Experiment #2

Band Spectrum of I2 Vapor

Introduction

The visible absorption spectrum of molecular iodine vapor in the 490 to 650 nm region displays discrete vibrational bands at moderate resolution.

The spectrum may be used to obtain vibrational frequencies, anharmonicities, bond energies, and other molecular parameters for the ground and excited states involved in this transition.

Electronic Transitions of I2En

ergy

Internuclear Distancero r*

Bonding orbital

Anti-Bonding orbital

Frank-Condon Principle

Electronic transitions occur so rapidly that the nuclears do not have time to change either their position or velocity

The most intense transitions from ” = 0 in the lower electronic state are those to vibrational states in the upper electronic state with a turning point at an internuclear separation r = re".

F-C factor

Wavefunction wavelap

2

' " ' "' ( ) " ( )v v v vQ r r dr

Frank-Condon PrincipleEn

ergy

spa

cing

Inte

nsity

dis

trib

utio

n

Transition Energy

For a diatomic molecule, the internal energyor

A transition between two electronic states

- = - - - el elT T T T G G F F %

FGThcE

T el intint

electronic vibrational rotational

Eint = Eel + Ev + Er

Anharmonic Correction to Vibrational Energy StatesG = e( + ½) e e( + ½)2 + eye( + ½)3 + …

= el + (G’ – G”)

= el + e’(’ + ½) ee’(’ + ½)2 e”(” + ½) + e e”(” + ½)2

Selection Rule = 0, ±1, ±2, ±3, …

""'' ,,, eeeeee

Linest fitting

y x1 x2 x3 x4

el,

De”, Do”, De’, Do’

Transition within An Electronic Sate

G

(’)

’

Birge-Sponer Plot

12 '''' eeeG

Energy spacing between two adjacent vibrational states

"'"'' ,,1 GGG Excited state

Bond Dissociation Energy

44

2

maxee

ee

ee GD

24

2e

ee

eoD

Ground-State Bond EnergyEn

ergy

Internuclear Distancero r*

Bonding orbital

Anti-Bonding orbital *'" IEDvD eele

E(I*) = 7598 cm-1

Force Constant

Near the minimum in the potential energy curve of a diatomic molecule, the harmonic oscillator model is usually quite good

A measure of the bond strength

2

2e 2 2

e

er

Uk cr

'ek "

ekvs

Morse Potential At large displacements from the

equilibrium position,

21 erree eDrrU

e

ehcDk

2

Bandhead Formation

The energy of a transition from a vibration-rotation (v”, J”) state in one electronic state to a vibration-rotation state (v’, J’) in another electronic state is:

' v ' " v" ' v ', ' " v", "e G G F J F J %

' "0 v ' v"' ' 1 " " 1B J J B J J %

Bandhead Formation

Setting J = J”, we have the following results R branch: P branch:

These two equations assume the same form if a new variable, m, is defined as m = J+1 for the R branch and m = -J for the P branch:

' "0 ' "1 2 1v vB J J B J J %

' "0 ' "1 1v vB J J B J J %

' " ' " 20 v ' v" v ' v"B B m B B m %

Bandhead Formation

For I2, Bv’ = 0.02903 cm-1 and Bv” = 0.03737 cm-1, so mvertex = 4 and vertex – 0 = 0.1316 cm-1

0ddm

%

' "v ' v"

' "v ' v"2vertex

B Bm

B B

2' "' "

0 ' "' "4

v vvertex

v v

B B

B B

-3 -2 -1 0 1

-15

-10

-5

0

5

10

15

20

m =

-J"

m =

J"

P br

anch

R b

ranc

h

I2 X -- B

m

- 0 (cm-1)

Red-shaded

Bandhead Formation The intensity of the transitions from individual

rotational states

""

0

" " 1( ' ") " ' 1 exp vB J J

I J J I J JkT

-100 -80 -60 -40 -20 0 20 40 60 80 1000

5

10

15

20

25

30

35Line intensities (I2 (B <-- X), T = 300 K)

Line

inte

nsity

m

-100 -80 -60 -40 -20 00

2

4

6

8

10

12

14I2 (B <-- X, T = 300 K) Red shaded bandhead

Abso

rptio

n

- 0 (cm-1)

How to do data analysis?

Data Analysis Assign each peak with a set of vibrational

quantum number (v’’ and v’) Make a table

(nm) v’’ (X) v’ (B)

541.2 0 27

539.0 0 28

571.6 1 18

568.6 1 19

592.0 2 14

588.5 2 15

McNaught, Ian J., The Electronic Spectra of Iodine Revisited, Journal of Chemical Education, 57(2):102 (1980).

v 0

v 1

v 2

v’ = 27

v’ = 28

v’ = 18

v’ = 19

Experimental Datav” v’ Peak

(nm)v”+½ (v”+½)2 v’+½ (v’+½)2 (cm-1)

0

0

…

1

1

…

2

2

…

Anharmonic Correction to Vibrational Energy StatesG = e( + ½) e e( + ½)2 + eye( + ½)3 + …

= el + (G’ – G”)

= el + e’(’ + ½) ee’(’ + ½)2 e”(” + ½) + e e”(” + ½)2

""'' ,,, eeeeee

Linest fitting

y x1 x2 x3 x4

el,

De”, Do”, De’, Do’

Sublimation Enthalpy

Beer’s law A = lC = l(P/RT) = 500 L mol-1 cm-1 at 500 nm

Clausius-Clapeyron equation

vapor pressure estimated from

optical absorbance

122

1 11lnTTR

HPP sub

Literature Results

Bond dissociation energy 152.5 KJ/mol http://www.newton.dep.anl.gov/askasc

i/chem00/chem00945.htm Sublimation enthalpy 60.4 KJ/mol

http://www.iodine.com/iodine.htm