Molecular Spectroscopy SCES/P2250
Spectroscopy Main Reference: Fundamentals of Molecular Spectroscopy Colin N Banwell and Elain M McCash Fourth Edition Tata McGraw-Hill Publishing Company Limited Reference book is imperative. Notes will refer to the book . Proforma of Molecular Spectroscopy Course Fakulti : Jabatan :
Sains Kimia
Program Pengajian :
B.Sc. (Hons.)
Kod Kursus : Tajuk Kursus : Jam Kredit :
SCES2250 Spektroskopi Molekul 3
Prasyarat / Keperluan Minimum Kursus :
Kimia Fizik II
Objektif Kursus :
Memberikan kefahaman tentang spektroskopi molekul sebagai alat utama untuk memahami struktur molekul dan sifat-sifatnya Spektroskopi putaran, getaran dan elektronik. Spektrum elektromagnet. elektromagnet. Asas-asas spetroskopi. Spektrum putaran dan getaran molekul dwiatom dan poliatom. Kesan Raman; spektrum Raman putaran dan dan getaran. Keadaan elektron dalam molekul; teori kumpulan asas
Sinopsis Kandungan Kursus :
untuk spektroskopi, pencirian keadaan elektron eralihan elektron, (term symbols). P eralihan spektroskopi elektronik, momen dwikutub peralihan. P endafluor endafluor dan pendafosfor.
Spektroskopi resonans magnet S ifat ifat magnet elektron dan nucleus. Kelakuan electron dan nucleus dalam medan magnet: peng kuantuman momentum sudut, tenaga spin, taburan B olt oltzmann spin, pemagnetan makroskopik. Resonans magnet dan eksperimen . P arameter arameter spectrum NMR: anjakan kimia, pengkupelan spin- spin spin dan masa relaksasi nucleus (T1 dan T2). F aedah aedah medan magnet tinggi. Resonans dubel. Kesan relaksasi dan resonans dubel ke atas spectrum NMR karbon-13. Masa relaksasi T1 dan maklumat gerakan molekul. Kelakuan nukleus magnet. . Skala- kuadrupol sebagai nukleus tak- magnet masa NMR; kesan fenomenon pertukaran ke atas spectrum NMR. P rinsip rinsip asas bagi NMR bagi keadaan pepejal, NMR dua- dimensi dimensi dan NMR mengimej.
Kaedah Penilaian :
P enilaian enilaian berterusan: 30% P eperi eperiksaan: 70%
E nglish nglish V ersion ersion Faculty : Department :
S cience cience C hemistry hemistry
Course programme:
B.S c. (H ons ons.)
Course code:
SCES2250/2132/SCEP2132/SCES2235
Course title: Credit hours:
Molecular S pectroscopy
Pre-requisite:
P hysical C hemistry II
Course objective:
T o give a fundamental understanding of molecular spectroscopy as the most important tool in understanding molecular structure and its characteristics Vibration, rotation and electronic spectroscopy. Electromagnetic spectrum . F undamentals of spectroscopy. Rotational and vibrational spectra of diatomic and polyatomic molecules. T he Raman effect ; rotational and vibrational Raman spectra . Elementary group theory for spectroscopy. Electronic states in molecules and term symbols. Electronic transition, transition dipole moment and electronic spectra. F luorescence and phosphorescence.
Synopsis of course content:
3
Magnetic resonance spectroscopy. Magnetic properties of the electron and nucleus: spin angular momentum and magnetic moment. B ehavior of electron and nucleus in magnetic field: space quantization of angular momentum, spin energy, B oltzmann distribution and macroscopic magnetization. Magnetic resonance and experiment . P arameters in the N MR spectrum: chemical shift, spin- spin coupling and nuclear relaxation time (T1 and T2). Advantages of high magnetic field. Double resonance . Effect of nuclear relaxation and double resonance on carbon-13 N MR spectra . Relaxation time T1 and molecular motion. B ehavior of quadrupolar nuclei as non- magnetic nuclei, N MR time- scale; effect of exchange phenomena on N MR spectra. B asic principles of solid- state N MR, two- dimensional N MR and N MR imaging.
Grading:
C ontinuous assessment: 30% Examination: 70%
Other references: 1) Modern S pectroscopy J. Michael H ollas S econd Edition Wiley 2) Molecular S pectroscopy John M B rown Oxford S cience P ublications 3) P hysical C hemistry P W Atkins Oxford Other S pectroscopy/P hysical C hemistry books available in the library 1
Introduction to Spectroscopy
1.1
Electroma g netic S pectrum
Molecular spectroscopy may be defined as the study of the interaction between electroma g netic waves (EMW) and matter (atoms or molecules).
When matter (molecules) absorb EMW, the molecules can under g o chan g es. T hese are broadly classified as: 1) rotation 2) vibration 3) redistribution of electrons. T he three types of chan g es occur when molecules absorb EMW of differin g ener g ies. 1.2 What is EMW? (p g. 1-3) EMW of which visible li g ht forms an obvious but very small part may be considered as a simple harmonic wave propa g ated from a source and travelin g in a strai g ht line except when refracted or reflected.
Diagram1.1: EMW
EMW applet http://mutuslab.cs.uwindsor.ca/schurko/animations/emwave/emwave.htm EMW consists of electric field and magnetic field parts; both waves are perpendicular to each other. Q 1: Write the equations of EMW:
Basi c wa ve equation is P!c/R where P is the wavelength in meters, c is the speed of light in ms-1 and R is the frequency in Hz (cycles s-1). In spectroscopy, a widely used unit is the wavenumber (cm-1), giving a generalized connotation of energy, frequency etc. T his is defined as: R
!1 / P
Using appropriate units for c (cms-1) and P (cm), it would be easy to convert from Hz to wavenumber and vice versa. A bar above R indicate units in cm-1
Q2 : Convert ² 133MHz to cm -1, 400cm -1 to Hz, 300nm to cm -1
1.3 EMW spectrum (pg. 5-9) To ans wer t he quest ion concern ing t he t ypes o f inter act ion t hat will occur when mo lecu les absor b EMW, we nee d to un derst an d t hat EMW e xists in different energ ies. T his c an be conven ient ly e xpresse d in terms o f an EM spectrum.
Visible light spectrum
Understand the EM spectrum presented (see a more lively EMW spectrum ² in folder ). Make sure you develop the sense of magnitude related to the spectrum. It is imperative that you understand, for example that EM in the microwave region, when absorbed by a molecule will cause the molecule to rotate. Q3 : Write brief notes on the EM spectrum and how it interacts with
matter:
1.4 Q uantization of Energy (pg. 3 -5) Initially matter was thought to be able to absorb energy in the form of EMW continuously, soaking up all the energy available over the whole spectrum of EMW. T his was found to be incompatible with reality. Max P lanck published a revolutionary paper suggesting that energy of an oscillator is discontinuous and change of energy can happen by means of a jump between two energy states. Extending this idea, a molecule can also be thought to possess energy in quantized form ² rotation, vibration, electronic . Etotal = Erotation + Evibration + Eelectronic (ET = Er + Ev + Ee )
T his is known as the B orn Oppenheimer approximation. Matter absorbs EM energy in a quantized manner. B est visualized via energy
level diagram: Diagram1.2 : Transitions between two energy levels
Upon absorption of EMW of a certain energy, a transition is said to occur. It is then said that the matter has absorbed a photon of EMW. T his transition can be described by an equation suggested by P lanck. ( E !
Where (E = En- Em. R s is
hR s
the frequency absorbed. T his is in Hz. T he symbol for frequency in cm-1
is usually
R s
unless different symbols are noted to have units of cm-1.
If we plot a graph of intensity of absorption vs. frequency, we get a spectrum with a peak at R s . T hree types of transitions are shown in diagram1.2. What are they? Q 4: Draw a spec tru m with ab sorption at R s .
In spectroscopy we can envisage the quantized energy levels as depicted below: Diagram1.3 : Magnitude of the different type of energy levels
T he physics that deals with quantized energies of molecules is quantum mechanics. T he basis of quantum mechanics is the S chrodinger equation. S olution to this equation basically gives two things. Energy (levels) (E) and wavefunctions () associated with each energy levels. As an example, lets jump straight into a real case ² the hydrogen atom. A S chrodinger equation for the kinetic and potential energy at play within the atom which consists of an electron and a proton is set up. It is then solved
to give energy levels and wavefunction. T hese wavefunctions are appropriately combined to result in atomic orbitals.
T hus, we have 1s, 2s, 3s, 2p etc. atomic orbitals (which are really combination of wavefunctions from the solutions of the schrodinger equation). Each orbital is identified with an energy level represented (or labelled) by its quantum number. T he details of this can be obtained from various P hysical C hemistry texts. S ince hydrogen atom is an atom, the only energy it possesses is the electronic energy (besides the continuous translational energy ). Absorption of EM in the region of UV/V is will cause electrons to be excited from one level to another, corresponding to the energy absorbed. A molecule, such as A-B on the other hand will have rotational and vibrational energy besides electronic energy. Q5 : Why do atoms lack rotation and vibrational energies?
Upon absorption of EM by a molecule, we ask three questions: 1) T he frequency of absorption 2) T he line intensity 3) T he linewidth of the spectral line.
T he frequency of the absorption can be read off the spectrum and the type of interaction depends on the value of the frequency (sense of magnitude? EM spectrum?)
Q6 : Draw a single line spectrum and illustrate the spectrum w ith labels
appropriate to the three questions :
Q uestions 2) and 3) w ill be answ ered below.
1.5 S pectral line intensity (pg. 18-20) S pectral line intensity is determined basically by three factors: a) T ransition probability ² A rigorous quantum mechanical treatment of EM- matter interaction w ill produce w hat is know n as the transition probability. It is represented by: Rnm !
m
´] n * Q] d X T
Where ] n and ] m are wavefunctions of states n and m respectively. Q is the electric dipole moment operator . T he spectral line intensity is proportional to Rnm2. If Rnm = 0 then there is no transition T
(forbidden), whereas if Rmn <> 0, there can be a transition (allowed). T his is also known as the gross selection rule for a transition. T he transition probability will be rationalized later for each type of transition; rotation, vibration and electronic. b) Population of states ² between two states, if the lower state is of higher population, and the upper one is lower in population, then the transition is very much favoured . B oltzmann distribution determines the relative population. Understand this properly. T his will be discussed further for each type of interaction Q7 : Write the B oltzmann distribution population ratio of two states m
and n
c) C oncentration of sample or path length of sample ² works within the B eer Lambert Law: log Io/I = Icl
Where I is the transmitted light intensity, Io is the incident light intensity, c is the concentration of sample, l is the path length and I is molar absorption coefficient ( a function of frequency). G ood applets on this can be obtained from : http://www.chm.davidson .edu/C hemistryApplets/#S pectrophotometr y
1.6 S pectral linewidth (pg. 17 -18) T here are 3 factors that effect line broadening:
a) N atural linewidth ² H eisenberg uncertainty principle. T his is natural in all spectroscopic measurements .
(R !
1
X
2T
T here will always be broadening because X can never be infinite. B roadening due to only one frequency ² homogeneous spectral line b) Doppler broadening ² due to Doppler shift ² based on Doppler effect
Diagram1.4 : Doppler effect As an example: S ound waves emanating from an ambulance moving to the right. T he perceived frequency is higher on the right, and lower on the left. Imagine molecules as source being stationary, or moving relative to the detector. Molecules move randomly ² as a result, you get many different frequencies centred around a mid frequency, each frequency overlapping with each other forming a gaussian envelope ² heterogeneous spectral line. Doppler effect applet- http://www.phy.ntnu.edu.tw/ java/Doppler/Doppler.html
c)
Pressure
broadening (collision broadening)
Due to continuous collision between molecules/atoms. T his causes perturbation to the energy levels, thus broadening it ² more severe in liquid. C an be reduced by taking spectrum in gas phase and lowering the pressure of gaseous samples
2 Representation of Spectra ² practical aspects of spectroscopy (pg. 9-17) T here are basically 3 types of spectroscopy experiments: 1) Absorption 2) Emission 3) S cattering Absorption spectrometer applet: http://artsci- ccwin.concordia.ca/facstaff/a- c/bird/c241/D2- part2.html We shall only look into the first two at the moment. 2.1 Absorption - UV/V is, IR (optical) and microwave (non- optical ) Q 8: Draw the complete diagram of a basic optical absorption experiment
complete with appropriate labels and explanation of the labels.
2 .2 Emission
- UV/Vis (o pti cal) Q9 : Dr aw the com ple te di a gr am of a b asi c o pti cal emission e xperimen t com ple te wi th appro pri ate labe ls and e xplan ation of the labe ls.
Diagram 1.4a ² typical arrangement of an absorption spectrometer Among the important parts of the spectrometer are: 1)
² the types of sources will depend on the types of interaction desired (refer to handouts). 2) Slit ² used to direct EMW to sample or to determine resolution. Unfortunately, slits also reduce the total intensity that could have been utilized. 3) Dispersing element or a grating ² used to disperse EMW into its constituent frequencies . Used in conjunction with a slit (see handout). T his part of the spectrometer is usually called a monochromator (below). An applet demonstrating the action of a grating can be found at: Source
http://www.mtholyoke.edu/~mpeterso/classes/phys301/laboratories /balmer .html
http://www.physics.uq.edu.au/people/mcintyre/applets/optics/grating.html
Diagram1.5 : Monochromator (action of a grating) 4)
holder ² to hold sample ² quartz and glass (UV/V is), KBR, N aCl salt slabs (IR) ² depending on the EMW region 5) Detector ² types of which are determined by the different EMW sources ² see handout 6) Display ² displays the spectrum ² computers, chart recorders. Sample
We should also consider the two types of operation in a spectrometer ² single beam and double beam operation ² this is done in order to compensate for the background which may affect the spectrum due to the presence of water vapour and carbon dioxide absorption. T his is especially true for IR spectroscopy (pg. 91-93) ² See brochure of Lambda series of spectrometers. 2 .3 Signal to N oise Ratio (pg. 15) Modern electronic instruments can·t escape from noise. T he noise can come
from the electronic cricuitry in the spectrometer or from the detector. N oise is usually described in termso fluctuation. T o differentiate between signal and noise, we need the signal to be at least 3 or 4 times larger than noise.
Signal- to- noise
ratio is an engineering term for the power ratio between a signal (meaningful information) and the background noise:
B ecause many signals have a very wide dynamic range, SNRs are often expressed in terms of the logarithmic decibel scale. In decibels, the SNR is 20 times the base-10 logarithm of the amplitude ratio, or 10 times the logarithm of the power ratio:
where P is average power and A is RMS amplitude
T here are various techniques to increase S/N ratio such as filtering and computer averaging (pg. 26). 2.4 Spectral resolution (pg. 16) Often used as a mesure of the performance of a spectrometer. Q 10: E xplain how the size of the output slits can affect the resolving power
of a spectrometer. Use appropriate illustrations.
2 .5 Fourier Transformation in Spectroscopy (pg. 20 -2 6) ,(pg. 9 3- 9 6)
Con ventiona lly a spectrum is taken by s weeping o ver t he who le range of frequencies wit hin t he spectra l domain. Say, a spectrum from 1 000 cm -1 to 4 000 cm -1 is to be recor de d. T he frequency is s wept smoot hly from 1000 to 4 000 cm -1 (by rotating t he grating in t he monoc hromator ). T his takes a long time. Very inefficient. Wit h FT tec hno logy, t he who le spectrum can be taken simu ltaneous ly wit hin t he require d region. To un derstan d FT, first look at beat frequency. Visit : http ://www.it hacasciencezone.com/e xp lrsci/ds wme dia/tone beat.htm http ://p hysics.pingry.org/Exp lorations/Acoustics/Beats/
for audio demonstration of beat frequency.
300Hz
+ about 300Hz (say 301 Hz) gives«. «.a beat frequency.
..which is an interference pattern. Imagine interfering more than 2 frequencies, in fact imagine interfering hundreds of frequencies together. Conceptually, a combination of many different frequencies will result in a particular interference pattern. T his pattern is in time domain (serial domain). You can·t tell what the different frequencies are«we have to convert this interference pattern into a frequency domain spectrum where interfering frequencies can be identified ² FT!! Note
that an interferogram shows an oscillating signal decaying smoothly to zero. T he oscillation is due to the beat pattern set up by all the superimposed, but slightly different sine waves emitted. T he decay can be imagined by considering that initially, all waves in the package are in step but as time goes by they start to be out of phase that on average, they cancel out (pg.22-23)
G ood applets to demonstrate time domain to frequency domain using FT..
http://storm.uni- mb.si/CoLoS/applets/fft/ftd.html http://sepwww .stanford .edu/oldsep/hale/F ftLab.html
B y using an interferometer, we can take the spectrum instantaneously and by using FT , the interferogram is transformed into a frequency domain spectrum. Read about the interferogram and understand how it works. A typical arrangement of an FTIR is depicted below (diagram 1.6). H ow does it work?
Diagram 1.6 : FTIR Demonstration of Michelson interferometer. http://www.physics.uq.edu.au/people/mcintyre/applets/michelson/michel.ht ml
Tutorial: 1) Convert 99.3MHz, 103.3MHz, 105.9 MHz dan 2.4GHz into wavenumber (cm-1). 2) Which region of the EMW causes molecular rotation? What are the selection rules required in order to observe rotational spectrum? 3) A molecule X absorbs EMW at 3500cm-1. What happened to it?
4)
Electron redistribution in a molecule or atom occurs in the EMW region of«. 5) Draw the diagram of a simple absorption spectrometer and explain the workings of this apparatus 6) What is the function of the first dispersion element of an emission spectrometer (in the monochromator before EMW enters the sample? 7) G ive example of the source of EMW for each identifiable region of the spectrum. 8) Write down the energies of a molecule based on the B orn Oppenheimer approximation. 9) List down the factors that influence the intensity of a spectral line 10)Discuss the three types of spectral line broadening 11) Discuss how an FTIR spectrometer works. 12) Explain why the natural linewidth in a rotational spectrum is smaller that the natural linewidth of a UV spectrum? 13) What is S/N ratio? 14) What is Rmn?