Download Biophysical Chemistry: NMR Spectroscopy

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
Functional characterisation
(binding studies,
enzymology,
in vivo studies)
Proteins (and
other biological
macromolecules)
Function and
dysfunction
Structural characterisation
(information about
larger complexes,
high-resolution structures
of the components)
High-resolution NMR
(HNMR)
X-ray crystallography
(diffraction)
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
of 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 qq0 ~
1r
4π0 r2
The deflection of an electron
between two charged plates is a
classical application of this idea:
and leads to the concept
of the electric field
emanating from one
charge and influencing
the other:
~
~E = F = 1 q ~1r
q0
4π0 r2
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 =
Bµ,z
µ0 µ
(3 sin(θ) cos(θ))
4π r3
Bµ,y = 0
µ0 µ
=
(3 cos2 (θ) − 1)
4π r3
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
of particles, just like their mass and charge, and cannot be
intepreted in terms of an actual physical rotation.
~
The spin angular
p 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 = 12 .
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, 21 , 1, 32 , 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
1H
2H
12 C
13 C
14 N
15 N
16 O
17 O
18 O
I
1
2
1
0
1
2
1
1
2
0
5
2
0
γ/107 radT −1 s−1
26.75
4.11
0
6.73
1.93
-2.71
0
-3.63
0
Lieven Buts
Abundance/%
99.985
0.015
98.89
1.108
99.64
0.36
99.756
0.037
0.205
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 × 10−34 J.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 = m~γB0
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 = 12 there are two possible energy levels with
m = + 12 (generally denoted α) and with m = − 21 (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 = cα α + cβ β
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
or wavelength λ, must match the energy difference
betwdeen the two states:
∆E = hν =
Lieven Buts
hc
= ~γB0
λ
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)
Gamma
rays
� (Hz) 1022
Visible
UV light IR
X rays
20
18
10
10
16
10
14
Micro
waves
12
10
Radio
waves
10
10
8
10
10
NMR
1
19
31
13
B0 = 9.4 T
400
376
162
100
63 40
B0 = 21.2 T
900
847
365
226
140 51
9
8
H
F
P
2
10
C
H
15
6
N
� (MHz)
� (ppm)
10
7
6
5
B0 = 9.4 T
4 kHz
B0 = 21.2 T
9 kHz
4
3
2
1
0
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 12 C, have a spin quantum number
I = 0 and are magnetically inert. Many biologically
important nuclides, including 1 H, 13 C and 15 N, have I = 12 .
Unpaired electrons are also in this category of "spins-1/2".
Other nuclei with I > 12 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 = 21 ) the magnetic quantum number m can
adopt two different values (+ 21 and − 12 ), 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