NMR Spectroscopy A short introduction. How it all began

NMR Spectroscopy

A short introduction

How it all began....

How it all began....

Bloch, Felix, (1905–83), Swiss-American physicist and Nobel laureate, born in Zürich, Switzerland, and educated at the Federal Institute of Technology there and in Germany at the University of Leipzig. He left Germany in 1933 and a year later he joined the faculty of Stanford University in California, where he taught until his retirement in 1971. Bloch’s doctoral dissertation (1928) is recognized as the basis of the modern theory of solids. He also made significant contributions to theoretical physics, particularly to the fields of superconductivity and magnetism. During World War II he worked on the Manhattan Project (the first atomic bomb) and on war-related counter-radar research. In 1946, Bloch became known for his method of determining the magnetic moment (a measure of magnetic strength) of the neutron and the development of the technique called nuclear magnetic resonance. He shared the 1952 Nobel Prize in physics with the American physicist Edward M. Purcell, who had independently discovered, in a different way, nuclear magnetic resonance at about the same time.

..and we need a magnetic field

400MHz = 9.395 T (tesla)

= 9.395*104 G (gauss)

..and we need a magnetic field

Basics of NMR Spectroscopy

Quantum spin number 0 nucleus is magnetically active

e.g. 1H, 13C, 15N, 19F, 31P (I = 1/2)

They will be observed at different (well separated ) frequencies.

We normally just detect one nucleus at a time!

15N 13C 31P 19F 1H

Nuclear Spins

The nucleus has a spin (rotation)

The angular momentum pp is a vector parallel to the axis of rotation

The magnitude of the angular momentum is given by the spin quantum number II::

p = h/2 * I(I+1)

pp

Nuclear Spins

A circulating current creates a ring current

The ring current creates a dipolar magnetic moment:

= p

: gyromagnetic ratio

The gyromagnetic ratio is a constant for each nucleus, describing its magnetic properties

pp

Nuclear Spins

The magnetic moment is a vector parallel to the angular momentum ppp

Nuclear Spins

Outside a magnetic field the nuclear spins have no orientation

N

S

NN

SS

NN

SS

NNSS

NN

SS

Nuclear Spins

Inside a magnetic field the nuclear spins will be aligned along the magnetic field axis

The picture shown here is not really correct: quantum mechanics allows only discrete orientations

The number of possible orientations is given by the spin quantum number I

N

S

NN

SS

NN

SS

NN

SS

NN

SS

NN

SS

Bo

Nuclear Spins

Not all nuclei align parallel

The number of nuclei with parallel and anti-parallel orientation is described by Boltzmann‘s law:

Nm = No

m

N

S

NN

SS

NN

SS

NN

SS

NN

SS

NN

SS

Bo

SS

NN

SS

NN

SS

NN

e-Em / kT

e-Em / kT

Nuclear Spins

Nm : number of spins in state m

No : total number of spins

Em : energy of state m

k : Boltzmann constant

T : temperature

Nm = No

m

N

S

NN

SS

NN

SS

NN

SS

NN

SS

NN

SS

Bo

SS

NN

SS

NN

SS

NN

e-Em / kT

e-Em / kT

Nuclear Spins

How many spins have parallel and anti-parallel orientation?

N+ - N- = No E /2kT

Assuming: Bo = 1 Tesla (43MHz)

No = 2‘000‘000

N+ = 1‘000‘001

N- = 999‘999

N

S

NN

SS

NN

SS

NN

SS

NN

SS

NN

SS

Bo

SS

NN

SS

NN

SS

NN

Nuclear Spins

N

S

NN

SS

NN

SS

NN

SS

NN

SS

NN

SS

Bo

SS

NN

SS

NN

SS

NN

Bo E

E = h Bo

m=-1/2

m=1/2

The energy levels are called Zeeman levels

What do we Observe ? (1)

In a magnetic field, the Zeeman levels are splitted according to:

type of the nucleus strength of the magnetic field

1H has a higher frequency than 13C at the same field strength

1H is more sensitive than 13C at the same field strength

E

field

13C splitting

1H splitting

What do we Observe ? (2)

Levels with different energies have different populations p:

Equilibrium population

We use rf pulses (MHz) in order to perturb the system :

Perturbed population

We observe populations going back to equilibrium: B A

E

p 0

E

p 0

A

B

Nuclear Spins: macroscopic magnetisation

E

m=-1/2

m=+1/2

From Microscopic to Macroscopic

M = magnetisation vectorB0 = static magnetic field

B 0

y

z

x

M

rf pulse 90° flip angle

y

z

xM

Macroscopic Signal

Magnetisation precesses at a frequency given by :

the type of nucleus the electronic environment in the molecule

Magnetisation relaxes towards equilibrium

The detected signal, the FID ("Free Induction Decay") shows :

frequency of precession damping due to relaxation

y

z

x M

time

T =1/

y

z

x M

Macroscopic Signal

Resonance Condition of NMR Spectroscopy:

I = I Bo

I : Larmor frequency

I : gyromagnetic ratio

Bo: magnetic field

y

z

x M

z

I

Signal Processing

To understand the signal, we go from the time domain signal, the FID, to the frequency domain signal, the spectrum

via the Fourier Transform

FT

time Frequency orchemical shift

Summary

• Nuclei have a spin which creates a magnetic moment.• Due to the magnetic moment the nuclei will orientate in the

magnetic field and thus create a net-magnetisation, called ‚macroscopic‘ magnetisation.

• The orientation of the macroscopic magnetisation will be disturbed by a RF pulse, thus creating a magnetisation vector in the x,y frame.

• The magnetisation rotates in the x,y, frame and induces a voltage in a receiver coil.

• The induced signal is processed by Fourier transformation

Laboratory and Rotating Frame

y’

z

x’

M

o

z

y

x

M

o

Laboratory Frame:•The x,y, frame is fix with respect to an

external observer.•The magnitization is seen rotating with the

Larmor frequency o

Rotating Frame:•The x,y, frame is rotating with the Larmor

frequency o

•The magnetisation is seen at a fix position

The RF pulse

z

y

x

B1

1. A coil is installed with its long axis oriented along the x axis.

2. This ‚transmitter coil‘ is feeded with an alternating current

3. A magnetic field oscillating linearly along the x axis

Laboratory FrameLaboratory Frame

The RF pulse

1. The oscillating B1 field can be considered as being composed of two opposite rotating components.

2. These two components are located in the x,y frame

B1

time

The RF pulse

1. The oscillation frequency of B1c and B1ac is: = 2

2. The oscillating frequency will be set equal to the frequency of the rotating frame:

= o3. One component, B1c or B1ac

then will be static with respect to the rotating frame

z

y

x B1

B1ac

B1c

B1ac: B1 component, rotates anti clockwise

B1c: B1 component, rotates clockwise

Laboratory FrameLaboratory Frame

The RF pulse

1. The macroscopic magnetization Mz will rotate along the static component of the B1 field.

2. Any macroscopic magnetization aligned exactly with the static component of the B1 field will not move.

z

y

xB1c static

Rotating FrameRotating Frame

Mz

The RF pulse

1. The rotation angle depends on how long the field B1 is applied

2. Definitions:

pulse or flip angle

tp: time of B1 switched on

tp(90) time required for a 90o rotation

90o pulse: RF flips a macroscopic magnetization by 90o

Rotating FrameRotating Framez

y

xB1c static

Mz

time

tp

RF

The RF pulse

1. The excitation bandwidth is defined by the length of the 90o pulse

2. The excitation profile is described by a SINC-function

2. A short duration for the 90o pulse is required for a uniform excitation over the entire spectral range

time

tp

RF

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frequency

+1/tp -1/tp

Excitation profile = sinc(0.5(Excitation profile = sinc(0.5(--)t)tpp))

The RF pulse

1. The intensity and phase of the NMR signal is given by the size and phase of the Mx,y magnetization

2. The magnetization vector can be described by the two projections to the z- and the x-/y-axis

3. The magnetization Mz does not create a NMR signal

z

y

x

M

My

Mz

The NMR experiment: what do we need?

1. The magnet2. The probe head3. Generation of RF pulses for excitation4. Preamplification of received signals5. Digital processing of analog NMR signal


1. The magnet:1. The magnet:

Requires control of field homogeneity SHIMRequires stabilisation of main field LOCKSHIM:SHIM:

additional coils with special field distribution,e.g. Z, Z2, Z3, X, Y, X3....We have cryo shims and room temperature shims

LOCKLOCK1.contineously determines frequency of 2H signal of the solvent (deuterated solvents)2. add a small extra field to the main field of the magnet to keep the overall field constant3. 2H signal also used for shimming

Basics of shims

Shims are used to compensate the magnetic field inhomogeneity in the sample area

Compensation is done by creating a magnetic field profile which has:– opposite sign compared to the inhomogeneity– same absolute intensity as inhomogeneity

Compensation requires a shim system to create the compensation field

Basics of shims

Shim field functional forms of some on-axis shims

Z

Z Z

Z Z

Z1 Z2 Z3

Z4 Z5

The Z axis is the axisof the magnet and the NMR sample tube

Basics of shims

Example: an inhomogeneity which would require the shim functions Z1 and Z2 to be adjusted

Z

Bo

Z

BShim

Z

B0

Z2

Z Z

Z1

The magnet‘s field before correction

correction field of the shim coil

superposition of magnet‘s field andthe correction field

1. The magnet:1. The magnet:

Requires control of field homogeneity SHIMRequires stabilisation of main field LOCKSHIM:SHIM:

additional coils with special field distribution,e.g. Z, Z2, Z3, X, Y, X3....We have cryo shims and room temperature shims

LOCKLOCK1.contineously determines frequency of 2H signal of the solvent (deuterated solvents)2. add a small extra field to the main field of the magnet to keep the overall field constant3. 2H signal also used for shimming


The lock: details

The lock channel can be understood as a ‚completely indepenant spectrometer within the spectrometer‘:

Transmitter 2H ProbeProbe Receiver 2H

Regulator

Shim systemShim system

amplitude,frequency

Ho

The resonance condition of NMR:

= Bo but: Bo is not stable

= (Bo+Ho) (Bo+Ho) = const.

The lock: lock phase

The lock receiver has two quadrature channels:

signal

=0o absorption:

=90o dispersion:

The lock: field homogenisation

The absorption signal is used for field homogenisation

The signal intensity is a measure for the field homogeneity:

sharp signal, high lock level

broad signal, low lock level

Intensity

The lock: field stabilisation

The dispersion signal is used for field stabilisation

The position of the zero-crossing of the signal is permanently checked

Determination of the zero-crossing frequency is more sensitive than determination of the frequency at maximum peak position

The lock: field stabilisation

(2H) (2H)

The lock: lock phase

If the lock phase is not adjusted correctly, absorption and dispersion signals will be mixed

Non-pure phases will result in:

– imperfect field homogenisation (shimming)– imperfect field homogenisation– field shifts during experiment using pulsed field

gradients

8.18.28.38.48.58.68.78.88.9 ppm

WATERGATE experiment:top: correct lock phasebottom: lock phase wrong by 30o

The lock: lock phase and GRASP

The lock: regulation parameters

Regulation parameters:Loop Gain: how strong to react on field disturbance

Loop Time: how fast to react „ „ „

Loop Filter: smoothing the lock signal to remove noise,

low pass filter

Wrong settings will result in:– instable signal position: suppression artifacts (NOE-

difference,...)

– noise around the signal

Use xau loopadj for adjusting the loop parameters

The lock: further parameters

Lock power:– 2H transmitter output power

– Due to different relaxation behavior of 2H for individual solvents, the lock power has to be adjusted for each solvent

– Too high lock power will result in an unstable lock signal

Lock gain:– receiver gain of the lock channel

– Gain too low: field homogenisation not optimum

– Gain too high:receiver is not linear, field homogenisation not optimum, spikes around NMR signals


2. The probe head:

Mainly is an antennatypically 3 RF channels:

2H: for the LOCK and shimming1H: for 1H-NMR and 1H-decouplingX: e.g. 13C, for 13C-NMR and 13C decoupling

The susceptibility of the coil material is crucial forbest line shape of the NMR signal

Helmholtz coils are mainly used for high resolution applications.

Example of a Helmholtz coil design

The NMR experiment: the probe

Sample location in the probehead


The probe

Pulse power:– Do not apply pulses at a power higher than specified for

the probe

– During endtest of the spectrometer the shortest possible pulses are calibrated. For pulse sequences those power levels might be too high, e.g. for 1H trim pulses in HSQC

– Carefully check the tuning and matching of the transmitter and decoupler channel

The probe

Additional notes:– Solvent volume: has to be adapted to the active length of

the coil used for observation

– Observe and decoupler coil: The decoupler coil is longer than the observe coil. Measuring a spectrum via the decoupler coil requires more solvent volumn:

• observe coil: >450l

• decoupler coil: >600l

The DEPT experiment

WALTZ16

90o 180o

90o 180o

1H

13C

1H channel:1H channel:different pulsespulse phases2 power levels

13C channel:13C channel:different pulsespulse phasesreceive signal

We have to create:We have to create:different frequencies with different phasesfast change of power levels for pulsesamplification of weak syntheziser outputexact timing of each actionswitch to the receiving modedigital preprocessing of the received data (FID)

The spectrometer

We have to create:We have to create:

•DPX,DRX,DMX:different frequencies with different phases FCU, syntheziserFCU, syntheziserfast change of power levels for pulses ASUASUamplification of weak syntheziser output BLAH, BLAXBLAH, BLAXexact timing of each action TCUTCUreceive signal HPPR, RX22 (SE451)HPPR, RX22 (SE451)digital preprocessing of the received data (FID) RCURCU

•Avance:different frequencies with different phases FCU, SGUFCU, SGUfast change of power levels for pulses SGUSGUamplification of weak syntheziser output BLAH, BLAXBLAH, BLAXexact timing of each action TCUTCUreceive signal HPPR, RX22HPPR, RX22digital preprocessing of the received data (FID) RCURCU

The Spectrometer: components

RF transmit path in the DRX console:RF transmit path in the DRX console:

FCU1

FCU2

Amplifier 1H

Syntheziser LOT ASU ROUTER

Amplifier X

Preamp 1H

Preamp X

BSMS 2H transmitter Preamp 2H

ProbeProbe


RF receive path in the DRX console:RF receive path in the DRX console:

Preamp 1H

Preamp X

Preamp 2H

FCU1

FCU2

Amplifier 1H


Amplifier X

BSMS 2H transmitter

ProbeProbe

BSMS 2HReceiver

RX22


RF receive path in the DRX console:RF receive path in the DRX console:

Preamp 1H

Preamp X

Preamp 2H

FCU1

FCU2

Amplifier 1H


Amplifier X

BSMS 2H transmitter

ProbeProbe

BSMS 2HReceiver

RX22

1. digitizing analog signal2. digital signal processing3. transfer to work station

1. digitizes analog signal2. analysis for field correction3. display signal

The receiver channel

Overview

ProbeProbeADC

Receiver Analog Digital Filters Antialiasing Filters

LO1 LO2

CH B

CH ARCU

The receiver channel

ProbeProbeADC

Receiver Analog Digital Filters Antialiasing Filters

LO1 LO2

CH B

CH ARCU

-40-20160 140 120 100 80 60 40 20 0 ppm

FID low frequency digitized FID digital filteringFID data reduction

The receiver: parameters for individual components

receiver gain of RX22 or SE451 rg, rga– RG chosen too low: bad dynamic, signals of low intensity

have bad sensitivity

– RG chosen too high: baseline distortion, phase cycles do not work,....

Analog antialiasing filters fw– automatically set by the software for RX22

– for SE451: fw=1.5*swh

Analog digital converter ADC– no parameters to set

The receiver: parameters for individual components

Digital filters on the RCU

User defined parameters:– DIGMOD: analog, digital or homodecoupling-digital

defines sampling rate of the ADC

– DSPFIRM: sharp, smooth or medium

defines number of coefficients for

the digital filter, depends on sweep width

– AQ_mod: qsim or DQD

DQD for perfect suppression of quadrature

images and O1-spikes

Some notes on digital filters

Digital filters and oversampling belong together

What is oversampling? – the FID is sampled faster than what is required for a

given spectral width

Dwell time DW


Sampling rate and spectral width SWH:

SWH = 1/2DW

-40-20160 140 120 100 80 60 40 20 0 ppm

DW[sec] SWH [Hz]

FT


Sampling rate and spectral width SWH:

SWHoversampling = 1/2DWoversampling

-40-20160 140 120 100 80 60 40 20 0 ppm

DW[sec] SWH [Hz]

FTDWoversampling

SWHoversampling [Hz]


The digital filter is a bandpass filter

The region of interest is extracted mathematically

-40-20160 140 120 100 80 60 40 20 0 ppm

SWH [Hz]

SWHoversampling [Hz]

A short demo of a digital filter

Demo using an audio WAV file:– selecting a frequency with a lowpass / highpass filter

– parameters for digital filter and filter quality

A short demo of a digital filter

Excitation parameters

Excitation frequency: O1, O1P

Spectral window: SW

Time domain data points: TD

Excitation sequence / pulse program: PULPROG

Excitation power e.g. for hard pulse: PL1

Length of 90o pulse: P1


Dwell time DW

TD

Time domain data points TD and acquisition time AQ:

AQ = TD * DW= TD/2SWH– The value for TD should result in an AQ which is long

enough to allow complete decay of the FID


O1 / O1P define the center of the spectral window:

-40-20160 140 120 100 80 60 40 20 0 ppm

SW/2 SW/2

O1 / O1P

Summary: essential acquisition parameters

Excitation:– excitation sequence: pulprog

– power level and 90o pulse: pl1, p1

– excitation center: o1p or o1

Acquisition:– attenuation of incoming RF: rg

– spectral window: sw

– # of sampled points: td

– mode for digital filters: digmod

– dummy scans ds

– coadded scans ns

Summary: essential processing parameters

General:– data points: si = 0.5* TD

– time domain baseline correction: bcmod

Window functions:– parameter for exponential window: lb

– parameter for gaussian window: lb, gb

– parameter for sin, sin2 window: ssb

End of document

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NMR Spectroscopy A short introduction. How it all began