Solid-state NMR Training Course
Making a measurement
EPSRC UK National Solid-state NMR Service at Durham
Routine set up of a CPMAS measurement
Assumptions:
Spin-½ nuclei
A standard sample (with known behaviour) is available
CaHPO4·2H2O
The spectrometer is operating correctly and is in a state such
that only fine tuning (checking/calibration) is required
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle
Method 1 – 79Br, maximising the rotary echoes/sidebands from KBr
Advantages:
79Br resonance is close to 13C
(@9.4 T 100.25 MHz vs. 100.56 for 13C)
No decoupling required
Shimming not critical
Good after repair or maintenance when
angle badly set
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle
Method 1 – maximising the rotary echoes/sidebands from KBr
FID
(Free Induction Decay)
Acquire
rotary echo (separation = rotor period)

Adjust
time / ms
centreband on resonance
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle
Method 1 – maximising the rotary echoes/sidebands from KBr


Acquire – adjust – acquire …….
EPSRC UK National Solid-state NMR Service at Durham
time / ms
The magic-angle
(Acquire)n – adjust – (acquire)n …..
gives more precision
n = 64 @ 0.2 s, 45o pulse @ 4 kHz (maybe
a problem)
Good for most samples …
… unless they contain highly
anisotropic environments
(>C=O, C-D, >M-)
EPSRC UK National Solid-state NMR Service at Durham
1
2
EPSRC UK National Solid-state NMR Service at Durham
Excitation methods
Direct excitation:
Pulse on X, observe on X
Cross polarisation:
EPSRC UK National Solid-state NMR Service at Durham
optional
Cross polarisation
Usually 1H to nX
1H
Transfer of magnetisation (polarisation)
nX
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
Almost all measurements are
…. pulse(s) – acquire – wait – pulse(s) – acquire – wait …..
DE
RD
RD depends on T1X
EPSRC UK National Solid-state NMR Service at Durham
RD
recycle delay
recycle
pulse delay
d1
Spin-lattice relaxation
T1 : Spin-lattice relaxation time constant
M z ( t ) = M 0 é1 - exp( - t / T1 ) ù
ë
û
Equilibrium magnetisation at
time t after excitation
(which will contribute to the
signal after the next excitation)
T1 : ultimately depends on molecular motion and is different
(in principle) for each nuclide and each type of environment
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
DE
RD
RD depends on T1X
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
DE
Repetition rate depends on T1X
CP
Repetition rate depends on T1H
X
H
T1 ? T1
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
T1H : a single, molecule-wide average is measured 1.7 s
T1C : different for each carbon. Average value
(excluding CH3) 190 s. T1C (CH3) is approximately 1 s.
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
Another advantage for CP over DE:
For efficient (100%) magnetisation transfer there is a signal
enhancement of
H
g
g
X
g : magnetogyric ratio (physical constant for every nuclide)
nuclide
g / 107 radT-1s-1
enhancement
time saving
factor
1H
26.752
-
-
31P
10.839
2.5
6.25
13C
6.728
4.0
16
29Si
-5.319
5.0
25
15N
-2.713
9.9
98
EPSRC UK National Solid-state NMR Service at Durham
Cross polarisation vs. direct excitation
CP: 448 repetitions, 3 s recycle
22 minutes
×2
DE: 448 repetitions, 3 s recycle
22 minutes
DE: 448 repetitions, 120 s recycle
15 hours
EPSRC UK National Solid-state NMR Service at Durham
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
Even complicated pulse sequences are built up from pulses with well
defined tip angle (30°, 45°, 90°, 180° ….)
low power element
high power element
modulated
decoupling
180°
90°
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
Terminology and relationships
n1 = gB1/2p = 1/(4t90)
(Bulk magnetisation,
rotating frame)
Vpp = 2√(2P × 50) or Vpp = 20√P
Vpp : volts (peak-to-peak), P: power
P(dB) = 10 × log10(P1/P2)
for dBm P2 = 1 mW
nRF
is the frequency at which it
is applied (MHz)
n1
is the nutation rate produced
by the pulse (kHz)
90o pulse
n1
B1 (13C)
3 ms
83.3 kHz
7.8 mT
400 W
50 dBm
53 dBm
400 V
100 W
200 W
56 dBm
200 V
283 V
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration (H-channel)
1. Set amplitude
2. Vary duration
2. Observe signal amplitude
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
Build up a nutation “curve”
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
Nutation “curve”
absolute value
t90 = (19-9.6)/2 = 4.7 ms
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
The sample is not excited uniformly through the
rotor (coil) – rf inhomogeneity
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
Nutation “curve”
t90 = (19-9.6)/2 = 4.7 ms
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration
It is important for the system to fully relax between successive
increments of the pulse duration. The nutation curve should
approximate to a damped sine wave.
EPSRC UK National Solid-state NMR Service at Durham
Pulse angles, RF field calibration (X-channel)
X relaxation can be slow (much slower than 1H), so calibrating X by direct
excitation can take time …. but there is a short cut
EPSRC UK National Solid-state NMR Service at Durham
Shimming
For solid-state NMR, once a good set of shims have been obtained for a
probe they do not need much adjustment.
[In practice, load the shims appropriate to the probe before starting any
calibration.]
EPSRC UK National Solid-state NMR Service at Durham
Shimming
Z1
Z2
Z3
Z4
X
Y
ZX
ZY
XY
X2-Y2
Z2 X
Z2 Y
ZXY
.
.
EPSRC UK National Solid-state NMR Service at Durham
Referencing
“Spectral referencing is with respect to an external
sample of neat tetramethylsilane (carried out by
setting the high-frequency signal from adamantane
to 38.5 ppm).”
EPSRC UK National Solid-state NMR Service at Durham
Referencing
Nuclide
Reference
(chemical shift /
ppm)
Nuclide
Reference
(chemical shift /
ppm)
1H
Adamantane (1.9)
7Li
LiCl (0)
13C
Adamantane (38.5,
CH2)
11B
BF3/O(CH2CH3)2 (0)
17O
H2O (0)
15N
Glycine (176.5, COO )
NH415NO3 (–5.1, NO3)
Glycine (–346.8)
19F
C6F6 ( –164.9)
23Na
NaCl (0)
29Si
tetrakis(trimethylsilyl)
silane (–9.8,–135.4)
27Al
Al(NO3)3 (0)
31P
CaHPO4.2H2O (1.0)
45Sc
Sc(NO3)3 (0)
77Se
(NH4)2SeO4 (1040)
51V
b-NaVO3 (–519)
(solid)
119Sn
Sn(C6H12) (–97.4)
59Co
K3Co(CN)6 (0)
199Hg
[Hg(dmso)6][O3SCF3]2
(–2313)
EPSRC UK National Solid-state NMR Service at Durham
ñ
1
Interaction between
nuclear quadrupole moment
and an
electric field gradient
2
EPSRC UK National Solid-state NMR Service at Durham
Quadrupolar nuclei
2 I + 1 energy levels
EPSRC UK National Solid-state NMR Service at Durham
Quadrupolar nuclei
The quadrupole coupling (χ or Cq) may be large
(relative to the Zeeman interaction) and this
complicates the response of the system to an RF
pulse.
To further complicate things, different
environments may have significantly different χ
values and therefore behave differently with
respect to a pulse.
EPSRC UK National Solid-state NMR Service at Durham
Quadrupolar nuclei
Response expected for
a spin-½ nuclide
Response obtained for a
quadrupolar nuclide
Calibrate on a solution (except for relaxation, unaffected by
quadrupole coupling )
EPSRC UK National Solid-state NMR Service at Durham
Quadrupolar nuclei
If:
EQ ?
ER F
æ
1ö
ç
n 1 = çI + ÷
g B1 / 2 p
÷
÷
çè
÷
2ø
For 27Al (spin-5/2) a 30o pulse (as calibrated on a solution)
would give maximum signal (central transition only fully
affected)
EQ = ER F
Response will behave like a spin-½ system
Intermediate – complex response.
Use a small angle (short pulse) [1 ms < 25o]
EPSRC UK National Solid-state NMR Service at Durham
EPSRC UK National Solid-state NMR Service at Durham
Matching
1H
nX
Hartmann-Hahn match condition:
H
X
g H B1 = g X B1
or
H
X
n1 = n1
or
EPSRC UK National Solid-state NMR Service at Durham
t
H
90
= t
X
90
H
Matching
X
B1
=
g H B1
so for X = C
gX
In practice do this first – it has
more impact on signal than minor
mis-set of 1H 90o duration.
t
X
H
Set B1 vary B1
For adamantane the match is very
dependent on spin-rate.
EPSRC UK National Solid-state NMR Service at Durham
H
90
= t
X
90
C
H
B1 : 4 B1
Matching
At low spin-rate a ramp
about “0” position is
adequate
EPSRC UK National Solid-state NMR Service at Durham
Matching
Hexamethylbenzene (HMB) is more tolerant of spin rate (up to about 10 kHz)
Typically the ramp is:
H
B1 ± 10 %
EPSRC UK National Solid-state NMR Service at Durham
Matching
At high spin-rate the match profile
can break up into a “sideband”
pattern
The
H
X
n1 = n1
match condition no longer
holds and is modified to:
H
X
n1 = n1 + n n r
The upshot is that the
centre of the ramp needs to
be repositioned.
Revary
H
n1
EPSRC UK National Solid-state NMR Service at Durham
Matching
EPSRC UK National Solid-state NMR Service at Durham
System (signal-to-noise ratio) test
Using HMB with well-defined acquisition parameters:
EPSRC UK National Solid-state NMR Service at Durham
Starting from scratch (David’s method)
For systems in an unknown state, probes after repair, installation of new
equipment.
Start with low RF powers and work upwards.
Can be useful to observe output with an oscilloscope or power meter to
understand how the instrument power control maps onto real output.
For example, we have two power controls:
(a) Goes from -16 to 63 (nominally dB)
(b) Goes from 0 to 4095 (linear)
So, 63(4000) is approximately full power (say 1 kW)
60(4000) = ½ power, 60(2000) = ¼ power …… 48(2000) = approximately 2%
of full power – should be very safe.
[Test this with an oscilloscope/power meter. Note high powers may need
to be attenuated to protect the measuring equipment.]
EPSRC UK National Solid-state NMR Service at Durham
Starting from scratch
(1) Using adamantane:
Observe 1H. Calibrate 90o pulse. Work upwards towards specification (e.g. 2.5
ms – see your manual). Line will be very broad (with sidebands).
(2) Observe 13C (directly) with decoupling (now you know a safe 1H setting).
Calibrate 90o pulse – as above. Recycle 5 s @ 9.4 T.
Broaden lines to mask poor line shape.
(3) Using KBr:
Set angle (use 13C power settings).
(4) Using HMB (or admantane):
Fine tune the match (remember
t
H
90
= t
X
90
).
(5) Using adamantane:
Shim and reference.
(6) Using HMB:
Test S/N (note for future reference).
EPSRC UK National Solid-state NMR Service at Durham
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle (2)
The resonance from any species in an anisotropic environment is potentially
sensitive to the angle of the spinning axis, e.g. the nitrate signal from ammonium
nitrate.
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle (2)
NH415NO3 (98%) @ 40.53 MHz.
CP: 1 repetition [30 s], contact 8 ms,
spin rate 5 kHz, 6 mm rotor,
acquisition time 100 ms.


Shims, cross polarisation,
decoupling required
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle (3)
Deuterium (spin-1) spectra can be extremely sensitive to the angle.
EPSRC UK National Solid-state NMR Service at Durham
The magic-angle (3)
Alanine-2-d (98%) @ 46.02 MHz
CP: 16 repetitions, 2 s recycle delay,
contact 1 ms, spin rate 8 kHz, 4 mm
rotor


EPSRC UK National Solid-state NMR Service at Durham
The magic-angle
Recap:
o For most measurements setting the angle with KBr is sufficient.
o Be wary of odd line shapes for resonances from highly anisotropic
species.
o For some experiments the angle must be set with very high precision,
e.g. 2H, STMAS (satellite transition MAS) for quadrupolar nuclei.
If a suitable set up compound cannot be found it may be necessary to set
the angle on the sample/experiment itself.
KBr is a cubic crystal, the
bromine environment is
isotropic
If we need anisotropy to observe
rotary echoes/sidebands where
does this come from?
EPSRC UK National Solid-state NMR Service at Durham
Nuclear Magnetic Resonance
The precession of magnetisation induced by the static field and manipulated by a
radiofrequency pulse produces a voltage detected by the coil.
EPSRC UK National Solid-state NMR Service at Durham
EPSRC UK National Solid-state NMR Service at Durham
Best S/N
Quantitative
The sample itself (recycle)
The sample itself (contact time)
Best S/N
EPSRC UK National Solid-state NMR Service at Durham
The sample itself

Recycle optimised

Contact time optimised
Optimise decoupling?

Check spin-rate/sideband positions
Check acquisition time


GO!
EPSRC UK National Solid-state NMR Service at Durham
Nitrogen-15 (from an organic compound)
Optimisation of the acquisition conditions rarely feasible
CP is only viable method (at natural abundance).
Repetition rate depends on T1H (from carbon).
Good spectra are often those where a long
contact time can be used.
EPSRC UK National Solid-state NMR Service at Durham
EPSRC UK National Solid-state NMR Service at Durham