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Overview and Context Nuclear Magnetic Resonance Summary

Biophysical Chemistry: NMR Spectroscopy

Nuclear Magnetism Lieven Buts

Vrije Universiteit Brussel

21st October 2011

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Context

Proteins (and

• ther biological

macromolecules) Function and dysfunction Functional characterisation (binding studies, enzymology, in vivo studies) Structural characterisation (information about larger complexes, high-resolution structures

• f the components)

X-ray crystallography (diffraction) High-resolution NMR (HNMR)

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Prerequisites and References

This part of the course assumes basic familiarity with the theory

• f 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, ISBN 0-19-855682-9 Spin Dynamics: Basics of Nuclear Magnetic Resonance (2nd edition), M.H. Levitt, Wiley, ISBN 978-0-470-51117-6 Understanding NMR Spectroscopy, J. Keeler, Wiley, ISBN 978-0-470-01786-9

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

The Electric Field

Coulomb’s law describes the force between two static charges q and q0:

• F =

1 4πǫ0 qq0 r2 1r and leads to the concept

• f the electric field

emanating from one charge and influencing the other:

• E =
• F

q0 = 1 4πǫ0 q r2 1r The deflection of an electron between two charged plates is a classical application of this idea:

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Magnetism

The magnetic field is introduced to describe interactions between moving charges:

• F = q ·

v × B

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Magnetic Dipoles (1)

A magnetic dipole produces a magnetic field with a characteristic pattern of field lines, and can be describe by the following equations: Bµ,x = µ0 4π µ r3 (3 sin(θ) cos(θ)) Bµ,y = 0 Bµ,z = µ0 4π µ r3 (3 cos2(θ) − 1)

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Magnetic Dipoles (2)

In certain positions the magnetic field vector has special properties: parallel with the dipole moment on the z axis antiparallel to the dipole moment on the x axis perpendicular to the dipole moment on a line making an angle θ = 54.7◦ (for which 3 cos2(θ) − 1 = 0) with the z axis.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Magnetic Dipoles (3)

The energy of a magnetic dipole in an external magnetic field is determined by their strengths and relative orientation: E = µ · B = | µ| · | B| · cos(θ)

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Induction and EM Waves

Electric currents give rise to magnetic fields, and changing magnetic fields induce currents in conductors. An alternating current produces electromagnetic waves, in which the electric and magnetic fields evolve in a coupled way, and both become functions of position and time:

• E =

E( r, t); B = B( r, t); B ⊥ E The most complete description of all EM phenomena is provided by the Maxwell equations.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

The Quantum Mechanical Atom

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

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Molecular Orbitals

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Nuclear Spin

Elementary particles, such as electrons, neutrons and protons, have been found to possess an intrinsic angular momentum, known as spin. Spin is a fundamental property

• f particles, just like their mass and charge, and cannot be

intepreted in terms of an actual physical rotation. The spin angular momentum is a vector quantity I with a magnitude of

• I(I + 1), where I is the spin quantum

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

2.

In atomic nuclei the spins of the component protons and neutrons partially or completely compensate each other, leaving the nucleus with a relatively small spin quantum number I of 0, 1

2, 1, 3 2, 2, ...

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Nuclear Magnetism

The intrinsic angular momentum I inevitably gives rise to a magnetic dipole moment µ:

• µ = γ

I in which the gyromagnetic ratio γ is a characteristic constant for each type of nucleus. Because the nuclei of different isotopes have different numbers of neutrons, they will have different spin quantum numbers and magnetogyric ratios. In NMR, isotopes are generally referred to as nuclides.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Biologically Relevant Nuclides

Nuclide I γ/107radT−1s−1 Abundance/%

1H 1 2

26.75 99.985

2H

1 4.11 0.015

12C

98.89

13C 1 2

6.73 1.108

14N

1 1.93 99.64

15N 1 2

• 2.71

0.36

16O

99.756

17O 5 2

• 3.63

0.037

18O

0.205

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Quantisation

The angular momentum, and therefore the dipole moment, are further quantised in a single direction, which is chosen to lie along the z axis by convention. The quantisation rule states that the z component of I can only adopt values of the form Iz = m . m is the magnetic quantum number, which can adopt values between −I and I, in integer steps: m = I, I − 1, I − 2, ..., −I + 1, −I =

h 2π, where h = 6.622 × 10−34J.s is the Planck constant.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

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 all magnetic substates have the same energy. In the presence of a strong external magnetic field ( B0 with magnitude B0), the direction of quantisation aligns with the field, and each substate acquires a different energy determined by its magnetic quantum number: E = mγB0 This gives rise to 2I energy differences, all equal to ∆E = γB0

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

The Simplest Case: I = 1/2

When I = 1

2 there are two possible energy levels with

m = +1

2 (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 mechanical superposition of the two stationary states. Its state is described by the general wave function Ψ, which is a linear combination of the wave functions of the stationary states: Ψ = cαα + cββ with cα, cβ ∈ C

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Interactions with EM Waves

A spin in an external field can absorb or emit electromagentic waves when two conditions are satisfied: the magnetic quantum numbers of the nuclear states before 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 ν

• r wavelength λ, must match the energy difference

betwdeen the two states: ∆E = hν = hc λ = γB0

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

Outline

1

Overview and Context Practical Matters Electromagnetism Refresher Organic Chemistry Refresher

2

Nuclear Magnetic Resonance Nuclear Spin and Magnetism Practical Implications

3

Summary

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

NMR in the EM Spectrum (1)

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Basic NMR Instrumentation

Nuclear magnetic resonance was first observed using relatively simple 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 T 400 H

1

C

13

100 B = 9.4 T B = 21.2 T 4 kHz 9 kHz

(Hz) 1022

1020 1018 1016 1014 1012 1010 108 106 NMR

(MHz)

63 H

2

40 N

15

376 F

19

P

31

162 900 226 140 51 847 365

(ppm)

10 9 8 7 6 5 4 3 2 1 Radio waves Gamma rays X rays Visible light Micro waves IR UV

Overview and Context Nuclear Magnetic Resonance Summary Nuclear Spin and Magnetism Practical Implications

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 of constant amplitude and frequency, while varying the intensity of the external magnetic field. The other is to generate a constant magnetic field, while varying the frequency of the RF source. Since in both cases the sample is continuously exposed to RF radiation, this approach is known as continuous wave NMR spectrosocpy. As we shall see, it is also possible to apply a short and powerful RF pulse to the sample, which simultaneously excites all nuclei in the sample, after which the different resonance frequencies can be deduced using a Fourier analysis. This pulse/FT approach has essentially completely displaced continuous wave methods because of its enormous practical advantages.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary

Summary (1)

Electrons and nuclei possess an intrinsic angular momentum I, which is subject to quantisation rules involving a spin quantum number I and a magnetic quantum number m. Some nuclei, including 12C, have a spin quantum number I = 0 and are magnetically inert. Many biologically important 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, but

will be ignored here. Any spin-1/2 behaves like a magnetic dipole with a magnetic moment µ = γ I, where γ is a characteristic gyromagnetic ratio.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary

Summary (2)

For a spin-1/2 (I = 1

2) the magnetic quantum number m can

adopt two different values (+1

2 and −1 2), corresponding to

two distinct energy states of the spin in an external magnetic field B0. A group of spins-1/2 can absorb electromagnetic radiation when the frequency ν of the photons matches the energy difference between the two magnetic states according to the relationship ∆E = hν = γB0

Lieven Buts Biophysical Chemistry: NMR Spectroscopy

Overview and Context Nuclear Magnetic Resonance Summary

Summary (3)

An NMR spectrometer has hardware capable of generating a strong magnetic field B0 as well as RF radiation of a defined frequency ν. It is capable of detecting resonance when the combination of these two parameters causes absorption of the RF energy by the nuclei in the sample. A complicated sample will contain nuclei of the same type experiencing different chemical environments, resulting in slightly different resonance frequencies and a spectrum with distinct lines.

Lieven Buts Biophysical Chemistry: NMR Spectroscopy