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Multinukleární NMR spektroskopie
C6800
 Jiří Pinkas, A12-224
 Materiály z přednášky v ISu
 Řešené úlohy ze spektroskopie nukleární
magnetické resonance
http://nmr.sci.muni.cz
 Úlohy – vyřešit a odevzdat
 Prezentace (na konci semestru) 10-15 min na
vybrané téma NMR
 Závěrečná písemná zkouška
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NMR – Historical Perspective
 1922 Electron spin is observed (Stern-Gerlach)
 1926 Nuclear spin - David Dennison (H2)
 1938 I. I. Rabi observes NMR
in a molecular beam of H2
 Isidor I. Rabi awarded Nobel prize in physics 1944
"for his resonance method for
recording the magnetic
properties of atomic nuclei"
(1898 – 1988)
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NMR – Historical Perspective
 1945 Purcell, Torrey, Pound @ Harvard solid paraffin
 1945 Bloch, Hansen, Packard @ Stanford liquid H2O
 Varian Bros. & Russell klystron for radars (WWII)
 1948 Pake, van Vleck solid state NMR
 1950 W. G. Proctor, F. C. Yu @ Stanford
 - chemical shift in 14NH4
14NO3
 1950 W. C. Dickinson @ MIT
 - chemical shift in 19F
 1952 Commercial NMR instruments used at DuPont, Shell, Humble Oil
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NMR – Historical Perspective
Edward M. Purcell (1912-1997) & Felix Bloch (1905-1983)
NP in physics 1952
"for their development of new methods for nuclear magnetic precision
measurements and discoveries in connection therewith"
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NMR – Historical Perspective
 1951 Proctor , Yu - the first observed J scalar coupling 121Sb-19F in NaSbF6
 1951 Gutowsky, McCall, Slichter @ U. of IL - J scalar coupling 31P-19F
 1952 Hahn, Maxwell @ Berkeley - J scalar coupling
 1955 Bloom, Shoolery spin decoupling
 1960 Shoolery integration
 1966 Ernst, Anderson FT NMR at Varian
 1968 Waugh @ MIT HR, multipulse NMR in solids
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NMR – Historical Perspective
 1971 Jeener - 2D NMR
 1971 Damadian - different NMR relaxation times of
tissues and tumors
 1972 CP, HP decoupling
 1972 The first routine 13C NMR spectrometer
(before mainly 1H, 19F, and 31P NMR)
 1973 Lauterbur - MRI
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MRI-Magnetic Resonance
Imaging
Paul C. Lauterbur
(1929-)
Sir Peter Mansfield
(1933-)
NP in physiology and medicine 2003
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NMR – Historical Perspective
 1974/1979 R. R. Ernst 2D COSY, NOESY
 1977 MAS
 1981 Bax, Freeman INADEQUATE
 1982 APT
 1983 Freeman BB decoupling, MLEV, WALTZ
 1990 3D and 1H/15N/13C Triple resonance
 1991 R. R. Ernst NP in chemistry
 2001 The first commercial 900 MHz instrument
 2002 K. Wüthrich NP in chemistry
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NMR – Historical Perspective
Richrad R. Ernst
(1933-)
NP in chemistry 1991
"for his contributions to the
development of the methodology
of high resolution nuclear
magnetic resonance (NMR)
spectroscopy"
Kurt Wüthrich
(1938-)
NP in chemistry 2002
"for his development of nuclear magnetic
resonance spectroscopy for determining the
three-dimensional structure of biological
macromolecules in solution"
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NMR – Historical Perspective
11
Nuclear Magnetic Resonance
 High resolution liquid state NMR
spectroscopy
 Solid state NMR spectroscopy
 High-pressure NMR
 NMR in the gas phase
 NMR spectroscopy in liquid crystalline
media
 Magnetic resonance imaging (MRI)
12
Hyperfine Interactions
• Interactions of nuclei with the electric and
magnetic fields
• Interactions between a nucleus and
electrons
• Transfer of chemical (electronic)
information from bonds and lone pairs to a
nucleus:
• Indirect
• Direct
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Hyperfine Interactions
Indirect
• Electric field gradient (EFG) with nuclear
electric quadrupole
• Induced magnetic field with nuclear
magnetic moments (shielding)
Direct
• s-electrons within nuclei, polarization of
bonding spins by nuclear spin (J-coupling)
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Direct Interactions
ONLY s-electrons can interact with nuclei
ONLY s-electrons have non-zero electron density at a nucleus
p, d - nodal planes
Which quantum number determines the number of angular nodes?
Which quantum number determines the number of radial nodes?
15
Relationship Between Wavelength,
Frequency and Energy
 Speed of light (c) is the same for all wavelengths
c = 2.9979 108 m s1
 Frequency (), the number of wavelengths per second, is
inversely proportional to wavelength:
 c
 Energy of a photon is directly proportional to frequency
and inversely proportional to wavelength:
E = h = hc/
h = Plank’s constant = 6.626176 1034 J s
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Electromagnetic Radiation
NMR
17
Method Energy Scale
18
Energy Scale Conversion Factors
Hz eV J mol1
Hz 1 4.136 1015 3.990 1010
eV 2.418 1014 1 9.649 104
J mol1 2.506 109 1.036 105 1
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Isotopes
Isotopes = a set of nuclides of an element, same Z, different A
there is about 2600 nuclides (stabile and radioactive)
340 nuclides found in nature
270 stabile and 70 radioactive
Monoisotopic elements:
9Be, 19F, 23Na, 27Al, 31P, 59Co, 127I, 197Au
Polyisotopic elements:
1H, 2H (D), 3H (T)
10B, 11B
Sn has the highest number of stabile isotopes – 10
112, 114, 115, 116, 117, 118, 119, 120, 122, 124Sn
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Natural Abundance, %
AHg I NA%
196 0 0.146
198 0 10.02
199 1/2 16.84
200 0 23.13
201 3/2 13.22
202 0 29.80
204 0 6.850
Mass number, A
Isotopic Compositions of the Elements
I = Nuclear Spin
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Natural Abundance, %
1H 99.985
2H 0.015
12C 98.89
13C 1.11
14N 99.63
15N 0.37
16O 99.759
17O 0.037
18O 0.204
32S 95.00
33S 0.76
34S 4.22
36S 0.014
Isotopic Compositions of the Elements
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Variability in Isotopic Compositions
Isotope Range Average
10B 18.927 - 20.337 19.9 (7)
11B 81.073 - 79.663 80.1 (7)
16O 99.7384 - 99.7756 99.757 (16)
17O 0.0399 - 0.0367 0.038 (1)
18O 0.2217 - 0.1877 0.205 (14)
Natural Abundance, %
23
Nuclear Spin
electron spin s = ½
proton and neutron I = ½
nuclear spin I = z ½ z = integer 0, 1, 2, 3, .....
Number of protons, Z Number of neutrons, N I
even even 0
odd odd integer
even odd
multiples of ½odd even
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Nuclear Spin
protons and neutrons are Fermions, obey Pauli exclusion principle
12C 13C
n np p
I = ½I = 0
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Nuclear Spin
 even – even: I = 0 4He, 12C, 16O, 20Ne,
24Mg, 28Si, 32S, 36Ar, 40Ca
 odd – odd: I = integer
ONLY 2H, 6Li, 10B, 14N, 40K, 50V, 138La, 176Lu
 even – odd and odd – even:
I = multiples of ½
13C ½, 17O 5/2, 33S 3/2
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Nuclear Spin
Number of protons
Z
Number of neutrons
N
Number of nuclides
even even 168
odd odd 8
odd even 50
even odd 57
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Nuclear Spin
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Nuclear Spin
 NO stable nucleus has spin 2
 the highest value of spin for a stable nucleus
is 7 176Lu
 unstable nuclei
highest integral spin 16 - isomer 178Hf
highest half-integer 37/2 - isomer 177Hf)
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Nuclear Spin
• Nuclei with spin ½ - a spherical charge distribution
• Nuclei with I > ½ - nonspherical charge distributions
(prolate or oblate)
• Nuclei with a non-zero spin → magnetic moment ()
• Nonspherical nuclei → electric quadrupole moment (eQ)
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Nuclear Spin
Rotating positive charge generates magnetic field
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Nuclear Spin
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Nuclear Spin
Nuclear spin = Spin angular momentum, P (vector)
(moment hybnosti)
Spin quantum number I
Magnetic quantum number mI
Magnitude of P is quantized:
Direction with respect to the magnetic
field B0 is quantized:
P
µ
 1
2
 II
h
P

Iz m
h
P
2

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Spin Angular Momentum, P
59Co, I = 7/2
mI
I = Nuclear spin quantum number
I = 0, ½, 1, 3/2, 5/2, 3, 7/2,.....
mI = Nuclear spin magnetic quantum
number
Multiplicity, M 2I + 1 values
mI = I, I  1, I  2, ..., I + 2, I + 1, I
1/2
3/2
5/2
-3/2
7/2
-1/2
-5/2
-7/2
B0 1
2
 II
h
P
 Iz m
h
P
2

 1
cos


II
m
P
P Iz

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Spin Angular Momentum, P
I [I (I + 1)]½
½ 0.866
1 1.414
3/2 1.936
5/2 2.958
3 3.464
7/2 3.969
4 4.472
9/2 4.975
 1
2
 II
h
P

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Spin Magnetic Moment, µ
The electrons, nucleons (protons, neutrons) and some
nuclei possess intrinsic magnetism, which is not due to a
circulating current.
Permanent magnetic moment similarly as spin angular
momentum.
Magnetic moment, µ, is directly proportional to the spin
angular momentum, P :
µ = γ P
γ is the gyromagnetic (magnetogyric) ratio
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Magnetogyric Ratio
γ - the magnetogyric ratio is the ratio of the
nuclear magnetic moment µ to the nuclear
angular momentum P.
µ = γ P
γ - Important characteristic of nuclei !!!
[rad T1 s1]
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Spin Magnetic Moment, µ
µ = γ P = γ ħ [I (I + 1)]½
µz = γ Pz = γ ħ mI
Nucleus 1H 2H 13C 15N 19F 29Si 31P
γ [10-7 rad T-1s-1] 26.75 4.11 6.73  2.71 25.18 5.32 10.84
electron
γe = 17 609  107
= 658 γ(H)
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Nuclear Spin in Magnetic Field
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Nuclear Spin in Magnetic Field
E =  absorbed light
Applied
Magnetic
Field
Hext
E =  absorbed light
Applied
Magnetic
Field
Hext
Random orientation
No Field Magnetic Field
Zeeman plitting to 2I + 1 levels
Alignment of spins
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Nuclear Spin in Magnetic Field
magnetic dipole
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Nuclear Spin in Magnetic Field
• An angular momentum is associated with each
rotating object
• A nuclear spin possesses a
magnetic moment µ arising from
the angular momentum of the
nucleus
• The magnetic moment µ is a
vector perpendicular to the
current loop
• In a magnetic field (B) the magnetic moment
behaves as a magnetic dipole
 = i A
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Nuclear Spin in Magnetic Field
In B0, a magnetic moment µ
is directed at some angle w.r.t.
B0 direction
the B0 field will exert a torque
on the magnetic moment.
This causes µ to precess about
the magnetic field direction
Torque is the rate of change
of the nuclear spin angular
momentum
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Nuclear Spin in Magnetic Field
Spin precession in the external magnetic field.
Quantum description of precession shows that the
frequency of the motion is:
ω0 =  γ B0 [rad s1] or ν0 =  γ B0/ 2π [Hz]
It is called the Larmor frequency (if γ > 0 then ν0 < 0)
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Larmor Frequency
ω0 =  γ B0 [rad s-1]
ν0 =  γ B0/ 2π [Hz]



2
0
0
B

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Larmor Frequency
Sir Joseph Larmor
(1857-1942)
ω0 =  γ B0 [rad s1] or ν0 =  γ B0/ 2π [Hz]
Ensemble of spins
Resonance Frequencies of Nuclei
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Resonance Frequencies of Nuclei
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Nucleus Magnetogyric
Ratio
11.74 T 7.05 T
1H 26.75 950 MHz 700 MHz 500 MHz 300 MHz
11B
13C 6.73
19F 25.18
27Al
29Si - 5.32
31P 10.84
103Rh
Nuclei are charged and
if they have spin, they
are magnetic
No Field
Applied
Magnetic
Field = B0
Energy of transition =
energy of radiowaves
Higher energy state: magnetic
field opposes applied field
Lower energy state: magnetic
field aligned with applied field
Nuclear Zeeman Effect - Splitting
mI ½
mI +½
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Nuclear Spin in Magnetic Field
Emag =  µ  B0 (a scalar product of 2 vectors)
Emag =  µz B =  γ Pz B
Emag =  mI ħ γ B
The magnetic energy depends on the interaction between the
magnetic moment and B0 field:
NMR selection rule ∆mI = ± 1
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Spin in Magnetic Field
∆ Emag = Em=-1/2  Em=1/2 = ∆mI ħ γ B = h ν  ν = γ B/2π
I = ½
E m = 1/2
E m = 1/2
The frequency of the electromagnetic radiation that
corresponds to the energy difference between the two
energy levels is equal to the precessional frequency of
the nuclei.
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Spin in Magnetic Field
 =  2.7116 107
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Amplitude
Frequency (Hz)
Excitation of NMR Spin
E


E

Irradiate with
Frequency so as
to satisfy Planck's
Law
E=h
Energy
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Energy Levels for I = ½
Protons
∆E = (6.626 1034 J s 26.75 107 rad T-1s-1 11.743 T)/2π = 3.313 1025 J
very small energy difference
∆ Emag = Em=-1/2  Em=1/2 = ∆mI ħ γ B = h γ B/2π
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Energy Levels for I = ½




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Energy Levels for I = ½
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Boltzmann Distribution
The excess of nuclei on the lower energy level is given by
Boltzmann distribution:
N↑↓/N↑↑ = exp(∆E/kBT) = exp(ħ γ B /kBT)
= exp(3.313 10-25/ 4.101 10-21) = exp(8.078 10-5) =
0.99991922
If N↑↑ = 1 000 000 then N↑↓ = 999919
Only 81 out of 2 million 1H nuclei contribute to NMR signal at 500 MHz!
ħ = 1.055 10-34 J s
γH = 26.75 107 rad T-1s-1
B = 11.7433 T (500 MHz)
kB = 1.3807 10-23 J K-1
T = 297 K











 



Tk
B
Tk
E
N
N
BB

expexp
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Boltzmann Distribution
N↑↓/N↑↑ = exp(∆E/kBT) = exp(ħ γ B /kBT)
the stronger the field and
the higher the
magnetogyric ratio, the
larger the population
difference
the higher the
temperature, the smaller
the population difference
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Boltzmann Distribution
The higher the field B,
the larger the energy difference,
the larger the population difference,
the larger the net magnetization,
and the bigger the NMR signal
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Nuclear Magnetic Resonance
(NMR)
 Nuclear – spin ½ nuclei (e.g. protons) behave as
tiny bar magnets.
 Magnetic – a strong magnetic field causes a small
energy difference between + ½
and – ½ spin states.
 Resonance – photons of radio waves can match the
exact energy difference between the + ½ and – ½
spin states resulting in absorption of photons as
the protons change spin states.
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Magnetization
More nuclei point in parallel to the
static magnetic field.
The macroscopic magnetic
moment, M0
M0 = Σ μi
In-Field
Bloch equations: the nuclear magnetization M = (Mx, My, Mz)
as a function of time and relaxation timesT1 and T2
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Longitudinal Magnetization
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Spin-Lattice Relaxation Time
R1 = 1/T1 [Hz] longitudinal relaxation rate constant
T1 [s] longitudinal relaxation time
spin-lattice relaxation time
enthalpy
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Transverse Magnetisation
Spin coherence
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Spin-Spin Relaxation Time
R2 = 1/T2 [Hz] transverse relaxation rate constant
T2 [s] transverse relaxation time constant
spin-spin relaxation time
entropy
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One RF Pulse
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Relaxation
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Free Induction Decay FID
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