microwave absorption excites molecular rotation, and
it requires the molecule have a permanent dipole.
For vibrational excitation
• Amount of vibration is quantized; we can use a quantum
number v (vee, not ν!) with v = 0, 1, 2 . . .
• Even when v = 0, molecules are still vibrating (this is called
the zero-point vibration, and is an expression of the Heisenberg Uncertainty Principle.
Vibrations are typically excited by wavelengths in the infrared
region of the spectrum.
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The rule on dipole moment is a little different:
Infrared absorption excites molecular vibration, and it
requires the molecule have a change in its dipole moment with excitation.
The Harmonic Oscillator
For a mass on a spring
F = −kx
The quantity k is the spring constant.
The system has a natural frequency given by
r
k
ν=
m
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Diatomic Molecules
Most diatomic molecules can be modeled very well as two masses
connected by a spring:
Clearly, the masses involved are just those of the atoms, but what
makes the spring?
If one atom is very heavy and one very light, we can treat just
the light atom. So for HI, we can write
r
kHI
ν≈
mH
In most cases (and for exactness in all cases), we need to account for the fact that both atoms are moving as the spring (bond)
stretches and compresses.
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The reduced mass:
µ=
m1 m2
m1 + m2
Note that for m2 m1 , m1 + m2 ≈ m2 , and µ ≈ m1 . So for CO,
the reduced mass is
m1 m2
12 amu · 16 amu
= 6.86 amu
µ=
=
m1 + m2
12 amu + 16 amu
A diatomic molecule with a dipole moment will always change
its dipole upon stretching or compressing, so any diatomic with
a dipole will also have an infrared absorption. This absorption will
be
• High energy for a large spring constant (a high bond order)
and light atoms (or a light atom attached to a heavy atom).
For HF,
E = hν = 4140 cm−1 = 49.5 kJ mol−1
• Low energy for a small spring constant (a low bond order)
and heavy atoms. For ICl:
E = hν = 382 cm−1 = 4.57 kJ mol−1
There is an important case where a diatomic molecule will not
have a dipole moment, and the dipole moment cannot change with
vibration; this is when you have a homonuclear diatomic.
Homonuclear diatomics—H2 , O2 , N2 , etc.—cannot absorb infrared radiation.
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Normal Modes
For polyatomics, we’ve got lots of masses connected by lots of
springs, and it makes sense to be a little more careful and use
a little more specificity in how we talk about vibrations. In our
taxonomy of vibrations, we say:
1. A vibration should not look like a translation.
2. Similarly, a vibration should not look like a rotation.
3. Finally, we want to describe molecules in terms of vibrations
that do not look like each other.
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