Nmr for friends

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1926: Pauli’s prediction of nuclear spin1932: Detection of nuclear magnetic moment by Stern1936: First theoretical prediction of NMR by Gorter1944: Nobel Prize in Physics to Rabi1945: First NMR of a liquid (H2O) by Bloch & solid (paraffin)

by Purcell1949: Discovery of chemical shifts1952: Nobel Prize in Physics to Bloch and Purcell

1992: Nobel Prize in Chemistry to Ernst2002: Nobel Prize in Chemistry to Wüthrich2003: Nobel Prize in Medicine to Mansfield and Lauterbur

Charithram

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Nuclear spin

Neutrons and protons have S = 1/2Nucleons are fermions

They obey Pauli (separately)Hence, there is “Nuclear Shell Model”

S(4He, 16O)=0S(1H, 13C)=1/2S(2H, 14N)=1

S(11B, 23Na)=3/2S(17O, 27Al)=5/2

S(45Sc, 133Sc)=7/2

S(93Nb, 115In)=9/2S(10B)=3S(40K)=4

S(138La)=5S(50V)=6

S(176Lu)=7

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Zeeman interaction

In the atom, the orbital angular momentumof the electrons gives rise to a magnetic

dipole moment which interacts with externalmagnetic fields

In the normal Zeeman effect, electronic stateswith angular momentum have split energylevels in the presence of a magnetic field

Similarly, a single nucleon with intrinsicangular momentum (spin) can interact with an

external magnetic field, with differentenergy configurations

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Precession model

B0

A B C

D E F G

Low energy High energy relaxing

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Nuclear Magnetic Resonance

Precession observablePrecession non-observable

The process of making precession observable is NMR

B0

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!

"L

=#B

0

2$

For a spin-1/2 nucleus

~ 100 MHz

Frequency of emission / absorption = ΔE/h

RF

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The population deference between the highand low energy levels by the Boltzmann distribution:

!

Na

Nb

= e

"hB0

kT

Population difference ∝ Signal intensity

Favorites:

a. High fieldb. Low temperature

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Bloch Equations:

Transverse (spin-spin) relaxation: T2Longitudinal (spin-lattice) relaxation: T1

T2 describes the line-width of your signalT1 asks you to wait until net magnetization comes back

to thermal equilibrium

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NMR interactions

There are five important NMR interactions

!

ˆ H N

= ˆ H Z

+ ˆ H Q

+ ˆ H D

+ ˆ H CS

+ ˆ H J

Zeeman interaction ~ 100 MHzQuadrupolar interaction ~ 1-10 MHzDipolar interaction ~ 100 kHzChemical shift interactions ~ 10 kHzScalar (J) interaction ~ 100 Hz

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Chemical shift

I feel shy..! Well, I don’t..!

e¯

I’m well-shieldedHmm.. Up-field

Haha.. Low freqs are enoughI’ve low chemical shifts

+ +

I’m de-shieldedI’m observed down-fieldYou need high frequenciesI’ve high chemical shifts

-CH3-OH

In comparison with TMS

1H NMR

chemicalinformation

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Chemical shift

ppm scale:

In a 9.4T (400 MHz) Magnet, 1H chemical shift of 1ppm =400HzIn a 9.4T (400 MHz) Magnet, 1H chemical shift of 1Hz =1/400ppmIn 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

In a 9.4T Magnet, 1H Larmor frequency =400MHzIn a 9.4T Magnet, 13C Larmor frequency=101MHz

1H chem. shift of 1ppm is the same for 9.4T and 11.7T1H chem. shift of 1Hz is 1/400ppm for 9.4T and 1/500ppm for 11.7T

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J-coupling

Through bond

Indirect interaction

Travels with Fermi and Pauli.

30 MHz

700 MHzbondinginformation

Remembern+1 rule

&Pascal’s triangle

Not visible in solid state..!

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Dipolar coupling

distanceinformation

!

d =µ0

4"

#

$ %

&

' ( h)

I)S

rIS

3

!

ˆ H DIS

= "d(3cos2# "1)ˆ I

zˆ S

z

!

"

Through space

Direct interaction

Averaged in solution state..!

vector

1H, 1H: 1Å: 120kHz1H, 13C: 1Å: 30kHz1H, 13C: 2Å: 3.8kHz13C, 13C: 2Å: 0.95kHz

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Quadrupolar coupling


Nuclei with Spin>1/2 have Electric Quadrupole Moments(non-spherical charge distribution on nucleons)

A quadrupole interacts withelectric field gradients (EFG)

symmetryinformation

c = 54,736° P2(c)=0

c = 30,55° or 70,11° P4(c)=0

P2Cosθ P4Cosθ!

CQ = eQVzz /h

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Chemical shift anisotropy (CSA)

Chemical shift is dependent on the orientation of thenuclei in the molecule in a solid

!

" PAS=

"11

0 0

0 "22

0

0 0 "33

#

$

% % %

&

'

( ( (

asymmetry (η)σ11, σ22, σ33 are the threeprincipal components of thechemical shielding tensor.

crystallographyinformation

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Magic Angle Spinning (MAS)

Spinning the powder sampleat magic angle rapidly withrespect to the externalmagnetic field averages theorientation dependent termsto zero..!

a) polycarbonate b) sodium citrate

1H MAS NMR

Experimental MAS speed canoften average CSA (~10kHz).But never the dipolar coupling(~100kHz)..!

Experimental MAS speed canaverage only the first orderquadrupolar interaction andnever the second order..!

20 kHz

0kHz

23Na MAS NMR

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Magic Angle Spinning (MAS)

7mm4mm

3.2mm

2.5mm

1.3mm

8kHz 18kHz35kHz

23kHz

70kHz

BN stator

in

Rotors Probe-head

ZrO2

KEL-F

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Spin decoupling

δ(19F)

Liquid SolidCombining MAS and dipolar decoupling

MAS alone reduces line-w idthfrom 5000 Hz to 200 Hz

Decoupling alone reduces line-w idth from 5000 Hz to 450 Hz

MAS & decoupling reduces line-w idth from 5000 Hz to 2 Hz

Similar to liquid state sample..!

δ(13C)

JFH

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Practical liquid state NMR

Locking:In high-field super-conducting NMR magnets, field drift happensoften. This is of very small magnitude (eg: 5Hz per Hr), but bigenough to affect liquid state NMR spectra.

A frequency lock to the deuterium signal in the deuterated solventhelps to avoid this problem. Each solvent has a different lockfrequency. So locking to a wrong solvent kills the spectrum.

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Shimming:The effective magnetic field experienced by the sample should behomogeneous all over the sample volume. In other words, thereshould not be any field gradient.

This is achieved by introducing various currents to the gradientshimming coils, so that a homogeneous magnetic field is effectedon a specific sample volume.

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Tuning and Matching:The NMR probe is an Inductor-Capacitor circuit. The capacitancehas to be changed for the inductor to deliver radio waves ofdifferent frequencies.In a 9.4T magnet, if I want to observe 1H, I have to change thecapacitance, so that the induction coil supplies me 400MHz RF.

This process, in practice, involves Tuning, where suitablefrequency is selected and Matching, where Q of circuit is matched.

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RF pulse:

FID

Advantage-no freq. sweep-no field sweep

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Referencing:Usually in liquid state NMR, a standard sample with most shieldednuclei is used as an internal chemical shift reference.Eg: TMS for 1H and 13C NMR (0ppm)

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 fromthe dispersion mode.

Fourier transformation:

The observed NMR signal is in time domain, which is a verycomplicated piece of information. FT is done to view this in thefrequency domain.

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NMR Magnet

probe is introduced from the bottom

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Nmr for friends