Basic principles of NMR NMR signal origin, properties, detection

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Transcript Basic principles of NMR NMR signal origin, properties, detection

Basic principles of NMR NMR signal origin, properties, detection, and processing Nils Nyberg NPR, Department of Drug Design and Pharmacology NTDR, 2014

Outline 10 00 – 10 45 • Establishing current knowledge level • Nuclear Magnetic Resonance phenomenon 10 45 • Vector model, in and out of the rotating frame – 11 00 • Short break 11 00 – 11 30 • The phase of pulses and signals • Effect of different chemical shifts in the vector model • Effect of homonuclear coupling in the vector model • The spin-echo sequence (homonuclear case) • The spin-echo sequence (heteronuclear case) 11 30 – 12 00 • Spin-echo exercise 12 15 – 13 15 • Lunch NTDR, 2014

Outline 12 15 – 13 15 13 15 • Lunch – 14 15 • Signal processing • Window functions • Fourier transform • Real and imaginary parts • Phasing • Topspin starter NTDR, 2014

Establishing current knowledge level Build (sketch) a NMR-instrument!

• Magnet • Probes • Amplifiers • Receiver • ADC • Gradients • Temperature control • Lock • Shimming NTDR, 2014

Establishing current knowledge level Draw a spectrum!

• Chemical shifts • Integrals • Phases • Coupling constants • Line widths • life time of signals, shimming, exchange, dynamics NTDR, 2014

Nuclear Magnetic Resonance phenomenon Nuclear: concerns the nuclei of atoms.

Magnetic: uses the magnetic properties of the nuclei.

Resonance: physics term describing oscillations.

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Resonance A system prefers some frequencies over others… A small energy input at the right frequency will give large oscillations… NTDR, 2014

The magnetic properties of atomic nuclei Atoms has a spin quantum number, I, and a magnetic quantum number, m = 2×I +1.

The magnetic quantum number = the number of different energy levels when the atom is placed in an external magnetic field.

Spin I = 0: Spin I = ½: Spin I = 1: Spin I = 1½: 12 C, 16 O 1 H, 13 C, 15 N, 19 F, 31 P, 77 Se 2 H, 14 N 33 S, 35 Cl, 37 Cl NTDR, 2014

Chemical shifts • The energy for a spin ½ nuclei can take two different levels in a magnetic field.

• The population of the two states is almost equal. A small surplus in the low energy α spin state and slightly fewer atoms in the higher β spin state.

• Stronger magnetic field = larger energy differences between the states.

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Chemical shifts • A magnet provides the static field (B 0 ) in the NMR instrument.

• The rest of the molecule provides a ’local magnetic field’, which is dependent on structure.

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NTDR, 2014 Chemical shifts • The chemical shifts are expressed on a frequency scale (by convention plotted in reverse direction).

• To make spectra comparable between instruments, the frequencies are expressed in parts per million [ppm] relative to a reference frequency.

• Early instruments with electromagnets worked by slowly change the magnetic field. Hence the terms ‘Downfield’ and ‘Upfield’. •Less shielded •More deshielded •Downfield •Higher frequency •More shielded •Less deshielded •Upfield •Lower frequency

Vector model (a statistical abstraction…) Unordered collection of ½-spin nuclei, with a magnetic moment (μ).

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Vector model Unordered collection of ½-spin nuclei, with a magnetic moment (μ).

In an external magnetic field, the magnetic moment starts to precess… NTDR, 2014

Vector model Unordered collection of ½-spin nuclei, with a magnetic moment (μ).

In an external magnetic field, the magnetic moment starts to precess… …and aligns, at an angle of 54.7°, with the external field… NTDR, 2014

Vector model Unordered collection of ½-spin nuclei, with a magnetic moment (μ).

In an external magnetic field, the magnetic moment starts to precess… …and aligns, at an angle of 54.7°, with the external field… …either up (along the field, slightly lower energy) or down (opposite the field, slightly higher energy) according to the Boltzmann distribution.

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Boltzmann distribution The distribution of spins in a -state relative those in the b state is described by the Boltzmann distribution.

The number of spins in each state is almost equal. There is a small surplus in the lower state.

Calculate how many spins in total you need to get one extra spin in the low energy state!

[ 1 H, 600 MHz, 298 K]

N

a  exp(

k

E

T

) 

e

( 

E k

T

)

N

b

e

 2 .

718 (natural logarithm) 

E

h

 

k

 1 .

4  10  23 J/K (Boltzmann constant)

h

 6 .

6  10  34 Js (Planck constant)   Frequency, Hz (s 1 ) T  Temperatur e in K (Tc  273.15) NTDR, 2014

Boltzmann distribution One spin extra in the low energy state!

[ 1 H, 600 MHz, 298 K] N β N α Σ = = = 12 922 12 923 25 845

N

b

N N

b  1 

N

b a  exp(

k

E

T

)

h

exp(

k

  

T

)

N

b  1 

N

b 

N

b exp( ( 1 

h k

  

T

) 

N

b

h

exp(

k

  

T

))

h

exp(

k

  

T

  1   1 ) 

N

b

N

b

N

b   ( 1   1

h

  exp(

k

  1

T

)) ( 1 

e

( 6 .

6  10  3 4  600  10 6 1 .

4  10  2 3  298 ) )  12922 NTDR, 2014

Vector model The ordered collection of spins can be handled from a common origin.

The Boltzmann distribution of up and down-spins, makes a net magnetic vector along the external field (green).

An external magnetic field (radio frequency pulse, B 1 ) perpendicular to the first (B 0 ) have two effects: NTDR, 2014

Vector model The ordered collection of spins can be handled from a common origin.

The Boltzmann distribution of up and down-spins, makes a net magnetic vector along the external field (green).

An external magnetic field (radio frequency pulse, B 1 ) perpendicular to the first (B 0 ) have two effects: • Creation of phase coherence (‘bunching of spins’) NTDR, 2014

Vector model The ordered collection of spins can be handled from a common origin.

The Boltzmann distribution of up and down-spins, makes a net magnetic vector along the external field (green).

An external magnetic field (radio frequency pulse, B 1 ) perpendicular to the first (B 0 ) have two effects: • Creation of phase coherence (‘bunching of spins’) • Switch from up- to down-spin (or down- to up- !) NTDR, 2014

Vector model The resultant magnetic vector is spinning at the precession frequency, which is the same as the frequency of the external magnetic field.

The spinning magnetic vector induces a current in the detector coil around the sample. The alternating current is recorded.

The detector senses the absolute length of the magnetic vector in the horizontal plane (XY-plane).

• Cosine curve along y-axis.

• Sine curve along x-axis.

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Vector model The resultant magnetic vector is spinning at the precession frequency, which is the same as the frequency of the external magnetic field.

The ‘rotating frame’ reference is used to simplify the model. The coordinate system is spun at the same speed as the vectors  the vectors appear as fixed.

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Relaxation T 1 -relaxation • Exponential recovery of magnetization along B 0 -axis • Back to equilibrium populations of up- and down-spin NTDR, 2014

Relaxation T 1 -relaxation • Exponential recovery of magnetization along B 0 -axis • Back to equilibrium populations of up- and down-spin T 2 -relaxation • Gradual ‘fanning’ out of individual magnetic vector.

• emission-absorption among spins (changes phase) • bad homogeneity of magnetic field NTDR, 2014

Relaxation T 1 -relaxation • Exponential recovery of magnetization along B 0 -axis • Back to equilibrium populations of up- and down-spin T 2 -relaxation • Gradual ‘fanning’ out of individual magnetic vector.

• emission-absorption among spins (changes phase) • bad homogeneity of magnetic field NTDR, 2014

Pulsed experiments The basic 1D-FT NMR experiment • Pulse (μseconds) • Broadband (covers a wide range of frequencies) • • • Acquisition (seconds) • Records all frequencies within a preset frequency width Relaxation delay (seconds) • To return the magnetization vector close to equilibrium Repeat and add results • signals increases linearly with n, while the noise partly cancels out and increases with n ½ .

S N

S N

n n n

    B 1  p 1 NTDR, 2014

Phase of pulses and signals Basic 1D NMR-experiment: With a 90°-pulse along the x-axis NTDR, 2014

Phase of pulses and signals Basic 1D NMR-experiment: With a 90°-pulse along the y-axis NTDR, 2014

Phase of pulses and signals The phase of the pulse gives the phase of the signal… NTDR, 2014

X Phase of pulses and signals Y X Y NTDR, 2014

X Phase of pulses and signals Y X Y NTDR, 2014

Different chemical shifts in the vector model Two signals with different chemical shifts rotates with different speed in the vector model • Interpreted as two different frequencies in the spectrum X Y NTDR, 2014

Different chemical shifts in the vector model Two signals with different chemical shifts rotates with different speed in the vector model • Interpreted as two different frequencies in the spectrum X Y NTDR, 2014

Different chemical shifts in the vector model One of the signals right on the carrier frequency • The other resonance will have a different speed X Y NTDR, 2014

Different chemical shifts in the vector model One of the signals right on the carrier frequency • The other resonance will have a different speed X Y NTDR, 2014

Coupling in the vector model A doublet with two signals • The same effect as two different chemical shifts, but usually depicted with the carrier frequency in the middle of the doublet.

• J = Coupling constant in Hz (Hz = rounds per seconds) NTDR, 2014

Spin-echoes in pulse sequences Chemical shifts are refocused NTDR, 2014

Spin-echoes in pulse sequences Chemical shifts are refocused NTDR, 2014

Spin-echoes in pulse sequences Chemical shifts are refocused NTDR, 2014

Spin-echoes in pulse sequences Couplings evolve (if both of the coupled nuclei are inverted) NTDR, 2014

Spin-echoes in pulse sequences Couplings evolve (if both of the coupled nuclei are inverted) NTDR, 2014

Spin-echoes in pulse sequences Couplings evolve (if both of the coupled nuclei are inverted) NTDR, 2014

Spin-echo example Explain the appearance of the normal 1 H spectrum of the hypothetical molecule.

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Spin-echo exercise I Explain the appearance of the spin-echo spectrum… • Use vector model • What delay was used around the 180-degree pulse?

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Spin-echo exercise II Explain the appearance of the spin-echo spectrum with simultaneous 180-pulses at both proton and carbon… • Use vector model • What delay was used around the 180-degree pulse?

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Spin-echo exercise I NTDR, 2014

Spin-echo exercise II NTDR, 2014

LUNCH The lunch is served in the cafeteria in building 22 12 15 -13 15 NTDR, 2014

Outline 12 15 – 13 15 13 15 • Lunch – 14 15 • Signal processing • Window functions • Fourier transform • Real and imaginary parts • Phasing • Topspin starter NTDR, 2014

Acquisition time The acquisition time is usually ~100 ms – 10 sec depending of type of experiment.

The best theoretical resolution in the spectrum is the inverse of the acquisition time (t a ).

t

a = 10 seconds  Δν= 0.1 Hz

t

a . = 0.1 seconds  Δν= 10 Hz NTDR, 2014

Acquisition time The line width is determined by the acquisition time and the relaxation!

Fast relaxation => the signal fades out fast => broad lines • long acquisition time will in this case only increase the noise NTDR, 2014

Spectral width, sampling rate & dwell time Dwell time Sampling rate Sampling rate Dwell time = Time between sampling points = Number of data points per second = Total no. of data points / acquisition time = (Sampling rate) -1 NTDR, 2014

Spectral width, sampling rate & dwell time Dwell time Sampling rate Sampling rate Dwell time = Time between sampling points = Number of data points per second = Total no. of data points / acquisition time = (Sampling rate) -1 Faster sampling Spectral width  larger spectral width (sw) = ½ × Sampling rate (according to Nyquist) NTDR, 2014

Experimental What is the acquisition time (t a ) for the 1D NMR experiment described in this article?

SW = 7.2 kHz  Sampling rate = 2 × 7.2 kHz = 14400 Hz TD = 32k = 32 × 1024 = 32768 data points Acquisition time; t a = 32768 / 14400 ≈ 2.3 seconds NTDR, 2014

Sweep width, dwell time and sampling rate The sampling rate must be high enough to determine the frequency of the signal (at least twice per period).

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Sweep width, dwell time and sampling rate The sampling rate must be high enough to determine the frequency of the signal (at least twice per period).

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Sweep width, dwell time and sampling rate The sampling rate must be high enough to determine the frequency of the signal (at least twice per period).

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Relaxation delay After a pulse: The magnetization returns to equilibrium • M z increases, M xy decreases • Exponentially = fast in the beginning, very slowly in the end • Time constant; T = longitudinal relaxation • Small molecules, 1 H: 0.5-5 sec, 13 C: 2-60 sec 100 80

M Z

 99 .

3 % 60 40 20

M Z

M

0  ( 1 

e

t

/

T

1 ) 0 0 1 2 3 4 Time (t/T 1 ) 5 6 7 8 NTDR, 2014

Relaxation delay Pulsed NMR! Add several transients!

• …but what if the recovery is slow and the repetition time too fast?

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Relaxation delay Pulsed NMR! Add several transients!

• …but what if the recovery is slow and the repetition time too fast? Use a small flip angle!

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Relaxation delay Pulsed NMR! Add several transients!

• …but what if the recovery is slow and the repetition time too fast? Use a small flip angle! Use the delay to acquire!

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Optimum flip angle Optimize the sensitivity with the Ernst angle!

For high resolution 1 H spectra (aq ≈3×T 1 ) For accurate quantitative measurements!

For carbons with long T 1 ’s cos( a

e

) 

e

t r

/

T

1 NTDR, 2014

Processing of spectra Fourier transform (time domain -> frequency domain) NTDR, 2014

Processing of spectra Fourier transform (time domain -> frequency domain) NTDR, 2014

Processing of spectra Fourier transform (time domain -> frequency domain) NTDR, 2014

Processing of spectra Fourier transform (time domain -> frequency domain) NTDR, 2014

Processing of spectra Window function: Exponential multiplication • Line broadening 0.3 Hz • Increases apparent T 2 • Apodization (‘removal of feet’), end of FID forced to zero.

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Processing of spectra Window function: Lorentz-Gauss • Line broadening -1.0 Hz, GB = 0.25

• Resolution enhancement, trade S/N for better resolved signals NTDR, 2014

Processing of spectra Window function: Lorentz-Gauss • Line broadening -0.3 Hz, GB = 0.5

• Resolution enhancement, trade S/N for better resolved signals NTDR, 2014

Processing of spectra Window function: Traficante • Line broadening 0.2 Hz • Keep line shape, increase S/N • Real and imaginary multiplied with two different functions NTDR, 2014

Processing of spectra Window function: Sine • Sine-bell shape, for data with few points • Strong apodization function NTDR, 2014

Processing of spectra Window function: 90 degree shifted sine • Cosine shape • Used in the indirect dimension of 2D-data NTDR, 2014

Processing of spectra Window function: Mixed cosine and sine bell shape • Mixture of sine and cosine shape • Used in the indirect dimension of 2D-data NTDR, 2014

Real and imaginary parts Two phase shifted signals detected simultaneously to separate frequencies on either side of the carrier frequency.

• Quadrature detection NTDR, 2014

Phasing Fourier transform => two components • ‘Real’ and ‘imaginary’ • Linear combinations => pure absorption dispersion + pure • The base of the dispersion signal is wide (unwanted feature) NTDR, 2014

Phasing Good phasing NTDR, 2014

Phasing 0:th order phase correction NTDR, 2014

Phasing 1:st order phase correction Freq. dep.

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Phasing 0:th order + 1:st order phase correction Freq. dep.

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Phasing, tips and tricks Reset the phase parameters (PHC0 and PHC1) to zero 1.) Adjust PHC0 on one signal in one end of the spectrum 2.) Adjust PHC1 on signals in the other end… Consider the relative phase (phase errors) of signals… NTDR, 2014

Topspin in D1 User name: Password: upnmr nmr2013!

Contact to license server (50 concurrent licenses) Folder hierarchy:

/data/ /nmr/ / = C:/data/ntdr2014/nmr/ NTDR, 2014

Topspin basics 1.Prepare data directory • Make a directory named ‘ data ’ in C:\ • Make a directory named ‘ NTDR2014 ’ in C:\data • Make a directory named ‘ nmr ’ in the ‘ NTDR2014 ’-folder 2.Download dataset • http://drug.ku.dk/research/npr/nmr/ntdr2014/ • Download ‘ Exercise3.zip

’ to ‘ C:\data\NTDR2014\nmr ’ • Unzip 3.Start Topspin 3.1

• Right click in browser pane and select “Add New Data Dir..”.

• Add “ C:\ ” 4.Fourier transform [ft] and phase.

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Topspin basics They try to be more like an apple… NTDR, 2014