obtaining an nmr spectra

Obtaining an NMR SpectraObtaining an NMR Spectra Basic Requirements:

NMR sample: compound of interest dissolved in 500-600 l 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)

sample lift

NMR Tube

RF coilscryoshims

shimcoils

Probe

Liquid He

Liquid N2

Superconducting Magnet

• solenoid wound from superconducting niobium/tin or niobium/titanium wire

• kept at liquid helium temperature (4K), outer liquid N2 dewarnear zero resistance minimal current lose magnet stays at field for years without external power source

Cross-section of magnet

Superconducting solenoidUse up to 190 miles of wire!

spinner

magnet

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: = Bo / 2


•Problems:− Field drifts (B0 changes)

Field Drift over 11 Hrs (~ 0.15Hz/hr = Bo/2Remember:

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

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


•Problems:

− Field is not constant over sample (spatial variation)

= Bo/2Again:

Magnetic Field Homogeneity

Frequency of absorption: = Bo / 2

Poor Homogeneity multiple peaks at different effective Bo

Resonance depends on position in NMR sample

Good Homogeneity single peak with frequency dependent on Bo

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

Sketch of shim coils

actual shim coils

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

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• 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• 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

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 shim (red) fit to 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 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:

− 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:

− transmitting the RF pulse

− detecting the NMR signal

− observing the lock signal

− 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 non-magnetic 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 Power submitted to transmitter and receiver is maximizedand receiver is maximized

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 50 )

Adjust two capacitors until the tuning and desired frequency match and you obtain a null

Affects:

signal-to-noiseaccuracy of 90o pulsesample heatingchemical shift accuracy


Tune and Match capacitors for a Bruker Probe


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 ProbeSide Notes: Impedance

− Impedance – any electrical entity that impedes the flow of current

a resistance, reactance or both Resistance – material that resists the flow of electronsResistance – material that resists the flow of electrons Reactance – property of resisting or impeding the flow of ac current or ac voltage Reactance – property of resisting or impeding the flow of ac current or ac voltage

in inductors and capacitors in inductors and capacitors

− Illustration of matching impedance

Consider a 12V car battery attached to a car headlight 12V car battery – low impedance 12V car battery – low impedance high power 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 8 1.5V AA batteries – high impedance low power low power

Now swap the arrangement What happens? Car battery can easily light the light bulb, but the headlight will quickly drain the Car battery can easily light the light bulb, but the headlight will quickly drain the

AA batteries AA batteries poor impedance match poor impedance match

Tuning the ProbeSide 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 rfAll inductors exhibit some extra resistance to ac or rf Q is the reactance of the inductor divided by this ac or rf resistance 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 sample increases losses in the resonant circuit by inducing eddy currents in

the solventthe solvent The more conductive the sample the more the losses and the lower the probe Q. The more conductive the sample the more the losses and the lower the probe Q.

– Water, high salt lower the Q of the probeWater, high salt lower the Q of the probe

– Lower Q Lower Q longer pulse widths longer pulse widths

L

XQ

R X – reactance of circuit in Ohms

RL – the series resistance of the circuit in Ohms

A radiofrequency pulse is a combination of a wave (cosine) of frequency wo and a step function

Pulse Generator & Receiver System• Radio-frequency generators and frequency synthesizers produce a signal at

essentially a single frequency.• RF pulses are typically short-duration (secs)

- produces bandwidth (1/4) centered around single frequency - shorter pulse width broader frequency bandwidth

o Heisenberg Uncertainty Principal: t- Shortest pulse length will depend on the probe Q and the sample property

FT

* =tp

Pulse length (time, tp)

The Fourier transform indicates the pulse covers a range of frequencies

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 11H 6 H 6 s 90s 90oo pulse pulse ±41666 Hz ±41666 Hz ±69.4 ppm at 600 MHz ±69.4 ppm at 600 MHz

Minimizes weaker perturbations of spins a edges of spectraMinimizes weaker perturbations of spins a edges of spectra

- There are also null points at ±1/PW Hz where nuclei are unperturbed 11H 6 H 6 s 90s 90oo pulse first null at ±1.67e pulse first null at ±1.67e55 Hz Hz ±277.8 ppm at 600 MHz ±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)

1313C 15 C 15 s 90s 90oo pulse pulse ±16666 Hz ±16666 Hz ±18.5 ppm at 900 MHz ±18.5 ppm at 900 MHz

Also, complex experiments (multiple pulses) depend on the accuracy and Also, complex experiments (multiple pulses) depend on the accuracy and consistency of pulse widthsconsistency 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)

Maximum at 90Maximum at 9000 and minimum at 360 and minimum at 360oo

Usually measure 90Usually measure 90oo pulse at 360 pulse at 360oo time point time point

Pulse Length Calibration

90o pulse (12 s)

180o pulse (24 s)

360o pulse (44 s)

270o pulse (32 s)

The pulse width was arrayed from 2 s to 60 s in steps of 2 s

90o pulse is ~ 11 s

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 probe’s 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

= Bo/2

Continuous Wave (CW) vs. Pulse/Fourier TransformContinuous 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


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


Fourier Transform NMR

• Observe each individual resonance as it precesses at its Larmor frequency (o) in the X,Y plane.

• Monitor changes in the induced current in the receiver coil as a function of time.

FID – Free Induction Decay

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:

o Gain in S/N will eventually plateauGain in S/N will eventually plateau

o The initial signal has to be strong The initial signal has to be strong enough to signal average.enough to signal average.

Increase signal-to-noise (S/N) by collecting multiple copies of FID and averaging signal.

/S N number of scans

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)

/S N number of scans


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)

o TT11 – NMR relaxation parameter that will be discussed in detail later – NMR relaxation parameter that will be discussed in detail later

in the coursein the course

− Most efficient recycle delay is 1.3 x T1

1.3T1

Relative S/N per unit time of data

collection

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 TT11 relaxation times also vary by nuclei, where relaxation times also vary by nuclei, where 1313C > C > 11HH

o Either estimates from related compounds or experimental Either estimates from related compounds or experimental measurements of Tmeasurements of T11 is required to optimize data collection is required to optimize data collection

especially for long data acquisitions.especially for long data acquisitions.

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


• NMR signal is collected in Time Domain, but prefer Frequency Domain

• Transform from time domain to frequency domain using the Fourier function


Sampling the NMR (Audio) Signal• Collect Digital data by periodically sampling signal voltage

− ADC – analog to digital converter

Continuous FID

Digitized FID

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

The Nyquist Theorem says that we have to sample at least twice as fast as the fastest (higher frequency) signal.

SR = 1 / (2 * SW)

Sample Rate

- Correct rate, correct frequency-½ correct rate, ½ correct frequency Folded peaks!Wrong phase!

SR – sampling rateSW – sweep width

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

Digital Resolution – number of data points

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

The FID is digitized

Equal delay between points (dwell time)

DT = 1 / (2 * SW)

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

Sampling the NMR (Audio) Signal

Sweep Width

(range of radio-frequencies monitored for nuclei absorptions)

Sweep width (Hz, ppm) needs to be set to cover the entire NMR spectra

If SW is too small or sampling rate is too slow, than peaks are folded or aliased (note phase change)

The phase of folded peaks can vary: (a) negative phase, (b) dispersive or (c) positive phase.


SW is decreased

Correct Spectra

Spectra with carrier offset resulting in peak folding or aliasing


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.

Higher Digital Resolution requires longer acquisition times

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


0 0.10 0.20 0.30 0.40 0.50t1 sec

All this noise All this noise added to spectraadded to spectra

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 FID signal is truncatedtruncated

Truncated FID leads

to artifacts


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)


Dwell time DW

TD

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 ValuablesALL Dependent Valuables


Dwell time DW

TD

Total Data Acquisition Time (AQ):

Should be long enough to allow complete delay of FID

AQ = TD * DW= TD/2SWH

Dwell time DW

TD


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


NMR data size• Increase in the number of data points increase in resolution

− Increases acquisition timeIn

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NMR data size

• Under sampling the data truncated FID

− Baseline distortions sinc wiggles

Sinc wiggles

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

time

voltage


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

Exponential in both t1 and t2

randomly sampled from an exponential

distribution in t1 and t2

Random in t1 and t2.

Graham A. Webb (ed.), Modern Magnetic Resonance, 1305–1311.


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

time

voltage

Traditional NMRFID is truncated because number of points and DW determine how much of the FID can be collected

NUS NMRFID is under-sampled, but the entire FID is sampled


Magn. Reson. Chem. 2011, 49, 483–491



− 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




− 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. – enhancementlw – line width

Magn. Reson. Chem. 2011, 49, 483–491




− 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

Sampling Density/LW = TSMP/T2

Truncated FID

Magn. Reson. Chem. 2011, 49, 483–491


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




− Dramatic gain in the quality of strychnine NMR spectrum with 25% sampling density

− The spectrum was collected 4x faster (10 min. vs. 40 min.)

Nat. Prod. Rep. 2013 30: 501-524

Uniform Sampling Non-Uniform 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


http://www.enmr.eu/webportal/mdd.html

http://newton.nmrfam.wisc.edu/newton/static_web/index.html

http://rnmrtk.uchc.edu/rnmrtk/RNMRTK.html


• 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 Increa

se in F

ID In

ten

sity with

nu

mb

er of tran

sients

Increa

se in F

ID In

ten

sity with

nu

mb

er of tran

sients

RG depends on NS

• 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.


• 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.



• Solvent suppression solvent concentration is significantly larger than the sample concentration

water is 55M compared to typical M – mM of compound

Without Solvent Suppression

With Solvent Suppression

• 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

Want to “see” weak peaks in the presence of intense peaks


• 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!!

1

32768

Peak intensity has to fit between range of 1:215

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

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

carrier

carrier

same frequency relative to the carrier, but opposite sign.

PW excites a corresponding bandwidth of frequencies

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 frequencyPrecession is difference from carrier frequency

− Possible to have resonances with same frequency but opposite direction

Clockwise – magnetization traveling faster than rotating frame

Counter clockwise – magnetization traveling slower than rotating frame

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

carriersame frequency relative to the carrier, but opposite sign.

Quadrature detection• How to differentiate between peaks upfield and downfield from carrier?

− observed peak frequencies are all relative to the carrier frequency

How to differentiate between magnetization that precesses clockwise and counter clockwise?

carrier

Same Frequency!Opposite sign


• 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

234 233 232 231 230 229 228 227 226 225 224 223f1 ppm

All this noise added to spectrumAll this noise added to spectrum

carrier

PW excites a corresponding bandwidth of frequencies centered on carrierPW excites a corresponding bandwidth of frequencies centered on carrier

(B1)

B

F

B

F

PH = 0

PH

= 9

0PH = 0

PH = 90

F

F

B

B

Use two detectors 90o out of phase.

Phase of Peaksare different.



Phase of Peaks are different allows differentiation of frequencies relative to carrier

Detector along X-axis(real component of

FT)

Detector along Y-axis(imaginary component of

FT)

Use two detectors 90o out of phase.

FT is designed to handle two orthogonal input functions called the real and imaginary component

Phase Correction of the NMR Spectrum

Phase Shift

Depending on when the FID data collection begins a phase shift in the data may occur.

Phase correction of the NMR spectrum compensates for this phase shift.

http://arrhenius.rider.edu/nmr/NMR_tutor/pages/anal/anal_b6_ph.html


Phase Shift

Phase shift depends on the frequency of the signal



Phase Shift

Phase Correct

Manually adjust zero-order (PO) and first-order (P1) parameters to properly phase spectra.



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(i)) to set to zero

we are effectively discarding the imaginary component of the spectrum



If you “over-phase” the spectrum, you get baseline “roll”


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

• 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

231.40 231.39 231.38 231.37 231.36 231.35 231.34 231.33 231.32 231.31 231.30 231.29 231.28 231.27 231.26 231.25 231.24f1 ppm

231.42 231.40 231.38 231.36 231.34 231.32 231.30 231.28 231.26 231.24 231.22 231.20f1 ppm

0 0.20 0.40 0.60 0.80 1.00 1.2 1.4 1.6 1.8 2.0 2.2t1 sec

8K data 8K zero-fill

8K FID 16K FID

No zero-filling 8K zero-filling

Zero Filling of the NMR Spectrum

No zero-filling 4AQ zero-filling

Zero Filling of the NMR Spectra

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

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

0 0.10 0.20 0.30 0.40 0.50t1 sec

Good stuff Mostly noise

Sensitivity Resolution

Applying a Window Function to NMR data

Simply Multiple FID with a Mathematical Function

0 0.10 0.20 0.30 0.40 0.50t1 sec X

0 0.10 0.20 0.30 0.40 0.50t1 sec

=

F(t) = e - ( LB * t )

Can either increase S/N or

Resolution

Not Both!

0 0.10 0.20 0.30 0.40 0.50t1 sec

1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm

0 0.10 0.20 0.30 0.40 0.50t1 sec0 0.10 0.20 0.30 0.40 0.50

t1 sec

1080 1060 1040 1020 1000 980 960 940 920 900f1 ppm

FT FT

LB = -1.0 HzLB = 5.0 HzIncrease Sensitivity Increase Resolution


A Variety of Different Apodization or Window functions


• 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

Xi & Roche BMC Bioinformatics (2008) 9:234

A number of factors lead to baseline distortions:

Intense solvent or buffer peaksPhasing problemsErrors in first data points of FIDShort recycle tinesShort acquisition timesReceiver gain

polynomial baseline correction

Baseline Correction of NMR Spectrum

http://www.biomedcentral.com/1471-2105/9/324/figure/F3?highres=y

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)

222/1

22/1

)(4)(

)(

XXLW

LWAY

o

LW1/2

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

HO-CH2-CH3 12

3Integral trace

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

meta

para

Unknown Xylene Mixture

from peakfrom peak heightsheights

17.7%

57.9%

24.4%

meta (21.3 ppm)meta (21.3 ppm)

para (20.9 ppm)para (20.9 ppm)

ortho (19.6 ppm)ortho (19.6 ppm)impuritiesimpurities

impuritiesimpurities

Methyl Region of NMR Spectrum

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

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 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)

Peak Picking NMR Spectra

obtaining an nmr spectra

Documents

nmr signal

lock signalif

observed lock signal

field strength

main field

small magnetic field

magnetposition sample

separate nmr spectrometer