Methane (CH4)

Ozone (O3)

Carbon Dioxide (CO2)Ammonia (NH3)

Nitrogen (N2)

Water Vapor (H2O)

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)?

Elementary Molecular Spectroscopy

E1

E2

Absorption emission

E=h

Quantum mechanics dictates that virtually all energy transitions are discrete:•Absorption: molecule increases its energy

•Emission: molecule decreases its energy.

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

Molecules can store energy in 4 discrete ways:

1.Translational (kinetic) energy – directly associated with the the TEMPERATURE of the gas. 2.Vibrational : Most molecules are constantly vibrating! (if their structures allow it)3.Rotational: Molecules can rotate on top of vibrating.4.Electronic: Relates to energy states of electrons inside a molecule

Energy storage potential in each type is :A.Electronic : HIGH (associated with visible/UV) B.Vibrational: MEDIUM-LOW (associated with IR/Microwave)C.Rotational: quite low – tacked on as a modified to vibrations, leading to “vibrational-rotational” absorption features.

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)

EEL > EVIB > ETRANS > EROT

The types of interactions that occurin matter depend on the rate ofoscillations that must be induced (i.e the wavelength of the incident radiation).

On the whole, shorter wavelength, radiation interacts with lighter andsmaller parts of matter whereas moresluggish slower oscillating radiationaffects the larger parts of matter.

We are mainly concerned with mechanisms affecting electrons, and atoms to more bulky molecules - mostly vibrational and rotational spectra

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.

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

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

*

*

*Induced through vibrations

THE OVERALL PICTURE

MODES OF VIBRATION

Degenerate!

Analog Models: Vibration of a Diatomic Molecule“It’s like a spring!”

Restoring Force F=-k(r-re)

harmonic oscillator predicts

the vibrationalquantum #

k=Spring constant

m’=“reduced mass”

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!

Analog Models: Rotation of a ‘Diatomic Molecule’

Rotating MoleculeCenter of mass: m1r1=m2r2

Moment of Inertia: I=m1r12+ m2r2

2

Energy: E=1/2 I2 =L2/2IAngular Momentum, L= I

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

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=00)

• SO ΔE =

• Leads to equally spaced lines (J=0,1,2,3 etc)

• Rotations are often a perturbation on vibrational transitions

Fundamental Vibrational Mode

First Harmonic VibrationalMode

ΔJ= -1

ΔJ= 0

ΔJ= +1

ROATIONAL-VIBRATIONAL Transitions

Rotation-Vibration Modes

vibrations + rotations typically occurtogether - at least < 20 m

selection rules (from q-theory) establishwhich 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

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)

P-Branch

R-Branch

Q-Branch

15 μm ν2 CO2 Transition

15 μm CO2 Transitions (mainly ν2)

The thermal IR spectrum, again

Isotopologues Matter!

Summary electricPermanent magnetic dipole - yes

Insert fig. 8.9

VERY LITTLE RHYME OR REASON

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.

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 = 34 takes 3 times more energy than J = 01 !

• The energy associated with Δv = ±1 does not depend on starting v state: they all take the same energy.