Transcript Chapter 5: Obtaining an NMR Structure

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
NMR Instrumentation (block diagram)
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
Superconducting
solenoid
Use up to 190
miles of wire!
Probe
Liquid N2
Liquid He
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
Superconducting Magnet
•
Problems:
−
Field drifts (B0 changes)
Field Drift over 11 Hrs (~ 0.15Hz/hr
Remember:
n = gBo/2p
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
Lock Feedback Circuit
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 Changes From
Off-resonance to
On-resonance
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 doesn’t move relative to a defined chemical shift
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!
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
o
Too high and lock signal is saturated  intensity of lock signal
fluctuates up and down
o
Too low and lock signal may not be observable
Superconducting Magnet
•
Problems:
− Field is not constant over sample (spatial variation)
Again:
n = gBo/2p
Magnetic Field Homogeneity
Frequency of absorption:
Poor Homogeneity  multiple
peaks at different effective Bo
Resonance depends on
position in NMR sample
n = g Bo / 2p
Good Homogeneity  single peak
with frequency dependent on Bo
Shim System
•
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Corrects for magnetic inhomogeneity
Spatial arrangement of 20 or more coils
actual shim coils
Sketch of shim coils
change current in each coil to “patch” differences in field and fix distortions in peak shape
Shim Coils
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electric currents in the shim coils create small magnetic fields which compensate for
inhomogenieties in the magnet
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shim coils vary in the geometric orientation and function (linear, parabolic, etc)
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Z0,Z1,Z2,Z3,Z4,Z5
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X, XZ,XZ2,X2Y2,XY,Y,YZ, YZ2, XZ3,X2Y2Z, YZ3,XYZ,X3,Y3
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
Shim Coils
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Examples of poor line-shapes due to shimming errors
Shim Coils
•
Examples of poor FID shape due to shimming errors
Perfectly Shimmed Magnet
Mis-shimmed Magnet
Spinning the Sample
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Improves effective magnetic field homogeneity by averaging inhomogeneities in
the magnet
−
•
Spinning the sample causes symmetric side-bands at intervals related to spinning
rate
−
•
Z – shims are also known as spinning shims
Non-spinning shims (X,Y) problems
Samples are never spun for multi-dimensional NMR experiments
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Creates artifacts  streaks or T1 ridges from spinning side-bands and
spinning instability
Spinning side-bands
symmetric about peak
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 H2O+D2O, CH3CN+D2O or CH3OH+D2O solvent
Shim Map
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
Gradient Shimming
Water resonance before and after Gradient Shimming
Gradient
Shimming
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:
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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
Environment Stability
Peak Chemical Shift and Shape
Change as Temperature Changes
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:
•
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transmitting the RF pulse
−
detecting the NMR signal
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observing the lock signal
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creating magnetic field gradients
Thermocouples and heaters to
maintain a constant temperature
Sample Probe
Important to note, because of the high magnetic
field, the probe has to be built with nonmagnetic material such as glass and plastics.
Thus, probes tend to be fragile and easy to break
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
Tune and Match System
•
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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
Tune and Match System
Tune and Match capacitors for a Bruker Probe
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!!
Tuning the Probe
Side Notes: Impedance
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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


Consider 8 1.5V AA batteries (12 volt total) attached to a very low wattage light
bulb


12V car battery – low impedance  high power
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
Tuning the Probe
Side Notes: Quality factor (Q)
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“Q” - dimensionless and important property of capacitors and inductors

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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 > 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
Q
RL
X – reactance of circuit in Ohms
RL – the series resistance of the circuit in Ohms
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
o
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
*
=
tp
Pulse length (time, tp)
The Fourier transform indicates the
pulse covers a range of frequencies
FT
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
6 ms 90o pulse  ±41666 Hz  ±69.4 ppm at 600 MHz

1H

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
Maximum affect
Null, no affect
Invert signal, 180o pulse
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 (>200 ppm)
15 ms 90o pulse  ±16666 Hz  ±18.5 ppm at 900 MHz

13C

Also, complex experiments (multiple pulses) depend on the accuracy and
consistency of pulse widths
- Selective pulse  long pulse width (ms) narrow band-width.
Maximum affect
Null, no affect
Invert signal, 180o pulse
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)
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Maximum at 900 and minimum at 360o
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Usually measure 90o pulse at 360o time point
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)
Pulse Generator & Receiver System
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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 probe’s receiver
coil resulting in an induced current in the nanovolt to microvolt range
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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
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
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
Continuous Wave (CW) vs. Pulse/Fourier Transform
Fourier Transform NMR
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Observe each individual resonance as it precesses at its Larmor frequency
(wo) in the X,Y plane.
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Monitor changes in the induced current in the receiver coil as a function of
time.
FID – Free Induction Decay
Fourier Transform NMR
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Signal-to-noise increases as a function of
the number of scans or transients
−
Increases data collection time
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There are inherent limits:
o
Gain in S/N will eventually plateau
o
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.
S / N  number of scans
Fourier Transform NMR
Increase signal-to-noise (S/N) by collecting multiple copies of FID and
averaging signal.
S / N  number of scans
But, total experiment time is proportional to the number of scans
exp. time ~ (number of scans) x (recycle delay; D1)
Fourier Transform NMR
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Recycle time (D1) – time increment between successive FID collection
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Maximum signal requires waiting for the sample to fully relax to
equilibrium (5 x T1)
o
−
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 …
Fourier Transform NMR
•
Recycle time (D1) – time increment between successive FID collection
−
Typical T1’s for organic compounds range from 50 to 0.5 seconds
o
T1 relaxation times also vary by nuclei, where 13C > 1H
o
Either estimates from related compounds or experimental
measurements of T1 is required to optimize data collection 
especially for long data acquisitions.
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
Sampling the NMR (Audio) Signal
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Collect Digital data by periodically sampling signal voltage
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ADC – analog to digital converter
Continuous FID
Digitized FID
Sampling the NMR (Audio) Signal
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Collect Digital data by periodically sampling signal voltage
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ADC – analog to digital converter
Sample intensity of voltage induced in
coil by y-vector of net magnetization
precessing in x,y-plane
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.
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
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
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)
Sampling the NMR (Audio) Signal
SW is
decreased
The phase of folded peaks can vary:
(a) negative phase, (b) dispersive or
(c) positive phase.
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.
Correct Spectra
Spectra with carrier offset resulting
in peak folding or aliasing
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
All this noise
added to spectra
Higher Digital Resolution requires longer acquisition times
Sampling the NMR (Audio) Signal
NMR data size
•
How long do you sample for?
−
Sample too short don’t collect all the data, lose resolution & get artifacts
FID signal is
truncated
Truncated
FID leads
to artifacts
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)
TD
Dwell time DW
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
TD
Dwell time DW
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
TD
Total Data Acquisition Time (AQ):
AQ = TD * DW= TD/2SWH
Should be long enough to
allow complete delay of FID
Dwell time DW
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
•
Sampling the NMR (Audio) Signal
NMR data size
•
Under sampling the data  truncated FID
−
Baseline distortions  sinc wiggles
FT
Sinc wiggles
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
voltage
time
−
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
Sampling the NMR (Audio) Signal
NMR Data Processing Software
• Non-uniform data sampling
− Significant improvement in resolution and sensitivity for nD NMR data
− Don’t 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 t1 and
linear in t2
randomly sampled from
an exponential
distribution in t1 and t2
Exponential in both
t1 and t2
Random in t1 and t2.
Graham A. Webb (ed.), Modern Magnetic Resonance, 1305–1311.
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
voltage
time
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
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, 483–491
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, 483–491
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
Truncated FID
Sampling Density/LW = TSMP/T2
Magn. Reson. Chem. 2011, 49, 483–491
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: 125–148
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.)
Uniform Sampling
Non-Uniform Sampling
Nat. Prod. Rep. 2013 30: 501-524
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/static_web/index.html
− RNMRTK: http://rnmrtk.uchc.edu/rnmrtk/RNMRTK.html
− mpiPipe: Available by contacting the Wagner Group
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
Digitizer has a finite data range
Increase in FID Intensity with number of transients
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.
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
o RG may be set to higher values, but no effect on the spectra will be observed
o RG may be set to non-factors of two, but adjusted to nearest factor of 2.
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
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
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
Want to “see” weak
peaks in the presence
of intense peaks
Peak intensity has
to fit between
range of 1:215
1
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
carrier
PW excites a corresponding bandwidth of frequencies
same frequency relative to
the carrier, but opposite sign.
carrier
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
o
−
Precession is difference from carrier frequency
Possible to have resonances with same frequency but opposite direction
same frequency relative to
the carrier, but opposite sign.
Clockwise – magnetization
traveling faster than rotating
frame
carrier
Counter clockwise –
magnetization traveling
slower than rotating frame
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?
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
Quadrature detection
PH = 0
B
B
PH = 90
Use two detectors
90o out of phase.
F
w (B1)
F
PH = 0
F
B
F
B
Phase of Peaks
are different.
PH = 90
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
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.
Phase Correction of the NMR Spectrum
Phase shift depends on the frequency of the signal
Phase Shift
Phase Correction of the NMR Spectrum
Phase Shift
Phase Correct
Manually adjust zero-order (PO) and first-order (P1) parameters to properly phase spectra.
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
Phase Correction of the NMR Spectrum
If you “over-phase” the spectrum, you get baseline “roll”
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
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 FID
No zero-filling
8K zero-fill
16K FID
8K zero-filling
Zero Filling of the NMR Spectra
• Better example of the resolution gain and benefits of zero-filling NMR spectra
No zero-filling
4AQ zero-filling
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
Good stuff
Mostly noise
Sensitivity
Resolution
Applying a Window Function to NMR data
Simply Multiple FID with a Mathematical Function
F(t) = e
X
- ( LB * t )
=
Applying a Window Function to NMR data
Can either increase S/N
or
Resolution
Not Both!
LB = 5.0 Hz
Increase Sensitivity
FT
LB = -1.0 Hz
Increase Resolution
FT
Applying a Window Function to NMR data
A Variety of Different Apodization or Window functions
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
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
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) 9:234
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
A( LW1 / 2 )2
Y
( LW1 / 2 )2  4( X o  X )2
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
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
ortho
from peak
heights
Methyl Region of NMR Spectrum
meta (21.3 ppm)
17.7%
meta
para (20.9 ppm)
57.9%
para
impurities
24.4%
ortho (19.6 ppm)
impurities
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
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
Peak#
1
2
3
4
5
6
7
8
9
10
11
12
.
.
.
15
N (ppm)
127.747
127.803
114.644
121.299
119.425
126.940
121.296
122.376
133.054
127.974
122.890
117.582
1
H (ppm)
9.537
9.405
9.312
9.287
9.225
9.181
9.107
9.090
8.983
8.934
8.944
8.928
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, 288–297 (1998)