Silvia BobeicaCHEM 382

Absorption Spectra of Iodine VaporAbstract:

This experiment involved the calculation of several diatomic constants for iodine in the vapor

phase using absorption spectroscopy in the visible region of 500 to 620 nm. The transitions were

assigned in the visible spectrum and from this the equilibrium wavenumber of the excited and ground

state was calculated to be 134 cm-1 and 230 cm-1 in good agreement with literature values. The

dissociation energy from the v=0 and the equilibrium dissociation energy for the excited state were

estimated 4328 and 4395 cm-1 respectively, reasonably close to literature values. The experimental bond

force constant was 67.5 N/m while the equilibrium radius of the iodine molecule in the excited state was

3.235 A, both these values comparing favorably to accepted values. The parameter β’ was also

calculated to be 1.965 A-1, in very good agreement with the literature value. The diatomic constants for the

ground state were not as accurate as those of the excited state. The experimental dissociation energy

from the v=0 state and the equilibrium dissociation energy were 8855cm-1 and 8964 cm-1, compared to

literature values of approximately 12000 cm-1. The bond force constant of the ground state 178 N/m was

in good agreement with the literature value. The parameter β’’ was estimated at 2.237 A -1 compared to

the literature value of 1.901 A-1. This experiment shows that while a good estimations can be obtained for

the excited state of the vapor phase iodine with this model, the ground state calculations are inaccurate

and do not provide a reliable information about the diatomic constants of a homonuclear halogen.

Introduction:

The visible spectrum of iodine has found applications as a convenient tool for the study of the

differential rotation of the Sun, or the improved efficiency of dye-sensitized solar cells when used to dope

titanium dioxide crystals.1,2 Spectra of small molecules in gas phase offer information on the potential

energy curves of the ground and excited electronic states. The absorption spectrum of iodine will be used

to deduce vibrational frequencies, and bond energies. Figure 1 represents some of the features this

experiment will analyze, such as the difference in energy between the minimum of the potential energy

curve and dissociated atoms, D’e and the dissociation energy from the ground vibrational level of the

potential D’0.

1

The internal energy of a diatomic molecule is given by the equation:

E∫¿=Eel+E v+Er(1)¿

where Eel is the electronic energy which designates the minimum value of the potential curve for a given

electronic state, Ev is the vibrational energy and Er is the rotational energy.4 Dividing by the quantity hc

with c expressed in cm/s, and changing notation of Ev/hc and Er/hc to G and F respectively, the term

value is obtained:

T∫¿ (cm−1)=

E∫ ¿

hc=T el+G+F (2 )¿¿

This equation allows for frequency expressed in reciprocal centimeters to be written as:

3

2

ν=T ' el−T' 'el+G (ν ' )−G (ν ' ' )+F (J ' )−F (J ' ' )=νel+G (ν ' )−G (ν ' ' )(3)

by considering the rotational term difference to be very small as this experiment will not resolve it.4

Therefore the transition frequency written as a function of the quantum numbers ν’ and ν’’ will be given by

the equation:

ν (v ' , v ' ' )=νel+ν ' el(v '+ 12 )−ν ' e x 'e(v '+ 12 )2

−ν ' ' e(v ' '+ 12 )+ν' 'e x ' ' e (v ' '+12 )❑2

(4)

or in a different form:

Δν (v ' )≅ ν (v '+1 , v ' ' )−ν (v ' , v ' ' )≈ ν ' e−2ν ' e x'e (v '+1 )(5)

From which, a Birge-Sponer plot with a slope of −2ν ' e x'e and an intercept of ν 'e−2ν

'e x

'e can be made.

This will allow for easy calculation of v’e and x’e and an analogous calculation can be used to obtain v’’e

and x’’e

The convergence limit is the energy at which the spacing between the absorption bands is too

small to be distinguished. Beyond this energy, called the dissociation energy, the molecule is split into its

constituent atoms. Knowing ν 'e x'e, the dissociation energy of the excited state can be calculated from:

De=G (vmax❑)=ν e(

1xe

−xe)

4(6)

The dissociation energy D0 to dissociate from the v=0 level is smaller than De by the zero point

energy G(0) and is therefore given by:

D0=νe(1xe

−2)

4(7)

A harmonic force constant ke for both the excited and the ground vibrational level can also be

obtained from the following equation near the minimum in the potential energy curve, where the harmonic

oscillator model holds well:

k e=μ (2 πc νe)2(8)

where μ is the reduced mass. 4

At large displacement from the equilibrium bond length, the Morse potential is used to replace the

harmonic oscillator model. The parameter β in the Morse potential is obtained by equating ke to the

curvature of the Morse potential r=re from:

β=(ke

2hc De)2

(9)

3

The transition of greatest intensity ν(v*’) can be obtained from the spectrum and used in the

following equation to obtain the difference between the equilibrium radius of the ground state and that of

the excited state:

U ' (r ' ' e−r 'e)=D 'e{exp [−β ' (r ' 'e−r 'e )]−1 }2+νel=ν (v ¿' )+ 1

2ν ' 'e−

14ν ' 'e x

' 'e(13)

Experimental:

A few crystals of iodine were placed in a 1.0 cm path length quartz cuvette, heated to 32oC to

obtain more iodine in vapor phase, and the spectrum between 500 and 620 nm was acquired using an

Ocean Optics HR 4000CG-UV-NIR High Resolution spectrometer running 40 counts. The experimental

values for the diatomic constants were compared to the values obtained by McNaught.3

Results:

The absorption spectrum of iodine in the vapor phase is represented in Figure 2. The quantum

numbers of the ground electronic state are also represented on the spectrum. Notable features include

the decreasing separation between the transitions when approaching the convergence limit as well as

variable intensities of the signals for each transition. The transition with maximum absorbance occurs at

535 nm (18691 cm-1).

Figure 2. Absorption spectrum of I2 vapor with the ground quantum numbers assigned.

Table 1. Deslandres table of PN bands with band-head frequencies in cm-1. Differences between energy levels used in the excited state calculations are in bold font, while differences between energy levels used in the excited state calculations are between brackets [ ].

4

v''Average Differences

between energy levels for the excited state

calculation (cm-1)0 1 2

5

v'

Average separation between energy levels for

the ground state calculation (cm-1)

215.5464268

Average separationbetween energy levels

for the groundstate calculation (cm-1)

208.1200221

11 16549.71534

128.3479984

12 16678.06334

106.9375799

13 16785.00092

104.0380905

14 17099.8632 [210.8241874] 16889.03901

99.99920001 99.27302764 99.63611382

15 17422.81692 17199.8624 [211.5503598] 16988.31204

99.52406372 98.18291978 101.323095 99.67669282

16 17522.34098 17298.04532 [208.4101846] 17089.63514

95.6998891 99.00761835 96.9249737 97.21082705

17 17618.04087 17397.05294 [210.4928292] 17186.56011

92.98601148 94.33255341 105.5028331 97.60713267

18 17711.02689 17491.38549 [199.3225495] 17292.06294

98.09494686 93.81480279 95.95487483

19 17809.12183 [223.9215368] 17585.2003

86.36850423 99.82932699 93.09891561

20 17895.49034 [210.460714] 17685.02962

94.00379899 92.11607906 93.05993903

21 17989.49414 [212.3483339] 17777.1457

76.70040136 94.9969897 85.84869553

22 18066.19454 [194.0518456] 17872.14269

97.45999051 80.2117601 88.8358753

23 18163.65453 [211.300076] 17952.35445

86.85192426 81.26020644 84.05606535

24 18250.50645 [216.8917938] 18033.61466

77.93929625 82.65556456 80.29743041

25 18328.44575 [212.1755255] 18116.27022

87.76051371 78.11862819 82.93957095

26 18416.20626 [221.817411] 18194.38885

74.23418078 78.12745774 76.18081926

27 18490.44044 [217.9241341] 18272.51631

73.80111562 82.84345683 78.32228623

28 18564.24156 [208.8817929] 18355.35977

71.61382785 69.5302902

29 18635.85539

78.47043065 78.4704307

30 18714.32582

6

60.08091233 68.0457493

31 18774.40673

69.6960093 69.690093

32 18844.10274

66.63856301 66.638563

33 18910.7413

62.0706594 62.0706594

34 18972.81196

60.3056642160.30566421

35 19033.11762

57.77411089 57.7741108936 19090.89174

53.3602028 53.360202837 19144.25194

57.71434299 57.7143429938 19201.96628

50.27660495 50.2766049539 19252.24289

51.65843216 51.6584321640 19303.90132

52.31105791 52.3110579141 19356.21238

44.68782541 44.6878254142 19400.9002

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 420

10

20

30

40

50

60

70

80

90

100

110

120

v'+1

v (c

m-1

)Δ

Figure 3. Birge- Sponer plot used to determine v’e and x’ e. Difference in wavenumber is ploted as a function of v’+1.

Figure 3 presents a Birge-Sponer plot with the difference in energies between the excited levels

as a function of the excited state quantum number v’. The best-fit line has a slope of -2.0203 and an

intercept of 130.24 which lead to calculated values of 134 cm-1 for v’ e and 1.1015 cm-1 for v’ e x’ e

(Table 2).

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0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5208.5

209

209.5

210

210.5

211

211.5

212

212.5

213

213.5

v''+1

v'Δ

Figure 4. Birge- Sponer plot used to determine v’’ e and x’’ e. Difference in wavenumbers is ploted as a function of v’’+1.

Figure 4 shows a Birge-Sponer plot used in the calculations v’’ e and x’’ e with the ground state

vibrational level as an independent variable and the difference in energies between transitions

starting at different ground levels. The slope of the line is -2.658 and the intercept is 215.64, which

lead to calculated values of 230 cm-1 for v’’e and 1.329 cm-1 for x’’e v’’e (Table 2).

Table 2 has a list of the experimental and calculated values for diatomic constants of iodine.

The calculated values for the excited state are in better agreement with literature values than the

experimental values for the ground state. The energy required to dissociate the molecule into atoms

was also calculated for the excited and the ground state to be 4395 cm-1 and 8964 cm-1, respectively.

The energy required to dissociate the molecule from the v=0 state was estimated at 4328 cm-1 for

the excited state and 8855cm-1 for the ground state. The harmonic bond force constant was

calculated to be 67.5 N/m for the excited state and 178 N/m for the ground state. The Morse

potential parameter β was calculated using the values for the force constant and the dissociation

energy to be 1.965 A-1 for the excited state and 2.237 A-1 for the ground state.

Table 2. Experimental and literature values for diatomic constants of iodine vapour. Literature values are those reported by McNaught.5

Calculated Literature5

x’e v’ e 1.1015 cm-1 0.735 cm-1

v’ e 134 cm-1 126 cm-1

D’ e 4395 cm-1 3805 cm-1

D’ 0 4328 cm-1 3742 cm-1

k’ e 67.5 N/m 59.5 N/mβ’r’ e

1.965 A-1

3.235 A1.982 A-1

3.025 Ax’’ e v’’ e 1.329 cm-1 0.67 cm-1

v’’ e 230 cm-1 214 cm-1

D’’ e 8964 cm-1 11973 cm-1

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k’’ eD’’ 0β’’r’’ e

178 N/m8855 cm-1

2.237 A-1

2.666 A

172 N/m11866 cm-1

1.901 A-1

2.666 A

Using the wavenumber of maximum absorbance (18691 cm-1) and equation 13, the difference in

radii was calculated to be 0.57 A between the excited state and the ground state. Using the accepted

literature value for r’’e of 2.666 A, the value for r’ e was calculated to be 3.235 A. Using the calculated

r’ e, the literature value for r’’ e and the calculated values for the parameter β of the excited state and

the ground state the Morse potential curves for the excited and the ground state were plotted in

Figure 5.

Figure 5 shows the bond dissociation energies for the ground state and the excited state at 4395

and 8964 cm-1 respectively, where the energy reaches a plateau, as well as the minimum in energy

when the internuclear distance is equal to the equilibrium radius for both states.

Figure 5. Morse potential curves for the excited state (red) and the ground state (blue). Harmonic

oscillator (green)

Discussion:

The absorption spectrum of iodine (Figure 2) approaches the convergence limit around 500 nm

(approximately 20000 cm-1). The different intensities of the bands is explained by the Franck-Codon

principle which states that the intensity of an electronic transition is proportional to the overlap of the

wavefunctions of the two states.4 The calculated diatomic constants were in better agreement with

literature values for the excited state of iodine. The calculated wavenumber of 134 cm -1 was in good

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agreement with the literature value of 126 cm-1. The dissociation energy of 4395 cm -1 was also

reasonably close to the accepted value of 3805 cm-1. The dissociation energy from the zero

vibrational level was reasonably close to the literature value of 3742 cm -1. The force constant for the

excited state was estimated to be 67.5 N/m, close to the literature value of 59.5 N/m. The parameter

β’ 1.965 A-1 was also very close to the literature value of 1.982 A-1.

The values for the diatomic constants of the ground state do not agree so well with the literature

values and one reason for this is the low number of data points used in the linear regression. The

equilibrium wavenumber was 230 cm-1, reasonably close to the literature value of 214 cm-1 with a 7.5

percent difference. The dissociation energy for the ground state was calculated to be 8964 cm-1, a

value far from the literature value of 11973 cm-1. The dissociation energy from the v=0 level of 8855

cm-1 was also not very accurate compared to the literature value of 11866 cm-1. The lack of accuracy

of these results can also be attributed to the fact that the wavelengths used in the linear regression

were estimated from the plot. The spectrometer resolution was not high enough to allow for

unambiguously discerning the signals of the spectrum. The literature value of the iodine equilibrium

radius was used instead of an experimental one. The differences in Table 1 used in each of the

calculations should be relatively constant, but upon a closer look a variation in these differences can

be observed. The source of this variation is the use of the band-head frequencies rather than the

band origins.4

Figure 5 confirms that the dissociation energy of the ground state iodine is much higher than that

of the excited that and that the minimum in energy is reached at radius equal to the equilibrium

radius of the respective state. The equilibrium radius of the ground state is also smaller than the

equilibrium radius of the excited state. The experimental estimate for the excited state radius of

3.235 is reasonably close to the literature value of 3.025 A. Figure 5 also shows that a harmonic

oscillator model would have been inadequate for the iodine molecule.

The calculations in this experiment depend largely on how many data points were included in the

linear regressions and how these data points were chosen from the visible spectrum of iodine, thus

leaving the possibility for large sources or error, especially for the ground state. For example, if the

transitions between v’’ 0 or 1 to v’ 15,16,17,18 were included, the best-fit line for the ground state

calculation would have had a slope of approximately -7 which would have afforded values

significantly different from the literature values. For the excited state calculations, at least three data

points were adjusted to not be the wavelengths on the short wavelength side of each peak, in order

to get decreasing separation between the excited state transitions as the convergence limit was

approached, as some of the estimations were skewing the best-fit line.

Conclusion:

The absorption spectrum of iodine could generate reasonably accurate results for the diatomic

constants of the excited state, but failed to afford good estimations for the constants of the ground

state. The results of this experiment depend heavily on the choice of the wavelengths and data

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points to be used in the linear regression and are therefore more inaccurate than analogous

calculations for smaller molecules with simpler spectra such as HCl.

Works Cited:

1. Takeda, Y., Ueno, S. Solar Physics, 2011, 270, p. 447-461. Iodine cell spectroscopy Applied to

Investigating Differential Rotation of the Sun.

2.  Hou, Q.Q.,  Zheng, Y.Z.,  Chen, J.F., Zhou, W.L., Deng, J., Tao, X. Journal of Materials

Chemistry 2011, 21, p. 3877-3883. Visible-light-response iodine-doped titanium dioxide

nanocrystals for dye-sensitized solar cells

3. Stafford, F.E. J. Chem. Educ. 1862, 39, p. 626. Band Spectra and Dissociation Energies – A

Physical Chemistry Experiment

4. Handout – Experiment 39. Absorption and Emission Spectra of Iodine. February 26th 2013.

5. McNaught, I.J. J. Chem. Educ. 1980, 57, p. 101. The electronic spectrum of iodine revisited.

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