Basics Concepts

• Nuclear spins

• Magnetic field B0

• Energy

• Sensitivity

• The NMR transition

• Larmor Frequency

• Magnetic field B1

• The rotating frame

• A pulse!

The energy of the NMR Transition

• Sensitivity

B0

E

m=+1/2

m=-1/2

E=h0

NUCLEUS

B0 MAGNETIC FIELD

Larmor Frequency

The two Zeeman level are degenerate at B0=0

E=(h/2)B0

E= -•B0

d/dt=(t)^B0(t)

B0

M0

I=1/2 E = B0

E = mB0

: m = +½

+½

E½B0

: m = ½½

E½B0

kT

E

eP

P

M0 = = Mz

Mx = My = 0

E = B0 = h

0=20=00

Mz=-1/2 h/2

E=-B0 = -hmzB0/2E=hB0/2

STILL, NO NMR EXPERIMENT

Mz=1/2 h/2

B1(t)= B1 cos 1t

B1 is a radiofrequency transmitter

A pulse!

dM(t)/dt= M(t)^B(t) B(t)= B0 + B1(t)dM(t)/dt= M(t)^B0 + M(t)^B1 (t) = M(t)^B0 + M(t)^|B1| cos1t (t)

Double precession

A pulse!

Precession around B0 (z axis)Precession around B1 (axis defined in the xyplane and rotating at speed 1)

Laboratory Frame

• Nuclear frequency 1= precession frequency of magnetic field B1

A pulse!

The Rotating frame

• X’,y’,z’ =laboratory frame• X,y,z,=rotating frame

(rotating at the frequency 1)

In the rotating frame,there is no frequency precession for and the radifrequency B1 is seen as a static magnetic field

The static magnetic field B0 is not observed in the rotating frame

Laboratory Frame

jam

Fly A (Laboratory Frame)

Fly B The movement of Fly B as seen by Fly A

Rotating Frame

Fly Bjam

The movement of Fly B as seen by Fly A

Fly A (Rotating frame)

Precession in the laboratory frame

0

dM/dt=M^B dM/dt=M^(B-)

L.F.R.F. at freq.

If = 0 dM/dt=0

If 0

dM/dt=M^B1 =

If = 0+B1

dM/dt=M^(B0 +B1 -0)

Rotation!

dM/dt=M^(B +B1 -0)

dM/dt=M^(B1+ (0))

dM/dt=M^(B1+ ())

B1

0

Precession in the laboratory frame

0

Mxy from any nuclear spin not exactly on resonance, will also precess in the x’y’ plane at the difference frequency 0.

Basics (II)

• Free Induction Decay (FID)

• Fourier transformation

A pulse

Free Induction Decay (FID)

Observed NMR signal in the time domain

Resonance frequencies are acquired as a function of time

Common case of observed FIDs

t t t

What happens?

Relaxation. Magnetization disappear from the xy plane because the system goes back to the equilibrium. The observed signal is always an Exponential DECAY.

Chemical shift precession. Different spins may have a different resonance frequency. When the resonance frequency is different from that of the field B1, the signal rotates on the xy plane, with a precession ferquency 1-0

Thank you, Mr. Fourier!

F() F(t)

FOURIER TRANSFORMATIONS

F()=(0)

F()=A(sin)/ centered at 0

F()=T2/1+(2T2)2 -i 2(T2)2/1+(2T2)20

F()=T2/1+(2T2)2 -i 2(T2)2/1+(2T2)20

F(t)=exp(-t/T2)

F(t)=exp(-t/T2)exp(i2A)

Why bother with FT?

FT allows to decompose a function in a sum of sinusoidal function(deconvolution).

In NMR FT allows to switch from the time domain, i.e. the signal emitted by the sample as a consequence of the

radiofrequency irradiation and detected by the receiving coil to the frequency domain (NMR spectrum)

The FT allows to determine the frequency content of a squared function

A “real” F.I.D.

Excitation pulses• A single resonance at Larmor frequency 1= excitation

frequency 0 (precession of the rotating frame)

Transmitter B1

A Pulse

B1 switched off

B1 on. A pulse!

The My magnetization is observed by the receiver coil

Received signal

• The received signal 1 is compared with the excitation frequency 0

• The resulting signal has observed frequency =0

• During acquisition time the signal relaxes (T2)

My=exp(t/T2)

Time (t)

Fourier Transformation

Frequency ()

=0

Excitation pulses• A single resonance at Larmor frequency 1different from

excitation frequency 0 (precession of the rotating frame)

Transmitter B1

Pulse

B1 switched off

B1 on. A pulse!

The My magnetization is observed by the receiver coil

Received signal

• The received signal 1 is compared with the excitation frequency 0

• The resulting signal has observed frequency obs=(1-0)

• During acquisition time the signal relaxes (T2)

My=cos(obs)texp(t/T2)

Time (t)

Fourier Transformation

Frequency ()

My=cos(obs)texp(t/T2)

=0=obs

FTrelax.

x90

Preparation Detection

x

y

z

x90 t2

0

dte)t(f)(F ti

Typical 1H NMR Spectrum

Absorbance

Protein 1H NMR spectrum: a “real spectrum”

Fourier Transformation

The NMR signal in the time domain

Free Induction Decay

A short pulse will excite all spinsAll spins will relax (all together) during time AQThe FT of FID gives the NMR spectrum