Obtaining an NMR Spectra

1
Obtaining an NMR Spectra

• Basic Requirements
• NMR sample compound of interest dissolved in
  500-600 ml of deuterated solvent.
• Higher the concentration ?higher the sensitivity
• Magnet differentiate spin states
  (aligned/unaligned).
• Higher the field strength ?higher the sensitivity
  and resolution
• Requires homogeneous field over the sample
• RF electronics generate RF pulse to perturb
  system equilibrium and observe NMR signal.
• Requires accurate control of pulse power and
  duration
• Stability of pulse
• Receiver electronics detection of induced
  current from nuclear precesson
• Requires high sensitivity
• Conversion of analog signal to digital signal

2
NMR Instrumentation (block diagram)
3

• Superconducting Magnet
• solenoid wound from superconducting niobium/tin
  or niobium/titanium wire
• kept at liquid helium temperature (4K), outer
  liquid N2 dewar
• near zero resistance ? minimal current lose ?
  magnet stays at field for years without external
  power source

Cross-section of magnet
magnet
spinner
sample lift
NMR Tube
RF coils
cryoshims
shimcoils
Probe
Superconducting solenoid Use up to 190 miles of
wire!
Liquid N2
Liquid He
4
NMR Sample

• Factors to Consider
• Maximize sample concentration
• Avoid precipitation or aggregation
• Use a single deuterated solvent
• Reference for lock
• Avoid heterogeneous samples ? distorts magnetic
  field homogeneity
• Avoid air bubbles, suspended particles, sample
  separation
• Avoid low quality NMR tubes ? distorts magnetic
  field homogeneity
• Breaks easily ? damage the NMR probe
• Chose appropriate temperature for the sample
• Freezing or boiling the sample may break the NMR
  tube and damage the NMR probe.
• Properly position NMR sample in the magnet
• Position sample in homogeneous region of magnet
  and between detection and RF coils
• Avoid positioning meniscus close to coil edge ?
  distorts magnetic field homogeneity

Frequency of absorption n g Bo / 2p
5

• Superconducting Magnet
• Problems
• Field drifts (B0 changes)

Field Drift over 11 Hrs ( 0.15Hz/hr
n gBo/2p
Remember
6

• Lock System
• Need to constantly correct for the field drift
  during data collection
• NMR probes contains an additional transmitter
  coil tuned to deuterium frequency
• changes in the intensity of the reference
  absorption signal controls a feedback circuit a
  frequency generator provides a fixed reference
  frequency for the lock signal
• if the observed lock signal differs from the
  reference frequency, a small current change
  occurs in a room-temperature shim coil (Z0) to
  create a small magnetic field to augment the
  main field to place the lock-signal back into
  resonance

Lock Feedback Circuit
Lock Changes From Off-resonance to On-resonance
7
Lock System Simply, the lock system can be
considered as a separate NMR spectrometer that is
constantly collecting a deuterium spectrum and
making sure the peak doesnt move relative to a
defined chemical shift
8

• Lock System things to consider
• Measures the resonance of the deuterated solvent
• a number of common solvents (D2O, methanol,
  chloroform) have known deuterium resonance
• Can only lock on one resonance, defined by user.
• Multiple deuterium resonances may confuse lock in
  automated acquisition
• NMR sample needs to contain at least 5-10 volume
  of a deuterated solvent

Consequence of locking wrong solvent wrong
chemical shifts and missing peaks!
9

• Lock System things to consider
• Maximize lock signal indicates on-resonance
• Use lock signal to shim sample
• Loss of lock during experiment is problematic?
  data not reliable
• NMR sample degraded
• Instrument problem
• Started with weak lock signal
• Increase lock signal by increasing lock gain
• Amplification of the detected lock signal
• Increases both signal and noise, so higher lock
  gain ? noisier lock signal
• Increase lock signal by increasing lock power
• Strength of RF pulse to detect lock signal
• Too high and lock signal is saturated ? intensity
  of lock signal fluctuates up and down
• Too low and lock signal may not be observable

10

• Superconducting Magnet
• Problems
• Field is not constant over sample (spatial
  variation)

n gBo/2p
Again
11
Magnetic Field Homogeneity
Frequency of absorption n g Bo / 2p
Good Homogeneity ? single peak with frequency
dependent on Bo
Poor Homogeneity ? multiple peaks at different
effective Bo Resonance depends on position in
NMR sample
12

• Shim System
• Corrects for magnetic inhomogeneity
• Spatial arrangement of 20 or more coils
• change current in each coil to patch
  differences in field and fix distortions in peak
  shape

actual shim coils
Sketch of shim coils
13

• Shim Coils
• electric currents in the shim coils create small
  magnetic fields which compensate for
  inhomogenieties in the magnet
• shim coils vary in the geometric orientation and
  function (linear, parabolic, etc)
• Z0,Z1,Z2,Z3,Z4,Z5
• X, XZ,XZ2,X2Y2,XY,Y,YZ, YZ2, XZ3,X2Y2Z,
  YZ3,XYZ,X3,Y3

14

• Shim Coils
• Optimize shims by i) minimizing line-width, ii)
  maximizing lock signal or iii) maximizing FID
• Examples of poor line-shapes due to shimming
  errors

15

• Shim Coils
• Examples of poor line-shapes due to shimming
  errors

16

• Shim Coils
• Examples of poor FID shape due to shimming errors

Perfectly Shimmed Magnet
Mis-shimmed Magnet
17

• Spinning the Sample
• Improves effective magnetic field homogeneity by
  averaging inhomogeneities in the magnet
• Z shims are also known as spinning shims
• Spinning the sample causes symmetric side-bands
  at intervals related to spinning rate
• Non-spinning shims (X,Y) problems
• Samples are never spun for multi-dimensional NMR
  experiments
• Creates artifacts ? streaks or T1 ridges from
  spinning side-bands and spinning instability

18

• Gradient Shimming
• Use pulse field gradients to automate the
  shimming (TopShim)
• Gradients - spatial changes to B0
• Gradients are used to probe (map) the Field (B0)
  profile
• A Shim Map is unique to each probe
• Requires a Strong Signal (Solvent)
• Requires H2OD2O, CH3CND2O or CH3OHD2O solvent

Shim Map
19

• Gradient Shimming
• Two General Approaches to Gradient Shimming
• 1D gradshim (Z-shims) seconds to minutes
• 3D gradient shimming (all shims) 5 to 30 minutes
• Shimming is accomplished by matching gradient
  shims for your sample to shim map

Gradient shim (red) fit to shim map
20
Gradient Shimming
Water resonance before and after Gradient Shimming
Gradient Shimming
21

• Environment Stability
• Changes in the environment during data
  acquisition may have strong negative impacts on
  the quality of the NMR data
• Common causes of spectra artifacts are
• Vibrations (building, HVAC, etc)
• Temperature changes
• The longer the data acquisition, the more likely
  these issues will cause problems
• The lower the sample concentration (lower S/N)
  the more apparent these artifacts will be

Noise peaks due to building vibrations
22
Environment Stability
Peak Chemical Shift and Shape Change as
Temperature Changes
23

• Sample Probe
• Holds the sample in a fixed position in the
  magnetic field
• Contains an air turbine to spin, insert and eject
  the sample
• Contains the coils for
• transmitting the RF pulse
• detecting the NMR signal
• observing the lock signal
• creating magnetic field gradients
• Thermocouples and heaters to
• maintain a constant temperature

24
Sample Probe Important to note, because of the
high magnetic field, the probe has to be built
with non-magnetic material such as glass and
plastics. Thus, probes tend to be fragile and
easy to break
25

• Tuning the Probe
• Placing the sample into the probe affects the
  probe tuning
• Solvent, buffers, salt concentration, sample
  concentration and temperature all have
  significant impact on the probe tuning
• Probe is tuned by adjusting two capacitors match
  and tune
• Goal is to minimize the reflected power at the
  desired frequency
• Tuning capacitor changes resonance frequency of
  probe
• Matching capacitor matches the impedance to a 50
  Ohm cable

Power submitted to transmitter and receiver is
maximized
26

• Tune and Match System
• Tune- corrects the differences between observed
  and desired frequency
• Match correct impedance difference between
  resonant circuit and transmission line (should be
  50W )
• Adjust two capacitors until the tuning and
  desired frequency match and you obtain a null

Affects signal-to-noise accuracy of 90o
pulse sample heating chemical shift accuracy
27
Tune and Match System Tune and Match
capacitors for a Bruker Probe
28
Tune and Match System Changing the Distance
Between the Plates or the Amount of Plate
Surface Area which overlaps in a Variable
Capacitor
Physical limits to how far the capacitor can be
turned in either direction. If turned too far
will easily break!!
29

• Tuning the Probe
• Side Notes Impedance
• Impedance any electrical entity that impedes
  the flow of current
• a resistance, reactance or both
• Resistance material that resists the flow of
  electrons
• Reactance property of resisting or impeding the
  flow of ac current or ac voltage in inductors and
  capacitors
• Illustration of matching impedance
• Consider a 12V car battery attached to a car
  headlight
• 12V car battery low impedance ? high power
• Consider 8 1.5V AA batteries (12 volt total)
  attached to a very low wattage light bulb
• 8 1.5V AA batteries high impedance ? low power
• Now swap the arrangement ? What happens?
• Car battery can easily light the light bulb, but
  the headlight will quickly drain the AA batteries
  ? poor impedance match

30

• Tuning the Probe
• Side Notes Quality factor (Q)
• Q - dimensionless and important property of
  capacitors and inductors
• Q - frequency of the resonant circuit divided by
  the half power bandwidth
• All inductors exhibit some extra resistance to ac
  or rf
• Q is the reactance of the inductor divided by
  this ac or rf resistance
• NMR probes Q gt 300
• Higher the probe Q the greater the sensitivity
• High Q for an NMR probe is required for high
  Signal-to-Noise
• Sample can effect the Q of the probe
• The sample increases losses in the resonant
  circuit by inducing eddy currents in the solvent
• The more conductive the sample the more the
  losses and the lower the probe Q.
• Water, high salt lower the Q of the probe
• Lower Q ? longer pulse widths

X reactance of circuit in Ohms RL the series
resistance of the circuit in Ohms
31

• Pulse Generator Receiver System
• Radio-frequency generators and frequency
  synthesizers produce a signal at essentially a
  single frequency.
• RF pulses are typically short-duration (msecs)
• - produces bandwidth (1/4t) centered around
  single frequency
• - shorter pulse width ? broader frequency
  bandwidth
• Heisenberg Uncertainty Principal Du.Dt 1/2p
• - Shortest pulse length will depend on the probe
  Q and the sample property

A radiofrequency pulse is a combination of a wave
(cosine) of frequency wo and a step function
The Fourier transform indicates the pulse covers
a range of frequencies
32

• Pulse Generator Receiver System
• RF pulse width determines band-width of
  excitation
• - Not a flat profile
• - All nuclei within 1/4PW Hz will be equally
  affected
• 1H 6 ms 90o pulse ? 41666 Hz ? 69.4 ppm at 600
  MHz
• Minimizes weaker perturbations of spins a edges
  of spectra
• - There are also null points at 1/PW Hz where
  nuclei are unperturbed
• 1H 6 ms 90o pulse first null at 1.67e5 Hz ?
  277.8 ppm at 600 MHz

33

• Pulse Generator Receiver System
• RF pulse width determines band-width of
  excitation
• - These issues become a problem at high magnetic
  field strengths (800 900 MHz) for 13C spectra
  that that have a large chemical shift range (gt200
  ppm)
• 13C 15 ms 90o pulse ? 16666 Hz ? 18.5 ppm at
  900 MHz
• Also, complex experiments (multiple pulses)
  depend on the accuracy and consistency of pulse
  widths
• - Selective pulse ? long pulse width (ms) ?narrow
  band-width.

34

• Pulse Length Calibration
• Need to experimentally determine 90o pulse
• - Measure intenisty of major peak (solvent) in
  spectrum as the function of 90o pulse length (P1)
• Maximum at 900 and minimum at 360o
• Usually measure 90o pulse at 360o time point

35
Pulse Length Calibration
90o pulse (12 ms)
180o pulse (24 ms)
360o pulse (44 ms)
The pulse width was arrayed from 2 ms to 60 ms in
steps of 2 ms 90o pulse is 11 ms
270o pulse (32 ms)
36

• Pulse Generator Receiver System
• A magnetic field perpendicular to a circular loop
  will induce a current in the loop.
• 90o NMR pulses places the net magnetization
  perpendicular to the probes receiver coil
  resulting in an induced current in the nanovolt
  to microvolt range
• preamp mounted in probe amplifies the current to
  0 to 10 V
• no signal is observed if net magnetization is
  aligned along the Z or Z axis

Rotates at the Larmor frequency
n gBo/2p
37
Continuous Wave (CW) vs. Pulse/Fourier Transform

• Continuous Wave sweep either magnetic field or
  frequency until resonance is observed
• absorbance observed in frequency domain

Pulse/Fourier Transform perturb and monitor all
resonances at once absorbance
observed in the time domain
38
Continuous Wave (CW) vs. Pulse/Fourier Transform
NMR Sensitivity Issue
A frequency sweep (CW) to identify resonance is
very slow (1-10 min.) Step through each
individual frequency.
Pulsed/FT collect all frequencies at once in time
domain, fast (N x 1-10 sec) All modern
spectrometers are FT-NMRs
39
Continuous Wave (CW) vs. Pulse/Fourier Transform

• Fourier Transform NMR
• Observe each individual resonance as it precesses
  at its Larmor frequency (wo) in the X,Y plane.
• Monitor changes in the induced current in the
  receiver coil as a function of time.

40

• Fourier Transform NMR
• Signal-to-noise increases as a function of the
  number of scans or transients
• Increases data collection time
• There are inherent limits
• Gain in S/N will eventually plateau
• The initial signal has to be strong enough to
  signal average.

Increase signal-to-noise (S/N) by collecting
multiple copies of FID and averaging signal.
41
Fourier Transform NMR
Increase signal-to-noise (S/N) by collecting
multiple copies of FID and averaging
signal. But, total experiment time is
proportional to the number of scans exp. time
(number of scans) x (recycle delay D1)

42

• Fourier Transform NMR
• Recycle time (D1) time increment between
  successive FID collection
• Maximum signal requires waiting for the sample to
  fully relax to equilibrium (5 x T1)
• T1 NMR relaxation parameter that will be
  discussed in detail later in the course
• Most efficient recycle delay is 1.3 x T1

Relative S/N per unit time of data collection
1.3T1
Repetition time (tT/T1)
Optimize your repetition time
43

• Fourier Transform NMR
• Recycle time (D1) time increment between
  successive FID collection
• Typical T1s for organic compounds range from 50
  to 0.5 seconds
• T1 relaxation times also vary by nuclei, where
  13C gt 1H
• Either estimates from related compounds or
  experimental measurements of T1 is required to
  optimize data collection ? especially for long
  data acquisitions.

44
Continuous Wave (CW) vs. Pulse/Fourier Transform

• Fourier Transform NMR
• NMR signal is collected in Time Domain, but
  prefer Frequency Domain
• Transform from time domain to frequency domain
  using the Fourier function

Fourier Transform is a mathematical procedure
that transforms time domain data into frequency
domain
45

• Sampling the NMR (Audio) Signal
• Collect Digital data by periodically sampling
  signal voltage
• ADC analog to digital converter

46

• Sampling the NMR (Audio) Signal
• Collect Digital data by periodically sampling
  signal voltage
• ADC analog to digital converter

Sample intensity of voltage induced in coil by
y-vector of net magnetization precessing in
x,y-plane
47

• Sampling the NMR (Audio) Signal
• To correctly represent Cos/Sin wave, need to
  collect data at least twice as fast as the signal
  frequency
• If sampling is too slow, get folded or aliased
  peaks

The Nyquist Theorem says that we have to sample
at least twice as fast as the fastest (higher
frequency) signal.
48
Digital Resolution number of data points
The FID is digitized
Equal delay between points (dwell time)
DT 1 / (2 SW)
Want to maximize digital resolution, more data
points increases acquisition time (AQ) and
experimental time (ET) AQ DT x NP ET AQ
x NS larger spectral width (SW) requires more
data points for the same resolution
49
Sampling the NMR (Audio) Signal
Sweep width (Hz, ppm) needs to be set to cover
the entire NMR spectra
Sweep Width
(range of radio-frequencies monitored for nuclei
absorptions)
If SW is too small or sampling rate is too slow,
than peaks are folded or aliased (note phase
change)
50
Sampling the NMR (Audio) Signal
SW is decreased
The phase of folded peaks can vary (a) negative
phase, (b) dispersive or (c) positive phase.
51
Sampling the NMR (Audio) Signal
Always set SW to be slightly larger than needed
to cover the entire spectrum. Allow for blank
space at both low and high chemical shifts.
52
Sampling the NMR (Audio) Signal

• NMR data size
• Analog signal is digitized by periodically
  monitoring the induced current in the receiver
  coil
• How many data points are collected?
• What is the time delay between data points?
• How long do you sample for?
• Sample too long ? collecting noise wasting time

Higher Digital Resolution requires longer
acquisition times
53
Sampling the NMR (Audio) Signal

• NMR data size
• How long do you sample for?
• Sample too short ?dont collect all the data,
  lose resolution get artifacts

Truncated FID leads to artifacts
54
Sampling the NMR (Audio) Signal

• NMR data size
• Digital Resolution (DR) number of Hz per point
  in the FID for a given spectral width.
• DR SW / TD
• where
• SW spectral width (Hz)
• TD data size (points)

55
Sampling the NMR (Audio) Signal

• NMR data size
• Dwell Time (DW) constant time interval between
  data points.
• SW 1 / (2 DW)
• From Nyquist Theorem, Sampling Rate (SR)
• SR 1 / (2 SW)
• DR, DW, SW, SR, TD are ALL Dependent Valuables

56
Sampling the NMR (Audio) Signal

• NMR data size
• Two Parameters that the spectroscopist needs to
  set
• SW spectral sweep width
• Should be just large enough to include the entire
  NMR spectra
• TD total data points
• Determines the digital resolution
• Contributes to the total experiment time
  (acquisition time)
• Should be large enough to collect entire FID

57
Sampling the NMR (Audio) Signal

• NMR data size
• Increase in the number of data points ? increase
  in resolution
• Increases acquisition time

Increase in data points, resolution and
acquisition time
58
Sampling the NMR (Audio) Signal

• NMR data size
• Under sampling the data ? truncated FID
• Baseline distortions ? sinc wiggles

Sinc wiggles
59
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Uniform Data Sampling
• Traditionally, NMR acquires EVERY data point with
  a uniform time-step (DW) between points
• avoids under-sampling frequencies
• FT algorithms expect uniform spacing of digital
  data
• Reason why nD NMR experiments take so long to
  collect
• Why FIDS are truncated
• Why spectra have low resolution and sensitivity
• No reason why the all the points of the FID need
  to be collected

60
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• Significant improvement in resolution and
  sensitivity for nD NMR data
• Dont need uniform sampling, just need
  alternative to FFT to process the data.
• The sampling non-uniform scheme is the primary
  decision and impact on the spectra

Exponential in both t1 and t2
exponential in t1 and linear in t2
randomly sampled from an exponential distribution
in t1 and t2
Random in t1 and t2.
Graham A. Webb (ed.), Modern Magnetic Resonance,
13051311.
61
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• VERY IMPORTANT POINT, tn is no longer defined by
  DW and number of points
• tn is now user defined since DW is no longer
  relevant.
• Avoid FID truncation, maximize resolution

Traditional NMR FID is truncated because number
of points and DW determine how much of the FID
can be collected
NUS NMR FID is under-sampled, but the entire FID
is sampled
62
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• Both noise (N) and signal to noise (SNR) are
  proportional to the total evolution time
• Optimal setting is 1.3T2 of the evolving
  coherence
• Maximize sensitivity

Magn. Reson. Chem. 2011, 49, 483491
63
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• What is the optimal sampling density?
• Increase enhancement by increase exponential
  bias, eventually regenerate truncated FID
• Highly resolved spectra is pT2

• TSMP time constant for the exponential
• weighting of the sampling.
• enhancement
• lw line width

Magn. Reson. Chem. 2011, 49, 483491
64
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• A 1.5 to 2.0 bias to early data points and a 4x
  reduction yields a 2x enhancement
• Or a 3T2 with a 3x reduction yields a 1.7
  enhancement

Magn. Reson. Chem. 2011, 49, 483491
65
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• Different sampling schemes have different
  performances at different sampling densities
• Sinusoidal Poisson Gap is currently the best
  random sampling, while minimizing gap size
  particularly at the beginning and end of the FID
• Some drastic sampling densities at 1 or less.

Top Curr Chem. 2012 316 125148
66
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• Dramatic gain in the quality of strychnine NMR
  spectrum with 25 sampling density
• The spectrum was collected 4x faster (10 min. vs.
  40 min.)

Non-Uniform Sampling
Uniform Sampling
Nat. Prod. Rep. 2013 30 501-524
67
Sampling the NMR (Audio) Signal

• NMR Data Processing Software
• Non-uniform data sampling
• How is the time-domain data processed?
• Use the partial data to reconstruct the full
  Nyquist grid then process as normal
• maximum entropy reconstruction is a common
  approach
• forward maximum entropy (FM), fast maximum
  likelihood reconstruction (FMLR)
• multi-dimensional decomposition (MDD) and
  compressed sensing (CS)
• MddNMR http//www.enmr.eu/webportal/mdd.html
• Newton http//newton.nmrfam.wisc.edu/newton/stati
  c_web/index.html
• RNMRTK http//rnmrtk.uchc.edu/rnmrtk/RNMRTK.html
• mpiPipe Available by contacting the Wagner Group

68
Sampling the NMR (Audio) Signal

• Adjusting the Receiver Gain (RG) electronic
  amplification of the signal
• There is an optimal setting guided by the limits
  of the ADC digitizer
• FID intensity changes as the number of
  transients increase during data acquisition

RG depends on NS
Increase in FID Intensity with number of
transients
69
Sampling the NMR (Audio) Signal

• Adjusting the Receiver Gain (RG) electronic
  amplification of the signal
• If RG set too high, the digitizer is full and
  the FID is clipped
• Fourier transform of a clipped FID results in
  sinc wiggles in the spectrum baseline.

70
Sampling the NMR (Audio) Signal

• Adjusting the Receiver Gain (RG) electronic
  amplification of the signal
• If RG is set too low, the spectrum will be
  noisy.
• RG should be set as increments of 2, where there
  is a maximum limit
• RG may be set to higher values, but no effect on
  the spectra will be observed
• RG may be set to non-factors of two, but adjusted
  to nearest factor of 2.

71
Sampling the NMR (Audio) Signal

• Solvent suppression
• solvent concentration is significantly larger
  than the sample concentration
• water is 55M compared to typical mM mM of
  compound

With Solvent Suppression
Without Solvent Suppression
72
Sampling the NMR (Audio) Signal

• Solvent suppression
• strong solvent signal can fill digitizer making
  it impossible to observe the sample signal
• Dynamic range problem
• 16K 32K range of intensities
• Need to suppress intense solvent signals with
  selective saturation pulse
• will discuss different NMR pulses in detail
  latter

The most intense peak is set to the largest value
in the digitizer and every other peak is scaled
accordingly
73
Sampling the NMR (Audio) Signal

• Dynamic range
• defines the range of signal amplitudes (peak
  intensities) observed in the spectrum
• Typically 16 bit or 18 bit digitizers
• 16 bit digitizer FID amplitudes range from
  -215 to 215
• peak smaller than 1/32768 (16 bit) or 1/131072
  (18 bit) of most intense peak is lost!!

32768
Peak intensity has to fit between range of 1215
1
74

• Quadrature detection
• Frequency of B1 (carrier) is set to the center of
  the spectrum.
• Small pulse length to excite the entire spectrum
• Minimizes folded noise

75

• Quadrature detection
• Frequency of B1 (carrier) is set to the center of
  the spectra.
• Rate of precession in X,Y plane is related to
  carrier frequency
• Precession is difference from carrier frequency
• Possible to have resonances with same frequency
  but opposite direction

76

• Quadrature detection
• How to differentiate between peaks upfield and
  downfield from carrier?
• observed peak frequencies are all relative to the
  carrier frequency

Same Frequency! Opposite sign
carrier
How to differentiate between magnetization that
precesses clockwise and counter clockwise?
77

• Quadrature detection
• If carrier at edge of spectrum, peaks are all
  positive or negative relative to carrier
• Excite twice as much noise, decrease S/N
• Half of the digital resolution
• Half of the spectrum is irrelevant noise

PW excites a corresponding bandwidth of
frequencies centered on carrier
carrier
All this noise added to spectrum
78
Quadrature detection
PH 0
B
F
B
Use two detectors 90o out of phase.
w (B1)
F
PH 90
PH 0
F
B
Phase of Peaks are different.
PH 90
F
B
79
Quadrature detection
Use two detectors 90o out of phase. FT is
designed to handle two orthogonal input functions
called the real and imaginary component
Detector along X-axis (real component of FT)
Detector along Y-axis (imaginary component of FT)
Phase of Peaks are different ? allows
differentiation of frequencies relative to
carrier
80
Phase Correction of the NMR Spectrum
Depending on when the FID data collection begins
a phase shift in the data may occur.
Phase Shift
Phase correction of the NMR spectrum compensates
for this phase shift.
81
Phase Correction of the NMR Spectrum
Phase shift depends on the frequency of the signal
Phase Shift
82
Phase Correction of the NMR Spectrum
Phase Shift
Phase Correct
Manually adjust zero-order (PO) and first-order
(P1) parameters to properly phase spectra.
83
Phase Correction of the NMR Spectrum

• What is happening mathematically during manual
  phasing of an NMR spectrum
• Fourier transformed data contains a real part
  that is an absorption Lorentzian and an imaginary
  part which is a dispersion Lorentzian
• we want to maintain the real absorption mode
  line-shape
• done by applying a phase factor (exp(iQ)) to set
  F to zero
• we are effectively discarding the imaginary
  component of the spectrum

84
Phase Correction of the NMR Spectrum
If you over-phase the spectrum, you get
baseline roll
85
Phase Correction of the NMR Spectrum

• Power or Magnitude spectrum
• obtain a pure absorption NMR spectrum without
  manual phasing
• results in broader spectrum that can not be
  integrated
• not a typical or preferred approach to
  processing an NMR spectrum

86
Zero Filling of the NMR Spectrum

• Improve digital resolution by adding zero data
  points at end of FID
• essential for n-Dimensional NMR data
• real gain in resolution is limited to
  zero-filling to 2AQ ( in theory) or 4AQ in
  practice

8K data
8K zero-fill
8K FID
16K FID
No zero-filling
8K zero-filling
87
Zero Filling of the NMR Spectra

• Better example of the resolution gain and
  benefits of zero-filling NMR spectra

4AQ zero-filling
No zero-filling
88

• Applying a Window Function to NMR data
• Emphasize the signal and decrease the noise by
  applying a mathematical function to the FID.
• Can also increase resolution at the expense of
  sensitivity
• Applied to the FID before FT and zero-filling

89
Applying a Window Function to NMR data
Simply Multiple FID with a Mathematical Function
F(t) e - ( LB t )
X

90
Applying a Window Function to NMR data
Can either increase S/N or
Resolution Not Both!
91
Applying a Window Function to NMR data
A Variety of Different Apodization or Window
functions
92
Applying a Window Function to NMR data

• A main goal in applying a window function for a
  nD NMR spectra is to remove the truncation by
  forcing the FID to zero.

Truncated FID with spectra wiggles
Apodized FID removes truncation and wiggles
93
Baseline Correction of NMR Spectrum

• It is not uncommon to occasionally encounter
  baseline distortions in the NMR spectra
• The baseline can be corrected by applying a
  linear fit, polynomial fit, spline fit or other
  function to the NMR spectrum.

Spline baseline correction
94
Baseline Correction of NMR Spectrum
A number of factors lead to baseline
distortions Intense solvent or buffer
peaks Phasing problems Errors in first data
points of FID Short recycle tines Short
acquisition times Receiver gain
polynomial baseline correction
Xi Roche BMC Bioinformatics (2008) 9234
95

• NMR Peak Description
• Peak height intensity of the peak relative to
  the baseline (average noise)
• Peak width width (in hertz) at half the
  intensity of the peak
• Line-shape NMR peaks generally resemble a
  Lorentzian function
• A amplitude or peak height
• (LW1/2) peak width at half height (Hz)
• Xo peak position (Hz)

LW1/2
96

• NMR Peak Integration or Peak Area
• The relative peak intensity or peak area is
  proportional to the number of protons associated
  with the observed peak.
• Means to determine relative concentrations of
  multiple species present in an NMR sample.

Relative peak areas Number of protons
97

• NMR Peak Integration or Peak Area
• Means to determine relative concentrations of
  multiple species present in an NMR sample.
• Need to verify complete or uniform relaxation

ortho
Methyl Region of NMR Spectrum
meta (21.3 ppm)
meta
para (20.9 ppm)
ortho (19.6 ppm)
para
impurities
impurities
98

• NMR Peak Integration or Peak Area
• NMR titration experiments are routinely used to
  monitor the progress of a reaction or interaction
  
• By monitoring changes in the area or intensity of
  an NMR peak

99
Peak Picking NMR Spectra

• One of the basic steps in analyzing NMR spectra
  is obtaining a list of observed chemical shifts
• Usually refereed to as peak picking
• Most programs have similar functionality, choice
  is based on personal preference
• display the data (zoom, traces, step through
  multiple spectra, etc)
• Peak-picking identify the X,Y or X,Y,Z or
  X,Y,Z,A chemical shift coordinate positions for
  each peak in the nD NMR spectra

Peak Picking List
100
Peak Picking NMR Spectra

• Critical for obtaining accurate NMR assignments
• Especially for software for automated
  assignments
• Only provide primary sequence and peak-pick
  tables
• Two General Approaches to Peak Picking
• Manual
• time consuming
• can evaluate crowded regions more effectively
• Automated
• pick peaks above noise threshold
• OR
• pick peaks above threshold with
• characteristic peak shape
• only about 70-80 efficient
• crowded overlap regions and noise
• regions (solvent, T2 ridges) cause problems
• noise peaks and missing real peaks cause
• problems in automated assignment software

J. OF MAG. RES. 135, 288297 (1998)