6 Topics to be covered. What is spectroscopy? 2Y Spectroscopy: Topic 1. Introduction to Spectroscopy. Quantitative Spectroscopy:

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1 Spectroscopy 3 lectures leading to one exam question Texts: Elements of Physical Chemistry 4 th ed. by Atkins & de Paula, Chapter 19 & Chapter 20 Foundations of Spectroscopy By Duckett & Gilbert, Chapter Various Specialist texts in Hardiman Library Need this for CH205 in second semester. Need this for 3, 4 year chemistry. Notes & Links available on my website. This version 22/11/2010: minor errors corrected. 6 Topics to be covered Introduction to Spectroscopy. Quantitative Spectroscopy: Beer-Lambert. Electronic spectroscopy. Vibrational Spectroscopy: FT-IR and Raman spectroscopy. Energies of Vibrational transitions. Polyatomic Vibrational spectroscopy Y Spectroscopy: Topic 1 Introduction to spectroscopy: Electromagnetic spectrum. Quantisation of energy & energy levels. Selection rules. Bohr condition. Absorption, Emission, & Scattering Spectroscopies. Need to Know: EM spectrum, how to interconvert from wavelength, wavenumber, or frequency to energy, and the different types of spectroscopy. What is spectroscopy? Interaction of electromagnetic radiation with matter: Absorption. Emission. Scattering. Many different scales: Astronomy (single stars). Microscopy (single molecules). Everything from forensics to living cells 3 4 Page 1

2 5 Spectrum (pl. spectra) Map of the energy states of a compound or molecule. In principle, each spectrum is unique. Spectrum is a molecular fingerprint : Tool for qualitative analysis (FT-IR, Raman). Also ideal for quantitative analysis via the Beer- Lambert Law: UV-Vis (exp. 2)..protein conc. in biochemistry. FT-IR, NIR, Raman spectroscopies in industry. The Electromagnetic Spectrum Region Frequency s 1 Wavelength Radio F m Micro Wave mm IR µm UV-VIS nm X-RAY pm γ-ray pm 6 Wavenumber (cm -1 ) Quantisation of energy. Quantum Theory.molecules exists in discrete energy levels (electronic, vibrational, rotational). Transitions between allowed energy states. Spectra reflect these defined changes (band structure). 500 nm = 0.5 x10-4 cm = 20,000 cm -1 Visible (high energy) 1000 nm = 1 x10-4 cm = 10,000 cm -1 Near IR 2000 nm = 2 x10-4 cm = 5,000 cm nm = 5 x10-4 cm = 2000 cm -1 IR (low energy) 7 8 INTENSITY (arb. units) Cocaine hydrochloride raman shift, cm -1. Page 2

3 E Schematic molecular energy levels UV-VISIBLE INFRARED MICROWAVE Selection Rules There are rules for each type of spectroscopy. In general: Interaction between oscillating electric (or magnetic field) with the dipole moment of the molecule. Transitions only between allowed energy levels (QChem). two electric charges +q and q separated by a distance R ELECTRONIC VIBRATIONAL ROTATIONAL TRANSLATIONAL 9 10 The Bohr frequency condition: E (molecule) = E (photon) PHOTON ENERGY Absorption spectroscopy Can refer to the absorption of any frequency of radiation, most common are: UV-visible absorption (electronic) IR absorption (vibrational) Microwave absorption (rotational) These are all types of molecular spectroscopy. Energy of the radiation energy of transition. 11 BEFORE DURING AFTER ε = hν = hc / λ = hcν 12 Page 3

4 Absorption spectrometer Light absorbed by sample. Grating/frequency analyser Single channel (PMT) or multichannel (CCD) detectors (visible) Emission spectroscopy Emission of any frequency of radiation. Concerned with the properties of emitted photons. UV-VIS-NIR (electronic transitions): Fluorescence, Phosphorescence, Chemiluminescence, photoluminescence. Fluorescence underpins nearly all of modern biology. Based on chemistry & physics Scattering spectroscopy We look at how light scatters from molecules: Not absorbed, doesn t have to pass thru. Can use everything from neutrons to x-rays etc. Most Important is Raman spectroscopy: Molecular technique. Great for forensics etc. 2Y Spectroscopy: Topic 2 Quantitative spectroscopy: Beer-Lambert Law. Absorbance & Transmittance. Molar Absorption co-efficient. Calculations. Limitations. Know the Beer-Lambert law & calculations, how to interconvert from transmittance to absorbance. Limitations of method. Sec & 19.2: Atkins (Elements of Phys. Chem, 4 ed ) Page 4

5 17 I 0 Beer-Lambert Law: Quantitative Sample, Concentration C I T Pathlength, l At a fixed temperature and a single wavelength: the intensity of light, I T, transmitted through a sample depends upon: the pathlength or sample thickness,l the concentration of the absorbing species, C the incident light intensity, I 0 18 Beer Lambert Law I = I 10 λ ( e l C) T 0... at constant Temp. and a single wavelength ( ) e molar absorptivity, l pathlength, C concentration of absorbing species log(i ) = log(i ) e l C.... rearrange to: T 0 log(i ) log(i ) = e l C... we know: log a T 0 0 IT a log b =log b ( ) ( ) I T I 0 log = e l C... rearrange to: log = e l C, I 0 I T I absorbance, A = log A = e l C Application of Beer-Lambert law (1) Calculate: Molar abs. Co-eff. of Tryptophan (comp. of proteins) 280 nm 1 mm pathlength Needed Info Aqueous solution, 0.50 mmol L -1 54% of light passes through A = - log T = εlc step 1, write eqn. ε = - log T / l C step 2, rearrange eqn. Application of Beer-Lambert law (2) What is the Absorbance for 1 mm & 5 mm? For 1 mm: A = -log T = -log 0.54 = 0.27 For 5 mm, A = εlc A = (5.4 x10 2 Lmol -1 mm -1 )(5 mm)(5.0 x 10-4 mol L -1 ) = 1.35 ε ε = ( moll ) x (1 mm ) = Lmol mm, or ε = log , Lmol cm Step 3, put in values. Simple equation, always check the units Defined wavelength 20 Page 5

6 21 Limitations of Beer-Lambert law Works with relatively dilute solutions Does not work with turbid samples Need to avoid scattering Fixed single wavelength / fixed temperature Most commonly used with UV-Visible absorption spectroscopy. Can be used with FT-IR etc. 22 2Y Spectroscopy: Topic 3 Electronic Spectroscopy: UV-Visible absorption. Franck-Condon Principle. Fluorescence. Phosphorescence. Stokes shift, Lifetimes, Quantum yield. Understand and be able to explain the different spectroscopies. Chapter 20, Elements of Physical Chemistry Sections 20.1, 20.3, 20.4, and 29.5 Visible spectrum Absorption spectrum 23 Complementary colours opposite ---- Numbers = nm (wavelength) Absorb Red looks Green Absorbs blue looks orange Useful rule of thumb, but not accurate enough for scientific purposes Observer dependant Absorption spectrum of chlorophyll in the visible region. Absorbs in the red and blue regions, green light is not absorbed. 24 Page 6

7 UV-Vis absorption 190 to 1000 nm Organic Chromophores absorb in UV/Vis/NIR C=C, C=O, C=N E = E E = hν ( photon) 2 1 Franck-Condon Principle Nuclei are much more massive than electrons, so Electronic transitions take place faster than nuclei can respond. most intense vibronic transition is from the ground vibrational state to the vibrational state lying vertically above it. Transitions to other vibrational levels also occur, but with lower intensity Absorption in gaseous state The electronic spectra of some molecules show significant vibrational structure. Absorption in solution Very broad, ill defined UV spectrum of gaseous SO 2 at 298 K. Sharp lines in this spectrum are due to transitions from a lower electronic state to different vibrational levels of a higher electronic state Page 7

8 Fluorescence Jablonski diagram Excitation of electron from ground to excited state S 0 to S 1 (or S 2 ) Vibrational Relaxation Emission of a photon of light S 1 to S 0 Phosphorescence Sometimes electron can cross over to triplet level (not allowed transition) Takes much longer for T 1 to S 0, not allowed. Triplet state..2 parallel electron spins ( ) Singlet paired spins ( ) Fluorescence Spectrometer Single channel Right angle excitation nm usually Quartz cuvettes Light source; lamps, LED, laser, Excite with a narrow band Photoluminescence Bioluminescence Chemiluminescence Fluorescence spectra Most spectra don t have features..energy gaps between vibrational levels is too small and if in condensed phase (liquid/solid) they overlap. Not seen at r.t. but if cooled down to LN2 temps can be observed Page 8

9 Stokes Shift Fluorescence Lifetime Born in Sligo longer wavelength than absorption Difference = Stokes Shift Sensitive to environment polarity Ion concentration Average time a molecule spends in the excited state: Nanosecond (10-9 s) to Picosecond (10-12 ) range Anthracene = 5.2 ns in cyclohexane solution For T 1 to S 0 transition lifetime can be seconds Quantum yield (Q) Measure of the efficiency with which absorbed light produces an effect: Ratio of No. of photons emitted to the No. of photons absorbed Good fluorophores have Q close to 1 Q ~ 0, means no fluorescence (or phosphorescence) Tricky to measure experimentally: Have to integrate the absorption and emission bands 36 2Y Spectroscopy: Topic 4 Vibrational Spectroscopy: Vibrations of molecules (stretching, bending, etc,) Selection rules. FT-IR absorption spectroscopy. Raman spectroscopy. Know the key concepts underlying vibrational spectroscopy, and the differences between Raman and IR absorption spectroscopy. Chapter 19, Elements of Physical Chemistry, Sections and Page 9

10 37 Concepts Wavenumber: 5000 nm = 5 x10-4 cm = 2000 cm -1 Molecules have bonds they can vibrate Some bonds are stronger than others: C C / C=C / C-C. Electronegativities..some atoms like electrons more than others. Stronger / weaker bonds. H + F - C-H Ionic..Covalent character. 38 Dipole Moment two electric charges (or partial charges) +q and q separated by a distance R For IR, the atoms can be Slightly different Carbon & Oxygen Nitrogen & Oxygen 39 Molecular Potential Energy Diagram Plot of energy versus internuclear distance: Minimum = equilibrium bond distance (R e ) 0 = dissociation, atoms far apart. MPE diagram For 2 different diatomics. Strong bond Weak bond 40 Molecular vibrations 1 All molecules capable of vibrating. Many different types of vibration (modes): Stretching, Bending, Wagging, Twisting The bigger the molecule, the more vib. modes Diatomics (1 mode) Proteins 10 s of thousands Vibrations excited by absorption of EM radiation of the right energy. Page 10

11 Molecular vibrations 2 Observing the frequencies of vibration can be used to ID molecules: Molecular Fingerprints. FT-IR and Raman spectroscopy used in this way for: Intensity(arb. units) Forensics (drugs, explosives, hazmat) Monitoring progress of reactions Heroin MDMA Cocaine Selection Rules Very important in vibrational spectroscopy. Used to predict which vibrations you should see. Rules are different for IR-Absorption and Raman scattering. Sometimes we see bands in IR and not in Raman..and visa-versa. Raman good for non-polar molecules. IR good for polar molecules Raman shift, cm IR-absorption spectroscopy Light absorbed by molecule: passes light through the sample Measure how much absorbed. Vibrational transitions (lowish energy) IR radiation (2 µm 1000 µm) (5000 cm -1 to 10 cm -1 ) Spectra from ~ cm -1 to 4000 cm -1 Obeys Beer-Lambert (linear with conc.) IR spectrometer Dispersive, like UV-visible, Light passes thru.scan across different wavelengths to make spectrum. Most modern IR spectrometers are Fourier-Transform (FT) based and use a Michelson Interferometer. All light frequencies at once. Faster than scanning Page 11

12 Typical IR spectrum Plot of % Transmittance Versus Wavenumber Vibration type C H C H V/cm C C stretch, bend C=C stretch C C stretch O H stretch C=O stretch C N stretch N H stretch Hydrogen bonds Raman spectroscopy (I) Light interacts with vibrational modes of molecule. A very small amount is scattered at longer/shorter wavelength. Photon hν 0 Stokes Virtual State ν = 4 ν = 3 ν = 2 ν = 1 ν = 0 Photon h(ν ν ) 0 1 Photon hν 0 anti-stokes Virtual State Photon h(ν +ν ) 0 1 ν = 4 ν = 3 ν = 2 ν = 1 ν = 0 Stokes shift to longer wavelength Anti-Stokes to shorter wavelength Electronic Ground State 47 Raman spectroscopy (II) RAMAN (STOKES) RAYLEIGH RAMAN (ANTI-STOKES) (υ 0 υ 1) υ 0 (υ 0 + υ 1) Frequency, cm -1 Stokes lines:- ~10 3 times weaker than Rayleigh scattering - shorter wavelength, gain of energy : Anti-Stokes lines:- ~ weaker than Stokes at ambient temps. Vibrational spectrum similar to an IR spectrum, Based on chemical structure of molecules, Spectra are unique.molecular fingerprints, 48 Raman spectroscopy (III) IR A b s o rp tio n b a n d s R a y le ig h s c a tte rin g R a m a n s a c tte rin g b a n d s Raman looks at the scattered light relative to the excitation line. Can use any wavelength excitation. P h o to n E n e rg y c m , / c m n m H e N e 1 8, / c m n m 2 0, / c m n m A r io n Page 12

13 Raman spectrometer Typical Raman Spectra Pure Cocaine taken using a Battery operated portable system Cocaine hydrochloride, pure. A11AUG13:11/8/ Pure Cocaine taken using a Laboratory system INTENSITY (arb.) Raman shift, cm -1. Gross selection rule: IR-Absorption Changing dipole moment The dipole moment, p, of the molecule must change during the vibration for it to IR active. 51 Does not have to have a permanent dipole can move Some vibrations cause no change in dipole moment (homonuclear diatomics) Transitions are restricted to single-quantum jumps to neighboring levels e.g. from v=0 to v=1, from v=1 to v=2, etc 52 Original molecule AB; 2 atoms + bond electron cloud. Draw bond dipole. Distort molecule. Draw new bond dipole. Has dipole changed? A r r +q -q p r +q -q p B Page 13

14 Gross selection rule: Raman spectroscopy Has to be a change in the polarizability for a vibration to be Raman active: CO 2 symmetric Stretch O C O O C O O C O Distortion of the electron cloud of a molecular entity by a vibration. Good for Homonuclear diatomics (N 2, O 2 etc.) Exclusion Rule: More exact treatment of IR and Raman activity of normal modes leads to the exclusion rule: If the molecule has a centre of symmetry (like CO 2 ), then no modes can be both infrared and Raman active: A mode may be inactive in both. often possible to judge intuitively if a mode changes the molecular dipole moment, use this rule to identify modes that are not Raman active Group theory is used to predict whether a mode is infrared or Raman active (3 rd year) IR vs. Raman spectra FT-IR. Raman.. Raman vs. IR spectroscopy How do the 2 different vibrational techniques compare? How do the selection rules work in practice for polyatomic molecules? What are the advantages/disadvantages? How can we use the techniques for advanced studies? Page 14

15 O-H stretch Ethanol (C 2 H 5 OH) O-H bend Scales not exact match Polar groups give strong IR bands.weaker in Raman Different selection rules Weak O-H bands mean can use OH containing solvents Applications in Microscopy Can use IR and Raman in microscopy. IR radiation = long wavelength = large spot size In practice spot ~10 µm. UV-Vis = shorter wavelength = smaller spot size For 488 nm excitation, spot < 1 µm. Water is a weak Raman scatterer: Can use Raman for analysis of cells & tissue. 57 Data from: ww.aist.go.jp/riodb/sdbs 58 IR versus Raman: comparison IR-absorption Raman Selection rule Change in Dipole moment Change in polarizability Good for Polar molecules (e.g. HCl) Non-polar molecules (e.g. N 2 ) Water Very strong absorption Very weak scattering Wavelength IR region of spectrum Any region Spectra Same ( cm -1 ) Same ( cm -1 ) Sensitivity Good Very weak Y Spectroscopy: Topic 5 Vibrational Energies: Spring Model. Force Constants. Effective mass. Vibrational Energy levels. Effect of bond strength on vibrational transitions. Understand the simple spring model. Be able to calculate force constants & energies of vibrational transitions. Chapter 19, Elements of Physical Chemistry, Sections and Page 15

16 H3C CH3 2 year Spectroscopy Handout: Modelling vibrations Close to R e the MPE curve.approximates to a parabola (y=x 2 ). Potential Energy (V) can be written: V = ½k(R-R e ) 2 Force Constant K Measure of the strength of the bond Parabola gets steeper as k increases. k = force constant (Nm -1 ) Diatomic Model: Both atoms move in a vibration.. Need to use detailed calculations: Schrödinger wave equation (3 rd year) υ = vibrational quantum number. Specific selection rule: υ = ±1 m 1 m 2 K 1 k ν =, µ = effective mass 2π µ (frequency in H z) E = ( υ +½)h ν, υ = 0,1,2,... v Vibrational Energy Levels: E υ ( 1 h k = υ + ), 2 2 π µ (Energy in Joules) 64 Effective Mass (µ) mamb µ =, m + m A B M A M B Na Na µ = in kg, M A M B + Na Na N = avogadros number M a = Atomic mass (in kg) Important for calculating vibrational energies Always a very small number: Page 16

17 65 Vibrational energy levels (diatomics) E (7/2)(h/2π) (k/µ) (5/2)(h/2π) (k/µ) (3/2)(h/2π) (k/µ) (1/2)(h/2π) (k/µ) Differences? Constant E = (h/2π) (k/µ) For photon Therefore 66 Calculating the wavenumber of a vibration An 1 H 35 Cl molecule has a force constant of 516 Nm 1. Calculate the vibrational stretching frequency: The wavenumber of a vibration can be calculated from the equation: 1 k 1 ν =, where ν is the vibrational wavenumber in m. 2π c µ mh mcl Step 1: Calculate the effective mass, µ =, m + m Na µ = Na in kg, Na = avogadros number Na Na µ = kg [ Always write this out longhand] H Cl 67 Calculating the wavenumber of a vibration The wavenumber of a vibr ation can be calculated from the equation: 1 k -1 ν =, whereν is the vibrational wavenumber in m. 2π c µ Step 2: input the values: 1 Nm ν = 2π ms (516 ) (516 kgms m ) , ν = ms ν = ms s kg , 2,[N = kgms ] kg ν = 299, 246 m = 2992 cm Calculating a force constant (step 1) 1 H 35 Cl has a fundamental stretching vibration at 2991 cm -1, Calculate the force constant. The force constant can be calculated from the equation: 1 k -1 ν =, where ν is the vibrational wavenumber in m. 2π c µ Step 1: Rearrange the equation: 1 k 1 k ν = = 2π c µ 4π c µ 4 c = k ν π µ k = 4 ( π c ) , ν, then: 2 2 ν µ Page 17

18 k = 4 Calculating a force constant (step 2) ( c ) π 2 2 ν 2 µ...remember mh mcl Step 2: Calculate the effective mass, µ =, m + m Na Na µ = in kg, Na = avogadros number Na Na µ = x kg [Always write this out longhand ] H Cl Calculating a force constant (step 3) ( c) ( c) k = 2 π ν µ... µ = 1.63 x 10 Step 3: Input values, [ Always write this out longhand] 2 2 k = 2π ν µ = (2π 2.9 = (3.54 kg ms ) (299,100 m ) ( kg) m s )( m )( kg) 2 2 = (517 kgs ) [1 Newton = 1 kgms ] = 517 Nm H 2 + Diatomic Molecules: V/cm 1 R e/pm k/(n m 1 ) D/(kJ mol 1 ) H H H 19 F H 35 Cl H 81 Br H 127 I N 2 235S O F Cl Y Spectroscopy: Topic 6 Polyatomic Molecules: Mass effect. Number of vibrational modes. Anharmonicity. Predicting active modes. Analysis of vibrational spectra. Comparison between Raman and IR spectra. Understand mass effect and factors that influence spectra of polyatomic molecules. Be able to calculate the number of vibrational modes, & predict which bands are IR or Raman active. Chapter 19, Elements of Physical Chemistry, Sections 19.12/13/15 71 p. 497, Atkins & DePaula, 4 th edition. 1 k ν = 2π c µ 72 Page 18

19 73 Polyatomic molecules..n>2 IR spectra are much more complex More than just stretching vibrations: Bending, wagging, twisting Combinations of vibrations 74 Polyatomics? N> Bond ν (cm ) Bond Energy (kjmol ) RC O R 2C = O R C-OR View polyatomic as collection of diatomics Force constants as per diatomics Correlates with bond strength (right-hand column) Mass effect? Yes, next ovhd. Group frequencies or wavenumbers, i.e., all ketones have IR band/peak near 1800 cm 1 Mass effect: CHCl 3 & CDCl 3 Compare CHCl 3 & CDCl 3 1 k 1 ν =, so ν = 2π c µ µ Step 1: Calculate the effective masses, µ µ µ µ H CCl3 H CCl3 D CCl3 D CCl3 75 ( )( ) (.001) + ( ) = in kg, Na = avogadros number N 1 = 1.65 x 10 kg, so... = µ = (.002)( ) (.002) + ( ) 3 Ratio = = a 35 1 N H CCl3 1 = x 10 kg, so... = µ H-CCl D-CCl a D CCl3 Is this seen experimentally? Peak at ~ 3,019 cm 1 due to C H stretch Shifted to ~ 2,258 cm 1 for D C stretch Ratio 3019/2300 = 1.34 (1.406 not bad.) 76 Page 19

20 How many vibrational modes? Rule: The number of modes of vibration N vib : 3N 5 for linear molecules (e.g. CO 2 ) 3N 6 for nonlinear molecules (e.g. H 2 O). 3n degrees of freedom (x, y, z) different displacements Take away the translational (change in x=y=z) so -3 2 angles needed to specify linear molecules orientation (A) 3 angles needed to specify linear molecules orientation (B) Where N = number of atoms in molecule The bigger the molecule the more vibrations If Linear H 2 O: Number of IR bands? Linear triatomic water How many vibrations? 3N-5 = = 4 Can only find three different: Symmetric stretch Asymmetric stretch 2 Bends (identical) Only two are IR active: Changes in dipole moment. H O H H O H H O H Symmetric stretch Asymmetric stretch Bend But we see three experimentally!! Page 20

21 Vibrational modes for bent H 2 O How many vibrations for non-linear molecule? 3N = 3 vibrations Sketch each mode & draw bond dipoles Sum to produce overall dipole Distort molecule for each vibration Redraw bond dipoles Sum to give overall dipole Has dipole changed during vibration? IR Spectra of simple cyanides Linear arrangement of atoms X-C-N 3N-5 vibrations; 3 different & all active Emergent Concept; Group frequencies X C C N B e n d HCN D CN FCN ClCN BrCN ICN HCN Vibrational modes H C N H C N H C N H C N H C stretch H C N H C N C-N stretch H-C stretch H-C-N bends All IR active Isotopic substitution? Identical structure D replacing H No change -8% Big change -20% Some change -20% 84 Band areas Functional group region O-H C-H Single bonds to H Fingerprint region Phenol Page 21

22 Analysis of vibrational spectra (I) Functional group region most important for interpreting IR spectra. In IR it is the polar covalent bonds than are IR "active In Raman spectra non-polar bonds are also active. In organic molecules these polar covalent bonds represent the functional groups. Hence, the most useful information obtained from an IR spectrum is what functional groups are present within the molecule. Analysis of vibrational spectra (II) Some functional groups are combinations of different bond types. Esters (CO 2 R) contain both C=O and C-O bonds, Both are typically seen in an IR spectrum of an ester. In the fingerprint region, spectra tend to be more complex and much harder to assign. But very important in Physics, Materials Science, etc.properties of materials Now some examples: Benzene vs Toluene, liquid CH 3 Environmental Influences (I) Covalent diatomic molecule H Cl Gas-phase 2,886 cm 1 Solid state 2,720 cm 1 Solution (aromatic solvent) 2,712 cm 1 Solution (ether solvent) 2,393 cm 1 Conclusion? NB: wavenumber of absorption (force constant) weak intermolecular bonding R 2 O... H Cl 87 Spectra from: 88 Page 22

23 Environmental Influences (II) Vibrational bands are usually broader in condensed media (solid liquid) than gas phase. Crystalline materials have sharper vibrational bands than amorphous materials. Can be used to distinguish polymorphs of pharmaceutical products 89 Page 23