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![Page 1: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/1.jpg)
NTDR, 2014
Nils NybergNPR, Department of Drug Design and Pharmacology
Basic principles of NMRNMR signal origin, properties, detection, and processing
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NTDR, 2014
Outline
1000 – 1045
• Establishing current knowledge level• Nuclear Magnetic Resonance phenomenon• Vector model, in and out of the rotating frame
1045 – 1100
• Short break1100 – 1130
• 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)
1130 – 1200
• Spin-echo exercise1215 – 1315
• Lunch
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NTDR, 2014
Outline
1215 – 1315
• Lunch1315 – 1415
• Signal processing• Window functions• Fourier transform• Real and imaginary parts• Phasing• Topspin starter
![Page 4: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/4.jpg)
NTDR, 2014
Establishing current knowledge level
Build (sketch) a NMR-instrument!
• Magnet• Probes• Amplifiers• Receiver• ADC• Gradients• Temperature control• Lock• Shimming
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NTDR, 2014
Establishing current knowledge level
Draw a spectrum!
• Chemical shifts• Integrals• Phases• Coupling constants• Line widths
• life time of signals, shimming, exchange, dynamics
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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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NTDR, 2014
Resonance
A system prefers some frequencies over others…
A small energy input at the right frequency will give large oscillations…
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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: 12C, 16OSpin I = ½: 1H, 13C, 15N, 19F, 31P, 77SeSpin I = 1: 2H, 14NSpin I = 1½: 33S, 35Cl, 37Cl
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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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NTDR, 2014
Chemical shifts
• A magnet provides the static field (B0) in the NMR instrument.
• The rest of the molecule provides a ’local magnetic field’, which is dependent on structure.
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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’.
NTDR, 2014
• Less shielded• More
deshielded• Downfield• Higher
frequency
• More shielded• Less deshielded• Upfield• Lower
frequency
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NTDR, 2014
Vector model (a statistical abstraction…)
Unordered collection of½-spin nuclei, with a magnetic moment (μ).
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NTDR, 2014
Vector model
Unordered collection of½-spin nuclei, with a magnetic moment (μ).
In an external magnetic field, the magnetic moment starts to precess…
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NTDR, 2014
Vector model
Unordered collection of½-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…
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NTDR, 2014
Vector model
Unordered collection of½-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![1H, 600 MHz, 298 K]
273.15) (TcK in eTemperatur T
)(s Hz Frequency,
constant)(Planck Js 106.6
constant) (BoltzmannJ/K 104.1
logarithm) (natural 718.2
)exp(
1-
34
23
)(
h
k
hE
e
eTk
E
N
N Tk
E
![Page 17: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/17.jpg)
NTDR, 2014
Boltzmann distribution
One spin extra in the low energy state![1H, 600 MHz, 298 K]
Nβ = 12 922
Nα = 12 923
Σ = 25 845
12922
)1(
1
))exp(1(
1
1))exp(1(
1)exp(
)exp(1
)exp(1
)exp(
)298104.1
10600106.6(
23
634
e
N
Tkh
N
Tk
hN
NTk
hN
NTk
hN
Tk
h
N
N
Tk
E
N
N
![Page 18: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/18.jpg)
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, B1) perpendicular to the first (B0) have two effects:
![Page 19: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/19.jpg)
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, B1) perpendicular to the first (B0) have two effects:
• Creation of phase coherence (‘bunching of spins’)
![Page 20: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/20.jpg)
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, B1) perpendicular to the first (B0) have two effects:
• Creation of phase coherence (‘bunching of spins’)
• Switch from up- to down-spin (or down- to up- !)
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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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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 ‘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
T1-relaxation• Exponential recovery of
magnetization along B0-axis• Back to equilibrium populations
of up- and down-spin
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NTDR, 2014
Relaxation
T1-relaxation• Exponential recovery of
magnetization along B0-axis• Back to equilibrium populations
of up- and down-spin
T2-relaxation• Gradual ‘fanning’ out of
individual magnetic vector.• emission-absorption
among spins (changes phase)
• bad homogeneity of magnetic field
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NTDR, 2014
Relaxation
T1-relaxation• Exponential recovery of
magnetization along B0-axis• Back to equilibrium populations
of up- and down-spin
T2-relaxation• Gradual ‘fanning’ out of
individual magnetic vector.• emission-absorption
among spins (changes phase)
• bad homogeneity of magnetic field
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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 n½.
nN
Sn
n
N
S
11 pB
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Phase of pulses and signals
Basic 1D NMR-experiment: With a 90°-pulse along the x-axis
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NTDR, 2014
Phase of pulses and signals
Basic 1D NMR-experiment: With a 90°-pulse along the y-axis
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NTDR, 2014
Phase of pulses and signals
The phase of the pulse gives the phase of the signal…
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NTDR, 2014
Phase of pulses and signals
X
Y
X
Y
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NTDR, 2014
Phase of pulses and signals
X
Y
X
Y
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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
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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
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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
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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
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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)
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Spin-echoes in pulse sequences
Chemical shifts are refocused
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NTDR, 2014
Spin-echoes in pulse sequences
Chemical shifts are refocused
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NTDR, 2014
Spin-echoes in pulse sequences
Chemical shifts are refocused
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NTDR, 2014
Spin-echoes in pulse sequences
Couplings evolve (if both of the coupled nuclei are inverted)
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NTDR, 2014
Spin-echoes in pulse sequences
Couplings evolve (if both of the coupled nuclei are inverted)
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NTDR, 2014
Spin-echoes in pulse sequences
Couplings evolve (if both of the coupled nuclei are inverted)
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Spin-echo example
Explain the appearance of the normal 1H spectrum of the hypothetical molecule.
12C 13C
Hb Ha
3JH,H=10 Hz
1JC,H=145 Hz
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Spin-echo exercise I12C 13C
Hb Ha
3JH,H=10 Hz
1JC,H=145 Hz
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?
12C 13C
Hb Ha
3JH,H=10 Hz
1JC,H=145 Hz
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NTDR, 2014
Spin-echo exercise I12C 13C
Hb Ha
3JH,H=10 Hz
1JC,H=145 Hz
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NTDR, 2014
Spin-echo exercise II12C 13C
Hb Ha
3JH,H=10 Hz
1JC,H=145 Hz
![Page 48: NTDR, 2014 Nils Nyberg NPR, Department of Drug Design and Pharmacology Basic principles of NMR NMR signal origin, properties, detection, and processing.](https://reader038.fdocuments.net/reader038/viewer/2022110320/56649cc15503460f9498862a/html5/thumbnails/48.jpg)
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LUNCH
The lunch is served in the cafeteria in building 22
1215-1315
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Outline
1215 – 1315
• Lunch1315 – 1415
• Signal processing• Window functions• Fourier transform• Real and imaginary parts• Phasing• Topspin starter
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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 (ta).
ta = 10 seconds Δν= 0.1 Hz
ta. = 0.1 seconds Δν= 10 Hz
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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
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Spectral width, sampling rate & dwell time
Dwell time = Time between sampling pointsSampling rate = Number of data points per secondSampling rate = Total no. of data points / acquisition timeDwell time = (Sampling rate)-1
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NTDR, 2014
Spectral width, sampling rate & dwell time
Dwell time = Time between sampling pointsSampling rate = Number of data points per secondSampling rate = Total no. of data points / acquisition timeDwell time = (Sampling rate)-1
Faster sampling larger spectral width (sw)Spectral width = ½ × Sampling rate (according to Nyquist)
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NTDR, 2014
Experimental
What is the acquisition time (ta) for the 1D NMR experiment described in this article?
SW = 7.2 kHz Sampling rate = 2 × 7.2 kHz = 14400 HzTD = 32k = 32 × 1024 = 32768 data pointsAcquisition time; ta = 32768 / 14400 ≈ 2.3 seconds
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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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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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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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NTDR, 2014
Relaxation delay
0 1 2 3 4 5 6 7 80
20
40
60
80
100
Mz (
%)
Time (t/T1)
)1( 1/0
TtZ eMM
%3.99ZM
After a pulse: The magnetization returns to equilibrium• Mz increases, Mxy decreases• Exponentially = fast in the beginning, very slowly in the
end• Time constant; T = longitudinal relaxation• Small molecules, 1H: 0.5-5 sec, 13C: 2-60 sec
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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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NTDR, 2014
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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NTDR, 2014
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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NTDR, 2014
Optimum flip angle
Optimize the sensitivity with the Ernst angle!
1/)cos( Tte
re
For carbons with long T1’s
For high resolution 1H spectra (aq ≈3×T1)
For accurate quantitative measurements!
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NTDR, 2014
Processing of spectra
Fourier transform (time domain -> frequency domain)
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NTDR, 2014
Processing of spectra
Fourier transform (time domain -> frequency domain)
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NTDR, 2014
Processing of spectra
Fourier transform (time domain -> frequency domain)
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NTDR, 2014
Processing of spectra
Fourier transform (time domain -> frequency domain)
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NTDR, 2014
Processing of spectra
Window function: Exponential multiplication• Line broadening 0.3 Hz• Increases apparent T2
• Apodization (‘removal of feet’), end of FID forced to zero.
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NTDR, 2014
Processing of spectra
Window function: Lorentz-Gauss• Line broadening -1.0 Hz, GB = 0.25• Resolution enhancement, trade S/N for better resolved signals
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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
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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
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NTDR, 2014
Processing of spectra
Window function: Sine• Sine-bell shape, for data with few points• Strong apodization function
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NTDR, 2014
Processing of spectra
Window function: 90 degree shifted sine• Cosine shape• Used in the indirect dimension of 2D-data
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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
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NTDR, 2014
Real and imaginary parts
Two phase shifted signals detected simultaneously to separate frequencies on either side of the carrier frequency.
• Quadrature detection
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NTDR, 2014
Phasing
Fourier transform => two components• ‘Real’ and ‘imaginary’• Linear combinations => pure absorption + pure
dispersion• The base of the dispersion signal is wide (unwanted
feature)
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NTDR, 2014
Phasing
Good phasing
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NTDR, 2014
Phasing
0:th orderphase correction
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NTDR, 2014
Phasing
1:st orderphase correction
Freq. dep.
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NTDR, 2014
Phasing
0:th order+1:st orderphase correction
Freq. dep.
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NTDR, 2014
Phasing, tips and tricks
Reset the phase parameters (PHC0 and PHC1) to zero
1.) Adjust PHC0 on one signal in one end of the spectrum2.) Adjust PHC1 on signals in the other end…
Consider the relative phase (phase errors) of signals…
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NTDR, 2014
Topspin in D1
User name: upnmrPassword: nmr2013!
Contact to license server (50 concurrent licenses)
Folder hierarchy:<Dir>/data/<user>/nmr/<experiment name><Dir>/<experiment name>
<Dir> = C:/data/ntdr2014/nmr/
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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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NTDR, 2014
Topspin basics
They try to be more like an apple…