Atomic and molecular vibrations correspond to excited energy levels

Absorption of EM radiation
Molecular absorption processes
~10-18 J
• Electronic transitions
• UV and visible wavelengths
• Molecular vibrations
• Thermal infrared wavelengths
Increasing energy
• Molecular rotations
• Microwave and far-IR wavelengths
~10-23 J
• Each of these processes is quantized
• Translational kinetic energy of molecules is unquantized
Absorption spectra of molecules
Hypothetical molecule
with three allowed
energy levels
Note relationship to
νij = ΔEij/h
(a) allowed transitions
(b) positions of the absorption lines in the spectrum of the molecule
• Line positions are determined by the energy changes of allowed transitions
• Line strengths are determined by the fraction of molecules that are in a
particular initial state required for a transition
• Multiple degenerate transitions with the same energy may combine
• Fluorescent lighting exploits this phenomenon: certain phosphors emit
visible light when bombarded with UV light. Much more efficient than
incandescent lighting.
• Also whitening agents in detergents...
Interaction of radiation with matter
• If there are no available quantized energy levels matching the quantum
energy of the incident radiation, then the material will be transparent to that
X-ray interactions
• Quantum energies of x-ray photons are too high to be absorbed by
electronic transitions in most atoms - only possible result is complete
removal of an electron from an atom
• Hence all x-rays are ionizing radiation
• If all the x-ray energy is given to an electron, it is called photoionization
• If part of the energy is given to an electron and the remainder to a lower
energy photon, it is called Compton scattering
Ultraviolet interactions
• Near UV radiation (just shorter than visible wavelengths) is absorbed very
strongly in the surface layer of the skin by electron transitions
• At higher energies, ionization energies for many molecules are reached
and the more dangerous photoionization processes occur
• Sunburn is primarily an effect of UV radiation, and ionization produces
the risk of skin cancer
UV SO2 and O3 absorption spectra
Visible light interactions
• Visible light is also absorbed by electron transitions
• Higher energies at blue wavelengths relative to red wavelengths: hence
red light is less strongly absorbed than blue light
• Absorption of visible light causes heating, but not ionization
• Car windshields transmit visible light but absorb higher UV frequencies
Infrared (IR) interactions
• Quantum energy of IR photons (0.001-1.7 eV) matches the ranges of
energies separating quantum states of molecular vibrations
• Vibrations arise as molecular bonds are not rigid but behave like springs
Microwave interactions
• Quantum energy of microwave photons
(0.00001-0.001 eV) matches the ranges of
energies separating quantum states of
molecular rotations and torsion
• Note that rotational motion of molecules is
quantized, like electronic and vibrational
transitions  associated absorption/emission
• Absorption of microwave radiation causes
heating due to increased molecular rotational
• Most matter transparent to µ-waves,
microwave ovens use high intensity µ-waves
to heat material
Molecular dipole moments
For a molecule to absorb IR radiation it must undergo a net change in dipole
moment as a result of vibrational or rotational motion.
The electric dipole moment for a pair of opposite charges of
magnitude q is the magnitude of the charge times the distance
between them, with direction towards the positive charge.
The total charge on a molecule is zero, but the nature of chemical bonds is
such that positive and negative charges do not completely overlap in most
molecules. Such molecules are said to be polar because they possess a
permanent electric dipole moment.
Water is a good example of a polar molecule:
Molecules with mirror symmetry like oxygen,
nitrogen and carbon dioxide have no
permanent dipole moments.
Key atmospheric constituents
• Diatomic, homonuclear molecules
(e.g., N2, O2) have no permanent
electric dipole moment (also CO2)
• Molecular N2, the most abundant
atmospheric constituent, has no
rotational absorption spectrum
• Oxygen (O2) has rotational
absorption bands at 60 and 118 GHz
• Linear and spherical top molecules
have the fewest distinct modes of
rotation, and hence the simplest
absorption spectra
• Asymmetric top molecules have the
richest set of possible transitions, and
the most complex spectra
• Note lack of permanent electric
dipole moment in CO2 and CH4
Vibration modes of simple molecules
Fundamental or normal modes
Symmetric stretch
Bend (Scissoring)
Asymmetric stretch
A normal mode is IR-active if
the dipole moment changes
during mode motion.
Overtones, combinations and
differences of fundamental
vibrations are also possible
(e.g., 2v1, v1+v3 etc.)
A non-linear molecule of N atoms has 3N-6 normal modes of vibration; a
linear molecule has 3N-5.
Absorption frequency for a diatomic molecule
k(m1  m2 )Av
m1, m2 = atomic mass of vibrating atoms
c = speed of light [3×108 m s-1]
V = wavenumber [cm-1]
Av = Avogadro’s number [6.023×1023 atoms mole-1]
k = force constant (bond strength) [dynes cm-1]
For a single bond, k = 5×105 dynes cm-1
For a double bond, k = 10×105 dynes cm-1
For a triple bond, k = 15×105 dynes cm-1
Infrared (IR) interactions
Vibrational transitions are associated with larger energies than ‘pure’
rotational transitions.
Vibrations can be subdivided into two classes, depending on whether
the bond length or angle is changing:
• Stretching (symmetric and asymmetric)
• Bending (scissoring, rocking, wagging and twisting)
Stretching frequencies are higher than corresponding bending
frequencies (it is easier to bend a bond than to stretch or compress it)
Bonds to hydrogen have higher stretching frequencies than those to
heavier atoms.
Triple bonds have higher stretching frequencies than corresponding
double bonds, which in turn have higher frequencies than single bonds
Infrared (IR) interactions
Wavenumber Type of
Far IR
50 - 1000
1.2 - 25
10 – 200
Mid IR
2.5 - 50
25 - 496
200 - 4000
Near IR
1 - 2.5
496 - 1240
4000 - 10000
Absorption spectra of molecules
V = Vibrational quantum number
J = Rotational quantum number
• Electronic, vibrational and rotational energy levels are superimposed
• The absorption spectrum of a molecule is determined by all allowed
transitions between pairs of energy levels, and whether the molecule
exhibits a sufficiently strong electric or magnetic dipole moment (permanent
or otherwise) to interact with the radiation field
Vibrational-rotational transitions
P branch (ΔJ = -1)
Q branch (ΔJ = 0)
(pure vibration)
R branch (ΔJ = +1)
• Relative positions of transitions in the absorption spectrum of a molecule
Hydrogen chloride (HCl) spectrum
Q branch (ΔJ = 0)
P branch
R branch
• Vibrational-rotational absorption spectrum of HCl: shows affect of two chlorine
isotopes with slightly different mass
Transmittance spectrum for ozone (O3)
Transmittance spectrum for CO2
Transmittance spectrum for H2O
Absorption line shapes
• Doppler broadening: random
translational motions of individual
molecules in any gas leads to Doppler
shift of absorption and emission
wavelengths (important in upper
• Pressure broadening: collisions
between molecules randomly disrupt
natural transitions between energy
states, so that absorption and emission
occur at wavelengths that deviate from
the natural line position (important in
troposphere and lower stratosphere)
• Line broadening closes gaps between
closely spaced absorption lines, so that
the atmosphere becomes opaque over
a continuous wavelength range.
Pressure broadening
• Absorption coefficient of O2 in the microwave band near 60 GHz at
two different pressures. Pressure broadening at 1000 mb obliterates
the absorption line structure.
Sulfur dioxide (SO2)
ν1: 1151 cm-1, 8.6 µm
ν3: 1361 cm-1, 7.3 µm
ν2: 519 cm-1, 19.2 µm
Sulfur dioxide (SO2)
ν1+ν3: 2500 cm-1, 4 µm
Water vapor (H2O)
• Most important IR absorber
• Asymmetric top → Nonlinear, triatomic molecule has complex line
structure, no simple pattern
• 3 vibrational fundamental modes
symmetric stretch
v1 = 2.74 μm
v2 = 6.25 μm
asymmetric stretch
v3 = 2.66 μm
• Higher order vibrational transitions (Δv >1) give weak absorption
bands at shorter wavelengths in the shortwave bands
• 2H isotope (0.03% in atmosphere) and 18O (0.2%) adds new (weak)
lines to vibrational spectrum
• 3 rotational modes (J1, J2, J3)
• Overtones and combinations of rotational and vibrational transitions
lead to several more weak absorption bands in the NIR
Transmission spectrum of
Explain the peaks in ni….
Carbon dioxide (CO2)
• Linear → no permanent dipole moment, no pure rotational spectrum
• Fundamental modes:
symmetric stretch
asymmetric stretch
v1 = 7.5 μm => IR inactive
v = 4.3 μm
v2 = 15 μm
bend v2
The v3 vibration is a parallel band (dipole moment oscillates parallel
to symmetric axis), transition ΔJ = 0 is forbidden, no Q branch,
greater total intensity than v2 fundamental
The v2 vibration is perpendicular band, has P, Q, and R branch
The v3 fundamental is the strongest vibrational band, but the v2
fundamental is most effective due to “matching” of vibrational
frequencies with terrestrial Planck emission function
13C isotope (1% of C in atmosphere) and 17/18O isotope (0.2%)
cause a weak splitting of rotational and vibrational lines in the CO2
IR Absorption Spectrum of CO2
Which is the
most potent
Ozone (O3)
• Ozone is primarily present in the stratosphere except anthropogenic
ozone pollution which exists in the troposphere
• Asymmetric top → similar absorption spectrum to H2O due to similar
configuration (nonlinear, triatomic)
• Strong rotational spectrum of random spaced lines
• Fundamental vibrational modes
symmetric stretch
v1 = 9.01 μm
v2 = 14.3 μm
asymmetric stretch
v3 = 9.6 μm
– 14.3 μm band masked by CO2 15 μm band
– Strong v3 band and moderately strong v1 band are close in
frequency, often seen as one band at 9.6 μm
– 9.6 μm band sits in middle of 8-12 μm H2O window and near peak
of terrestrial Planck function
– Strong 4.7 μm band but near edge of Planck functions
IR Absorption Spectrum of O3
Methane (CH4)
• Spherical top
• 5 atoms, 3(5) – 6 = 9 fundamental modes of vibration
• Due to symmetry of molecule, 5 modes are degenerate, only v3 and
v4 fundamentals are IR active
• No permanent dipole moment => No pure rotational spectrum
• Fundamental modes
v3 = 3.3 µm
v4 = 7.7 µm
IR Absorption Spectrum of CH4
• 7.6 µm band in otherwise largely transparent part of atmosphere
• Methane concentrations also directly/indirectly affected by human activities
Nitrous oxide (N2O)
• Linear, asymmetric molecule (has permanent dipole moment)
• Has rotational spectrum and 3 fundamentals
• Absorption band at 7.8 μm broadens and strengthens methane’s 7.6
μm band.
• 4.5 μm band less significant as it is at the edge of the Planck function.
• Fundamental modes:
symmetric stretch
v1 = 7.8 μm
asymmetric stretch
v3 = 4.5 μm
bend v2
v2 = 17.0 μm
IR Absorption Spectrum of N2O
v3=4.5 µm
v1=7.8 µm
v2=17 µm
Mineral and rock reflectance spectra
• Electronic transitions in solids; Fe2+ (iron)
particularly important in remote sensing –
minerals contain Fe2+ ions
• Fundamental vibrational modes of H2O:
2.74 µm, 6.25µm, 2.66 µm
• In rock spectra, whenever water is
present we see 2 absorption bands in
near-IR spectra – one near 1.45 µm (2ν3
overtone) and one near 1.9 µm (v2+v3
combination). Sharpness of bands relates
to sites in crystal structure occupied by the
water molecules.
• Note that penetration depth into natural
surfaces is usually restricted to the upper
few microns. Consequences?
Geological mapping/prospecting
Escondida Mine, Atacama Desert, Chile
ASTER visible
ASTER short-wave IR (SWIR)
Why are most plants
green and then red or
yellow in the fall?
• Chlorophyll absorbs in the red and blue, and
hence reflects in the green.
• Its absorption spectrum is due to electronic
In the fall, trees produce
carotenoids, which reflect yellow,
and anthocyanins, which reflect
orange and red.