Basics of NMR

Shashank Deep

NMR

• Absorbed photon promotes a nuclear spin from its ground state to its excited state.

• The degeneracy of the energy levels is lifted by the interaction of nuclear dipole

moment with an intense external magnetic field.

• Excitation of transitions between energy

levels is stimulated using radio-frequency electromagnetic radiation.

Difference with other spectroscopy

• The generation of the ground and excited NMR

states requires the existence of an external

magnetic field.

• NMR excited state has a life time that is on the

order of 109 times longer than the lifetime of

excited electronic states.

• According to Heisenberg Uncertainty principle,

ΔEΔt ≈h/2π. The longer an excited state exist,

the narrower the line width.

Difference …..

• Longer lifetime also facilitates multi-dimensional spectroscopy by allowing the resonance frequency information

associated with one spin to be passed to another.

• The longer life-time permits the

measurement of molecular dynamics over a wide-range of time scales.

rvmJ

All nucleons, that is neutrons and protons, composing any

atomic nucleus, have the intrinsic quantum property of spin.

As the name

suggests, spin

was originally

conceived as the

rotation of a particle around

some axis. This

picture is correct

so far as spin

obeys the same mathematical

laws as

quantized

angular

momenta do.

Since these particles are also charged, one expects a magnetic

field will be induced

Magnetic moment

JJm

e

rA

er

ci

Qx

c

t

Qi

cdx

dQ

dt

dQi

Ai

avg

2

.2

.

2

Gyromagnetic ratio

The gyromagnetic ratio g determines the ratio of

the nuclear magnetic moment to the nuclear spin.

•It is a fundamental property of each nuclear isotope

Hz)(in

1)-s rad(in

Hz)(in

1)-s rad(in

0

0

0

0

0

0

m

m

BmE

mI

IH

IH

IBH

m

mmZ

Z

Z

Z

No field

X Y

Z

Apply field wait

X Y

Z

X Y

Z

With field not at equilibrium With field at equilibrium

Bulk Magnetization

Larmor precession

Ma

gn

eti

c fi

eld

Z

X Y

Tip away magnetization from the Z-axis

Nuclear spins

precess in a magnetic field • Nuclear spins precess

because:

1. they are magnetic

2. they have angular

momentum

• Precession frequency =

Larmor frequency

• Negative γ = positive

sense of precession

• Positive γ = negative

sense of precession

Larmor Precession

Z

X Y

Apply RF Field

Two counter-rotating field is equivalent to field

oscillating along the x-axis (RF field)

Larmor frequency in rotating frame

The effective field

On-resonance pulse

Effect of On-line pulse

Organic Structure Analysis, Crews, Rodriguez and Jaspars

ONE-PULSE SEQUENCE

1H

(90o)x

Preparation Detection

Organic Structure Analysis, Crews, Rodriguez and Jaspars

Mo

x

y

z

Bo

Excess of spin

population along

the direction of

applied magnetic

field.

(90o)x

x

y

z

Bo

After 90o

pulse

magnetization

is tipped into

the xy plane.

M

time t2

M=Magnetization which

produces the FID. It decays

as magnetization in xy

plane diminishes after

resonance

FT

frequency f2

preparation detection

ONE-PULSE SEQUENCE

Effect of pulses

X

Y

X

Y

Mx

My

time = 0

time = t

Mx My

time time

Fourier transformation (transformation of time-domain data to frequency domain)

Two key idea

(i) Any time-domain function can be represented by the sum of cosine waves of different frequencies and amplitude.

(ii) Cosine waves are orthogonal to each other, i.e. integral, taken between t=0 and t = ∞, of the product of any two cosine waves of different frequency is zero.

Cosine wave of 15 Hz

cosine wave of 15 Hz

-1.5

-1

-0.5

0

0.5

1

1.5

0 6 12 18 24 30 36 42 48 54 60 66

TIME (t/15)

AM

PL

ITU

DE

Multiplication of cosine wave of 15 Hz with cosine

wave of different frequency

Multiplication by 5 Hz

-1.5

-1

-0.5

0

0.5

1

1.5

0 6 12 18 24 30 36 42 48 54 60 66

time (t/15)

Am

pli

tud

e

Multiplication by 10 Hz

-4

-3

-2

-1

0

1

2

0 6 12 18 24 30 36 42 48 54 60 66

time ( t/15)

Am

pli

tud

e

Multiplication by 15 Hz

-2

-1

0

1

2

0 6 12 18 24 30 36 42 48 54 60 66

time (t/15)

Am

pli

tud

e

Multiplication by 20 Hz

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 6 12 18 24 30 36 42 48 54 60 66

time (t/15)

Am

pli

tud

e

∑ A= - 0.97 ∑ A= - 3.24

∑ A= 30.98 ∑ A=-4.91

Fourier Transformation of complex

signal

22

22

)(

RD

R

RA

FT

22

22

)(

RD

R

RA

Height of the peak at

R

S1

When R

S2

R- ,2/1 R

Width at half height = 2R

Phase correction

Phase correction

Second order phase correction

Sensitivity Enhancement

Sensitivity Enhancement

Resolution enhancement

Optimum

Sine-bell function

Zero-Filling

Hard pulse

The effective field

Pulse calibration