Molecular Biology Course 2012 Introduction to Spectroscopy · Infrared 2.5-100µm 3-120 THz...

Molecular Biology PhD Programme 2012

Molecular Biology Course 2012

Introduction to SpectroscopyTim Grüne

University of GöttingenDept. of Structural Chemistry

http://[email protected]

Tim Grüne Week 0: Spectroscopy 1/53

http://shelx.uni-ac.gwdg.de


Spectroscopy

Spectroscopic methods investigate properties of substances by how the substance modifies electromagneticradiation.

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



The Electromagnetic Spectrum

The term “electromagnetic radiation” is a generalisation of “light”. It is characterised by its wavelength:

800nm 400nm

Radio Micro Infrared X−raysVisible UV −raysγ

30cm10km 1mm 1nm 10pm

wavelength

123keV1.23keV3.09eV1.54eV0.00123eV4.12µV energy

Naturally we can only observe visible light. Some snakes can detect infrared, and bees observe UV light (butno red).

Yet, we still react to the whole spectrum, as you can see e.g. by the sun-burnt face.



Light as Waves

Classically, electromagnetic radiation is considered a wave.

The wave is described by its wavelength λ or frequency ν whichare connected by the speed of light c:

ν =c

λ=

2.99 · 108msλ

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.


/home/tg/workspace/lectures/molbio/2011/week0/movies/wave_movie.sh


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=

1.237 · 10−6eV m

λ

The energy is measured in eV, corresponding to 1.6 · 10−19 J.

(A light spot as accumulation of photons; http://www.lightandmatter.com/html books/6mr/ch03/ch03.html )


http://www.lightandmatter.com/html_books/6mr/ch03/ch03.html


Wave-Particle-Duality

• A photon has properties both like a particle and a wave. But that is rather impossible to understand orimagine.

• 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 thetwo without warning.



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 andmomentum between the two electrons. At an atomic/ molecular level this picture is often more helpful thanthe wave picture.

(Feynman diagram from wikipedia.org)



Units and Unit Conversion

Apart from SI-units (m, s, J ,. . . ) there are a couple of widely used units in spectroscopy.

Conversions

From unit To unit Conversion

Energy [eV] Wavelength [Å] λ = 12.37E/eV

Å

Wavelength [Å] Energy [eV] E = 12.37λ/Å

eV

Wavelength [Å] Wavelength [m] 1Å= 10−10mEnergy [eV] Energy [J] 1eV = 1.602 · 10−19 J

Units

h Planck constant 6.626 · 10−34 Js = 4.136 · 10−15 eVs~ “h bar” = h/2π 6.583 · 10−16 eVsc Speed of light 299792458m

sNA Avogadro’s number 6.022 · 1023/molk Boltzmann constant 1.381 · 10−23J/K = 8.617 · 10−5eV/K



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) oneuses prefixes to units.

p pico ×10−12 n nano ×10−9 µ micro ×10−6

m milli ×10−3 k kilo ×103 M mega ×106

G giga ×109 T tera ×1012 P peta ×1015

So1,000,000,000 Hz = 1× 109Hz = 1 GHz, and0.000,001 g = 1× 10−6 g = 1 µg.

Except for the “kilo”, lower case letters are small and upper case letters are large.



Spectrum and Spectroscopy

A wavelength (of visible light) correspondsto one colour. Colours can be added.Adding all visible colours together resultsin white light.





What could happen if one places a yellowfoil into the light path?





What could happen if one places a yellowfoil into the light path?

Not the yellow light is left over, but its com-plement (some greenish-blueish) is re-moved from the spectrum. The remainingfrequency add up to the colour yellow.

This was our first spectroscopic experiment. We found out that inside the foil something is happeningwhich requires the energy of the particular wavelength removed from the spectrum.



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.



Energy Range and Molecular Processes

Radiation λ ν Energy Process Method

Radio > 10cm < 3GHz < 10 µeV Nuclear Spin nuclear magnetic reso-nance (NMR)

Micro 1-10cm 3-30 GHz 0.01 - 0.1meV Electron Spin electron spin resonance(ESR)

mol. rotation IR-spectroscopyInfrared 2.5-100µm 3-120 THz 0.01-0.5eV mol. rotation IR-spectroscopy

mol. vibration IR-spectroscopyUV/Vis 200-700nm 0.4-1.5 PHz 1.7-6eV mol. vibration UV/Vis-spectroscopy

electronic stateX-rays < 10nm >30 PHz 120 eV transitions of inner

shell electronsX-ray fluorescence (XRF),X-ray photoelectron spec-troscopy (XPS)

source: Bergmann, Schaefer, “Lehrbuch der Experimentalphysik”, Vol. 4



Spectroscopy and Discrete Spectra



The “Real” World

Tourismusverband Sächs.Schweiz, Frank Richter ht

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de.w

ikip

edia

.org

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rrad

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iene

rP

rate

r

potential energy

m · g · h

kinetic energy12mv2

rotational Energy12Iω

2

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.


http://de.wikipedia.org/wiki/Fahrrad

http://de.wikipedia.org/wiki/Wiener_Prater


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• . . .



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 val-

ues.– ...



The “Shape” of Spectra

Photons can transfer their energy. Particles prefer those photons that match the change of energy they undergoby their transition to a new state.





Energy transfer can go in two directions. In the case of Sodium (Na) this is thecause for its typical 589nm spectral line.




In principle a particle could absorb the energy it requires from a high-energy photon and emit the extraneousenergy 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 amanifold of spectroscopic experiments.

http://www.chemie.uni-kl.de/forschung/oc/kubik


http://www.chemie.uni-kl.de/forschung/oc/kubik


Resonance

The technical term for “preference of the matching energy” is resonance. It also exists in the macro-world (“our”world).

http://en.wikipedia.org/wiki/Tacoma 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).


http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)


NMR & ESR

The two spectroscopic methods nuclear magnetic resonance and electron spin resonance both exploit the spinof particles.

electron, neutron, proton

• spin 12

• measured effect: ±12

nucleus (composition of neutrons and protons)

• spin 0, 12,1,112, . . .

• measured effect: ±0,±12,±1,±11

2, . . .



The Spin of Particles

In 1921, Otto Stern and Walther Gerlach carried out their famous experiment which led to the notion of the spinof elementary particles.

• Silver-atoms were run through a strong (inhomogeneous)magnetic field onto a detector.

• “Classically” the electrons orbit around the nucleus and cre-ate a small magnetic field. This would create one smear ofsilver atoms on the detector, depending on the arbitrary ori-entation of the electron orbits w.r.t. the magnetic field.

• Stern and Gerlach expected one single spot because of thequantisation of space. They observed two distinct spotson the detector which was explained by new property ofelementary particles which interacts with magnetic fields —the spin.

http://en.wikipedia.org/wiki/Stern-Gerlach experiment


http://en.wikipedia.org/wiki/Stern-Gerlach_experiment


Angular Momentum and Spin

The quantum mechanical description of the electron spin resembles that of the orbital angular momentum of anelectron 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 thesethree 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, 12,0,

12,1, . . .

• x- and y-components cannot be determined (somewhere on cir-cle)



Fine Structure, Hyperfine Structure, . . .

The more closely we look the more details we observe.

E.g. the 589nm spectral line of Na is actuallysplit into two lines 588.995 nm & 588.592 nm

589nm ✪✪✪✪

✦✦✦

588.592 nm, ms =12

588.995 nm, ms = −12

“good” “better” measurement

One line is due to ms = +12 and the other

one is due to ms = −12

An electron is charged and interacts with its own spin. This leads to a splitting of spectral lines as in the case ofthe 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 (andrequires even better techniques to be observed).



Quantum Mechanical Conventions

Physicists are very conservative about the letters they use (e.g. E for energy, v for speed, m for mass, . . . ). Theimportant quantum numbers in spectroscopy are:

• l or L: orbital angular momentum number(electron orbits/ shells, but also rotating molecules).- ml: z-component of l, also magnetic quantum number ; ml = −l,−l+1, . . .− 1,0,1, . . .+ l.• s or S: spin number; for electrons, neutrons, protons: s = 1

2

- ms: z-component of s; ms = ±12 for electrons, neutrons, protons.

• j or J total angular momentum (the composition of s and l, which affects the experiment)- mj: z-component of j; mj = −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 quantifi-

cation of these properties.

The energy of a system with (experimentally determined) moment of inertia I is EJ = J(J + 1)~2

2I , i.e. it isindependent 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-Gerlach-experiment and as in NMR and ESR.



Selection Rules

1. Conservation of energy, momentum, angular momentum: if we take all particles of an experiment intoaccount, 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 onlyincrease or decrease by one., and it changes its direction of travelvirb



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)



IR-Spectroscopy

The energy range for vibrations and rotations of (small) molecules is the range of IR-radiation (λ =800nm-1mm).

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Vib

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Rotation

Cl

H

ClH

ClH

ClH

The Cl-atom attracts the electron of the H-atom. The Cl-side is rathernegatively charged, the H-side rather positively: the molecule has adipole moment.

The two atoms can vibrate along their bond and they can rotate abouteach other.

The energy for both motions lies in the range of infrared radiation.

The presence of dipole moment is important to allow interaction withthe photon.



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 num-ber ν) of state.

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R-S

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P-branchR-branch

Q-branch

The graph shows the allowed transitions for a two-atommolecule like HCl.The rotational energy in IR-spectroscopy can change its quan-tum number J only by 1, because this changes the angularmomentum 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 bythe selection rules, therefore the Q-branch is missing.


http://de.wikipedia.org/wiki/IR-Spektroskopie


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



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 strengthof 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 largersteps between the energy levels.



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)



Circular Dichroism of Proteins: Secondary Structure

Depending on their secondary structure, proteins change the circular polarisation of light.

−6 × 104

−4 × 104

−2 × 104

0 × 100

2 × 104

4 × 104

6 × 104

8 × 104

190 200 210 220 230 240 250

Θ [°

cm2 /d

mol

]

wavelength [nm]

α−lysineβ−lysine

coiled lysine

CD-Spectra of 3 different conformations of poly-Lys:1. purely α-helical2. purely β-sheets3. purely coiled-coil

• 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.



Circular Dichroism of Proteins: Thermal Stability

Proteins are thermally unstable: loss of secondary structure with increased temperature.

−110

−100

−90

−80

−70

−60

−50

−40

−30

−20

20 25 30 35 40 45 50 55 60 65 70

slop

e [°

/K]

Temperature [°C]

slope (window = 4)data4+5 samples

“Meltung Curve” of a protein sample:Green Curve: Reduction of circular dichroism

with temperature measured at wavelengthλ = 208 nm

Red Curve: Slope of green curve. Peaks corre-spond to “melting events”.

⇒ Multiple domain protein, one domain thermallyless stable than the other



Nucleic Magnetic Resonance (NMR)



Nucleic Magnetic Resonance (NMR)

The nuclei of elements consist of neutrons (uncharged) and pro-tons (charge: 1e).Both are spin=1

2 particles.The total spin quantum number I of a nucleus is the composi-tion of the neutrons’ and protons’ spin (but not the sum).Element I Element I

12C 0 16O 0 invisible to NMR13C 1/2 31P 1/2 allow specific labelling19F 1/2 14N 1

By replacing only some e.g. 12C isotopes with 13C, one la-bels the structure and can selectively make certain parts of thestructure visible by NMR.



NMR Experiment

The spin quantum number I gives rise to mI = −I, (−I +1), . . .−1,0,1, . . . I different states. In the case ofI = 1/2,mI = ±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

EmI = −γ~BmI

γ: magnetogyric ratio. Its value depends on the nucleus type.

Sometimes one alternatively writes γ~ = gIµN , with the nuclear g-factorgI , and the nuclear magneton µN = 5.05 × 10−27J/T (T : Tesla, unit of

magnetic field).

The term γB has the unit 1/s like frequencies and is called the Larmorfrequency ω, i.e. EmI = −mI~ω.

B

En

erg

y

B

m I=+1

m I= 0

m I=−1

m I=+1

m I= 0

m I=−1

0



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 (Em↑) according to Boltzmann distribution

Nm↓

Nm↑

= e−(Em↓

−Em↑)/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.



NMR Measurement

In its simplest form, NMR uses two electromagnetic fields:

• One strong homogeneous field (measured in Tesla) in order to make the spin statesof the nucleus distinguishable.

• One (“probing”) field (measured in MHz) with energy in the range of the difference ofthe energy levels.

The “probing” field scans the region of the expected energy levels. When it matches a transition, resonanceoccurs, i.e. the photon of the correct energy is absorbed in order to make the nucleus change its state.

En

erg

y

B

m I=+1

m I= 0

m I=−1

0

B

m I=+1

m I= 0

m I=−1Eprobe



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 greateror smaller than B.

NMR experiments measure the difference between the probe and a reference sample. Usually the relative shiftwith respect to a standard chemical is determined.

δ =ν − ν0ν0

· 106ppm

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 compound1H (Si(CH3))4 = tetramethylsilane (TMS)13C (Si(13CH3))431P 85%H3(

31P )O4(aq)

The chemical shifts δ of the reference compounds are definedto be 0.

The shift δ is independent of the strength of the homogeneous field B but becomes easier to measure thestronger the field.



NMR: Typical Shifts

0ppm100p

pm

200p

pm

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Shifts of 13C depending onits chemical environment.

The chemical shift is in the range of only a fewppm for 1H and a few hundred ppm for 13C.

This means that for a typical energy differencecorresponding to a photon of 500 MHz, theNMR machine must detect the small differencebetween 500,000,000 Hz and 500,000,500 Hz.

It is like telling whether the weight of a jumbo jetis 500t or 500t and 500g!!!

Therefore, NMR machines are large and expen-sive. . .

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21.2T NMR machine.


http://en.wikipedia.org/wiki/Carbon-13_NMR

http://en.wikipedia.org/wiki/NMR_spectroscopy


Electron Spin Resonance



Electron Spin Resonance

There are several types of magnetism.

Diamagnetism is caused by the movement of the electrons: When electrons are exposed to an ex-terior magnetic field and move, their movement itself creates a magnetic field which is opposedto 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 ofan atom are filled with electrons (as e.g. in noble gases or CF4), all electrons are paired, andso 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 param-agnetic 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 aparamagnetic sample by the reaction of the electron spin to a magnetic field.



Magnetic Field splits Spin States

= g e µB B∆ E

s=+1/2m

0

Energ

y

ms=−1/2

B

Just as in the case of NMR, a homogeneous magnetic field splits the energylevels of the spin.Because electrons always have spin s = 1/2, there are always two energylevels E↑ and E↓.Their difference is E↑ − E↓ = geµBB.µB is called the Bohr-magneton.For a typical ESR spectrometer, B = 0.3T . This corresponds to an energydifference of 10 GHz, i.e. microwave radiation.

The factor geµB can be considered the response of the electron to the magnetic field B. It is about 600 timeslarger than the response gIµN of a nucleus. Therefore, ESR is susceptible to much weaker effects or longrange effects compared to NMR.

(Note: E↓ is the lower energy state for electrons while for nuclei it is E↑.)



ESR Experimental Setup

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Sample

B−field

Mic

ro−

wa

ve

s

Reference wave

Comparison

N

SSplitter

At an ESR experiment, the microwave fre-quency is kept constant and the B-field is var-ied.This way the microwaves can be compared witha reference beam and a resonance detected ata specific strength of B.

This is opposed to NMR, where the magnetic field is kept constant and the energy range at which a transitionoccurs is scanned.



The g-factor

Just as in NMR, the chemical environment of an electron alters the magnetic field the electron experienceslocally.

Because the difference B − Bloc is only small, we can approximate that the difference is proportional to theexternal field B:

B −Bloc = σB ⇒ Bloc = (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)ge 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 = gµBB.



The g-Tensor

In solid material, notably crystals with crystal defects, the effect of the magnetic field can depend on the orien-tation of the field w.r.t. the sample.

Mg2+ O2− Mg2+

O− Mg O2−

Mg2+ O2− Mg2+

⇑ B⊥

⇐ B‖

An MgO crystal with a defect (missing Mg2+ ion) can have anO− radical.The radical is shifted slightly away from the “hole”.The g-factor varies depending on whether the magnetic fieldapplied from the side (B‖ → g‖) or from the bottom (B⊥ →

g⊥).In a general description, the g-factor becomes a 3 × 3-matrixcalled the g-tensor.

ESR is sensitive enough to determine the nine entries of the g-tensor which gives even more information aboutthe chemical environment of the considered radical.



Hyperfine Structure

As in NMR, the magnetic field from the spin of the nucleus affects the spin of the surrounding electrons. If welook 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 numberof sub-levels for both ↑ and ↓ state of an electron.

m I= −1/2

m I= +1/2

m I= −1/2

m I= +1/2

h ν

Microwave

photon

0

En

erg

y B−field

Example of hyperfine structure with an I = 1/2 nu-cleus.The microwave energy is kept constant, so there aretwo values for the (varying) B-field at which transitionsare possible.When the B-field is too weak or the detector not sensi-tive enough, these two lines appear as one.



Use of ESR

The hyperfine structure can become very complicated with several nuclei. The resulting spectrum is like afingerprint 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 of10-100 nm).



Further Reading

• P. Atkins, Physical Chemistry, Oxford University Press (quantum mechanical theory, selection rules, tech-niques)


Molecular Biology Course 2012 Introduction to Spectroscopy · Infrared 2.5-100µm 3-120 THz...

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Transcript of Molecular Biology Course 2012 Introduction to Spectroscopy · Infrared 2.5-100µm 3-120 THz...