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
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
4
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
5

• Superconducting Magnet
• solenoid wound from superconducting niobium/tin
  or niobium/titanium wire
• kept at liquid helium temperature (4K), outer
  liquid N2 dewar
• 1) 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
6

• 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

7

• 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

8

• 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

9

• 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
10

• Lock System
• NMR magnetic field slowly drifts with time.
• Need to constantly correct for the field drift
  during data collection
• c) Deuterium NMR resonance of the solvent is
  continuously irradiated and monitored to maintain
  an on-resonance condition
• 1) changes in the intensity of the reference
  absorption signal controls a
• feedback circuit
• 2) a frequency generator provides a fixed
  reference frequency for the lock
• signal
• 3) 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
• d) NMR probes contains an additional transmitter
  coil tuned to deuterium frequency

Lock Feedback Circuit
Field Drift over 11 Hrs ( 0.15Hz/hr
11

• Lock System
• 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
• 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

Lock Changes From Off-resonance to On-resonance
12

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

13

• 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
14

• Tuning the Probe
• Side Notes Impedance and Quality factor (Q)
• 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

15

• Tuning the Probe
• Side Notes Impedance and 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

16

• Pulse Generator Receiver System
• Radio-frequency generators and frequency
  synthesizers produce a signal of essentially a
  single frequency.
• RF pulses are typically short-duration (msecs)
• 1) produces bandwidth (1/4t) centered around
  single frequency
• 2) shorter pulse width ? broader frequency
  bandwidth
• i. Heisenberg Uncertainty Principal Du.Dt
  1/2p
• 3) 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
17

• Pulse Generator Receiver System
• RF pulse width determines band-width of
  excitation
• 1) Not a flat profile
• 2) 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
• 3) 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
• 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)
• Also, complex experiments (multiple pulses)
  depend on the accuracy and consistency of pulse
  widths
• Selective pulse ? long pulse width (ms) ?narrow
  band-width.

18

• 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
• e) preamp mounted in probe amplifies the
  current to 0 to 10 V
• f) no signal is observed if net magnetization
  is aligned along the Z or Z axis

Rotates at the Larmor frequency
n gBo/2p
19
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
20
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
21
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.

FID Free Induction Decay
Increase signal-to-noise (S/N) by collecting
multiple copies of FID and averaging signal.
S/N r number of
scans

22

• 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.

S/N r number of scans
23

• 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
• 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.

24
Continuous Wave (CW) vs. Pulse/Fourier Transform
Fourier Transform NMR c) NMR signal is collected
in Time domain, but prefer frequency domain d)
Transform from the time domain to the frequency
domain using the Fourier function
Fourier Transform is a mathematical procedure
that transforms time domain data into frequency
domain
25

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

Continuous FID
Digitized FID
26
Sampling the NMR (Audio) Signal b) To correctly
represent Cos/Sin wave, need to collect data at
least twice as fast as the signal
frequency c) 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.
Sample Rate
- Correct rate, correct frequency
SR 1 / (2 SW)

• ½ correct rate, ½ correct frequency Folded peaks!
• Wrong phase!

SR sampling rate SW sweep width
27
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)
28
Sampling the NMR (Audio) Signal
Correct Spectra
Spectra with carrier offset resulting in peak
folding or aliasing
The phase of folded peaks can vary (a) negative
phase, (b) dispersive or (c) positive phase.
29
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
• Sample too short ?dont collect all the data
  lose resolution

All this noise added to spectra
FID signal is truncated
Higher Digital Resolution requires longer
acquisition times
30
Sampling the NMR (Audio) Signal
NMR data size c) 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)
d) Dwell Time (DW) constant time interval
between data points. SW 1 / (2
DW) e) From Nyquist Theorem, Sampling Rate (SR)
SR 1 / (2 SW) f) ALL Dependent Valuables
31
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 (acquisition
  time)
• Should be large enough to collect entire FID

32
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
33
Sampling the NMR (Audio) Signal

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

Sinc wiggles
34
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

Digitizer has a finite data range
35
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.

36
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
• 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

With Solvent Suppression
Without Solvent Suppression
37

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

carrier
PW excites a corresponding bandwidth of
frequencies
carrier
same frequency relative to the carrier, but
opposite sign.
38

• Quadrature detection
• a) 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

carrier
same frequency relative to the carrier, but
opposite sign.
Counter clockwise magnetization traveling
slower than rotating frame
Clockwise magnetization traveling faster than
rotating frame
39
Quadrature detection b) How to differentiate
between peaks upfield and downfield from
carrier? 1) observed peak frequencies are
all relative to the carrier frequency
c) If carrier is at edge of spectra, then peaks
are all positive or negative relative to
carrier 1) Excite twice as much noise, decrease
S/N
How to differentiate between magnetization that
precesses clockwise and counter clockwise?
PW excites a corresponding bandwidth of
frequencies
carrier
All this noise added to spectra
40
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
41
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
42
Phase Correction of the NMR Spectra
Depending on when the FID data collection begins
a phase shift in the data may occur.
Phase Shift
Phase correction of the NMR spectra compensates
for this phase shift.
43
Phase Correction of the NMR Spectra
Phase shift depends on the frequency of the signal
Phase Shift
44
Phase Correction of the NMR Spectra
Phase Shift
Phase Correct
Manually adjust zero-order (PO) and first-order
(P1) parameters to properly phase spectra.
45
Phase Correction of the NMR Spectra

• What is happening mathematically during manual
  phasing of an NMR spectra
• 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 spectra

46
Phase Correction of the NMR Spectra
If you over-phase the spectra, you get baseline
roll
47
Phase Correction of the NMR Spectra

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

48
Zero Filling of the NMR Spectra

• Improve digital resolution by adding zero data
  points at end of FID
• essential for nD 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
49
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
50

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

Good stuff
Mostly noise
Resolution
Sensitivity
F(t) 1 e - ( LB t ) line broadening
Effectively adds LB in Hz to peak Line-widths
51
Applying a Window Function to NMR data
Can either increase S/N or
Resolution Not Both!
LB -1.0 Hz
LB 5.0 Hz
Increase Sensitivity
Increase Resolution
FT
FT
52
Applying a Window Function to NMR data

• A Variety of Different Apodization or Window
  functions
• Some common window functions with the
  corresponding NMRPipe command

53
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
54
Baseline Correction of NMR Spectra

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

Spline baseline correction
55

• 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
56

• 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
3
Integral trace
HO-CH2-CH3
2
1
57

• 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

Unknown Xylene Mixture (0.4 g in 0.6 ml CDCl3
with 2mg of Cr(acac)3 relaxation agent)
Methyl Region
6 ms pulse instead of 8.5 us 5 sec delay, 2.5 sec
acq 256 transients in 0.5 hr.
from peak heights
DHcomb
ortho
meta (21.3 ppm)
17.7
1091.7
meta
para (20.9 ppm)
57.9
1088.4
ortho (19.6 ppm)
impurities
para
impurities
1089.1
24.4
58

• 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

59
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
• manual and automated approaches
• 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
60
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)