### Lab Report on The electronic absorption spectrum of iodine

The lab report below was submitted as part of the coursework for CM2101 Principles of Spectroscopy. Please do not plagiarise from it as plagiarism might land you into trouble with your university. Do note that my report is well-circulated online and many of my juniors have received soft copies of it. Hence, please exercise prudence while referring to it and, if necessary, cite this webpage.

Aim
To analyse the vibrational fine structures of the electronic excited state of iodine from the electronic absorption spectrum and to obtain harmonic frequency, ν̃e, anharmonicity constant, χe, spectroscopic dissociation energy, D0 and thermodynamic dissociation energy, De.
Results and calculation
The peaks that corresponded to transitions beginning from v’=0 were chosen. In order to ensure that the assignments are consistent, the results from the overlapping region – 556.00 to 568.40 nm – were not chosen for calculations.

Sample calculation for determining wavenumber:
Wavelength of peaks from spectrum obtained are matched with the 541.2 nm wavelength at v’ = 27. The closest value is 541.00 nm at peak number 21. Hence, range of v’ are obtained.
At v’ = 27, l = 541.00 nm = 541.00 x 10-7 cm
Wavenumber = 1 /(541.00 x 10-7) = 18484.29 cm-1 (2 d.p)

Table 1. Wavelength and corresponding wavenumbers of each peak due to v’’ = 0 ® v’
 Peak Number (from spectrum) v’ λ (nm) Wavenumber, G (cm-1) Peak Number (from spectrum) v’ λ (nm) Wavenumber, G (cm-1) 12 22 553.40 18070.11 35 41 516.80 19349.85 14 23 550.80 18155.41 36 42 515.40 19402.41 16 24 548.20 18241.52 37 43 514.20 19446.69 18 25 545.60 18328.45 38 44 513.00 19493.18 20 26 543.20 18409.43 39 45 512.00 19531.25 21 27 541.00 18484.29 40 46 511.00 19569.47 22 28 538.80 18559.76 41 47 510.00 19607.84 23 29 536.80 18628.91 42 48 509.00 19646.37 24 30 534.60 18395.88 43 49 508.20 19677.29 25 31 532.60 18775.82 44 50 507.40 19708.32 26 32 530.80 18839.49 45 51 506.60 19739.44 27 33 529.00 18903.59 46 52 506.00 19762.85 28 34 527.20 18968.13 47 53 505.40 19786.31 29 35 525.60 19025.88 48 54 504.60 19817.68 30 36 523.80 19091.26 49 55 504.00 19841.27 31 37 522.40 19142.42 50 56 503.60 19857.03 32 38 520.80 19201.23 51 57 503.00 19880.72 33 39 519.40 19252.98 52 58 502.60 19896.54 34 40 518.00 19305.02 53 59 501.40 19944.16

v’’=0, v=22, ∆G at v’ + ½ = 22.5, ∆G = wavenumber v’=23 - wavenumber v’=22
= 18155.41 – 18070.11
= 85.30 cm-1

Table 2. Values of separation (∆G) and (v’+ ½)
 v’ + ½ ∆G (cm-1) v’ + ½ ∆G (cm-1) v’ + ½ ∆G (cm-1) v’ + ½ ∆G (cm-1) 22.5 85.30 30.5 70.24 38.5 51.76 46.5 38.37 23.5 86.11 31.5 63.67 39.5 52.04 47.5 38.52 24.5 86.93 32.5 64.10 40.5 44.83 48.5 30.93 25.5 80.98 33.5 64.54 41.5 52.56 49.5 31.02 26.5 74.86 34.5 57.74 42.5 45.28 50.5 31.12 27.5 75.47 35.5 65.38 43.5 45.49 51.5 23.41 28.5 69.14 36.5 51.16 44.5 38.07 52.5 23.46 29.5 76.66 37.5 58.81 45.5 38.22 53.5 31.37

Gradient of a modified Birge-Sponer plot = -2 ν̃eχe = -2.009
ν̃eχe = 1.0045
χe = 1.0045 / ν̃e                                             ------- (1)
Vertical intercept = ν̃e - ν̃eχe = 130.9             ------- (2)
Substitute (1) into (2):
ν̃e ν̃e (1.0045 / ν̃e) = 130.9

Harmonic frequency, ν̃e = 130.9 + 1.0045= 131.9045 cm-1 = 131.90 cm-1 (2 d.p.)
Anharmonicity constant, χe = 1.0045 / 131.90 = 0.0076153 = 0.007615 cm-1(4 s.f)

Spectroscopic dissociation energy, D0 = (ν̃e - ν̃eχe)2 ÷ 4ν̃eχe
= (130.90)2 / (4 x 1.0045)
= 4264.51cm-1
= 4265 cm-1 (4 s.f)
Thermodynamic dissociation energy, De = ν̃e2 ÷ 4ν̃eχe
= 131.90452/ (4 x 1.0045)
= 4330.21 cm-1
= 4330 cm-1 (4 s.f)

Discussion
Descriptions of and reasons behind the electronic absorption spectrum of iodine
Iodine crystals sublimes easily even at room temperature because of its high vapour pressure. Iodine molecules absorb wavelength belonging to yellow visible region of electromagnetic spectrum and emit its complimentary colour, purple, when iodine promoted from the ground electronic state, X( 1Σ g+) , to an upper excited state, B( 3πu+).
Homonuclear diatomic molecules – including  I2 – do not have a pure rotational and vibrational transition as they do not have permanent dipole moments and  experiences no change in dipole moment upon vibrational excitation. However, they do produce electronic spectrum. This is because all molecules including such diatomic homonuclear molecules, will experience changes in electronic distribution upon excitation.  Linear molecules like I2 can have 3N-5 fundamental vibrational modes, where N is number of atoms in a molecule. Thus, I2 only has 1 normal vibrational mode.

The absorption spectrum of iodine yields information about the excited state (B). This information is valuable since such molecules may only exist in such unstable, excited states for a very short time.

Due to simultaneous vibrational excitation, the visible absorption spectrum of iodine shows overlapping progressions and fine structures are observed over the main peak. From about 500 to 545 nm, the spectrum is uncomplicated and lines within this region are known to originate from the v’’ = 0 vibrational level in the ground electronic state to all values of v in the upper excited electronic state. Beyond 545 nm the spectrum becomes more complicated due to the appearance of  hot bands, that is, bands originating from v’’= 1 and v’’ = 2 or higher.
After a molecule has undergone an electronic transition into an excited state, there are several ways by which its excess energy may be lost. Phosphorescence of iodine can occur when two excited states of different total spin have comparable energies.  When the singlet and triplet states (1Σ g+,3πu+) energy curves overlap, the excited iodine may undergo intersystem crossing, a non-radiative transition between states of different multiplicity and become a triplet state. By spin selection rule, transition from triplet to singlet state is forbidden. Singlet-triplet transition is possible as spin-orbit coupling occurs because iodine is a heavy molecule. Once the molecule has arrived in the triplet state and undergone some loss of vibrational energy in that state, it cannot return to the excite singlet state. It will reach the v’=0 level of the triplet sate and may emit radiation slowly and weakly for a long period of time.

Electronic transitions can occur between populated vibrational states of the ground state and various vibrational states of the excited states. These transitions are governed by the Frank-Condon
principle states that since the nuclei is much heavier than electrons, an electronic transition occurs on a much faster timescale than nuclei motion,  it is as if the nuclei has not moved during the transition. 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. 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 which is the equilibrium internuclear distance. The intensity of peaks are the highest when the electronic transition is from v’’=0 to v’ vibrational energy levels as according to the Boltzmann distribution, most iodine molecules are in their ground vibrational level at room temperature. The B <= X transition is allowed according to the electronic selection rules.  Hot bands, transitions from v’’=1 to higher levels, are also observed in spectrum but with weak intensity.

From table 2, it can be observed that as v’ increases, the vibrational energy spacing, ΔG, decreases. The continuum limit occurs when the energy gap between excited state vibrational levels is zero. This means that the energies form a continuum rather than being quantized. It is at this limit that bond dissociation occurs. From the 500-640 nm spectrum data, a continuum tail was observed towards the end of the spectrum at longer wavelengths. This continuum tail arises due to the dissociation of the I2 molecule. The dissociated I2 molecule can take up any amount of kinetic energy, meaning that the transitions which occur are no longer quantised and thus a continuum tail results.
Graph of ΔG against (v’ + ½)

The separation between neighbouring levels in B state, ΔG, was plotted against (v’ + ½) in a modified Birge-Sponer plot to obtain values of dissociation energies. The equation is as follow: ∆G= ν̃e- ν̃eχe - 2 ν̃eχe (v’+1/2). Thus, by integrating this equation which is the area under the Birge-Sponer curve, ground vibrational state dissociation energy D0 is obtained. A R2 value of 0.966 reflects a strong collinear relationship between ∆G and (v’+1/2) and implies that Birge-Sponer extrapolation holds.
The literature values of D0 and De are 4335 and 4398 cm-1 respectively. Thus, values of D0, De, ν̃e and χe are quite accurate and Birge-Sponer plot proved to be useful. There is a slight difference between literature and experimental values because of the assumption that that ∆G approach 0 linearly used by Birge-Sponer extrapolation is only an approximation. At high v’ values, ∆G decrease more sharply as cubic and quadratic terms of vibrational energy equation become more significant. Thus, this limits the accuracy of experimental values obtained.

The spectroscopic dissociation energy of iodine measured from the zero point energy is 4265 cm-1. Thus, the frequency of incident beam radiated by spectrophotometer should not reach and exceed this value as iodine will then dissociate and the spectrum obtained will be a continuum plot. This will then affect the clarity of spectrum and the assignment of peaks. 4330 cm -1 is the thermodynamic dissociation energy for the B electronic state of I2 molecule, which is imaginary. Thus the energy required to dissociate the bond is not 4330 but 4265 cm-1.

Other useful information can be derived from this experiment, such as zero point energy (ZPE) and vmax. ZPE is the difference between these 2 values, ZPE = De -D0 = 4330 - 4265 = 65 cm-1. This energy is the energy of iodine at vibrational state v = 0. vmaz, which is the vibrational quantum number before dissociation of iodine is obtained by vmax=1/(2χe) – ½ = 1/(2 x 0.007615) – ½ ≈ 66. Thus, as iodine go beyond vibrational quantum state of 66, it will dissociate.

Precautions

Empty gas cells were recorded as the background spectra for subsequent subtraction of ambient absorption. This is because molecules in air that are present in the gas cell will also produce a spectrum. Hence, subtracting the background noise ensures that the spectra recorded belongs to sample and gives a better resolution and clarity of spectrum.

The sides of the gas cell was also not touched as fingerprint markings will scatter the light passing through, thus affecting the transmittance readings. Hot bands will appear more frequently if temperature increases. In order to prevent the hot bands from affecting the clarity of spectrum, experiment should be kept at acceptable temperatures.

Conclusion
The electronic absorption spectrum of iodine was measured and the vibrational fine structures of the electronic excited state was analysed. The values found are as follows:
harmonic vibrational frequency, ν̃e = 131.90 cm-1
anharmonicity constant, χe = 0.007615 cm-1
spectroscopic dissociation energy, D0 = 4265 cm-1 and
thermodynamic dissociation energy, De = 4330 cm-1.

Exercises
1)      Broadening of band spectrum is due to the increase of the natural lifetime of the states involved in a transition by anharmonic vibrations. When a molecule is vibrationally excited, it can also be rotationally excited simultaneously. At higher wavelengths, the energy that the molecule absorbs is much lower. Due to the inclusion of the anharmonicity, the average inter-nuclei distance (r) increases for higher vibrational states. Since the rotation constant, B, is inversely proportion to the square of r (i.e. B α 1/r2), B becomes progressively smaller with increasing rotations. This causes the rotation line peak separation under a vibration line to be separated by a larger B constant, resulting in the broadening of the band. As so, a longer wavelength indicates lower vibration states and a greater peak separation.
2)   1Σg+ indicates that the total spin angular momentum is zero whereby all the electrons are paired. X refers to the ground state of iodine while B is the excited state with the labeling 3Πu+. The spin multiplicity in B is 3, total spin angular momentum is 1. Thus, there are 2 unpaired electrons in B.
The electronic configurations of I2 in electronic states B and X are:

I2 (X state) (1Σg+) : [Kr2](4d10)2 (5sσg)2(5sσu*)2(5pσg)2(5pπu)4(5pπg*)4(5pσu*)0

I2 (B state) (3Πu+): [Kr2] (4d10)2 (5sσg)2(5sσu*)2(5pσg)2(5pπu)4(5pπg*)3(5pσu*)1

3) The sample cells used in this experiment were 10 cm long because this experiment involved gaseous iodine instead of a liquid sample, which is routinely used in 1-cm cell for spectrophotometry. Gaseous iodine molecules have a low density because the intermolecular forces of attraction are only weak dispersion forces. Thus iodine crystals sublime easily at room temperature. Furthermore, gas molecules are much less closely packed than a liquid sample. Hence, iodine molecules will tend to spread out over a larger space, resulting in a small number of molecules per unit volume. This results in a very low iodine concentration. According to Beer-lambert law, A = εcl, where A = absorbance, ε = molar absorptivity and l = path length. In order to compensate for the low gas concentration to obtain a reasonable absorbance, a longer path length hence longer sample cell must be used. A longer path length will result in more iodine molecules undergoing electronic excitations. This will then result in higher sensitivity of measuring absorbance in the UV/visible spectrophotometer.

2 cells were used so that one of them (A) act as a standard zero reference to eliminate background radiation absorbance. The other cell (B) is used to measure the absorbance of background radiation and gaseous iodine. Hence, the signal of background radiation will be subtracted from cell B. Thus, the absorbance of iodine recorded will only belong to the gaseous iodine, excluding the background radiation. Hence, an accurate absorbance spectrum would be obtained.

References
 Inorganic Chemistry 4th Edition, Shriver & Atkins, Oxford University Press

 Banwell and McCash, Fundamentals of Molecular Spectroscopy, 4th edition.

 P. Atkins, J. P. Paula, Physical Chemistry, Oxford University Press, 8th Ed

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