Chemistry 330
Vibrational and Rotational Spectroscopy
The Electromagnetic Spectrum
The electromagnetic spectrum and
the classification of the spectral
regions.
The band at the bottom of the
illustration indicates the types of
transitions that absorb or emit in the
various regions.
The Electromagnetic Spectrum
(Cont’d)
Transition Intensity
The intensity of a
transition is the area
under a plot of the
molar absorption
coefficient against
the wavenumber of
the incident
radiation.
Absorption and Emission
Absorption and emission
of radiation and the
attainment of thermal
equilibrium.
The excited state can
return to the lower state
– spontaneously
– stimulated by radiation
already present at the
transition frequency.
Forbidden Transitions
When a 1s electron becomes a 2s
electron, there is a spherical migration
of charge
There is no dipole moment associated
with this migration of charge
This transition is electric-dipole
forbidden
Forbidden Transitions
When a 1s electron
becomes a 2p
electron, there is a
dipole associated
with the charge
migration
This transition is
allowed.
Doppler Broadening
The shape of a
Doppler-broadened
spectral line
The distribution
reflects the Maxwell
distribution of
speeds in the
sample
Lines broaden as T
increases
The Definition of Moment of
Inertia
In this molecule
– three identical atoms
attached to the B atom
– three different but
mutually identical atoms
attached to the C atom.
Centre of mass lies on
the C3 axis
Perpendicular distances
are measured from the
axis passing through
the B and C atoms.
Asymmetric Rotor
An asymmetric rotor
has three different
moments of inertia;
all three rotation
axes coincide at the
centre of mass of
the molecule.
Types of Rigid Rotors
A schematic illustration of the classification
of rigid rotors.
Spherical Rotors
The rotational
energy levels of a
linear or spherical
rotor. Note that the
energy separation
between
neighbouring levels
increases as J
increases.
The significance of the
quantum number K.
When |K| is close to its
maximum value, J,
most of the molecular
rotation is around the
principal axis.
When K = 0 the
molecule has no
angular momentum
about its principal axis:
it is undergoing endover-end rotation.
The significance of the
quantum number MJ.
When MJ is close to its
maximum value, J,
most of the molecular
rotation is around the
laboratory z-axis.
An intermediate value
of MJ.
When MJ = 0 the
molecule has no
angular momentum
about the z-axis.
Linear Rotor
The effect of an
electric field on the
energy levels of a
polar linear rotor. All
levels are doubly
degenerate except
that with MJ = 0.
Absorption and Emission
The processes that
account for absorption
and emission of
radiation and the
attainment of thermal
equilibrium.
The excited state can
return to the lower state
– spontaneously
– by stimulated emission
Centrifugal Distortion
The effect of rotation on
a molecule. The
centrifugal force arising
from rotation distorts
the molecule, opening
out bond angles and
stretching bonds
slightly. The effect is to
increase the moment of
inertia of the molecule
and hence to decrease
its rotational constant.
The Gross Selection Rule for
Rotations
A rotating polar
molecule looks like
an oscillating dipole
which can stir the
electromagnetic field
into oscillation.
Classical origin of
the gross selection
rule for rotational
transitions.
Photon Absorption
When a photon is
absorbed, the angular
momentum of the
combined system is
conserved.
If the molecule is
rotating in the same
sense as the spin of the
incoming photon, then J
increases by 1.
The Linear Rotor
The transitions allowed
by the selection rule J
= 1
The intensities reflect
the populations of the
initial level in each
case and the strengths
of the transition dipole
moments.
Polarizability
An electric field
applied to a
molecule results in
its distortion, and
the distorted
molecule acquires a
contribution to its
dipole moment
Polarizability (cont’d)
The polarizability may be different when
the field is applied
– parallel
– perpendicular to the molecular axis
The molecule has an anisotropic
polarizability.
The Raman Selection Rules
The distortion induced
in a molecule by an
applied electric field
returns to its initial value
after a rotation of only
180
Origin of the J = 2
selection rule in
rotational Raman
spectroscopy.
A Rotational Raman Spectrum
The rotational
energy levels of a
linear rotor and the
transitions allowed
by the J = 2
Raman selection
rules.
The form of a typical
rotational Raman
spectrum
A molecular potential energy
curve
The energy may be
approximated by a
parabola near the
bottom of the well.
The parabolic
potential leads to
harmonic
oscillations.
The Definition of the Force Constant
The force constant
measures of the
curvature of the
potential energy
close to the
equilibrium
extension of the
bond.
Nonpolar Species
The oscillation of a
molecule, even if it
is nonpolar, may
result in an
oscillating dipole
that can interact with
the electromagnetic
field.
The electric dipole
moment of a
heteronuclear diatomic
molecule varies as
shown by the green
curve. For small
displacements the
change in dipole
moment is proportional
to the displacement.
Morse Potentials
The Morse potential
energy curve
reproduces the general
shape of a molecular
potential energy curve.
The number of bound
levels is finite.
– Note the relation
between the dissociation
energy, D0, and the
minimum energy, De, of
the curve.
The Dissociation Energy
The dissociation
energy is the sum of
the separations of
the vibrational
energy levels up to
the dissociation limit
just as the length of
a ladder is the sum
of the separations of
its rungs.
Birge-Sponer Plot
The area under a
plot of transition
wavenumber
against vibrational
quantum number is
equal to the
dissociation energy
of the molecule.
The Birge-Sponer
extrapolation.
The HCl Spectrum
A high-resolution vibration-rotation absorption
spectrum of HCl.
The lines appear in pairs because H35Cl and
H37Cl both contribute!
Note - no Q branch,
P, Q, R Branches
The formation of P,
Q, and R branches
in a vibrationrotation spectrum.
The intensities
reflect the
populations of the
initial rotational
levels.
O, Q, S Branches
The formation of O,
Q, and S branches
in a vibrationrotation Raman
spectrum of a linear
rotor.
Note the frequency
scale runs in the
opposite direction to
those of the P, Q, R
branches.
The Vibrations of CO2.
The stretching modes are not
independent, and if one CO
group is excited the other begins
to vibrate.
The symmetric and
antisymmetric stretches are
independent, and one can be
excited without affecting the
other: they are normal modes.
The two perpendicular bending
motions are also normal modes.
The Normal Modes of Water
The three normal
modes of H2O. The
mode v2 is
predominantly
bending, and occurs
at lower
wavenumber than
the other two.
Symmetry and Normal Modes
The atomic
displacements of
CH4 and the
symmetry
elements used to
calculate the
characters.