Simple Laser-Induced Fluorescence Setup to Explore Molecular Spectroscopy

S. B. Bayram∗ and M.D. Freamat†

Miami University, Department of Physics, Oxford, OH 45056

(Dated: July 23, 2012)

Abstract

We will demonstrate a relatively simple, affordable and highly visual experiment to explore molecular

spectroscopy by measuring the laser-induced fluorescence (LIF) spectrum of the iodine molecules at room

temperature. Iodine is a uniquely suited molecule for LIF measurements since it conveniently absorbs about

20,000 lines in the 490- to 650-nm visible region of the spectrum and serves excellent example of displaying

discrete vibrational bands at moderate resolution and rotational structure at high resolution.

The apparatus consists of a diode laser 532 nm (or a laser pointer), an iodine cell, and a handheld

spectrometer. We will scrutinize the LIF spectrum about the potentials associated with the vibrational states

of the diatomic molecules and assign spectral lines based on the transition probability between vibrational

levels, build vibrational energy level diagram and tabulate Deslandres table, evaluate the harmonic and

anharmonic characteristics of two states and thereof the merits of the harmonic approximation for the

molecular oscillator, and finally extract the molecular constants such as dissociation energies of the molecular

potentials.

∗Electronic address: bayramsb@muohio.edu†Electronic address: freamamv@muohio.edu

1

I. INTRODUCTION

Iodine is the heaviest common halogen (atomic number=53, atomic mass=127) and like the

other halogens, iodine vapor consists of a weakly bound diatomic molecule. The vapor has the

appearance of a violet gas, indicating a visible absorption. This absorption corresponds to a spin-

forbidden transition from the lowest vibrational levels of the singlet electronic ground state to high

vibrational levels of a triplet excited state.

In this experiment we are going to study the laser induced fluorescence of iodine in the gas phase

at room temperature. The aim of the study is to determine the molecular parameters, that is the

dissociation energy of the ground X and excited B states, vibrational frequency, anharmonicity

constant and the force constant, of iodine in the ground state. This will be done by measuring the

vibrational spectrum of the fluorescence from an iodine vapor, which is excited by a 532-nm laser

beam.

Laser induced emission can be analyzed to give a great deal of information about the molec-

ular structure and potential energy curves for ground and excited electronic states. The visible

absorption spectrum of iodine vapor in the 490- to 650-nm region serves as excellent example,

displaying discrete vibrational bands at moderate resolution and extensive rotational structure at

high resolution. The rotational structure is not seen at a resolution of ∼0.2 nm, a common limit for

commercial ultraviolet-visible spectrometers, but the vibrational features can be easily discerned

in both absorption and emission measurements. A green 532 nm laser is used to excite the iodine

in its B state from the lowest v′′=0 vibrational level of the ground electronic state to higher level

vibrational level of the excited state. The excited molecule will relax to different vibrational levels

in the ground state.

The spectrum of the X1Σ+g →B3Π+

g transitions has more than 20,000 absorption lines in the

visible and some of them near 532 nm, and it complements the absorption spectrum. Observation

of emission spectrum from the Laser Induced Fluorescence (LIF) using a green laser pointer at 532

nm exhibits Stokes and anti-Stokes emissions, and offers not only vibrational structure but also

rotational structure with adequate resolution.

In this experiment, we concentrate on the LIF spectrum of I2 in order to obtain vibrational

frequencies, anharmonicities, and other molecular parameters for the ground X1Σ+g and excited

B3Π+g states involved in this electronic transition.

2

A. Background theory

The relevant potential energy curves for I2 are shown in Fig. 1, which also shows some of the

parameters to be determined from the spectra. The spacing between levels in the two electronic

states can be measured by laser induced fluorescence spectrum. The total energy of a diatomic

molecule has

E = Ee + Evib + Erot. (1)

where electronic Ee, vibrational Evib and rotational Erot energies are individually quantized.

FIG. 1: A partial potential energy diagram for I2: the curves X and B are associated with the respective

ground and excited electronic states. The horizontal lines within the curves indicate the vibrational energy

levels of the electronic state.

There is no strict selection rule for the change in vibrational quantum number during an elec-

tronic transition; thus sequences of transitions are observed. The selection rules for electronic

transitions are based on conservation of angular momentum (which govern which electronic states

3

can be accessed), and on the Franck-Condon Principle (which governs which vibrational states can

be accessed). The X → B transition is allowed according to the electronic selection rules. Thus, we

must turn to the Franck-Condon principle to understand which vibronic transitions we can expect

to see. This principle, also based on the fact that electrons are much lighter than nuclei, says

the electron redistribution which results from an electronic transition occurs instantaneously with

respect to nuclear motion. That is, the nuclei do not move during a transition, they only adjust

after the absorption event is complete. Since the internuclear distance does not change during the

absorption of a photon, the transition is drawn with a vertical line on the potential energy diagram:

we say that electronic transitions must be vertical as seen in Fig. 1. Furthermore, transitions of

the highest intensities occur when the overlap between the ground and excited state wavefunctions

is largest. This means that the most intense transitions originate from the center of the v′′=0 level

(i.e. the equilibrium internuclear distance).

There are two main consequences of the Franck-Condon principle for the absorption spectrum

of I2:

• Because the potential wells for iodine are substantially offset along the x-axis, transitions

to low-lying vibrational states, (X, 0)→(B, small v′), are not observed (that is, vertical

transitions are not possible to small v′).

• For iodine, observable vertical transitions terminate at vibrational levels in the region of v′

= 26-50. Transitions to very large v′ are not observed because the overlap between ground

and excited state wavefunctions is too poor.

Thus, Franck-Condon selection rules predict that the absorption spectrum for iodine at room

temperature will primarily consists of transitions such as (X, v′′) → (B, v′ = 20, ..., 50).

In order to define the energies in terms of wavenumbers, it is convenient to divide Eq. (1) by

the quantity hc, where c is expressed in units of cm−1, to get the so-called term value T , which

has units of cm−1. Thus

T = E/hc = Te + G(v) + F (J), (2)

where Te is the electronic term value (Ee/hc), G(v) is the vibrational term value (Ev/hc), and

F (J) is the rotational term value (Erot/hc). The advantage of this change is that the frequency

(expressed in cm−1) for a transition between two electronic states can be simply expressed by

T ′ − T ′′ = (T ′e − T ′′e ) + (G(v′)−G(v′′)) + (F (J ′)− F (J ′′)), (3)

4

where primed (′) parameters are properties of the upper state, while the double-primed (′′) param-

eters are lower state properties. Here, T ′′e is zero since it refers to the ground electronic energy

state and T ′e is the frequency of the transition between X and B. Since the rotational energies will

not be resolved in the experiment, we will ignore the rotational contribution. The vibrational term

value is

G(v) = Ev/hc = ωo(v + 1/2)− ωoxo(v + 1/2)2, (4)

where ωo (calculated in cm−1) is the fundamental frequency of the vibration. Because the product

ωoxo quantifies the first order energy deviation from that of a harmonic oscillator, it is termed

anharmonicity.

II. EXTRACTING MOLECULAR CONSTANTS

To take into account of the anharmonicity of the vibrations, we use the Morse potential to

describe the potential curve

V (r) = De

(1− e−β(r−r0)

)2, (5)

where De is the dissociation energy given by the depth of the potential well, and β relates to the

force constant k as

β = (k/2De)1/2. (6)

The fundamental frequency of the vibration, ω0, is naturally related with the other parameters of

the oscillator:

ω0 =1

2πc

√k

µ=

β

c

√De

2π2µ, (7)

where µ is the reduced mass of the iodine. By subtracting the energies of successive levels v within

a state characterized by (ω0, ω0x0), one obtains the vibrational energy spacing:

∆G(v) = ∆Ev/hc = ω0 − 2ω0x0 (v + 1) (8)

which suggests that the energy steps are fairly constant at low v, as confirmed experimentally by

the regularity of the spectrum peaks within each progression and the inter-level energies, but reduce

5

gradually at high v, up to a maximum level vmax = 1/2x − 1 corresponding to the dissociation

energy De. This argument stays behind the so called Birge-Sponer treatment [1] that uses the

linear plot of ∆G against (v + 1). Based on this linear plot, fundamental frequency ωo can be

found by extrapolating the linear fit to the ∆G axis. The anharmonic term ωoxo is the slope of

the line. The dissociation energy D0 with respect to the zero-point level is simply given by the

area under the linear plot in the interval (0, vmax). Since ∆E0/hc ≈ ω0 whereas ∆Evmax → 0,

the zero-point dissociation energy is D0/hc = ω20/4ω0x0. Combining with equation 4, the students

can furthermore calculate the dissociation energy De relative to the equilibrium point (that is, the

bottom of the potential well) as shown in Fig. 1.:

De/hc = E0/hc + D0/hc =12ω0 − 1

4ω0x0 +

ω20

4ω0x0. (9)

Insofar as De and ω0 can be substituted in Eq. (7) to find β. Theoretical constants are given in

references [2, 3]. Franck Condon table for the 532 nm excitation was given in reference [4]. In

our earlier paper [5], we showed how to extract upper level molecular potential well using a simple

nitrogen capillary discharge tube.

III. CALIBRATION

After obtaining the spectrum, one can calibrate the spectrum using various light sources. A

reference spectrum can be obtained from Hg source which exhibits a bright green at 546.1 nm

and two yellow lines at 579 nm and 577.1 nm as seen in the figure below. Neon lines can be

used to further calibrate the spectrum at 533.078 nm, 534. Helium light source gives many lines

in between 400 nm and 600 nm, and can be used to calibrate the spectrum as well. The most

important information about the atoms and their strong emission lines, transition probabilities

and etc. can be found at http://www.nist.gov/pml/data/handbook/index.cfm. When you

enter the site, click on Periodic Table to select the atom of interest.

FIG. 2: Typical Hg strong lines.

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IV. TASKS

Next 4 pages (4 TASKS) will guide you through the basics of how to extract molecular constants

quickly and easily without using sophisticated programs or computer. The figures 3 below show

a typical spectrum you will obtain from the experiment and our simple experimental apparatus.

500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 8000

5000

10000

15000

Inte

nsity

(arb

.)

Wavelength (nm)

Vibrational spectrum of I2excited by 532 nm laser

FIG. 3: Typical LIF spectrum and experimental apparatus consists of an iodine cell, a 532 nm laser, and a

handheld spectrometer with fiber.

7

500520

540560

580600

620640

660680

700720

740760

780800

0

5000

10000

15000I n t e n s i t y ( a r b . )

Wavelength (nm)

Task 1: Spectral line assignmentUse the Franck-Condon factors in the insert to assign each peak on the spectrum a possible B(v’) to X(v’’) transitions. Assign at least 20 of them.

Transition from B(v’=32)

Task 2: D

ata tabulation in a Deslandres table for iodine

Use once again the I2 em

ission spectrum to fill out the table below

with the follow

ing parameters for each spectral line:

The em

itted wavelength, λ (nm

). Employ the program

provided to verify the values.

The transition energy, G v′→

v″ (cm–1).

The energy separation betw

een successive levels, ΔG = G

v′→v″ – G

v′→v″+1 (cm

–1) Then, to get a sense of the vibrational fine structure, use any pair of successive lines to estim

ate the energy separation within the X

-state.

v″ λ (nm

) G

v′→v″ (cm

–1) ΔG

(cm–1)

Transition energy in cm–1 from

wavelength:

71

110

nmcm

cmnm

vv

G

Transition energy in eV from

wavelength:

1240 nmeV

eVnm

vv

hcE

Apply this expression to tw

o arbitrary consecutive vibrational levels and subtract to estim

ate the separation betw

een energy levels in eV:

1________

eVv

vv

vE

EE

Task 3: D

ata analysis using Birge-Sponer treatm

ent A

s explained in the manual, the energy separation betw

een vibrational levels varies linearly with the ground level quantum

numbers v″, as given by

ΔG = ω

0 – 2ω0 x

0 (v″ + 1). Collect a sufficient num

ber of (ΔG, v″ + 1)-values from

the table and build a graph on the frame provided below

. Then

A

pproximate a linear fit and sketch a sm

ooth straight line through the distribution.

Notice that the ΔG

-axis intercept is ω0 , that is, the fundam

ental frequency of the diatomic m

olecule if it were a perfect sim

ple harmonic

oscillator. Extrapolate the linear fit, estimate ω

0 and feed the value in the provided box.

On the other hand, the slope is –2ω

0 x0 , that is, the anharm

onic term describing how

much the m

olecular quantum oscillator deviates from

the sim

ple harmonic m

odel. Estimate it and feed the value in the provided box.

ω0 = intercept =

ω0 x

0 = – ½ slope =

250 240 230 220 210 200 190 180 170 160 150

ΔG

(cm–1)

v″ + 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Task 4: Sum

marizing the results

As explained in the m

anual, the fundamental frequency and the anharm

onic term can be used to determ

ine other parameters of the m

olecular vibrational state under scrutiny: the force constant k

0 of the bond, the dissociation energies D0 and D

e with respect to the low

est level and the equilibrium

position (bottom of the potential w

ell), and the factor β in the Morse potential. U

se the provided formulas to estim

ate these parameters

for the ground level X of the iodine m

olecule, and list them in the table below

.

Parameter

Experim

ent Literature

ω0 (cm

–1)

214.248

ω0 x

0 (cm–1)

0.6074

k0 (N

/m)

172.1

D0 (eV

)

1.55

De (eV

)

β (cm–1)

SHO

force constant:

2

00

2k

c

Dissociation energy from

v″ = 0 level: 20

00

04

Dx

Dissociation energy from

equilibrium position:

oo

oo

ex

DD

4 12 1

Factor β in the Morse potential

0

()

1r

re

Vr

De

:

0

2e

kD

Conversions:

from

cm–1 to eV

:

1

4eV

cm1.24

10 cm

eVE

E

from

cm–1 to J:

1

23J

cm1.99

10 cm

JE

E

reduced m

ass of iodine molecule:

2563.5 am

u1.05

10 kg

1 cm–1 = 1.23985x10

–4 eV

Acknowledgments

The financial support from the Research Corporation and the Dean of the College of Arts and

Science at Miami University are greatly acknowledged.

[1] R. T. Birge and H. Sponer. Phys. Rev., 28:259, 1926.

[2] Ian J. McNaught. The electronic spectrum of iodine revisited. J. Chem. Educ., 57:101, 1980.

[3] L. Mathieson and A.L.G. Rees. Electronic states and potential diagram of the iodine molecule. J. Chem.

Phys., 25:753, 1956.

[4] J. Tellinghuisen. Laser-induced fluorescence in gaseous I2 excited with a green laser pointer. J. Chem.

Educ., 84:336, 2007.

[5] S. B. Bayram and M.V. Freamat. Vibrational spectra of N2: An advanced undergraduate laboratory in

atomic and molecular spectroscopy. Am. J. Phys., 80:664, 2012.

8