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Principles of NMR spectroscopy

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Title: Principles of NMR spectroscopy


1
Principles of NMR spectroscopy
Dieter Freude, Institut für Experimentelle Physik
I der Universität Leipzig Skiseminar in the
Dortmunder Hütte in Kühtai, Sunday 30 March
2008, 730?830 p.m.
2
NMR is far from nuclear spectroscopy
3
NMR is near to Nobel Prizes
Physics 1952 Chemistry 1991 2002 Medicine
2003                  Felix Bloch and Edward
Purcell Richard R. Ernst Kurt Wüthrich Paul
Lauterbur and Peter Mansfield Stanford Harvard
University ETHZ ETHZ Urbana Nottingham USA USA Sw
itzerland Switzerland USA England
4
Some of the 130 NMR isotopes
WEB of Science 35 of NMR studies focus to the
nuclei 1H, 25 to 13C, 8 to 31P, 8 to 15N, 4
to 29Si,and 2 to 19F. In these nuclei, we have a
nuclear spin I  ½. If we look at nuclei with a
quadruple moment and half-integer spin I gt ½, we
find 27Al in 3 of all the NMR papers and 1 for
each of the nuclei 11B, 7Li, 23Na and 51V. For
even numbered spin, only the I  1-nuclei are
frequently encountered 2H in 4 and 14N and 6Li
in 0.5 of all NMR papers.
5
Chemical shift of the NMR

We fragment hypothetically a water molecule into
hydrogen cation plus hydroxyl anion. Now the 1H
in the cation has no electron shell, but the 1H
in the hydroxyl anion is shielded (against the
external magnetic field) by the electron shell.
Two signals with a distance of about 35 ppm
appear in the (hypothetical) 1H NMR spectrum.
6
Chemical shift and J-coupling

The figure shows at left the free induction decay
(FID) as a function of time and at right the
Fourier transformed 1H NMR spectrum of alcohol in
fully deuterated water. The individual spikes
above are expanded by a factor of 10. The singlet
comes from the OH groups, which exchange with the
hydrogen nuclei of the solvent and therefore show
no splitting. The quartet is caused by the CH2
groups, and the triplet corresponds to the CH3
group of the ethanol. The splitting is caused by
J-coupling between 1H nuclei of neighborhood
groups via electrons.
An NMR spectrum is not shown as a function of the
frequency n (g / 2p) ? B0(1-s), but rather on
a ppm-scale of the chemical shift d 106 ? (nref
-n) /nL, where the reference sample is
tetramethylsilane (TMS) for 1H, 2H, 13C, and 29Si
NMR.
7
Chemical shift range of some nuclei

Ranges of the chemical shifts of a few nuclei and
the reference substances, relative to which
shifts are related.
8
NMR spectrometer
Bruker's home page
H. Pfeifer Pendulum feedback receiver Diplomarbe
it, Universität Leipzig, 1952
AVANCE 750 wide-bore in Leipzig
9
NMR spectrometer for liquids
10
Structure determination by NMR
H
C
Structure
NMR-Spektrum
1H-NMR
13C-NMR
HH-COSY
HC-COSY HETCOR
NOESY
R. Meusinger, A. M. Chippendale, S. A. Fairhurst,
in Ullmanns Encyclopedia of Industrial
Chemistry, 6th ed., Wiley-VCH, 2001
11
How works NMR a nuclear spin I 1/2 in an
magnetic field B0
Many atomic nuclei have a spin, characterized by
the nuclear spin quantum number I. The absolute
value of the spin angular momentum is
The component in the direction of an applied
field is   Lz  Iz ? ? m ? ? ½ ? for I 1/2.
Atomic nuclei carry an electric charge. In
nuclei with a spin, the rotation creates a
circular current which produces a magnetic moment
µ. An external homogenous magnetic field B
results in a torque T  µ ? B  with a related
energy of  E  - µB.
The gyromagnetic (actually magnetogyric) ratio g
is defined by µ  g L. The z component of the
nuclear magnetic moment is µz   g Lz   g Iz ?
 ?  g m ?. The energy for I 1/2 is split into
2 Zeeman levels Em  - µz B0  - g m?B0 ?g
?B0/2 ?wL ?/2.
Pieter Zeeman observed in 1896 the splitting of
optical spectral lines in the field of an
electromagnet.
12
Larmor frequency
Classical model the torque T acting on a
magnetic dipole is defined as the time
derivative of the angular momentum L. We get
By setting this equal to T  µ ? B , we see that
The summation of all nuclear dipoles in the unit
volume gives us the magnetization. For a
magnetization that has not aligned itself
parallel to the external magnetic field, it is
necessary to solve the following equation of
motion
We define B  (0, 0, B0) and choose
M(t  0)  M (sina, 0, cosa). Then we obtain
Mx  M sina coswLt, My  M sina
sinwLt, Mz  M cosa with wL    -gB0. The
rotation vector is thus opposed to B0 for
positive values of g. The Larmor frequency is
most commonly given as an equation of magnitudes
wL   gB0 or
Joseph Larmor described in 1897 the precession of
electron orbital magnetization in an external
magnetic field.
13
Macroscopic magnetization
hnL  kT applies at least for temperatures above
1 K and Larmor frequencies below 1 GHz. Thus,
spontaneous transitions can be neglected, and the
probabilities P for absorption and induced
emission are equal. It follows P  B½,-½ wL
B-½,½ wL, where B refers to the Einstein
coefficients for induced
transitions and wL is the spectral radiation
density at the Larmor frequency. A measurable
absorption (or emission) only occurs if there is
a difference in the two occupation numbers N. In
thermal equilibrium, the Boltzmann distribution
applies to N and we have
If nL  500 MHz and T  300 K, hnL/kT ? 8 ? 10-5
is very small, and the exponential function can
be expanded to the linear term
14
Longitudinal relaxation time T1
All degrees of freedom of the system except for
the spin (e.g. nuclear oscillations, rotations,
translations, external fields) are called the
lattice. Setting thermal equilibrium with this
lattice can be done only through induced
emission. The fluctuating fields in the material
always have a finite frequency component at the
Larmor frequency (though possibly extremely
small), so that energy from the spin system can
be passed to the lattice. The time development
of the setting of equilibrium can be described
after either switching on the external field B0
at time t  0 (difficult to do in practice) with
T1 is the longitudinal or spin-lattice relaxation
time an n0 denotes the difference in the
occupation numbers in the thermal equilibrium.
Longitudinal relaxation time because the
magnetization orients itself parallel to the
external magnetic field. T1 depends upon the
transition probability P as 
1/T1   2P  2B-½,½ wL.
15
T1 determination by IR
The inversion recovery (IR) by p-p/2
16
Line width and T2
A pure exponential decay of the free induction
(or of the envelope of the echo, see next page)
corresponds to G(t) exp(-t/T2).
The Fourier-transform gives fLorentz const. ? 1
/ (1 x2) with x (w - w0)T2, see red line.
The "full width at half maximum" (fwhm) in
frequency units is
Note that no second moment exists for a Lorentian
line shape. Thus, an exact Lorentian line shape
should not be observed in physics.
Gaussian line shape has the relaxation function
G(t) exp(-t2 M2 / 2) and a line form fGaussian
exp (-w2/2M2), blue dotted line above, where M2
denotes the second moment. A relaxation time can
be defined by T22 2 / M2. Then we get
17
Correlation time tc, relaxation times T1 and T2
The relaxation times T1 and T2 as a function of
the reciprocal absolute temperature 1/T for a
two spin system with one correlation time. Their
temperature dependency can be described by
tc  t0 exp(Ea/kT). It thus holds that T1  T2 ?
1/tc when wLtc 1 and T1 ? wL2 tc when wLtc
1. T1 has a minimum of at wLtc ? 0,612 or nLtc ?
0,1.
18
Rotating coordinate system and the offset
For the case of a static external magnetic field
B0 pointing in z-direction and the application of
a rf field Bx(t) 2Brf cos(wt) in x-direction we
have for the Hamilitonian operator of the
external interactions in the laboratory sytem
(LAB) H0
Hrf hwLIz 2hwrf cos(wt)Ix, where wL 2pnL
-g B0 denotes the Larmor frequency, and the
nutation frequency wrf is defined as wrf -g Brf.
The transformation from the laboratory frame to
the frame rotating with w gives, by neglecting
the part that oscillates with the twice radio
frequency,
H0 i Hrf i h Dw Iz hwrf Ix, where Dw
wL - w denotes the resonance offset and the
subscript i stays for the interaction
representation.
Magnetization phases develop in this interaction
representation in the rotating coordinate system
like b wrf t
or a Dw t. Quadratur detection yields
value and sign of a.
19
Bloch equation and stationary solutions
We define Beff  (Brf, 0, B0-w /g) and introduce
the Bloch equation
Stationary solutions to the Bloch equations are
attained for dM/dt  0
20
Hahn echo
p/2 pulse FID, p
pulse around the dephasing around the
rephasing echo y-axis
x-magnetization x-axis x-magnetization
a(r,t)  Dw(r)t
a(r,t)  - a(r,t) Dw(r)(t - t)
21
T2 and T2
22
EXSY, NOESY, stimulated spin echo
23
NMR diffusometry (PFG NMR)
Pulsed field gradient NMR diffusion measurements
base on NMR pulse sequences that generate a spin
echo, like the Hahn echo (two pulses) and the
stimulated spine echo (three pulses). At right,
the 13-intervall sequence for alternating
gradients consisting of 7 rf pulses, 4 gradient
pulses of duration ?, intensity g, and diffusion
time ? and 2 eddy current quench pulses is
described.
The self-diffusion coefficient D of molecules in
bulk phases, in confined geometries and in
biologic materials is obtained from the amplitude
S of the free induction decay in dependence on
the field gradient intensity g by the equation
Application of MAS technique in addition to PFG
(pulsed field gradient) improves drastically the
spectral resolution, allowing the study of
multi-component diffusion in soft matter or
confined geometry.
24
The difference between solid-state and liquid
NMR, the lineshape of water
solid water (ice)

Dn / kHz

-10
10
20
30
40
0

-30
-20
-40
liquid water
Dn / Hz

-0.1
0.1
0.2
0.3
0.4
0

-0.3
-0.2
-0.4
25
High-resolution solid-state MAS NMR
Fast rotation (1-60 kHz) of the sample about an
axis oriented at 54.7 (magic-angle) with respect
to the static magnetic field removes all
broadening effects with an angular dependency of
rotor with sample in the rf coil
zr
B0
?rot
?
That means chemical shift anisotropy, dipolar
interactions, first-order quadrupole
interactions, and inhomogeneities of the magnetic
susceptibility. It results an enhancement in
spectral resolution by line narrowing also for
soft matter studies.
gradient coils for MAS PFG NMR
26
Laser supported high-temperature MAS NMR for
time-resolved in situ studies of reaction
steps in heterogeneous catalysis the NMR batch
reactor
27
Some applications of solid-state NMR spectroscopy
Dieter Freude, Institut für Experimentelle Physik
I der Universität Leipzig Skiseminar in the
Dortmunder Hütte in Kühtai, 31 March 2008,
730?830 p.m.
28
NMR on the top
WEB of Science refers for the year 2006 to about
16 000 NMR studies, mostly on liquids, but
including also 2500 references to solid-state
NMR. Near to 12 000 studies concern magnetic
resonance imaging (MRI). The next frequently
applied technique, infrared spectroscopy, comes
with about 9 000 references in the WEB of
Science.
29
Solid-state NMR on porous materials
  • 1H MAS NMR spectra including TRAPDOR
  • 29Si MAS NMR
  • 27Al 3QMAS NMR
  • 27Al MAS NMR
  • 1H MAS NMR in the range from 160 K to 790 K

1H MAS NMR on molecules adsorbed in porous
materials
  • Hydrogen exchange in bezene loaded H-zeolites
  • In situ monitoring of catalytic conversion of
    molecules in zeolites by 1H, 2H and 13C MAS NMR
  • MAS PFG NMR studies of the self-diffusion of
    acetone-alkane mixtures in nanoporous silica gel

30
1H MAS NMR spectra, TRAPDOR
31
1H MAS NMR spectra, TRAPDOR
Without and with dipolar dephasing by
27Al high power irradiation and difference
spectra are shown from the top to the bottom. The
spectra show signals of SiOH groups at framework
defects, SiOHAl bridging hydroxyl groups, AlOH
group.
2.2 ppm
4.2 ppm
2.9 ppm
2.9 ppm
1.7 ppm


2.2 ppm
H-ZSM-5 activated at 550 C
H-ZSM-5 activated at 900 C
4.2 ppm
1.7 ppm
without dephasing
with dephasing
4.2 ppm
2.9 ppm
2.9 ppm
4.2 ppm
difference spectra
?4

?2
2
4
6
8
10
?2
0
4
6
8
10
?4
2
0







? / ppm
? / ppm
32
1H MAS NMR of porous materials
33
29Si MAS NMR spectrum of silicalite-1
SiO2 framework consisting of 24 crystallographic
different silicon sites per unit cell (Fyfe 1987).
34
29Si MAS NMR
35
Determination of the Si/Al ratio by 29Si MAS NMR
For Si/Al  1 the Q4 coordination represents a
SiO4 tetrahedron that is surrounded by four
AlO4-tetrahedra, whereas for a very high Si/Al
ratio the SiO4 tetrahedron is surrounded mainly
by SiO4-tetrahedra. For zeolites of faujasite
type the Si/Al-ratio goes from one (low silica X
type) to very high values for the siliceous
faujasite. Referred to the siliceous faujasite,
the replacement of a silicon atom by an aluminum
atom in the next coordination sphere causes an
additional chemical shift of about 5 ppm,
compared with the change from Si(0Al) with n 0
to Si(4Al) with n 4 in the previous figure.
This gives the opportunity to determine the Si/Al
ratio of the framework of crystalline
aluminosilicate materials directly from the
relative intensities In (in ) of the (up to
five) 29Si MAS NMR signals by means of the
equation
Take-away message from this page Framework Si/Al
ratio can be determined by 29SiMAS NMR. The
problem is that the signals for n 0-4 are
commonly not well-resolved and a signal of SiOH
(Q3) at about -103 ppm is often superimposed to
the signal for n 1.
36
29Si MAS NMR shift and Si-O-Si bond angle a
Considering the Q4 coordination alone, we find a
spread of 37 ppm for zeolites in the previous
figure. The isotropic chemical shift of the
29Si NMR signal depends in addition on the four
Si-O bonding lengths and/or on the four Si-O-Si
angles ai, which occur between neighboring
tetrahedra. Correlations between the chemical
shift and the arithmetical mean of the four
bonding angles ai are best described in terms of
The parameter r describes the s-character of the
oxygen bond, which is considered to be an s-p
hybrid orbital. For sp3-, sp2- and
sp-hybridization with their respective bonding
angles a  arccos(-1/3) ? 109.47, a  120,
a  180, the values r  1/4, 1/3 and 1/2 are
obtained, respectively. The most exact NMR data
were published by Fyfe et al. for an
aluminum-free zeolite ZSM-5. The spectrum of the
low temperature phase consisting of signals due
to the 24 averaged Si-O-Si angles between 147.0
and 158.8 (29Si NMR linewidths of 5 kHz) yielded
the equation for the chemical shift
Take away message from this page Si-O-Si bond
angle variations by a distortion of the
short-range-order in a crystalline material
broaden the 29Si MAS NMR signal of the material.
37
27Al MAS NMR
38
27Al MAS NMR shift and Al-O-T bond angle
Aluminum signals of porous inorganic materials
were found in the range -20 ppm to 120 ppm
referring to Al(H2O)63. The influence of the
second coordination sphere can be demonstrated
for tetrahedrally coordinated aluminum atoms In
hydrated samples the isotropic chemical shift of
the 27Al resonance occurs at 75-80 ppm for
aluminum sodalite (four aluminum atoms in the
second coordination sphere), at 60 ppm for
faujasite (four silicon atoms in the second
coordination sphere) and at 40 ppm for AlPO4-5
(four phosphorous atoms in the second
coordination sphere). In addition, the isotropic
chemical shift of the AlO4 tetrahedra is a
function of the mean of the four Al-O-T angles a
(T Al, Si, P). Their correlation is usually
given as d /ppm  -c1   c2. c1 was
found to be 0.61 for the Al-O-P angles in AlPO4
by Müller et al. and 0.50 for the Si-O-Al angles
in crystalline aluminosilicates by Lippmaa et al.
Weller et al. determined c1-values of 0.22 for
Al-O-Al angles in pure aluminate-sodalites and of
0.72 for Si-O-Al angles in sodalites with a Si/Al
ratio of one. Aluminum has a nuclear spin I
5/2, and the central transition is broadened by
second-order quadrupolar interaction. This
broadening is (expressed in ppm) reciprocal to
the square of the external magnetic field. Line
narrowing can in principle be achieved by double
rotation or multiple-quantum procedures.
39
27Al 3QMAS NMR study of AlPO4-14
AlPO4-14, 27Al 3QMAS spectrum (split-t1-whole-echo
, DFS pulse) measured at 17.6 T with a rotation
frequency of 30 kHz. The parameters dCS, iso
1.3 ppm, Cqcc 2.57 MHz, h 0.7 for aluminum
nuclei at position 1, dCS, iso 42.9 ppm, Cqcc
1.74 MHz, h 0.63, for aluminum nuclei at
position 2, dCS, iso 43.5 ppm, Cqcc 4.08 MHz,
h 0.82, for aluminum nuclei at position 3,
dCS, iso 27.1 ppm, Cqcc 5.58 MHz, h 0.97,
for aluminum nuclei at position 5, dCS, iso
-1.3 ppm, Cqcc 2.57 MHz, h 0.7 were taken
from Fernandez et al.
40
27Al MAS NMR spectra of a hydrothermally treated
zeolite ZSM-5

Take-away message A signal narrowing by MQMAS
or DOR is not possible, if the line broadening is
dominated by distributions of the chemical shifts
which are caused by short-range-order distortions
of the zeolite framework.
41
Mobility of the Brønsted sites and hydrogen
exchange in zeolites
one-site jumps around one aluminum atom
multiple-site jumps along several aluminum atoms
Proton mobility of bridging hydroxyl groups in
zeolites H-Y and H-ZSM-5 can be monitored in the
temperature range from 160 to 790 K. The full
width at half maximum of the 1H MAS NMR spectrum
narrows by a factor of 24 for zeolite H-ZSM-5
and a factor of 55 for zeolite 85 H-Y. Activation
energies in the range 20-80 kJ mol-1 have been
determined.
42
Narrowing onset and correlation time
40 C
120C
17 kHz
dn  dnrigid/2
3,2 kHz
dn  dnrigid/2
2H MAS NMR, deuterated zeolite H-ZSM-5, loaded
with 0.33 NH3 per crossing
1H MAS NMR, zeolite H-Y, loaded with mit 0.6  NH3
per cavity
The correlation time corresponds to the mean
residence time of an ammonium ion at an oxygen
ring of the framework.
The correlation time corresponds to the mean
residence time of an ammonium ion at an oxygen
ring of the framework.
2H NMR, H-Y at50 C tc5 µs 1H NMR, H-Y at 40
C tc20 µs 2H NMR, H-ZSM-5 at 120 C tc3,8 µs
43
1D 1H EXSY (exchange spectroscopy)
  • EXSY pulse sequence

Evolution time t1  1/4 Dn . Dn denotes the
frequency difference of the exchanging species.
MAS frequency should be a multiple of Dn
Two series of measurements should be performed at
each temperature Offset Dn right of the right
signal and offset Dn left of the left signal.
44
Result of the EXSY experiment
  • Stack plot of the spectra of zeolite H-Y loaded
    with 0.35 ammonia molecules per cavity. Mixing
    times are between tm  3 ms and15 s.

Intensities of the signals of ammonium ions and
OH groups for zeolite H-Y loaded with 1.5 ammonia
molecules per cavity. Measured at 87 C in the
field of 9,4 T. The figure on the top and bottom
correspond to offset on the left hand side and
right hand side of the signals, respectively.
45
Basis of the data processing
diagonal peaks

cross peaks

dynamic matrix (without spin diffusion)
46
Laser supported 1H MAS NMR of H-zeolites
  • Spectra (at left) and Arrhenius plot (above) of
    the temperature dependent 1H MAS NMR measurements
    which were obtained by laser heating. The zeolite
    sample H-Y was activated at 400 C.

47
Proton transfer between Brønsted sites and
benzene molecules in zeolites H-Y
  • In situ 1H MAS NMR spectroscopy of the proton
    transfer between bridging hydroxyl groups and
    benzene molecules yields temperature dependent
    exchange rates over more than five orders of
    magnitude.

H-D exchange and NOESY MAS NMR experiments were
performed by both conventional and laser heating
up to 600 K.
48
Exchange rate as a dynamic measure of Brønsted
acidity
Arrhenius plot of the H-D and H-H exchange rates
for benzene molecules in the zeolites 85 H-Y and
92 H-Y. The values which are marked by blue or
red were measured by laser heating or
conventional heating, respectively.
The variation of the Si/Al ratio in the zeolite
H-Y causes a change of the deprotonation energy
and can explain the differences of the exchange
rate of one order of magnitude in the temperature
region of 350?600 K. However, our experimental
results are not sufficient to exclude that a
variation of the pre-exponential factor caused by
steric effects like the existence of
non-framework aluminum species is the origin of
the different rates of the proton transfer.
49
In situ monitoring of catalytic conversion of
molecules in zeolites by 1H, 2H and 13C MAS NMR
13C CP/MAS NMR spectra of 2-13C-n-but-1-ene
adsorption on H-FER in dependence on reaction
time. Asterisks denote spinning side-bands. The
appearance of the signals at 13 and 17 ppm and
decreasing intensity of the signal at 126 ppm
show the label scrambling.
2H MAS NMR spectra of n-but-1-ene-d8 adsorbed on
H-FER (T 333K). n-But-1-ene undergoes readily
a double-bond-shift reaction, when it is adsorbed
on ferrierite. The reaction becomes slow enough
to observe the kinetics , if the catalyst
contains only a very small concentration of
Brønsted acid sites.
1H MAS NMR spectra of n-but-1-ene-d8 adsorbed on
H-FER2 (T360K). Hydrogen transfer occurs from
the acidic hydroxyl groups of the zeolite to the
deuterated butene molecules. Both methyl and
methene groups of but-2-ene are involved in the
H/D exchange. The ratio between the intensities
of the CH3 and CH groups in the final spectrum is
31.
Kinetics of a double-bond-shift reaction,
hydrogen exchange and 13C-label scrambling of
n-butene in H-ferrierite
50
MAS PFG NMR for NMR diffusometry
51
MAS PFG NMR studies of the self-diffusion of
acetone-alkane mixtures in nanoporous silica gel
The self-diffusion coefficients of mixtures of
acetone with several alkanes were studied by
means of magic-angle spinning pulsed field
gradient nuclear magnetic resonance (MAS PFG
NMR). Silica gels with different nanopore sizes
at ca. 4 and 10 nm and a pore surface modified
with trimethylsilyl groups were provided by
Takahashi et al. (1). The silica gel was loaded
with acetone alkane mixtures (110). The
self-diffusion coefficients of acetone in the
small pores (4 nm) shows a zigzag effect
depending on odd or even numbers of carbon atoms
of the alkane solvent as it was reported by
Takahashi et al. (1) for the transport diffusion
coefficient.
(1) Ryoji Takahashi, Satoshi Sato, Toshiaki
Sodesawa and Toshiyuki Ikeda Diffusion
coefficient of ketones in liquid media within
mesoporesPhys. Chem. Chem. Phys.5 (2003)
24762480
52
Stack plot of the 1H MAS PFG NMR spectra at 10
kHz of the 110 acetone and octane mixture
absorbed in Em material as function of increasing
pulsed gradient strength for a diffusion time D
600 ms
Semi-logarithmic plot of the decay of the CH3
signal of ketone in binary mixture with acetone
at 298 K. The diffusion time is D 600 ms and a
gradient pulse length is d 2 ms
Diffusion coefficient of acetone in mixture
within Em in dependence of the number of carbons
in the alkane solvent. The measurements were
carried out with diffusion time D 600 ms, D
800 ms and D 1200 ms and the gradient pulse
length d 2 ms.
53
Horst Ernst Moisés Fernández Clemens
Gottert Johanna Kanellopoulos Bernd Knorr Thomas
Loeser Toralf Mildner Lutz Moschkowitz Dagmar
Prager Denis Schneider Alexander
Stepanov Deutsche Forschungsgemeinschaft Max-Buch
ner-Stiftung
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