Introduction to Spectroscopy Tim Grüne University of Göttingen Dept. of Structural Chemistry

Transcription

1 Molecular Biology Course 2012 Introduction to Spectroscopy Tim Grüne University of Göttingen Dept. of Structural Chemistry Tim Grüne Week 0: Spectroscopy 1/53

2 Spectroscopy Spectroscopic methods investigate properties of substances by how the substance modifies electromagnetic radiation. It is mostly suitable to observe (and interpret) energy levels of the material. Biologically oriented methods based on spectroscopy include Nuclear Magnetic Resonance Electron Spin Resonance UV-/Vis-spectroscopy X-Ray Fluorescence Tim Grüne Week 0: Spectroscopy 2/53

3 The Electromagnetic Spectrum The term electromagnetic radiation is a generalisation of light. It is characterised by its wavelength: Radio Micro Infrared Visible UV X rays γ rays 4.12µV eV 1.54eV 3.09eV 1.23keV 123keV energy wavelength 10km 30cm 1mm 800nm 400nm 1nm 10pm Naturally we can only observe visible light. Some snakes can detect infrared, and bees observe UV light (but no red). Yet, we still react to the whole spectrum, as you can see e.g. by the sun-burnt face. Tim Grüne Week 0: Spectroscopy 3/53

4 Light as Waves Classically, electromagnetic radiation is considered a wave. The wave is described by its wavelength λ or frequency ν which are connected by the speed of light c: ν = c λ = m s λ The wavelength is measured in meter m. The unit of frequency is 1 s = 1Hz. Humans observe different wavelengths (of visible light) as differnt colours. Tim Grüne Week 0: Spectroscopy 4/53

5 Light as Particle: the Photon Quantum-mechanically, light can be considered both a wave or a particle. This light-particle is called photon. A photon with wavelength λ carries the energy E = hc λ = evm λ The energy is measured in ev, corresponding to J. (A light spot as accumulation of photons; books/6mr/ch03/ch03.html ) Tim Grüne Week 0: Spectroscopy 5/53

6 Wave-Particle-Duality A photon has properties both like a particle and a wave. But that is rather impossible to understand or imagine. In order to understand a phenomenon, we can choose whether we consider light as wave or as photons, which ever makes the phenomenon easier to understand. Caveat: Spectroscopy makes heavy use of both appearances and an explanation can switch between the two without warning. Tim Grüne Week 0: Spectroscopy 6/53

7 Photons vs. Matter Two negatively charged electrons e repel each other. wave picture both electrons create an electro-magnetic field, which travels like a wave away from the electrons. When the wave reaches the other electron, it experiences a repulsive force. particle picture a photon is transferred from one eletron to the other. The photon interchanges energy and momentum between the two electrons. At an atomic/ molecular level this picture is often more helpful than the wave picture. (Feynman diagram from wikipedia.org) Tim Grüne Week 0: Spectroscopy 7/53

8 Units and Unit Conversion Apart from SI-units (m, s, J,... ) there are a couple of widely used units in spectroscopy. Conversions Units From unit To unit Conversion Energy [ev] Wavelength [Å] λ = E/eV Å Wavelength [Å] Energy [ev] E = λ/å ev Wavelength [Å] Wavelength [m] 1Å= m Energy [ev] Energy [J] 1eV = J h Planck constant Js = evs h bar = h/2π evs c Speed of light N A Avogadro s number m s /mol k Boltzmann constant J/K = ev/k Tim Grüne Week 0: Spectroscopy 8/53

9 Number Prefixes In order to avoid the writing of very large (like 1,000,000,000 Hz) or very small numbers (like 0.000,001g) one uses prefixes to units. p pico n nano 10 9 µ micro 10 6 m milli 10 3 k kilo 10 3 M mega 10 6 G giga 10 9 T tera P peta So 1,000,000,000 Hz = Hz = 1 GHz, and 0.000,001 g = g = 1 µg. Except for the kilo, lower case letters are small and upper case letters are large. Tim Grüne Week 0: Spectroscopy 9/53

10 Spectrum and Spectroscopy A wavelength (of visible light) corresponds to one colour. Colours can be added. Adding all visible colours together results in white light. Tim Grüne Week 0: Spectroscopy 10/53

11 Spectrum and Spectroscopy A wavelength (of visible light) corresponds to one colour. Colours can be added. Adding all visible colours together results in white light. What could happen if one places a yellow foil into the light path? Tim Grüne Week 0: Spectroscopy 11/53

12 Spectrum and Spectroscopy A wavelength (of visible light) corresponds to one colour. Colours can be added. Adding all visible colours together results in white light. What could happen if one places a yellow foil into the light path? Not the yellow light is left over, but its complement (some greenish-blueish) is removed from the spectrum. The remaining frequency add up to the colour yellow. This was our first spectroscopic experiment. We found out that inside the foil something is happening which requires the energy of the particular wavelength removed from the spectrum. Tim Grüne Week 0: Spectroscopy 12/53

13 Energy transfer What Photons are used for A photon can transfer energy to matter (molecules, atoms). There are various atomic processes that can pick up a photons energy. Depending on the wavelength range we use, we can investigate different processes/ characteristics. Tim Grüne Week 0: Spectroscopy 13/53

14 Energy Range and Molecular Processes Radiation λ ν Energy Process Method Radio > 10cm < 3GHz < 10 µev Nuclear Spin nuclear magnetic resonance (NMR) Micro 1-10cm 3-30 GHz meV Electron Spin electron spin resonance (ESR) mol. rotation IR-spectroscopy Infrared µm THz eV mol. rotation IR-spectroscopy mol. vibration IR-spectroscopy UV/Vis nm PHz 1.7-6eV mol. vibration UV/Vis-spectroscopy electronic state X-rays < 10nm >30 PHz 120 ev transitions of inner shell electrons source: Bergmann, Schaefer, Lehrbuch der Experimentalphysik, Vol. 4 X-ray fluorescence (XRF), X-ray photoelectron spectroscopy (XPS) Tim Grüne Week 0: Spectroscopy 14/53

15 Spectroscopy and Discrete Spectra Tim Grüne Week 0: Spectroscopy 15/53

16 The Real World potential energy m g h kinetic energy rotational Energy 1 2 mv2 1 2 Iω2 Tourismusverband Sächs. Schweiz, Frank Richter Prater We are used to a continuous world: objects can have arbitrary mass, arbitrary speed, arbitrary velocity, etc.. We can measure these quantities with nearly arbitrary precision - it is only a matter of our instruments. Tim Grüne Week 0: Spectroscopy 16/53

17 Quantum Mechanics At an atomar or molecular scale, the world is quantised. Electrons orbit the nucleus at certain levels molecules can only vibrate or rotate at certain frequencies... Tim Grüne Week 0: Spectroscopy 17/53

18 The Small World A spectrum is usually associated with discrete lines. Nucleus: n,p + Electrons: e Particles at an atomic scale are described by a state. A state encompasses properties that we know (energy, charge,... ) and properties that are new (spin,... ) Most atomic" properties of a state are quantised: electrons are in certain orbits around the nucleus charges are always integer multiples of the electron or proton charge The energy of particles can only assume distinct values.. Tim Grüne Week 0: Spectroscopy 18/53

19 The Shape of Spectra Photons can transfer their energy. Particles prefer those photons that match the change of energy they undergo by their transition to a new state. Tim Grüne Week 0: Spectroscopy 19/53

20 The Shape of Spectra Photons can transfer their energy. Particles prefer those photons that match the change of energy they undergo by their transition to a new state. Tim Grüne Week 0: Spectroscopy 20/53

21 The Shape of Spectra Photons can transfer their energy. Particles prefer those photons that match the change of energy they undergo by their transition to a new state. Energy transfer can go in two directions. In the case of Sodium (Na) this is the cause for its typical 589nm spectral line. Tim Grüne Week 0: Spectroscopy 21/53

22 The Shape of Spectra Molecular Biology PhD Programme 2012 In principle a particle could absorb the energy it requires from a high-energy photon and emit the extraneous energy by a photon of lower energy. This would yield continuous spectra, at least above a energy cut-off. However, the preference of a matching photon is so strong that we obtain the typical discrete spectra in a manifold of spectroscopic experiments. Tim Grüne Week 0: Spectroscopy 22/53

23 Resonance The technical term for preference of the matching energy is resonance. It also exists in the macro-world ( our world). Narrows Bridge (1940) When the energy is right, the system (the bridge) takes up all energy from the exciting force (the wind). Another example: radio tuners when set to the correct frequency of the radio station we want to listen to, the signal is best (no noise). Tim Grüne Week 0: Spectroscopy 23/53

24 NMR & ESR The two spectroscopic methods nuclear magnetic resonance and electron spin resonance both exploit the spin of particles. electron, neutron, proton spin 1 2 measured effect: ± 1 2 nucleus (composition of neutrons and protons) spin 0, 1 2,1,11 2,... measured effect: ±0,± 1 2,±1,±11 2,... Tim Grüne Week 0: Spectroscopy 24/53

25 The Spin of Particles In 1921, Otto Stern and Walther Gerlach carried out their famous experiment which led to the notion of the spin of elementary particles. experiment Silver-atoms were run through a strong (inhomogeneous) magnetic field onto a detector. Classically the electrons orbit around the nucleus and create a small magnetic field. This would create one smear of silver atoms on the detector, depending on the arbitrary orientation of the electron orbits w.r.t. the magnetic field. Stern and Gerlach expected one single spot because of the quantisation of space. They observed two distinct spots on the detector which was explained by new property of elementary particles which interacts with magnetic fields the spin. Tim Grüne Week 0: Spectroscopy 25/53

26 Angular Momentum and Spin Molecular Biology PhD Programme 2012 The quantum mechanical description of the electron spin resembles that of the orbital angular momentum of an electron orbiting the nucleus. Both are vectorial quantities, i.e. they consist of three components, one for the x-, y-, and z-direction each. Because of Heisenberg s uncertainty principle, we can only determine its vector length and one out of these three components. By convention one usually calls this z-direction. z Example: Total momentum somewhere on dashed sphere Radius = Strength. z-component is quantised - can only be..., 1, 1 2,0, 1 2,1,... x- and y-components cannot be determined (somewhere on circle) Tim Grüne Week 0: Spectroscopy 26/53

27 Fine Structure, Hyperfine Structure,... The more closely we look the more details we observe. E.g. the 589nm spectral line of Na is actually split into two lines nm & nm 589nm nm, m s = nm, m s = 1 2 good better measurement One line is due to m s = one is due to m s = 1 2 and the other An electron is charged and interacts with its own spin. This leads to a splitting of spectral lines as in the case of the Na-D-line. The interaction between electron spin and its charge is often referred to as fine structure. The interaction between electron spin and the spin of the nucleus is often referred to as hyperfine structure (and requires even better techniques to be observed). Tim Grüne Week 0: Spectroscopy 27/53

28 Quantum Mechanical Conventions Physicists are very conservative about the letters they use (e.g. E for energy, v for speed, m for mass,... ). The important quantum numbers in spectroscopy are: l or L: orbital angular momentum number(electron orbits/ shells, but also rotating molecules). - m l : z-component of l, also magnetic quantum number; m l = l, l+1,... 1,0,1,...+l. s or S: spin number; for electrons, neutrons, protons: s = m s : z-component of s; m s = ± 2 1 for electrons, neutrons, protons. j or J total angular momentum (the composition of s and l, which affects the experiment) - m j : z-component of j; m j = j, j +1,... 1,0,1,...+j. These numbers are integers (-2, -1, 0, 1,... ) or half-integers (1/2, 3/2,... ), a fact that expresses the quantification of these properties. The energy of a system with (experimentally determined) moment of inertia I is E J = J(J + 1) 2I 2, i.e. it is independent of the z-component. One says, the energy level is (2J +1)-fold degenerate. The degeneration can be removed by e.g. an external magnetic field as in the case of the Stern-Gerlachexperiment and as in NMR and ESR. Tim Grüne Week 0: Spectroscopy 28/53

29 Selection Rules 1. Conservation of energy, momentum, angular momentum: if we take all particles of an experiment into account, the total energy does not change. This holds both in the macro- and the quantum-world. 2. Pauli Exclusion Principle: two particles cannot be in the same state. These two rules lead to the selection rules for spectroscopic experiments: Only certain changes of state are possible. These rules help understanding the experimental results. E.g. for some transitions which involve the angular momentum quantum number J, this number can only increase or decrease by one., and it changes its direction of travelvirb Tim Grüne Week 0: Spectroscopy 29/53

30 Types of Spectroscopy The following spectroscopic methods will be discussed in a little more detail: Infrared (IR) Spectroscopy Light- and Ultraviolet (UV/Vis) Spectroscopy Electron Parametric (or Spin) Resonance (EPR/ ESR) Nuclear Magnetic Resonance (NMR) Tim Grüne Week 0: Spectroscopy 30/53

31 IR-Spectroscopy The energy range for vibrations and rotations of (small) molecules is the range of IR-radiation (λ =800nm- 1mm). H Cl Rotation Cl H Vibration H H Cl Cl The Cl-atom attracts the electron of the H-atom. The Cl-side is rather negatively charged, the H-side rather positively: the molecule has a dipole moment. The two atoms can vibrate along their bond and they can rotate about each other. The energy for both motions lies in the range of infrared radiation. The presence of dipole moment is important to allow interaction with the photon. Tim Grüne Week 0: Spectroscopy 31/53

32 IR: P- and R-branch Since we are looking at molecules, quantum mechanics applies and only discrete changes of state are possible. IR-spectroscopy detects both rotational changes (quantum number J) and vibrational changes (quantum number ν) of state. P-branch Q-branch R-branch The graph shows the allowed transitions for a two-atom molecule like HCl. The rotational energy in IR-spectroscopy can change its quantum number J only by 1, because this changes the angular momentum by the amount transferred to or from a photon. Transitions which lower J by 1 are called the P-branch. Transitions which increase J by 1 are called the R-branch. Purely vibrational transitions with J = 0 are not allowed by the selection rules, therefore the Q-branch is missing. Tim Grüne Week 0: Spectroscopy 32/53

33 IR: Example Spectrum for HCl gap : missing Q-branch right from gap : P-branch with decreasing energy left from gap : R-branch with increasing energy Tim Grüne Week 0: Spectroscopy 33/53

34 Evaluation of Spectra Other than for the simplest molecules, the expected spectra become too complicated to be calculated. Spectra (not only IR) are usually interpreted by measuring the deviation from known standards, e.g. the strength of the hydrogen bond R C H would vary depending on the residual R. The strength of the bond is directly related to the energy of the vibrational transitions, a strong bond has larger steps between the energy levels. Tim Grüne Week 0: Spectroscopy 34/53

35 UV/Vis-Spectroscopy The energy of visible and UV-light corresponds to the transitions of valence electrons of molecules. UV/Vis-spectroscopy investigates bonding effects and is mostly used to investigate organic compounds. Some applications of UV/Vis-spectroscopy: determination of pk-values determination of equilibrium constants quantitative determination of solutions of transition metal ions secondary structure composition and thermal stability of proteins (circular dichroism (CD)-spectroscopy) Tim Grüne Week 0: Spectroscopy 35/53

36 Circular Dichroism of Proteins: Secondary Structure Depending on their secondary structure, proteins change the circular polarisation of light α lysine β lysine coiled lysine Θ [ cm 2 /dmol] CD-Spectra of 3 different conformations of poly-lys: 1. purely α-helical 2. purely β-sheets 3. purely coiled-coil wavelength [nm] Proteins = mixtures of α-helices, β-sheets, loop-regions CD-spectrum = mixture of the above deconvolution of spectrum: insight into secondary structure composition of protein. Tim Grüne Week 0: Spectroscopy 36/53

37 Circular Dichroism of Proteins: Thermal Stability Proteins are thermally unstable: loss of secondary structure with increased temperature. slope [ /K] slope (window = 4) data 4+5 samples Temperature [ C] Meltung Curve of a protein sample: Green Curve: Reduction of circular dichroism with temperature measured at wavelength λ = 208 nm Red Curve: Slope of green curve. Peaks correspond to melting events. Multiple domain protein, one domain thermally less stable than the other Tim Grüne Week 0: Spectroscopy 37/53

38 Nucleic Magnetic Resonance (NMR) Tim Grüne Week 0: Spectroscopy 38/53

39 Nucleic Magnetic Resonance (NMR) The nuclei of elements consist of neutrons (uncharged) and protons (charge: 1e). Both are spin= 1 2 particles. The total spin quantum number I of a nucleus is the composition of the neutrons and protons spin (but not the sum). Element I Element I 12 C 0 16 O 0 invisible to NMR 13 C 1/2 31 P 1/2 allow specific labelling 19 F 1/2 14 N 1 By replacing only some e.g. 12 C isotopes with 13 C, one labels the structure and can selectively make certain parts of the structure visible by NMR. Tim Grüne Week 0: Spectroscopy 39/53

40 NMR Experiment The spin quantum number I gives rise to m I = I,( I +1),... 1,0,1,...I different states. In the case of I = 1/2,m I = ±1/2 one usually speaks of spin up and spin down. These states are separated by a strong homogeneous magnetic field B with energy levels E mi = γ Bm I m I = 1 γ: magnetogyric ratio. Its value depends on the nucleus type. m I = 1 Sometimes one alternatively writes γ = g I µ N, with the nuclear g-factor g I, and the nuclear magneton µ N = J/T (T : Tesla, unit of magnetic field). 0 Energy m I = 0 m I =+1 m I = 0 m I =+1 The term γb has the unit 1/s like frequencies and is called the Larmor frequency ω, i.e. E mi = m I ω. B B Tim Grüne Week 0: Spectroscopy 40/53

41 NMR Sample Preparation A strong homogeneous field B serves two purposes: 1. Separation of energy levels easier to detect. 2. Greater population of lowest energy state (E m ) according to Boltzmann distribution N m N m = e (E m E m )/kt so that more transitions (m m ) can be observed. This means that a strong, homogeneous magnetic field improves the signal we want to detect. At 12T (Tesla), the photon required to excite a proton from E to E must have a frequency of 500MHz. Current NMR machines create magnetic fields with a separation of 900 MHz. Tim Grüne Week 0: Spectroscopy 41/53

42 NMR Measurement In its simplest form, NMR uses two electromagnetic fields: One strong homogeneous field (measured in Tesla) in order to make the spin states of the nucleus distinguishable. One ( probing ) field (measured in MHz) with energy in the range of the difference of the energy levels. The probing field scans the region of the expected energy levels. When it matches a transition, resonance occurs, i.e. the photon of the correct energy is absorbed in order to make the nucleus change its state. E probe m I = 1 m I = 1 0 m I = 0 m I = 0 Energy m I =+1 B m I =+1 B Tim Grüne Week 0: Spectroscopy 42/53

43 NMR: The Chemical Shift The chemical environment of a nucleus influences the local magnetic field that the nucleus experiences: The spin levels are not separated by a magnetic field of strength B, but a slightly different B which can be greater or smaller than B. NMR experiments measure the difference between the probe and a reference sample. Usually the relative shift with respect to a standard chemical is determined. δ = ν ν 0 ν ppm The unit ppm is just like the % -sign: % = parts per hundred ppm = parts per million It reflects how small the changes really are. nucleus reference compound 1 H (Si(CH 3 )) 4 = tetramethylsilane (TMS) 13 C (Si( 13 CH 3 )) 4 31 P 85%H 3 ( 31 P)O 4 (aq) The chemical shifts δ of the reference compounds are defined to be 0. The shift δ is independent of the strength of the homogeneous field B but becomes easier to measure the stronger the field. Tim Grüne Week 0: Spectroscopy 43/53

44 NMR: Typical Shifts NMR 200ppm 100ppm 0ppm Shifts of 13 C depending on its chemical environment. The chemical shift is in the range of only a few ppm for 1 H and a few hundred ppm for 13 C. This means that for a typical energy difference corresponding to a photon of 500 MHz, the NMR machine must detect the small difference between 500,000,000 Hz and 500,000,500 Hz. It is like telling whether the weight of a jumbo jet is 500t or 500t and 500g!!! Therefore, NMR machines are large and expensive... spectroscopy 21.2T NMR machine. Tim Grüne Week 0: Spectroscopy 44/53

45 Electron Spin Resonance Tim Grüne Week 0: Spectroscopy 45/53

46 Electron Spin Resonance There are several types of magnetism. Diamagnetism is caused by the movement of the electrons: When electrons are exposed to an exterior magnetic field and move, their movement itself creates a magnetic field which is opposed to the exterior field, they weaken the exterior field. A similar effect is used in dynamos to generate current and in eddy current brakes. Paramagnetism is a reaction of the electron spin to an exterior magnetic field. When all shells of an atom are filled with electrons (as e.g. in noble gases or CF 4 ), all electrons are paired, and so their spins and cancel pairwise. Such material is not paramagnetic. Therefore, if one wants to investigate the response of electrons to a magnetic field, only paramagnetic samples (i.e. with at least one unpaired electron) can be used. The chemical term for such a molecule is a radical. Hence Electron Paramagnetic Resonance is the same as Electron Spin Resonance : Characterisation of a paramagnetic sample by the reaction of the electron spin to a magnetic field. Tim Grüne Week 0: Spectroscopy 46/53

47 Magnetic Field splits Spin States 0 Energy m s =+1/2 E = g e µ B B m s = 1/2 B Just as in the case of NMR, a homogeneous magnetic field splits the energy levels of the spin. Because electrons always have spin s = 1/2, there are always two energy levels E and E. Their difference is E E = g e µ B B. µ B is called the Bohr-magneton. For a typical ESR spectrometer, B = 0.3T. This corresponds to an energy difference of 10 GHz, i.e. microwave radiation. The factor g e µ B can be considered the response of the electron to the magnetic field B. It is about 600 times larger than the response g I µ N of a nucleus. Therefore, ESR is susceptible to much weaker effects or long range effects compared to NMR. (Note: E is the lower energy state for electrons while for nuclei it is E.) Tim Grüne Week 0: Spectroscopy 47/53

48 ESR Experimental Setup Micro waves Splitter Reference wave N S Sample Comparison B field At an ESR experiment, the microwave frequency is kept constant and the B-field is varied. This way the microwaves can be compared with a reference beam and a resonance detected at a specific strength of B. This is opposed to NMR, where the magnetic field is kept constant and the energy range at which a transition occurs is scanned. Tim Grüne Week 0: Spectroscopy 48/53

49 The g-factor Just as in NMR, the chemical environment of an electron alters the magnetic field the electron experiences locally. Because the difference B B loc is only small, we can approximate that the difference is proportional to the external field B: B B loc = σb B loc = (1 σ)b σ is a (very) small number which depends on the chemical environment of the electron under consideration. In ESR one calls g = (1 σ)g e the g-factor of the radical or complex under consideration. The energy of the (microwave) photon required to transfer the electron from to is E = gµ B B. Tim Grüne Week 0: Spectroscopy 49/53

50 The g-tensor In solid material, notably crystals with crystal defects, the effect of the magnetic field can depend on the orientation of the field w.r.t. the sample. Mg 2+ O 2 Mg 2+ O Mg O 2 Mg 2+ O 2 Mg 2+ B B An MgO crystal with a defect (missing Mg 2+ ion) can have an O radical. The radical is shifted slightly away from the hole. The g-factor varies depending on whether the magnetic field applied from the side (B g ) or from the bottom (B g ). In a general description, the g-factor becomes a 3 3-matrix called the g-tensor. ESR is sensitive enough to determine the nine entries of the g-tensor which gives even more information about the chemical environment of the considered radical. Tim Grüne Week 0: Spectroscopy 50/53

51 Hyperfine Structure As in NMR, the magnetic field from the spin of the nucleus affects the spin of the surrounding electrons. If we look close enough, we can see the effect. Because this is a quantum mechanical effect, the (2I + 1) levels of the nucleic spin create the same number of sub-levels for both and state of an electron. m I = +1/2 0 Energy m I = 1/2 B field m I = 1/2 h ν Microwave photon Example of hyperfine structure with an I = 1/2 nucleus. The microwave energy is kept constant, so there are two values for the (varying) B-field at which transitions are possible. When the B-field is too weak or the detector not sensitive enough, these two lines appear as one. m I = +1/2 Tim Grüne Week 0: Spectroscopy 51/53

52 Use of ESR The hyperfine structure can become very complicated with several nuclei. The resulting spectrum is like a fingerprint of a radical. One of the main purposes of ESR therefore is the detection of compounds/ radicals with known spectrum. In the presence of more than one parametric centre, one can also determine their distance (in the range of nm). Tim Grüne Week 0: Spectroscopy 52/53

53 Further Reading P. Atkins, Physical Chemistry, Oxford University Press (quantum mechanical theory, selection rules, techniques) Tim Grüne Week 0: Spectroscopy 53/53