Biophysical Chemistry: NMR Spectroscopy - Vrije …more.vub.ac.be/LievenButs/slides/NMR_en_1.pdfOverview and Context Nuclear Magnetic Resonance Summary Biophysical Chemistry: NMR Spectroscopy

Overview and ContextNuclear Magnetic Resonance

Summary

Biophysical Chemistry: NMR SpectroscopyNuclear Magnetism

Lieven Buts

Vrije Universiteit Brussel

21st October 2011

Lieven Buts Biophysical Chemistry: NMR Spectroscopy


Summary

Outline

1 Overview and ContextPractical MattersElectromagnetism RefresherOrganic Chemistry Refresher

2 Nuclear Magnetic ResonanceNuclear Spin and MagnetismPractical Implications

3 Summary



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Practical MattersElectromagnetism RefresherOrganic Chemistry Refresher

Outline



3 Summary



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Context

Proteins (andother biological

macromolecules)

Function anddysfunction

Functional characterisation(binding studies,

enzymology,in vivo studies)

Structural characterisation(information aboutlarger complexes,

high-resolution structuresof the components)

X-ray crystallography(diffraction)

High-resolution NMR(HNMR)



Summary


Prerequisites and References

This part of the course assumes basic familiarity with the theoryof electromagnetism and organic chemistry.The following books are used as reference material:

Nuclear Magnetic Resonance (Oxford Chemistry Primers#32), P.J. Hore, Oxford Science Publications, ISBN0-19-855682-9Spin Dynamics: Basics of Nuclear Magnetic Resonance(2nd edition), M.H. Levitt, Wiley, ISBN 978-0-470-51117-6Understanding NMR Spectroscopy, J. Keeler, Wiley, ISBN978-0-470-01786-9



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The Electric Field

Coulomb’s law describesthe force between twostatic charges q and q0:

~F =1

4πε0

qq0

r2~1r

and leads to the conceptof the electric fieldemanating from onecharge and influencingthe other:

~E =~Fq0

=1

4πε0

qr2~1r

The deflection of an electronbetween two charged plates is aclassical application of this idea:



Summary


Magnetism

The magnetic field isintroduced to describeinteractions betweenmoving charges:

~F = q ·~v× ~B



Summary


Magnetic Dipoles (1)

A magnetic dipoleproduces a magnetic fieldwith a characteristicpattern of field lines, andcan be describe by thefollowing equations:

Bµ,x =µ0

4πµ

r3 (3 sin(θ) cos(θ))

Bµ,y = 0

Bµ,z =µ0

4πµ

r3 (3 cos2(θ)− 1)



Summary


Magnetic Dipoles (2)In certain positions themagnetic field vector hasspecial properties:

parallel with thedipole moment on thez axisantiparallel to thedipole moment on thex axisperpendicular to thedipole moment on aline making an angleθ = 54.7◦ (for which3 cos2(θ)− 1 = 0) withthe z axis.



Summary


Magnetic Dipoles (3)

The energy of a magneticdipole in an externalmagnetic field is determinedby their strengths andrelative orientation:

E = ~µ · ~B = |~µ| · |~B| · cos(θ)



Summary


Induction and EM Waves

Electric currents give rise to magnetic fields, and changingmagnetic fields induce currents in conductors. An alternatingcurrent produces electromagnetic waves, in which the electricand magnetic fields evolve in a coupled way, and both becomefunctions of position and time:

~E = ~E(~r, t);~B = ~B(~r, t);~B ⊥ ~E

The most complete description of all EM phenomena isprovided by the Maxwell equations.



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The Quantum Mechanical Atom

The classical "solar system" model with particles following awell-defined trajectory is replaced by a probabilistic descriptionwith an inherent uncertainty principle.


Molecular Orbitals


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Nuclear Spin and MagnetismPractical Implications

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Nuclear Spin

Elementary particles, such as electrons, neutrons andprotons, have been found to possess an intrinsic angularmomentum, known as spin. Spin is a fundamental propertyof particles, just like their mass and charge, and cannot beintepreted in terms of an actual physical rotation.The spin angular momentum is a vector quantity~I with amagnitude of

√I(I + 1)~, where I is the spin quantum

number of the particle. For electrons, neutrons andprotons, I = 1

2 .In atomic nuclei the spins of the component protons andneutrons partially or completely compensate each other,leaving the nucleus with a relatively small spin quantumnumber I of 0, 1

2 , 1, 32 , 2, ...



Summary


Nuclear Magnetism

The intrinsic angular momentum~I inevitably gives rise to amagnetic dipole moment ~µ:

~µ = γ~I

in which the gyromagnetic ratio γ is a characteristicconstant for each type of nucleus.Because the nuclei of different isotopes have differentnumbers of neutrons, they will have different spin quantumnumbers and magnetogyric ratios. In NMR, isotopes aregenerally referred to as nuclides.



Summary


Biologically Relevant Nuclides

Nuclide I γ/107radT−1s−1 Abundance/%1H 1

2 26.75 99.9852H 1 4.11 0.01512C 0 0 98.8913C 1

2 6.73 1.10814N 1 1.93 99.6415N 1

2 -2.71 0.3616O 0 0 99.75617O 5

2 -3.63 0.03718O 0 0 0.205



Summary


Quantisation

The angular momentum, and therefore the dipole moment,are further quantised in a single direction, which is chosento lie along the z axis by convention. The quantisation rulestates that the z component of~I can only adopt values ofthe form Iz = m~ .m is the magnetic quantum number, which can adoptvalues between −I and I, in integer steps:

m = I, I − 1, I − 2, ...,−I + 1,−I

~ = h2π , where h = 6.622× 10−34J.s is the Planck constant.



Summary


Effect of an External Magnetic Field

In the absence of any significant external magnetic field,the direction of quantisation (the z axis) is arbitrary, and allmagnetic substates have the same energy.In the presence of a strong external magnetic field (~B0 withmagnitude B0), the direction of quantisation aligns with thefield, and each substate acquires a different energydetermined by its magnetic quantum number:

E = m~γB0

This gives rise to 2I energy differences, all equal to∆E = ~γB0



Summary


The Simplest Case: I = 1/2

When I = 12 there are two possible energy levels with

m = +12 (generally denoted α) and with m = −1

2 (β).α and β are two special, stationary states of a spin-1/2.In general, a spin-1/2 exists as a quantum mechanicalsuperposition of the two stationary states. Its state isdescribed by the general wave function Ψ, which is a linearcombination of the wave functions of the stationary states:

Ψ = cαα+ cββ

with

cα, cβ ∈ C



Summary


Interactions with EM Waves

A spin in an external field can absorb or emit electromagenticwaves when two conditions are satisfied:

the magnetic quantum numbers of the nuclear statesbefore and after the interaction can differ by only one unit(this is the selection rule):

∆m = ±1

the energy of the photons, determined by their frequency νor wavelength λ, must match the energy differencebetwdeen the two states:

∆E = hν =hcλ

= ~γB0



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NMR in the EM Spectrum (1)


Basic NMR InstrumentationNuclear magnetic resonance was first observed using relativelysimple experimental setups:

The first experiments were done on simple pure compounds,such as water and ethanol (shown here):

NMR in the EM Spectrum (2)

B = 9.4 T

B = 21.2 T0

0

400

H1 C13

100

B = 9.4 T

B = 21.2 T0

0

4 kHz

9 kHz

� (Hz) 1022

1020

1018

1016

1014

1012

1010

108

106

NMR

� (MHz)

63

H2

40

N15

376

F19 P31

162

900 226 140 51847 365

� (ppm) 010 9 8 7 6 5 4 3 2 1

Radiowaves

Gammarays X rays

Visiblelight

MicrowavesIRUV


Summary


Continuous Wave versus Puls/FT

There are two obvious ways of recording an NMR spectrum.One possibility is to irradiate the sample with an RF source ofconstant amplitude and frequency, while varying the intensity ofthe external magnetic field. The other is to generate a constantmagnetic field, while varying the frequency of the RF source.Since in both cases the sample is continuously exposed to RFradiation, this approach is known as continuous wave NMRspectrosocpy.As we shall see, it is also possible to apply a short and powerfulRF pulse to the sample, which simultaneously excites all nucleiin the sample, after which the different resonance frequenciescan be deduced using a Fourier analysis. This pulse/FTapproach has essentially completely displaced continuouswave methods because of its enormous practical advantages.



Summary

Summary (1)

Electrons and nuclei possess an intrinsic angularmomentum~I, which is subject to quantisation rulesinvolving a spin quantum number I and a magneticquantum number m.Some nuclei, including 12C, have a spin quantum numberI = 0 and are magnetically inert. Many biologicallyimportant nuclides, including 1H, 13C and 15N, have I = 1

2 .Unpaired electrons are also in this category of "spins-1/2".Other nuclei with I > 1

2 can also be studied by NMR, butwill be ignored here.Any spin-1/2 behaves like a magnetic dipole with amagnetic moment ~µ = γ~I, where γ is a characteristicgyromagnetic ratio.



Summary

Summary (2)

For a spin-1/2 (I = 12 ) the magnetic quantum number m can

adopt two different values (+ 12 and −1

2 ), corresponding totwo distinct energy states of the spin in an externalmagnetic field B0.A group of spins-1/2 can absorb electromagnetic radiationwhen the frequency ν of the photons matches the energydifference between the two magnetic states according tothe relationship

∆E = hν = ~γB0



Summary

Summary (3)

An NMR spectrometer has hardware capable of generatinga strong magnetic field B0 as well as RF radiation of adefined frequency ν. It is capable of detecting resonancewhen the combination of these two parameters causesabsorption of the RF energy by the nuclei in the sample.A complicated sample will contain nuclei of the same typeexperiencing different chemical environments, resulting inslightly different resonance frequencies and a spectrumwith distinct lines.


Documents

Biophysical Chemistry: NMR Spectroscopy - Vrije …more.vub.ac.be/LievenButs/slides/NMR_en_1.pdfOverview and Context Nuclear Magnetic Resonance Summary Biophysical Chemistry: NMR Spectroscopy