Amirul Hakim Bin Abdul Malik Chia

73 Pages·2016·4.44 MB·English

PC4199 HONOURS PROJECT IN PHYSICS - FINAL REPORT
VIBRATIONAL-ROTATIONAL STRUCTURE OF THE
ETHYLENE (12C HD ) MOLECULE BY
2 3
HIGH-RESOLUTION FOURIER TRANSFORM
INFRARED (FTIR) SPECTROSCOPY
A0097131J AMIRUL HAKIM BIN ABDUL MALIK CHIA
SUPERVISOR: DR AUGUSTINE TAN TUCK LEE
CO-SUPERVISOR: DR DZMITRY MATSUKEVICH
SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR
DEGREE OF BACHELOR OF SCIENCE (HONOURS) IN PHYSICS
DEPARTMENT OF PHYSICS, NATIONAL UNIVERSITY OF SINGAPORE
APRIL 2016

Contents
Acknowledgments 5
1 Introduction 7
1.1 An Introduction on Ethylene . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Theoretical Background 10
2.1 Regions of the Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . 10
2.2 Molecular Absorption of Electromagnetic Radiation . . . . . . . . . . . . . . . 12
2.3 The Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . . 15
2.4 Rotational Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 Moments of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Rigid Rotor Approximation for Linear Molecules . . . . . . . . . . . . . 17
2.4.3 Centrifugal Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.4 Non-linear Polyatomic Molecules: Symmetric Rotors . . . . . . . . . . . 20
2.4.5 Non-linear Polyatomic Molecules: Asymmetric Rotors . . . . . . . . . . 23
2.5 Vibrational Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.1 Quantisation of Vibrational Energy: Simple Harmonic Oscillator . . . . 25
2.5.2 Anharmonicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.3 Normal Vibrational Modes . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 Vibration-Rotation Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.7 Classification of Vibrational Bands . . . . . . . . . . . . . . . . . . . . . . . . 31
2.8 Inertial Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 Ground State Combination Differences (GSCDs) . . . . . . . . . . . . . . . . 33
2.10Coriolis Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3
3 Fourier Transform Infrared (FTIR) Spectroscopy 36
3.1 FTIR Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Experimental Details 40
4.1 Experimental Details and Procedure . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Calibration of Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Spectral Line/GSCDs Fit Procedure . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Perturbation Analysis of Coriolis Interactions . . . . . . . . . . . . . . . . . . 48
5 Results and Discussion 51
5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 Conclusion 58
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
References 61
Appendix 63
4
Acknowledgments
I would like to thank my supervisor, Dr Augustine Tan Tuck Lee for allowing me to pursue
an Honours Project in High-Resolution Molecular Spectroscopy at the Nanyang Institute of
Education. The theory behind Vibrational-Rotational Spectroscopy of molecules has greatly
intrigued me in my last few years in university, and I am grateful to him for the opportunity
to conduct research in this area of study. His willingness to offer positive feedback on my
presentations and report despite his busy schedule is also deeply appreciated.
I would also like to thank Dr Dzmitry Matsukevich from the Center for Quantum Technolo-
gies, for agreeing to be the co-supervisor in NUS for my project. Without his help, my Final
Year Project would not have been possible.
Finally, IwanttoextendmythankstothemembersofDrTan’sresearchgroup; myacademic
mentor Ms Alicia Ng and Ms Marissa Gabona for all the help they have given me throughout
mytimeinNIE.TheirinstructionandadvicehavehelpedmefurthermyprogresswheneverI
haveencounteredproblemsinmyproject, andtheirpatiencewithmyquestionsandmistakes
was always reassuring.
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1.1 An Introduction on Ethylene Introduction
CHAPTER 1
Introduction
1.1. An Introduction on Ethylene
Ethylene, also known as ethene, is an organic molecule with the formula H C=CH . It is
2 2
the simplest molecule in the class of hydrocarbons called alkenes which have the general
chemical formula C H (n = 2,3,4,...). At room temperature, it is a colourless, odourless
n 2n
gas that is also flammable. The carbon and hydrogen atoms lie in the same plane when the
molecule is at rest.
Figure 1.1: Left: C H ethylene molecule. Right: 12C HD ethylene molecule. Bond lengths and
2 4 2 3
angles are not to scale.
Ethylene is a naturally occuring hydrocarbon gas in Earth’s atmosphere. Living sources of
ethylene include the vegetative and reproductive tissue and fruit of plants which are ripening
or rotting, while nonliving sources include improperly adjusted or uncleaned greenhouse
heating units, leaky gas lines, and exhausts from combustion engines. Ethylene serves as
a plant hormone, and is highly active at low concentrations. Some of ethylene’s effects on
crops are malformed leaves and flowers, thickened stems and leaves, stunting of growth and
abortion of flowers and leaves [1].
Also, ethylene has been detected on other planets and moons in the solar system. With the
use spectrometers onboard satellites such as the Infrared Space Observatory (ISO) Satellite
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1.2 Project Objectives Introduction
operated by the European Space Agency (ESA), ethylene has been detected in the strato-
spheres of the gas giants Jupiter, Saturn and Neptune, and also Saturn’s lagest moon, Titan
[2]. As ethylene is naturally occuring on Earth, its existence on other celestial bodies within
the solar system is of interest to astronomists.
1.2. Project Objectives
The detrimental effect of ethylene on crops, even at low concentrations, highlights the need
to monitor the levels of ethylene in agricultural systems. Also, the detection of ethylene in
the atmospheres of planets and moons in the solar system requires accurate rovibrational
parameters,which have to be obtained through high resolution Fourier Transform Infrared
(FTIR) spectral analysis of the ethylene spectrum.
Due to its simplicity in structure and chemical composition, and abundance in nature in
gaseousform,ethylenehasbeenamoleculeofgreatinteresttospectroscopistsandtheoretical
chemists. To understand the rotational-vibrational structure of ethylene and accurately
determine its rovibrational parameters, research on several isotopologues (molecules with
different isotopic composition) of ethylene have been done in the past using high resolution
Fourier Transform Infrared Spectroscopy, including but not limited to 12C H D [3], 12C D
2 3 2 4
[4], cis-12C H D [5] and trans-12C H D [6].
2 2 2 2 2 2
The main focus of this project is the ethylene isotopologue 12C HD , where three of the
2 3
hydrogen atoms of ethylene are replaced with deuterium (Figure 1.1). 12C HD ethylene
2 3
is relatively asymmetric compared to 12C H , and this makes it an interesting molecule
2 4
for spectroscopists and quantum chemists to study and refine the rotational-vibrational
structure theory of asymmetric molecules . This interest has led to studies being carried out
on the vibrational and rovibrational structures of 12C HD by low resolution [7, 8] and high
2 3
resolution infrared spectroscopy [9, 10].
In 1973, Duncanet al. identified the12 fundamental vibrationalmodesof ethylene12C HD ,
2 3
and identified the band center frequencies of the vibrations with an accuracy of 1 cm-1 [7].
Later in 1993, he and his team carried out analysis on the infrared spectrum of 12C HD
2 3
at low resolution (0.5 cm-1) [8]. In 1995, all 12 fundamental vibrational band centers of
12C HD were derived by Martin et al. using accurate ab initio calculations [11].
2 3
8
1.2 Project Objectives Introduction
In 2011, Tan and Lebron carried out high resolution Fourier Transform Infrared (FTIR)
analysis on the ν vibrational band of 12C HD and derived rovibrational constants for the
8 2 3
ground state and upper state (ν = 1) of the band, up to all five quartic centrifugal distortion
8
terms for the first time [9]. Later in 2015, Ng et al. further improved on the work by Tan
and Lebron [10].
With reference to the previous works by Tan and Lebron and Ng et al. on the ν vibrational
8
band of 12C HD , in this work we study the 2ν vibrational band of 12C HD , which is the
2 3 8 2 3
2nd excited state of the ν vibrational mode of 12C HD . Through careful spectral analysis
8 2 3
of the FTIR spectrum of the 2ν band, this work aims to derive accurate rovibrational
8
constants of the 2ν vibrational band of 12C HD . The 2ν vibrational band of 12C HD has
8 2 3 8 2 3
yet to be studied through high resolution FTIR analysis, and this work will be the first to
report it.
The main objectives of this project are:
1. To collect and measure the mid-infrared spectra of ethylene 12C HD using high-
2 3
resolution Fourier transform infrared spectroscopy.
2. Using Watson’s A-reduced Hamiltonian model, carry out non-linear least-squares fit-
ting analyses of the transmittance spectrum lines in the 2ν vibrational band of ethy-
8
lene 12C HD .
2 3
3. To accurately determine the rotation-vibration parameters of the ground state and
upper state of 2ν vibrational band of ethylene 12C HD .
8 2 3
4. Correct for perturbation caused by Coriolis interactions experienced by the spectral
lines of the 2ν vibrational band 12C HD .
8 2 3
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2.1 Regions of the Electromagnetic Spectrum Theoretical Background
CHAPTER 2
Theoretical Background
2.1. Regions of the Electromagnetic Spectrum
Electromagnetic radiation, or EM radiation, can be considered as small packets of energy
that have wave-particle dual behavior. As a wave, EM radiation can be represented as
transverse waves where the electric and magnetic parts of the radiation are in phase and
in mutually perpendicular planes. The electric component of the radiation is an oscillating
electric field of strength E while the magnetic component of the radiation is an oscillating
magnetic field of strength H. If the direction of E and H are y and z, respectively, we have
E = Asin(ωt−kx)
y
H = Asin(ωt−kx)
z
Both waves oscillate in phase with each at the same amplitude A and radial frequency ω.
In the interaction of EM radiation with atoms and molecules, the oscillating electric field is
more involved that the magnetic field [12].
All EM radiation travels at the speed of light, which in vacuum has a constant value of
c = 2.998×108 m s-1. This constant is related to the frequency f and wavelength λ of the
electromagnetic radiation by
c = fλ (2.1)
The EM spectrum is divided into several regions shown in Figure 2.1 and Table 2.1.
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