4. Molecular spectroscopy. Basel, 2008

Transcription

1 4. Molecular spectroscopy Basel, 008

2 4.4.5 Fluorescence radiation The excited molecule: - is subject to collisions with the surrounding molecules and gives up energy by decreasing the vibrational levels (vibrational relaxation) radiationless decay. - the rest of energy is released by emission of a photon > fluorescence occur at a lower frequency that of the incident radiation! Fluorescence microscopy CLSM micrograph of convolaria

3 Fluorescence correlation spectroscopy A fluorescent labeled molecule in solution emits photons as long as it moves through a laser spot, those number depends on: 1. number of molecules (concentration). diffusion time (mass of molecule) 3. spot size (instrumental parameter) 4. quantum yield (property of dye) 5. bleaching, triplet states (laser power and dye) What can we learn by using FCS? - Diffusion time of fluorescent particles size - Concentration of fluorescent molecules - Molecular brightness number of dye molecules/diffusing particle - Binding constant (8x diff. in M W, knowledge of brightness necessary) for proteinligand interactions

4 FCS: example Diffusion times of fluorescent particles passing through the confocal volume are proportinal with the molecular mass of these particles: τ r D ω1 6πη = r 4 kt (4.17) 3 = 3m 4πρ N A τ D = diffusion time of the molecule ω 1 = radius of laser focus η= viscosity of the solution r = hydrodynamic radius of the molecule T = absolute temperature k = Boltzmann constant N A = Avogadro number ρ= mean density of the molecule m = molecular mass of the molecule G(τ) Increasing diffusion time - mass G (t) SOD+Dye SOD+Dye+Polymer (4.18) SOD - τ D = 10 SOD+ vesicles τ D =.3 ± 0.5 ms Time [µs] Example: encapsulation of superoxide dismutase in nanocontainers

5 4.5 MW spectroscopy Domain: - λ = m - ν = Hz - ~ ν = cm -1 -> E x Hypothesis: the molecule is a collection of mass points (for each atom one mass point), and can rotate as a whole (rigid rotor). The moment of inertia around the centre of the mass: I = m xx i i x i (4.19) x i - coordinate x of the particle of mass m i from the centre of the mass.

6 Rotor types The molecule is considered as a rigid rotor: Spheric rotor: CH 4 Symmetric rotor: NH 3 Linear rotor: CO, HCl Asymmetirc rotor: H O

7 Diatomic molecules: Triatomic linear molecules: I m m = m Moments of inertia I mam = m B R ma ( R + R' ) + ( m R m R' ) A C + A If m A =m C, R=R : I m = m R A C (4.0) (4.1) (4.) Spherical rotors: I = 8 3 m A R (4.3) I = m R A (4.4)

8 Symmetric rotors I // = mar I m m C = m A R' R ( 1 cosθ ) m m A ( 1 cosθ ) + ( m + m ) R ( 1+ cosθ ) 1 3 ( 3m + m ) R' + 6m R ( 1+ cosθ ) A B A B (4.5) C 1 + (4.6) I I I I // = m R I = m A R A ( 1 cosθ ) m m m (4.7) A B ( 1 cosθ ) + R ( 1+ cosθ ) (4.8) I // = 4mAR (4.9) I = ma R + mc R' (4.30)

9 4.5.. Rotational energy levels Rotational energy levels: E J h = J J 8π I ( + 1) (4.31) B = h /(8π I) (4.3) B - rotational constant of the molecule Example: CCl 4 has I = 4.85x10-45 kgm, and thus a rotation constant B = 1.04x10 - J = 5.4 cm -1 Rotational energy levels of a diatomic rigid rotor are: E J = B J(J+1) (4.33) J = rotational quantum number J = 0, 1,, 3... I = mr (4.34) m = m A m B /(m A +m B ) (4.35)

10 4.5.3 Rotational transitions The transition energy between two rotational levels (spherical rotors, or linear rotors), when J > J 1 is: ( J + 1 ) BJ ( J 1) = BJ E J = BJ (4.36) For large molecules, the inertia momentul increases > B decreases > E J decreases! E / B J 0 J = 4 8 J 0 -> 1 1 -> -> 3 3 -> 4 4 -> 5 1 J = J = 0 4 J = 1 J = 0 B 4B 6B 8B 10B cm -1

11 Rotational transitions for linear rotors Linear rotors: HCl, CO, C H... Rotational energy levels of a linear rigid rotor are: E J = B J(J+1) J = 0, 1,, 3... Centrifugal distortion: when the molecules is rotating, the atmos are subject to centrifugal forces which induce distortions of the molecular geometry change in I! Rotational energy levels for a diatomic molecule (centrifugal distortion induces a stretch of the bond): E J = B J(J+1) - DJ (J+1) (4.37) A high D value indicates a high stretch of the bond D - centrifugal distortion constant

12 4.5.4 Selection rules: rotational transitions 1. The molecule must have a permanent electric dipole moment. A molecule gives a pure rotational spectrum only if it is polar (it possess a fluctuating dipole momentul when rotating) Inactive molecules (in normal conditions do not have a pure rotational spectrum): Homonuclear diatomic molecules Symmetric linear molecules Spherical rotors if they are not significantly centrifugal distorted. Active molecules: OCS, H O, NO, NO.... Specific rules for linear molecules: J = ± 1 and M J = o, ±1 M J quantum number of the projection of J on Oz axis.

13 Rotational spectra Wavenumbers of the allowed J > J+1 absorptions for a linear rotor are: ~ ( J + 1 J ) = B( J + 1) ν (4.38) J = 0, 1,, 3... Pure rotational spectrum: a serie of lines with wavenumbers B, 4B, 6B,... and of separation B. > Determine the moment of inertia perpendicular to the principal axis of the molecule. Example: Rotation spectrum of the Orion nebula, showing the fingerprint of diatomic and poliatomic molecules present in the interstellar cloud.

14 4.6 IR spectroscopy Molecules vibrate in a a large number of different modes: - benzen has 30 different vibration modes (swelling or shrinking of the ring, and buckling in distorted shapes) - one protein has thousends of different ways of vibration (twisting, stretching, buckling in different regions). λ m ν Hz E J ν ~ cm -1 -> E Electromagnetic waves can induce a change in the dipole moment of molecules (IR waves can resonate with the molecules vibrations, as they have comparable frequency). x

15 Vibrations of diatomic molecules As vibrations in a large molecule can be considered as the summ of motions of each two bonded atoms, we describe first the diatomic molecules. a. Harmonic potential energy curve (see chapter 3..3) 1 V ( r) = k e ( r r ) (4.39) k - force constant of the bond r - internuclear distance r e internuclear distance at equilibrium Solutions of the Schrödinger equation for a harmonic oscillator: 1 Ev = v + hν (4.40) v vibration quantum number v = 0,1,,3... µ - efective mass, or reduced mass 1 k v = π µ mamb µ = m + m A B (4.41) (4.4)

16 4.6. Low vibrational states Vibration energy levels in the harmonic aproximation (in the regions close to the equilibrium) Low vibrational states V(R) 9 / hν 7 / hν v = 4 v = 3 E v = hν (v+1/) v = 0, 1,, 5 / hν 3 / hν v = 1 v = v = 0 > E v = hν zero point energy (4.43) 1 / hν r e v = 0 R Isotopic effect: substitution of an atom in a bond by different isotopes induces a change in vibrational frequency > change in vibrational energy, E v Heavier isotopes > decrease in vibrational frequency (see reduced mass formula 4.4)

17 Selection rules for IR transitions: IR- Selection rules During the vibration of the molecule the dipole momentum is oscillating, too, and if it changes, will interact with the electromagnetic radiation (IR domain). Change of dipole moment during the transition ( µ 0) v = ± E v = v + hν v + hν = (4.44) (4.45) hν At T = 93K, the most important vibration transition: v = 0 to v = 1 energy levels. Examples: CO group of a peptide link has k = 1. kn m -1. Thus it absorbes at = 1700cm -1 ~ ν HCl has k = kn m -1. Thus it absorbes at ~ ν = 990cm -1

18 IR transitions Clasification of molecules with respect of their IR spectra: 1. Homonuclear molecules are IR inactive (the stretching motion does not change the dipole momentum).. Heteronuclear molecules are IR active. Transitions frequencies: - bending modes are less stiff that the stretching modes: ν bend. < ν str. - high ν appear for large k (stiff bonds), and small reduced mass.

19 4.6.4 High vibrational states For high vibrational states (high v) the energy levels are not equally spaced > harmonic oscillator approximation is not appropriate! Anharmonic oscillator (the force is not proportional with the displacement) > potential energy is not a parabola! E v = v hν v + χehν (4.46) χ e - anharmonicity constant Transition energy: E ( v 1) χ ν = hν + h e (4.47) Wavenumber of the transition: ~ ν ~ ~ ν ( v + 1 v) = ν 0 ( v + 1) χe 0 (4.48) r e

20 High vibrational states The number of vibrational levels of an anharmonic ascillator is finite because the second term in 4.31 is negative and induces the convergence of the levels at high vibrational quantum numbers. > v max In the IR spectra appear overtones (additional weak absorption lines) with v =, 3,... E v - not equal for high vibrational states Explanation of the overtones: the selection rules are derived for harmonic oscillator, thus a slight anharmonicity will induce weak overtones (allow forbidden transitions, but with weak intensity).

21 3. The intramolecular potential 3..1 Internal and external degrees of of freedom of of a molecule Aim: determine the number of independent coordinates (=degrees of freedom, dof) to describe the motions of a molecule. Analyse the possible types of motion: 1. An atom can move in all three dimensions in 3D space -> 3 dof. A molecule consisting of N atoms can be regarded as a cluster of the constituent atoms -> 3N dof However, the motions of the atoms inside a molecule are not independent from one another: The molecule can move as a hole: Translation -> 3 dof The molecule can rotate as a whole: Rotation: linear molecule -> dof non-linear molecule -> 3 dof The remaining 3N-3-=3N-5 (linear mol.) or 3N-6 (non-linear mol.) dof account for the internal vibrations of the molecule.

22 4.6.5 Normal modes of vibration The description of the vibration motion of a polyatomic molecule is simpler if we consider combinations of the stretching and bending motions of individual bonds. > normal modes of vibration Definition: Normal mode of vibration represents an independent, synchronous motion of atoms or groups of atoms which may be excited without leading to the excitation of any other normal mode. Example 1: Normal modes for H O molecule: O O O ν ~ H H H H H H Symm. stretching bending Asymm. stretching Normal modes of vibration = combination of vibrational displacement of atoms

23 Normal modes of vibration - examples Example : Normal modes for CO molecule: ν ~ Each normal mode of vibration = an independent harmonic oscillator Number of normal modes of vibration = number of vibration modes of the molecule How many normal modes of vibration are in a protein of 6000 atoms?

24 4.6.6 Selection rules for normal modes Energy levels in the harmonic aproximation (similar as formula to 4.5 and 4.6): 1 Ev = v + hν 1 v = π k µ (4.49) (4.50) BUT: k = the extent to which bonds bend and stretch during the vibration µ = extent to which each atom contributes to the vibration Observation: atoms which do not move during the vibration, do not contribute to µ! Selection rules: - the motion of a normal mode of vibration should induce a change in the dipole momentul of the molecule ( µ 0) - v = ± 1

25 Active Normal modes: CO Example CO : Symmetric stretching mode inactive IR Antisymmetric stretching mode active IR Bending modes active IR

26 IR spectra have two regions: IR spectra - fingerprint region (some of the normal modes of vibration of organic molecules can be regarded as collective motions of the molecule as a whole, thus they are characteristic for that molecule) ν < 1500 cm -1 Confirm the presence of a molecule in a mixture (usually the bending normal modes belong to this region) -stretching normal modes with ν > ν fingerprint region Identify an unknown compound (Tables of stretching ν).

27 Stretching frequencies: examples

28 Example: thioacetic acid IR spectrum: example

29 peaks (with double maxima) : CO in gas phase - fundamental absorption - Transition v=0 > v=1, at 143 cm -1 ~4.56x10-0 J - first overtone - Transition v=0 > v=, at 460 cm -1 ~ 8.46x10-0 J Energy of the overton is double as that of the fundamental transition. Ist intensity is weaker as it is allowed due to the anharmonicity of the oscillator. In gas phase a vibration spectrum of a heteronuclear diatomic molecule can be analysed at high resolution > each line consists of a large number of closely spaced components. The structure of components for each vibrational line is due to the rotational transitions which accompagne each vibration transition.

30 4.6.8 Rotation structure of a vibration transition Energy levels of a diatomic molecule taking into acount the vibration and the rotation movements (in the harmonic approximation): 1 = v + hν + BJ J ( 1) Ev, J + (4.51) Selection rule: J = ±1, 0 Rotational structure of vibrational transition v > v+1 ~ ~ P branch( J = -1) ν =ν 0 BJ ~ ~ Q branch ( J = 0) ν = ν 0 ~ ν = ~ ν + B J R branch ( J = +1) ( 1) 0 + (4.5) (4.53) (4.54) P Q R

31 Rotation structure of a vibration transition Transition v > v+1 : P branch ( J = -1) Q branch ( J = 0) R branch ( J = +1)

32 4.7 Magnetic resonance Magnetic resonance: resonant absorption of radiation (microwave or radio) by molecules which contains magnetic spins (electronic or nuclear), when they are placed in a magnetic field. NMR (Nuclear Magnetic Resonance) describes the resonant absorption of radiofrequency radiation ( 500 MHz) by molecules which contain magnetic nuclei (I 0), when they are located in a static magnetic field. EPR (Electron Paramagnetic Resonance) or ESR (Electron Spin Resonance) are synonymous terms which describe the resonant absorption of microwave radiation (10 10 Hz) by paramagnetic ions or molecules when they are located in a static magnetic field.

33 4.7.1 EPR systems EPR spectra are obtained from paramagnetic transition ions in crystals, chemical complexes, biomolecules, defect centers in semiconductors and the samples can be: Single crystals Solutions Frozen solutions Powders In paramagnetic substances magnetic moments are weekly coupled they can be considered as isolated from oneanother. µ r i

34 4.7. Two energy levels system A two-level system is characteristic for a paramagnetic centre with an electron spin ½ (such as free radicals, conduction electrons in metals, F-centers trapped in alkali halides, transition metal ions, etc) When the paramagnetic system is placed in a static magnetic field (B), the energy of interaction between the paramagnetic ion and the magnetic field is: E r = µ B r (4.55) B µ r µ r - magnetic moment

35 Two energy levels system The relation between magnetic moment and the spin S associated to electron is: r µ = r gβ S (4.56) β - Bohr magneton g- electronic splitting factor The potential energy of the dipol in magnetic field is: V = gβ S r B r (4.57) E ± = gβ M s B (4.58) where: M s = ± 1 M S quantum number associated to the projection of the spin to Oz axis.

36 4.7.3 Resonance condition When the energy of the radiofrequency source (hν c ) is equal with the difference between the energy levels at a resonance value of magnetic field B 0, an absorption takes places. hν c = gβ B 0 (4.59) Resonance condition g gyromagnetic factor ν c microwave frequency For a free electron (g=.003) in a magnetic field B=330mT, the ν c =9.48 GHz (so called X-band frequency) B 0 ( mt ) = ν c ( GHz ) 1 g (4.60)

37 EPR for two energy levels system EPR line

38 4.7.4 Selection rules - EPR EPR spectra are based on magnetic dipolar transitions, while electronic spectra are based on electric-dipole transitions. Selection rule: the magnetic dipolar transitions take place when the magnetic quantum number M s (which has as values: S, S-1, -S) changes according to: M s = 1 In some cases the forbidden transitions can also be observed in the spectra.

39 4.7.5 Paramagnetic transition ions List of most used paramagnetic transition ions. Biologically important elements: V, Fe, Mn, Co, Cu, Mo and Ni.

40 4.7.6 EPR spectrometer Microwave source: klistron, of gun diode Detector: detector sensitive for phase detection Sample cavity: microwave resonant cavity Magnet system Sample types: - solid, single crystals - fluid (frozen solutions, or fluid solutions) - gas phase