1. Charithram
1926: Pauli’s prediction of nuclear spin
1932: Detection of nuclear magnetic moment by Stern
1936: First theoretical prediction of NMR by Gorter
1944: Nobel Prize in Physics to Rabi
1945: First NMR of a liquid (H2O) by Bloch & solid (paraffin)
by Purcell
1949: Discovery of chemical shifts
1952: Nobel Prize in Physics to Bloch and Purcell
1992: Nobel Prize in Chemistry to Ernst
2002: Nobel Prize in Chemistry to Wüthrich
2003: Nobel Prize in Medicine to Mansfield and Lauterbur
1
2. Nuclear spin
Neutrons and protons have S = 1/2
Nucleons are fermions
They obey Pauli (separately)
Hence, there is “Nuclear Shell Model”
S(4He, 16O)=0 S(11B, 23Na)=3/2 S(93Nb, 115In)=9/2 S(138La)=5
S(1H, 13C)=1/2 S(17O, 27Al)=5/2 S(10B)=3 S(50V)=6
S(2H, 14N)=1 S(45Sc, 133Sc)=7/2 S(40K)=4 S(176Lu)=7
2
3. Zeeman interaction
In the atom, the orbital angular momentum
of the electrons gives rise to a magnetic
dipole moment which interacts with external
magnetic fields
In the normal Zeeman effect, electronic states
with angular momentum have split energy
levels in the presence of a magnetic field
Similarly, a single nucleon with intrinsic
angular momentum (spin) can interact with an
external magnetic field, with different
energy configurations
3
4. Precession model
A B C
B0
D E F G
Low energy High energy relaxing
4
5. Nuclear Magnetic Resonance
B0
Precession non-observable Precession observable
The process of making precession observable is NMR
5
6. Nuclear Magnetic Resonance
For a spin-1/2 nucleus
RF ~ 100 MHz
Frequency of emission / absorption = ΔE/h
#B0
"L =
2$
6
7. Nuclear Magnetic Resonance
The population deference between the high
and low energy levels by the Boltzmann distribution:
"hB 0
Na
=e kT
Nb
Population difference ∝ Signal intensity
Favorites:
a. High field
b. Low temperature
! 7
8. Nuclear Magnetic Resonance
Bloch Equations:
Transverse (spin-spin) relaxation: T2
Longitudinal (spin-lattice) relaxation: T1
T2 describes the line-width of your signal
T1 asks you to wait until net magnetization comes back
to thermal equilibrium
8
9. NMR interactions
There are five important NMR interactions
ˆ ˆ ˆ ˆ ˆ ˆ
H N = H Z + HQ + H D + HCS + H J
Zeeman interaction ~ 100 MHz
Quadrupolar interaction ~ 1-10 MHz
Dipolar interaction ~ 100 kHz
! Chemical shift interactions ~ 10 kHz
Scalar (J) interaction ~ 100 Hz
9
10. Chemical shift
1H NMR
I feel shy..! Well, I don’t..!
+ chemical +
information
e¯
I’m de-shielded I’m well-shielded
I’m observed down-field Hmm.. Up-field
You need high frequencies Haha.. Low freqs are enough
I’ve high chemical shifts I’ve low chemical shifts
-OH -CH3
In comparison with TMS
10
11. Chemical shift
ppm scale:
In a 9.4T Magnet, 1H Larmor frequency =400MHz
In a 9.4T Magnet, 13C Larmor frequency=101MHz
In a 9.4T (400 MHz) Magnet, 1H chemical shift of 1ppm =400Hz
In a 9.4T (400 MHz) Magnet, 1H chemical shift of 1Hz =1/400ppm
In a 9.4T (400 MHz) Magnet, 13C chemical shift of 1ppm=101Hz
In a 9.4T (400 MHz) Magnet, 13C chemical shift of 1Hz=1/101ppm
1H chem. shift of 1ppm is the same for 9.4T and 11.7T
1H chem. shift of 1Hz is 1/400ppm for 9.4T and 1/500ppm for 11.7T
11
12. J-coupling
30 MHz
Indirect interaction
Remember
n+1 rule
&
Pascal’s triangle
bonding 700 MHz
information
Through bond
Travels with Fermi and Pauli.
Not visible in solid state..!
12
13. Dipolar coupling
Direct interaction
ˆ = "d(3cos 2 # "1) I S
H D IS ˆˆ
z z
distance
information vector
! # µ0 & h) I ) S
d =% ( 3 "
$ 4 " ' rIS
Through space !
1 H, 1 H: 1Å: 120kHz
1 H, 13C: 1Å: 30kHz
! 1 H, 13C:
13C, 13C:
2Å: 3.8kHz
2Å: 0.95kHz
Averaged in solution state..!
13
14. Quadrupolar coupling
Nuclei with Spin>1/2 have Electric Quadrupole Moments
(non-spherical charge distribution on nucleons)
A quadrupole interacts with
electric field gradients (EFG)
CQ = eQVzz /h symmetry
information
! P2Cosθ P4Cosθ
c = 54,736° P2(c)=0
c = 30,55° or 70,11° P4(c)=0
Averaged in solution state..!
14
15. Chemical shift anisotropy (CSA)
Chemical shift is dependent on the orientation of the
nuclei in the molecule in a solid
σ11, σ22, σ33 are the three asymmetry (η)
principal components of the
chemical shielding tensor.
crystallography
information
#"11 0 0&
% (
" PAS = % 0 " 22 0 (
%0
$ 0 " 33 (
'
!
Averaged in solution state..!
15
16. Magic Angle Spinning (MAS)
Experimental MAS speed can
average only the first order
quadrupolar interaction and
never the second order..!
1H MAS NMR 23Na MAS NMR
Spinning the powder sample
at magic angle rapidly with
respect to the external 0kHz
magnetic field averages the
orientation dependent terms
to zero..!
20 kHz
Experimental MAS speed can
often average CSA (~10kHz).
But never the dipolar coupling
(~100kHz)..! a) polycarbonate b) sodium citrate
16
18. Spin decoupling
Liquid Solid
JFH Combining MAS and dipolar decoupling
MAS alone reduces line-w idth
from 5000 Hz to 200 Hz
MAS & decoupling reduces line-
w idth from 5000 Hz to 2 Hz
Decoupling alone reduces line-
w idth from 5000 Hz to 450 Hz Similar to liquid state sample..!
δ(19F) δ(13C)
18
19. Practical liquid state NMR
Locking:
In high-field super-conducting NMR magnets, field drift happens
often. This is of very small magnitude (eg: 5Hz per Hr), but big
enough to affect liquid state NMR spectra.
A frequency lock to the deuterium signal in the deuterated solvent
helps to avoid this problem. Each solvent has a different lock
frequency. So locking to a wrong solvent kills the spectrum.
19
20. Practical liquid state NMR
Shimming:
The effective magnetic field experienced by the sample should be
homogeneous all over the sample volume. In other words, there
should not be any field gradient.
This is achieved by introducing various currents to the gradient
shimming coils, so that a homogeneous magnetic field is effected
on a specific sample volume.
20
21. Practical liquid state NMR
Tuning and Matching:
The NMR probe is an Inductor-Capacitor circuit. The capacitance
has to be changed for the inductor to deliver radio waves of
different frequencies.
In a 9.4T magnet, if I want to observe 1H, I have to change the
capacitance, so that the induction coil supplies me 400MHz RF.
This process, in practice, involves Tuning, where suitable
frequency is selected and Matching, where Q of circuit is matched.
21
23. Practical liquid state NMR
Fourier transformation:
The observed NMR signal is in time domain, which is a very
complicated piece of information. FT is done to view this in the
frequency domain.
Phasing:
Signals obtained in NMR are having a real and an imaginary part.
To observe the ‘real-only’ part, an absorptive mode is helpful.
Phasing of the signal helps to achieve the absorption mode from
the dispersion mode.
Referencing:
Usually in liquid state NMR, a standard sample with most shielded
nuclei is used as an internal chemical shift reference.
Eg: TMS for 1H and 13C NMR (0ppm)
23
24. NMR Magnet
probe is introduced from the bottom
24
