Methane (CH4)

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

2. 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. E2 E=h E1 Absorption emission Elementary Molecular Spectroscopy • Quantum mechanics dictates that virtually all energy transitions are discrete: • Absorption: molecule increases its energy • Emission: molecule decreases its energy.

4. Elementary Molecular Spectroscopy Bright lines of emission’ Dark lines of absorption 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 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! • N2 generally unimportant in stratospheric chemistry • Because of O2/O3, no photons make it below mid- stratosphere that can excite more electronic transitions. UV-B UV-C UV-A

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 P&R Branch 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. electric Summary 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.