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

2. BUT: 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)?

3. Elementary Molecular Spectroscopy
Absorption emission
E=h
Quantum mechanics dictates that virtually all energy transitions are discrete:
Absorption: molecule increases its energy
Emission: molecule decreases its energy.

4. Elementary Molecular Spectroscopy
One of the real clues as to the nature of the absorption emission process (and for that matter the nature of matter itself) came from the realization that bright and dark lines occur in the same spectral location
Bright lines of emission’
Dark lines of absorption
Wavelength or frequency

5. 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.

6. EEL > EVIB > ETRANS > 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)

7. 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

8. ELECTRONIC TRANSITIONS ARE IMPORTANT IN the UltraViolet – It’s How Ozone protects us!
UV-A
UV-B
UV-C
N2 generally unimportant in stratospheric chemistry
Because of O2/O3, no photons make it below mid- stratosphere that can excite more electronic transitions.

9. 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

10. Dipole Moments (electric or magnetic) ARE REQUIRED to interact with E-M radiation

11. * *
*Induced through vibrations

12. THE OVERALL PICTURE

13. MODES OF VIBRATION
Degenerate!

14. Analog Models: Vibration of a Diatomic Molecule
“It’s like a spring!”
Restoring Force F=-k(r-re)
harmonic oscillator predicts
k=Spring constant
m’=“reduced mass”
the vibrational
quantum #

15. VIBRATION INFORMATION!
Linear diatomic molecules have a single mode of vibration at fundamental frequency ν1.
Triatomic (linear& nonlinear) have : ν1, ν2, ν3
Energy of vibration E = (v+½) hν; v=0,1,2,3…
QM rules require Δv=±1 !!!
SO ΔE = hν (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!

16. Analog Models: Rotation of a ‘Diatomic Molecule’
Rotating Molecule
Center of mass: m1r1=m2r2
Moment of Inertia: I=m1r12+ m2r22
Energy: E=1/2 I2 =L2/2I
Angular Momentum, L= I 

17. 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, I1=I2,I3
Spherical symmetric top (CH4) - non linear, I1=I2=I3
Asymmetric top (H2O) - non linear and all moments of inertia are
different - complex (random) spectrum

18. 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: ΔJ=±1 only
Degenerate: ΔJ=±1, or 0 (not J=00)
SO ΔE =
Leads to equally spaced lines (J=0,1,2,3 etc)
Rotations are often a perturbation on vibrational transitions

19. ROATIONAL-VIBRATIONAL Transitions
First Harmonic
Vibrational
Mode
Fundamental Vibrational Mode
ΔJ= -1
ΔJ= +1
ΔJ= 0

20. Rotation-Vibration Modes
vibrations + rotations typically occur
together - at least < 20 m
selection rules (from q-theory) establish
which transitions are permitted
Diatomic molecule v=  1, J=  1
P&R Branch
Triatomic (linear) molecule (CO2)
v=  1, J=  1
v= 1, J= 0
Q Branch

21. 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)

22. 15 μm ν2 CO2 Transition
R-Branch
P-Branch
Q-Branch

23. 15 μm CO2 Transitions (mainly ν2)

24. The thermal IR spectrum, again

25. Isotopologues Matter!

26. Summary
electric
Permanent
magnetic
dipole -
yes
Insert fig. 8.9

28. VERY LITTLE RHYME OR REASON

29. 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 > 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 > 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.

30. 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.
ΔJ = -1  “P-branch”
ΔJ = 0  “Q-branch” if it exists! Only allowed if the vibrational transition is “degenerate” , e.g. the ν2 transition of CO2!
ΔJ = +1  “R-branch”
The energy associated with ΔJ = ±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 Δv = ±1 does not depend on starting v state: they all take the same energy.