2. Molecular stucture/Basic The electromagnetic

Spectral region fooatocadr atomic and molecular spectroscopy

E. Hecht (2nd Ed.) , Addison-Wesley Publishing Company,1987 Per-Erik Bengtsson Spectral regions Mo lecu lar spec troscopy o ften d ea ls w ith ra dia tion in the ultraviolet (UV), visible, and (IR) spectltral regi ons.

• The visible region is from 400 nm – 700 nm • The ultraviolet region is below 400 nm • The infrared region is above 700 nm.

400 nm 500 nm 600 nm 700 nm

Spectroscopy: That part of science which uses emission and/or absorption of to deduce atomic/molecular properties Per-Erik Bengtsson Some basics about spectroscopy

E = Energy difference  = c /c h = Planck's constant, 6.63 10-34 Js ergy

nn  = E hn = h/hc /l E = h = hc / c = Velocity of , 3.0 108 m/s = 0 Often the wave number, , is used to express energy. The unit is cm-1.  = E / hc = 1/

Example The energy difference between two states in the OH- is 35714 cm-1. Which wavelength is needed to excite the molecule? Answer  = 1/ =35714 cm -1   = 1/ = 280 nm. Other ways of expressing this energy: E = hc/ = 656.5  10-19 J E / h = c/ = 9.7  1014 Hz

Per-Erik Bengtsson Species in combustion

Combustion involves a large number of species

Atoms (O), (H), etc. formed by dissociation at high

Diatomic (N2), oxygen (O2)

(CO), hydrogen (H2) nitri coxide (NO), hy droxy l (OH), CH, e tc.

Tri-atomic molecules (H2O), (CO2)etc), etc.

Molecules with more fuel molecules such as ,,, ethene, etc. than three also molecules formed in rich flames

Per-Erik Bengtsson

According to quantum mechanics all energy levels in atoms and molecules are discrete and are given by the solution to the Schrödinger equation: 2    2    V r   E = wavefunction  2  h = h/2 (h = Plancks constant)

m m   1 2 reduced m1  m2

E = energy levels VilV = potential energy

Since the selections rules only permit certain transitions a spectrum can be very precisely calculated Diatomic molecules: Structure

A consists of two - - - nuclilei an d an e lec tron c lou d. - + - + - - The positive nuclei repel each other. - - The negative attract the positive nuclei and prevent them from separation. rgy ee When all electrons have their lowest En possible energies, the molecule is in its ground electronic state. Ground electronic 0 state

Per-Erik Bengtsson Diatomic molecules: electronic states

We observe an outer loosely bound .

By the addition of energy, it can be moved to another ”orbit” at higher energy, and the molecule end up in an excited electronic state. + + rgy ee

En Different electronically excited states

Ground 0 electronic state Per-Erik Bengtsson Absorption

For many molecules of interest in combustion, absorption of radiation in the ultraviolet and visible spectral region can lead to electronic excitation of a + + molecule.

This absorption process can be represented in an diagram:

The energy levels are discrete, and the rgy ee energy difference can be used to En calculate the exact wavelength of the E radiation needed for absorption: E = hc/ 0 Per-Erik Bengtsson Diatomic molecules: Structure The electronic states of molecules are in analogy with electronic states of atoms. In addition molecules can vibrate and rotate . In - - - the Born-Oppenheimer approximation these - motions are initially treated separately: + - + - - - Etot= Eel + Evib + Erot - To more easily describe vibrational and rotational energies, a simpler model for the molecule will be used.

Consider the diatomic molecule as two atoms joined by a string.

Time scales: Electronic interaction ~10-15s Vibrations ~10-14s Rotations ~10-13-10-12 s Per-Erik Bengtsson Diatomic molecules: vibrations

Molecules can also vibrate at different .

BtBut onl y specifi ifidic discre te vibrational frequencies occur, corresponding to specific energies.

Per-Erik Bengtsson Vibrational energy levels

The vibrational energy states give v=2 a fine structure to the electronic yy Excited states. v=1 Electronic v=0 }state Energ v=0 is the lowest vibrational frequency, then higher v numbers correspond to higher vibrational frequencies.

While th e separati on b et ween electronic energy states is around 20000 cm-1,,p the separation between vibrational energy states is on the order of 2000 cm-1. v=2 Ground v=1 Electronic }state 0 v=0 Per-Erik Bengtsson Vibrational energy levels

Solutions to Schrödinger equation for harmonic oscillator with 2 give V(r) = ½ k (re-r)

1 Ev/hc = Gv  ω(v1/2) [cm ] G0= 1/2 ,G1= 3/2 , G2= 5/2 

v = 1   = G(v') - G(v") = (v + 1 + 1/2) - (v + 1/2) = 

V'- corresponds to levels in the excited state V" – corresponds to levels in the ground state Vibrational energy levels

A better description of the energy is given by the Morse function:

2 V  Deq.[1exp{a(req. r)}]

Dissociation energy, D . where a is a constant for a particular e molecule. Energy corrections can now be introduced.

2 1 Gv  e (v1/ 2)exe (v1/ 2) [cm ]

v = 1, 2,

Per-Erik Bengtsson Vibrational population The transition from v=0 to v=1 then occurs at;

2 2 1 Gv 1  G v  0  e 11/ 2e xe 11/ 2 e 1/ 2 e xe 1/ 2  e 1 2xe cm

Whereas the transition from v=1 to v=2 (hot band) occurs at

G(v=2) - G(v=l) =  (1-4 ) cm-1 Population distributiondistribution of of N N2 e e 2

1

0,9 n oo 0,8 v=0

0,7 v=1 Population Nv; 0,6 v=2

l populati 0,5

aa vv3=3 0,4 Nv ~ exp[-G(v)/kT] 0,3 0,2 Fraction 0,1

0 200 700 1200 1700 2200 2700 3200 (K) Per-Erik Bengtsson Diatomic molecules: rotations

Molecules can also rotate at different frequencies.

But only specific discrete rotational frequencies occur, corresponding to specific energies.

Per-Erik Bengtsson Rotational energy levels J = 6 The rotational energy states give a v=2 fine structure to the vibrational yy states. v=1 v=0 Energ J=0 is the lowest rotational energy state, then higher J numbers correspond to higher rotational J = 5 states.

While th e separati on b et ween vibrational energy states is around J = 4 2000 cm-1,,p the separation between rotational energy states is on the order of a few to hundreds of cm-1. v=2 J = 3 v=1 J =2= 2 J = 1 0 v=0 J = 0 Per-Erik Bengtsson Energy levels for rigid rotator Solutions to Schrödinger equation with V(r) = 0, gives m1 m C 2

2 h r r EJ  J(J 1) 1 2 8 2I r0

2 m1m2 I  r0   m1  m2

E h F  r  J(J 1)  BJ(J 1) [cm1] J hc 82cI Rotational transitions F = F (J') - F (J") = B J'(J'+l) - B J" (J"+l)

J=J = ±l  F=2BJF = 2BJ J' - corresponds to levels in the excited state J" – corresponds to levels in the ground state Rotational population distribution

The rotational population distribution can be N  (2J 1)eBJ(J 1)hc/kT calculated as

If f (J)  (2J 1)eBJ(J1)hc/kT 0,09

0,08 Nitrogen f (J) 0,07

then on  0 0,06 T=300 K

T 0,05

0,04 populati

kT 1 0,03ee gives Jmax   0,02 T=1700 K

2Bhc 2 0,01Relativ

0 0 3 6 9 12 15 18 21 24 27 30 33 36 39 Rotational , J

Per-Erik Bengtsson A coupling rotation-vibration

Total energy Tv,j given by:

2 Tv,J  Gv FJ e v 1/ 2 e x e v 1/ 2  BJJ 1

A transition from v’ to v’’ occurs at:

    BJ'J'1 BJ"J"1

Consider two cases: A coupling rotation-vibration: Exampl e HCl ab sorpti on HITRAN

HITRAN is an acronym for high- resolution transmission molecular ABSORPTION, which is a database using spectroscopic parameters to predict and simulate the absorption spectra of different molecules Example: The CO vibrational band (0-1)

P Branch R Branch Different broadening mechanisms: Collisional broadeninggppg and Doppler broadening

Lorentz profile: 1 b g ()  L L () 22 b  0 L

Doppler profile:   exp( (ln 2)(0 )2 ) ln 2 bD gD ()   bD

Voigt profile— of Doppler andLd Loren tz ian line s hape func tion:

 ''' gggdVDL()  ( ) ( )  Absorption simulation

H2O+CO2

H2O+CO2 CO2 H2O

Isotope abundance: 1% Simulated : 500 ppm Detect limit: 5 ppm Transitions between electronic states

Absorption and emission spectra are A spppecies specific

The energy difference (and thereby v=1 the wavelength) can be calculated v=0 using molecular parameters for the involved electronic states. nn bsorptio mission X AA EE

Rotational energy levels in the first excited vibrational state. v=1 } v=0 } Rotational energy levels in the ground vibrational state.

Equilibrium distance

Per-Erik Bengtsson Molecular structure - OH

Q

P R

Per-Erik Bengtsson Summaryyp 1: Temperature effects

At low tempp(erature (room-T) Molecules generally • rotate at lower frequencies. • vibrate at lower frequencies

At high temperature (flame-T) Molecules generally • rotate at higher frequencies. • vibrate at higgqher frequencies

Per-Erik Bengtsson Summaryyp 2: Temperature effects

Population distribution over energy states at flame temperature, ability bb (also high rotational frequencies, not only lowest vibrational frequency) Pro yy Population distribution over energy states at room temperature,

obabilit (Low rotational frequencies, lowest vibrational frequency) rr P

0 Energy The population distribution is often what is probed when temperatures are measured

Per-Erik Bengtsson Summary: Molecular

Each molecule is at a certain time in a specific rotational state, J, in a specific vibrational energy level, v, and in a specific electronic energy level.

There is a higgph probabilit y that a molecule chan ges state as a result of a molecular collision. However, the population distribution over all possible states is the same at a constant temperature (because of the large number of molecules) .

To excite an or a diatomic molecule a must be tuned to an exact wavelength for the excitation.

A larger molecule, such as a 3-pentanone or , has many more close-lilying s tttates. To excit e such a mol ecu le, any wave leng thithith within a range can be used for the excitation.

Per-Erik Bengtsson Summary

• Molecules have different energies; rotational energies, vibrational energies, and electronic energies.

• Information about the energy levels for molecules is used to interpret spectroscopic information from laser-based techniques and other optical techniques.

• Absorption and laser-induced are techniques for which we need to know at which wavelength a certain species can bitdbe excited.

•Temppypgpperatures can be measured by probing the population distribution over different energy levels, for example in Raman and CARS techniques.

Per-Erik Bengtsson