Methane (CH4)

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Carbon Dioxide (CO2)
Methane (CH4)
Ammonia (NH3)
Nitrogen (N2)
Ozone (O3)
Water Vapor (H2O)
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MOLECULAR ABSORPTION

• From Previous lectures we know how to use
  absorption coefficients cross sections to
  calculate absorption and emission by gases in the
  atmosphere.
• BUT
• How do gases absorb radiation?
• Why do only certain gases absorb radiation?
• What dictates the nature of the absorption
  (wavelength,strength)?

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Elementary Molecular Spectroscopy

• Quantum mechanics dictates that virtually all
  energy transitions are discrete
• Absorption molecule increases its energy
• Emission molecule decreases its energy.

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Elementary Molecular Spectroscopy
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• Molecules can store energy in 4 discrete ways
• Translational (kinetic) energy directly
  associated with the the TEMPERATURE of the gas.
• Vibrational Most molecules are constantly
  vibrating! (if their structures allow it)
• Rotational Molecules can rotate on top of
  vibrating.
• Electronic Relates to energy states of electrons
  inside a molecule
• Energy storage potential in each type is
• Electronic HIGH (associated with visible/UV)
• Vibrational MEDIUM-LOW (associated with
  IR/Microwave)
• Rotational quite low tacked on as a modified
  to vibrations, leading to vibrational-rotational
  absorption features.

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EEL gt EVIB gt ETRANS gt EROT
IMPORTANT NOTES Because molecules are
constantly colliding when in Local Thermodynamic
Equilibrium (LTE), the energies are constantly
redistributed amongst kinetic, electronic,
vibrational, and rotational modes of energy
storage. TRANSLATIONAL ENERGY is not quantized,
but plays an important role in energy
redistribution. Molecules that are excited by
electronic/vibrational transitions will
redistribute some of this extra energy to
translational energy (ie HEATING)
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The types of interactions that occur in matter
depend on the rate of oscillations that must be
induced (i.e the wavelength of the incident
radiation). On the whole, shorter wavelength,
radiation interacts with lighter and smaller
parts of matter whereas more sluggish slower
oscillating radiation affects the larger parts of
matter. We are mainly concerned with mechanisms
affecting electrons, and atoms to more bulky
molecules - mostly vibrational and rotational
spectra
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ELECTRONIC TRANSITIONS ARE IMPORTANT IN the
UltraViolet Its How Ozone protects us!

• N2 generally unimportant in stratospheric
  chemistry
• Because of O2/O3, no photons make it below mid-
  stratosphere that can excite more electronic
  transitions.

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The Electric Dipole Separation of and - charge
The electric dipole is a characteristic of matter
important to how E-M radiation interacts with
matter.
The displacement or oscillation of charge in this
the dipole creates a time varying dipole moment
(ie. dp/dt) and in turn a time varying e-field
and thus EM radiation
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Dipole Moments (electric or magnetic) ARE
REQUIRED to interact with E-M radiation
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Induced through vibrations
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THE OVERALL PICTURE
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MODES OF VIBRATION
Degenerate!
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Analog Models Vibration of a Diatomic
Molecule Its like a spring!
Restoring Force F-k(r-re) harmonic oscillator
predicts
kSpring constant
mreduced mass
the vibrational quantum
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VIBRATION INFORMATION!

• Linear diatomic molecules have a single mode of
  vibration at fundamental frequency ?1.
• Triatomic (linear nonlinear) have ?1, ?2, ?3
• Energy of vibration E (v½) h? v0,1,2,3
• QM rules require ?v1 !!!
• SO ?E h? (for a given vibrational mode)
• If you could only change one mode at a time, CO2
  (e.g.) could only have 3 absorption regions. In
  reality it has a lot more!

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Analog Models Rotation of a Diatomic Molecule
Rotating Molecule Center of mass
m1r1m2r2 Moment of Inertia Im1r12 m2r22
Energy E1/2 I?2 L2/2I Angular
Momentum, L I ?
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The more complex the molecule geometry, the more
rotational degrees of freedom exist, and thus the
more complex is the rotational absorption
spectrum. Linear molecules (CO2, N2O) - only one
I, simple evenly spaced
distribution of lines)
Symmetric top molecules (NH3, CF3Cl) - non
linear, I1I2,I3 Spherical symmetric top (CH4) -
non linear, I1I2I3 Asymmetric top (H2O) - non
linear and all moments of inertia are
different - complex
(random) spectrum
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ROTATION INFORMATION!

• In reality, most atmospheric gas molecules have
  one or two nonzero moments of inertia
• Angular momentum is quantized by
• E ½L2/I
• QM rules require
• Usually ?J1 only
• Degenerate ?J1, or 0 (not J0?0)
• SO ?E
• Leads to equally spaced lines (J0,1,2,3 etc)
• Rotations are often a perturbation on vibrational
  transitions

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ROATIONAL-VIBRATIONAL Transitions
First Harmonic Vibrational Mode
Fundamental Vibrational Mode
?J -1
?J 1
?J 0
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Rotation-Vibration Modes vibrations rotations
typically occur together - at least ?lt 20
?m selection rules (from q-theory)
establish which transitions are
permitted Diatomic molecule ?v ? 1, ?J ? 1
PR
Branch Triatomic (linear) molecule (CO2)
?v ? 1, ?J ? 1
PR Branch
?v 1, ?J 0
Q Branch
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IMPORTANT SOLAR ABSORPTION BANDS From Liou,
Chapter 3

• Most useful in remote sensing! Can often derive
  column-integrated quanties of these gases.
• Can be important for energy balance (H2O
  especially)

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15 µm ?2 CO2 Transition
R-Branch
P-Branch
Q-Branch
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15 µm CO2 Transitions (mainly ?2)
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The thermal IR spectrum, again
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Isotopologues Matter!
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electric
Summary
Permanent magnetic dipole - yes
Insert fig. 8.9
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VERY LITTLE RHYME OR REASON
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Summary in Words of Gas Transitions (1)

• 3 types of quantized transitions important to us
• Electronic (highest energy UV-Vis)
• Vibrational (medium energy Vis-NIR-Thermal IR)
• Rotational (Far IR Microwave)
• Other types of absorption are not quantized
• Photo-Ionization Ripping electronic off to make
  ion
• (Occurs when photon energy gt ionization energy of
  molecule)
• Photo-Dissociation Tearing an atom off a
  molecule
• (E.g. O3 ? O2 O - critical for stratospheric
  chemistry)
• (Occurs when photon energy gt dissociation energy
  of molecule)
• Pure rotational transitions can happen ONLY if
  molecule has a permanent electric dipole moment
  (e.g. H2O, CO, O3).
• Symmetric linear molecules (N2, CO2, N2O) do not
  have a permanent dipole moment.

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Summary in Words of Gas Transitions (2)

• Rotational transitions often accompany
  vibrational transitions
• Rotational quantum number J changes by (-1,0, or
  1) when vibrational quantum number v changes by
  1.
• ?J -1 ? P-branch
• ?J 0 ? Q-branch if it exists! Only allowed
  if the vibrational transition is degenerate ,
  e.g. the ?2 transition of CO2!
• ?J 1 ? R-branch
• The energy associated with ?J 1 is
  proportional to the starting J state
• For example J 3?4 takes 3 times more
  energy than J 0?1 !
• The energy associated with ?v 1 does not
  depend on starting v state they all take the
  same energy.