Nuclear Magnetic Resonance A.) Introduction:

Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency region (~4-900 MHz)

- nuclei (instead of outer electrons) are involved in absorption process- sample needs to be placed in magnetic field to cause different

energy states

NMR was first experimentally observed by Bloch and Purcell in 1946 (received Nobel Prize in 1952) and quickly became commercially available and widely used.

Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins.

NMR is routinely and widely used as the preferred technique to rapidly elucidate the chemical structure of most organic compounds.

One of the One of the MOSTMOST Routinely used Analytical Techniques Routinely used Analytical Techniques

1937 Rabi predicts and observes nuclear magnetic resonance1946 Bloch, Purcell first nuclear magnetic resonance of bulk sample1953 Overhauser NOE (nuclear Overhauser effect)1966 Ernst, Anderson Fourier transform NMR1975 Jeener, Ernst 2D NMR1985 Wüthrich first solution structure of a small protein (BPTI)

from NOE derived distance restraints1987 3D NMR + 13C, 15N isotope labeling of recombinant proteins

(resolution)1990 pulsed field gradients (artifact suppression)1996/7 new long range structural parameters:

- residual dipolar couplings from partial alignment in liquid crystalline media

- projection angle restraints from cross-correlated relaxation

TROSY (molecular weight > 100 kDa)Nobel prizes1944 Physics Rabi (Columbia)1952 Physics Bloch (Stanford), Purcell (Harvard)1991 Chemistry Ernst (ETH)2002 Chemistry Wüthrich (ETH)2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham)

NMR HistoryNMR History

NMR HistoryNMR History First NMR Spectra on Water

Bloch, F.; Hansen, W. W.; Packard, M. Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment.The nuclear induction experiment. Physical Review (1946), 70 474-85. Physical Review (1946), 70 474-85.

11H NMR spectra of waterH NMR spectra of water

NMR HistoryNMR History First Observation of the Chemical Shift

11H NMR spectra ethanolH NMR spectra ethanol

Modern ethanol spectra Modern ethanol spectra

Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. 1919: p. 507. : p. 507.

Typical Applications of NMR:1.) Structural (chemical) elucidation

> Natural product chemistry> Synthetic organic chemistry

- analytical tool of choice of synthetic chemists- used in conjunction with MS and IR

2.) Study of dynamic processes> reaction kinetics> study of equilibrium (chemical or structural)

3.) Structural (three-dimensional) studies> Proteins, Protein-ligand complexes> DNA, RNA, Protein/DNA complexes

> Polysaccharides4.) Drug Design

> Structure Activity Relationships by NMR5) Medicine -MRI

MRI images of the Human Brain

NMR Structure of MMP-13 complexed to a ligand

O

O

O

O

OH

OO

O

HO

NH

OH

OO

O

O

Taxol (natural product)

2-phenyl-1,3-dioxep-5-ene2-phenyl-1,3-dioxep-5-ene

1313C NMR spectraC NMR spectra

11H NMR spectraH NMR spectra

Each NMR Observable Nuclei Yields a Peak in the SpectraEach NMR Observable Nuclei Yields a Peak in the Spectra““fingerprint” of the structurefingerprint” of the structure

Information in a NMR SpectraInformation in a NMR Spectra

ObservableObservable NameName QuantitativeQuantitative InformationInformation

Peak position Chemical shifts () (ppm) = obs –ref/ref (Hz) chemical (electronic)

environment of nucleus

Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles)

Peak Intensity Integral unitless (ratio) nuclear count (ratio) relative height of integral curve T1 dependent

Peak Shape Line width = 1/T2 molecular motion peak half-height chemical exchange

uncertainty principaluncertainty in

energy

A Basic A Basic ConceptConcept in ElectroMagnetic Theory in ElectroMagnetic Theory

A Direct Application to NMR

A perpendicular external magnetic field will induce an electric current in a closed loop

An electric current in a closed loop will create a perpendicular magnetic field

Theory of NMR

Quantum Description

Nuclear Spin (think electron spin)

a) Nucleus rotates about its axis (spin)

a) Nuclei with spin have angular momentum (p)1) quantized, spin quantum number I2) 2I + 1 states: I, I-1, I-2, …, -I3) identical energies in absence of

external magnetic field

c) NMR “active” Nuclear Spin (I) = ½: 1H, 13C, 15N, 19F, 31P Odd atomic mass

I = +½ & -½

NMR “inactive” Nuclear Spin (I) = 0:12C, 16O Even atomic mass &

number

Quadrupole Nuclei Nuclear Spin (I) > ½: 14N, 2H, 10B Even atomic mass & odd

number I = +1, 0 & -1

l

Magnetic Moment ()

a) spinning charged nucleus creates a magnetic field

b) magnetic moment () is created along axis of the nuclear spin

= pwhere:

p – angular momentum – gyromagnetic ratio (different

value for each type of nucleus)

c) magnetic moment is quantized (m)m = I, I-1, I-2, …, -I

for common nuclei of interest: m = +½ & -½

Similar to magnetic field created by electric current flowing in a coil

Magnetic moment

Bo

= h / 4

Magnetic alignmentMagnetic alignment

In the absence of external field,each nuclei is energetically degenerate

Add a strong external field (Bo).and the nuclear magnetic moment: aligns with (low energy) against (high-energy)

Energy Levels in a Magnetic Field

a) Zeeman Effect -Magnetic moments are oriented in one of two directions in magnetic field

b) Difference in energy between the two states is given by:

E = h Bo / 2where:

Bo – external magnetic field units:Tesla (Kg

s-2 A-1) h – Planck’s constant 6.6260 x 10-34

Js

– gyromagnetic ratio unique value per nucleus

1H: 26.7519 x 107 rad T-1 s-

c) Frequency of absorption: = Bo / 2 (observed NMR frequency)

d) From Boltzmann equation: Nj/No = exp(-hBo/2kT)

Frequency of absorption: = Bo / 2

Energy Levels in a Magnetic Field• Transition from the low energy to high energy spin state occurs through an

absorption of a photon of radio-frequency (RF) energy

RF

NMR Theory: Classical Description

Spinning particle precesses around an applied magnetic field

a) Angular velocity of this motion is given by:

o = Bo

where the frequency of precession or Larmor frequency is:

= Bo/2

Same as quantum mechanical description

Net Magnetization in a Magnetic Field

Mo

y

x

z

x

y

z

Bo Bo

Bo > 0 E = h

Bo

Classic View:- Nuclei either align with or against external magnetic field along the z-axis.

- Since more nuclei align with field, net magnetization (Mo) exists parallel to external magnetic field

Quantum Description:- Nuclei either populate low energy (, aligned with field) or high energy (, aligned against field)

- Net population in energy level.

- Absorption of radio- frequency promotes nuclear spins from .

An NMR ExperimentAn NMR Experiment

Mo

y

x

z

x

y

z

Bo Bo

We have a net magnetization precessing about Bo at a frequency of o with a net population difference between aligned and unaligned spins.

Now What?

Perturbed the spin population or perform spin gymnasticsBasic principal of NMR experiments

The Basic 1D NMR ExperimentThe Basic 1D NMR Experiment

Experimental details will effect the NMR spectra and the corresponding interpretation

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

Right-hand rule

resonant condition: frequency (1) of B1 matches Larmor frequency (o)energy is absorbed and population of and states are perturbed.

An NMR ExperimentAn NMR Experiment

And/Or:And/Or: Mo now precesses about B1

(similar to Bo) for as long as the B1 field is applied.

Again, keep in mind that individual spins flipped up or down(a single quanta), but Mo can have a continuous variation.

RF pulse

B1 field perpendicular to B0Mxy

Mz

Classical Description

• Observe NMR Signal Need to perturb system from equilibrium.

B1 field (radio frequency pulse) with Bo/2frequency

Net magnetization (Mo) now precesses about Bo and B1

MX and MY are non-zero Mx and MY rotate at Larmor frequency System absorbs energy with transitions between aligned and unaligned states

Precession about B1stops when B1 is turned off

Classic View:- Apply a radio-frequency (RF) pulse a long the y-axis

- RF pulse viewed as a second field (B1), that the net magnetization (Mo) will precess about with an angular velocity of 1

-- precession stops when B1 turned off

Quantum Description:- enough RF energy has been absorbed, such that the population in / are now equal

- No net magnetization along the z-axis

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

1 = B1

90o pulse

Bo > 0

E = h

Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization

Absorption of RF Energy or NMR RF Absorption of RF Energy or NMR RF PulsePulse

An NMR ExperimentAn NMR Experiment

What Happens Next?

The B1 field is turned off and Mxy continues to precess about Bo at frequency o. z

x

Mxy

Receiver coil (x)

y

NMR signal

o

FID – Free Induction Decay

y y y

Mxy is precessing about z-axis in the x-y plane Time (s)

The oscillation of Mxy generates a fluctuating magnetic field which can be used to generate a current in a receiver coil to detect the NMR signal.

An NMR ExperimentAn NMR Experiment

A magnetic field perpendicular to a circular loop will induce a current in the loop.

NMR Probe (antenna)

NMR Signal Detection - NMR Signal Detection - FIDFIDThe FID reflects the change in the magnitude of Mxy as

the signal is changing relative to the receiver along the y-axis

Again, the signal is precessing about Bo at its Larmor Frequency (o).

RF pulse along Y

Detect signal along X

NMR Signal Detection - Fourier NMR Signal Detection - Fourier TransformTransform

So, the NMR signal is collected in the Time - domain

But, we prefer the frequency domain.

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

NMR Signal Detection - Fourier NMR Signal Detection - Fourier TransformTransformAfter the NMR Signal is Generated and the B1 Field is Removed, the

Net Magnetization Will Relax Back to Equilibrium Aligned Along the Z-axis

T2 relaxation

Two types of relaxation processes, one in the x,y plane and one along the z-axis

Peak shape also affected by magnetic field homogeneity or shimmingPeak shape also affected by magnetic field homogeneity or shimming

NMR Relaxation

a) No spontaneous reemission of photons to relax down to ground state Probability too low cube of the frequency

b) Two types of NMR relaxation processes spin-lattice or longitudinal relaxation (T1)

i. transfer of energy to the lattice or solvent material

ii. coupling of nuclei magnetic field with magnetic fields created

by the ensemble of vibrational and rotational motion of the

lattice or solvent.

iii. results in a minimal temperature increase in sample

Mz = M0(1-exp(-t/T1))

Recycle Delay: General practice is to wait 5xT1 for the system to have fully relaxed.

NMR Relaxationspin-spin or transverse relaxation (T2)

i. exchange of energy between excited nucleus and low energy

state nucleus

ii. randomization of spins or magnetic moment in x,y-plane

iii. related to NMR peak line-widthMx = My = M0 exp(-t/T2)

(derived from Heisenberg uncertainty principal)

Please Note: Line shape is also affected by the magnetic fields homogeneity

NMR SensitivityNMR Sensitivity

Bo = 0

Bo > 0 E = h

N / N = e E / kTBoltzmman distribution:

The applied magnetic field causes an energy difference between aligned() and unaligned() nuclei

The population (N) difference can be determined from

The E for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol

Very Small !Very Small !~64 excess spins ~64 excess spins per million in lower per million in lower statestate

Low energy gap

NMR SensitivityNMR Sensitivity

EhBo /2

NMR signal depends on:

1) Number of Nuclei (N) (limited to field homogeneity and filling factor)2) Gyromagnetic ratio (in practice 3)3) Inversely to temperature (T)4) External magnetic field (Bo

2/3, in practice, homogeneity)

5) B12 exciting field strength

N / N = e E / kT

Increase energy gap -> Increase population difference -> Increase NMR signal

E ≡ Bo≡

- Intrinsic property of nucleus can not be changed.

signal (s) ~ 44BBoo22NBNB11g(g()/T)/T

- Intrinsic property of nucleus can not be changed.

C)3 for 13C is 64xN)3

for 15N is 1000x

1H is ~ 64x as sensitive as 13C and 1000x as sensitive as 15N !

Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%relative sensitivity increases to ~6,400x and ~2.7x105x !!

NMR SensitivityNMR Sensitivity

• Relative sensitivity of 1H, 13C, 15N and other nuclei NMR spectra depend on Gyromagnetic ratio (Gyromagnetic ratio ()) Natural abundance of the isotope Natural abundance of the isotope

1H NMR spectra of caffeine8 scans ~12 secs

13C NMR spectra of caffeine8 scans ~12 secs

13C NMR spectra of caffeine10,000 scans ~4.2 hours

NMR SensitivityNMR Sensitivity

Increase in Magnet Strength is a Major Means to Increase Sensitivity

NMR SensitivityNMR Sensitivity

But at a significant cost!

~$800,000 ~$2,00,000 ~$4,500,000

Chemical Chemical ShiftShift

Up to this point, we have been treating nuclei in general terms.Simply comparing 1H, 13C, 15N etc.

If all 1H resonate at 500MHz at a field strength of 11.7T, NMR would not be very interesting

Beff = Bo - Bloc --- Beff = Bo( 1 - )

is the magnetic shielding of the nucleus

The chemical environment for each nuclei results in a unique local magnetic field (Bloc) for each nuclei:

Beff = Bo - Bloc --- Beff = Bo( 1 - )

Chemical Shift

Beff = Bo - Bloc --- Beff = Bo( 1 - )

HO-CH2-CH3

de-shielding high shieldingShielding – local field opposes Bo

= Bo/2

– reason why observe three distinct NMR peaks instead of one based on strength of B0

Effect of Magnetic Anisotropy1) external field induces a flow (current) of electrons in system – ring current effect

2) ring current induces a local magnetic field with shielding (decreased chemical shift) and deshielding (increased chemical shifts)

Decrease in chemical shifts

Increase in chemical shifts

Chemical Shift

The NMR scale (The NMR scale (, ppm), ppm)

- ref

= ppm (parts per million) ref

Instead use a relative scale, and refer all signals () in the spectrum to the signal of a particular compound (ref).

Bo >> Bloc -- MHz compared to Hz

Comparing small changes in the context of a large number is cumbersome

Tetramethyl silane (TMS) is a common reference chemicalH3C Si CH3

CH3

CH3

IMPORTANT: absolute frequency is field dependent ( = Bo / 2)

The NMR scale (The NMR scale (, ppm), ppm)

Chemical shift is a relative scale so it is independent of Bo. Same chemical shift at 100 MHz vs. 900 MHz magnet

IMPORTANT: absolute frequency is field dependent ( = Bo / 2)

At higher magnetic fields an NMR spectra will exhibit the same chemical shifts but with higher resolution because of the higher frequency range.

NMR Spectra TerminologyNMR Spectra Terminology

Increasing field (Bo)Increasing frequency ()Increasing Increasing energy (E, consistent with UV/IR)

1H 13C 2H600 MHz 150 MHz 92 MHz

TMS

CHCl3

7.27 0 ppmincreasing decreasing low field high field down field up fieldhigh frequency () low frequencyde-shielding high shielding Paramagnetic diamagnetic

Chemical Shift TrendsChemical Shift Trends

Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

For protons, ~ 15 ppm:For carbon, ~ 220 ppm:

Chemical Shift TrendsChemical Shift Trends

0TMS

ppm

210 7 515

Aliphatic

Alcohols, protons to ketones

Olefins

AromaticsAmidesAcids

Aldehydes

ppm

50150 100 80210

Aliphatic CH3,CH2, CH

Carbons adjacent toalcohols, ketones

Olefins

Aromatics,conjugated alkenes

C=O of Acids,aldehydes, esters

0TMS

C=O inketones

CHARACTERISTIC PROTON CHEMICAL SHIFTS

Type of Proton Structure Chemical Shift, ppm

Cyclopropane C3H6 0.2

Primary R-CH3 0.9

Secondary R2-CH2 1.3

Tertiary R3-C-H 1.5

Vinylic C=C-H 4.6-5.9

Acetylenic triple bond,CC-H 2-3

Aromatic Ar-H 6-8.5

Benzylic Ar-C-H 2.2-3

Allylic C=C-CH3 1.7

Fluorides H-C-F 4-4.5

Chlorides H-C-Cl 3-4

Bromides H-C-Br 2.5-4

Iodides H-C-I 2-4

Alcohols H-C-OH 3.4-4

Ethers H-C-OR 3.3-4

Esters RCOO-C-H 3.7-4.1

Esters H-C-COOR 2-2.2

Acids H-C-COOH 2-2.6

Carbonyl Compounds H-C-C=O 2-2.7

Aldehydic R-(H-)C=O 9-10

Hydroxylic R-C-OH 1-5.5

Phenolic Ar-OH 4-12

Enolic C=C-OH 15-17

Carboxylic RCOOH 10.5-12

Amino RNH2 1-5

Common Chemical Shift Ranges

Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)

Coupling ConstantsCoupling Constants

through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities

1) The spacing in hertz (hz) between the peaks is a constant i. coupling constant (J)

bonding electrons convey spin states of bonded nuclei

1) spin states of nuclei are “coupled”

2) alignment of spin states of bonded nuclei affects energy of the ground () and excited states () of observed nuclei

3) Coupling pattern and intensity follows Pascal’s triangle

Coupling ConstantsCoupling Constants

Energy level of a nuclei are affected by covalently-bonded neighbors spin-states

13C

1H 1H 1H

one-bond

three-bond

I SS

S

I

I

J (Hz)

Spin-States of covalently-bonded nuclei want to be aligned.

The magnitude of the separation is called coupling constant (J) and has units of Hz.

+J/4

-J/4

+J/4

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

Coupling ConstantsCoupling Constants

singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1

Common NMR Splitting Patterns

Coupling Rules:1. equivalent nuclei do not interact

2. coupling constants decreases with separation ( typically 3 bonds)

3. multiplicity given by number of attached equivalent protons (n+1)4. multiple spin systems multiplicity (na+1)(nb+1)

5. Relative peak heights/area follows Pascal’s triangle6. Coupling constant are independent of applied field strength

IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.

Multiplets consist of 2nI + 1 lines I is the nuclear spin quantum number (usually 1/2) andn is the number of neighboring spins.

Karplus Equation – Coupling Constants Karplus Equation – Coupling Constants

Relates coupling constant toTorsional angle.

Used to solve Structures!

J = const. + 10Cos

ExampleExample: : The proton NMR spectrum is for a compound of empirical formula The proton NMR spectrum is for a compound of empirical formula CC44HH88O. Identify the compoundO. Identify the compound

Strong singlet at ~2.25 ppm Strong singlet at ~2.25 ppm methyl next to carbonylmethyl next to carbonyl

Absence of peak at ~9.7 Absence of peak at ~9.7 ppm ppm eliminates aldehyde groupeliminates aldehyde groupAnd suggests ketoneAnd suggests ketone

O

CH2

H3C

CH3

Quartet at ~2.5 ppm suggests Quartet at ~2.5 ppm suggests a methylene next to a a methylene next to a carbonyl coupled to a methylcarbonyl coupled to a methyl

Triplet at ~1.2 ppm suggests a Triplet at ~1.2 ppm suggests a methyl group coupled to a methyl group coupled to a methylene groupmethylene group

a) Interaction between nuclear spins mediated through empty space (5Å) like ordinary bar magnets

b) Important: effect is time-averagedc) Gives rise to dipolar relaxation (T1 and T2) and specially to

cross-relaxation

Perturb 1H spin populationaffects 13C spin population NOE effect

Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)

Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)

Nuclear Overhauser Effect (NOE, ) – the change in intensity of an NMR resonance when the transition of another are perturbed, usually by saturation.

Saturation – elimination of a population difference between transitions (irradiating one transition with a weak RF field)

i = (I-Io)/Io

where Io is thermal equilibrium intensity

N N

N+

N-X

X A

A

irradiate

Populations and energy levels of a homonuclear AX system (large chemical shift difference)

Observed signals only occur from single-quantum transitions

Nuclear Overhauser Effect (NOE)Nuclear Overhauser Effect (NOE)

N+½

I

I S

S

Populations and energy levels immediately following saturation of the S transitions

N+½N-½

N-½

Saturated(equal population)

Saturated(equal population)

saturate

W1

A

W1A

W1X

W1X

W2

W0

Observed signals only occur from single-quantum transitions

Relaxation back to equilibrium can occur through:Zero-quantum transitions (W0)Single quantum transitions (W1)Double quantum transitions (W2)

N-½

N+½

N+½

N-½

The observed NOE will depend on the “rate” of these relaxation pathwaysThe observed NOE will depend on the “rate” of these relaxation pathways

NMR Instrumentation (block diagram)

sample lift

NMR Tube

RF coilscryoshims

shimcoils

Probe

Liquid He

Liquid N2

Superconducting Magnet

a) solenoid wound from superconducting niobium/tin or niobium/titanium wire

b) 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

Superconducting Magnet

a)Problems:Field drifts (B0 changes)

Field is not constant over sample (spatial variation)

Field Drift over 11 Hrs (~ 0.15Hz/hr

= Bo/2Remember:

Lock System a) Corrects for magnetic field driftc) 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

Shim System

a) Corrects for magnetic inhomogeneityc) Spatial arrangement of 20 coils

change current in each coil to “patch” differences in field and fix distortions in peak shape

Sketch of shim coils

actual shim coils

Tune and Match System

a) Tune- corrects the differences between observed and desired frequencyc) 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

Receiver Gain

a) Amplifies the radio frequency FID signal from the probeb) Set to maximize signal-to-noisec) Signal is dependent on sample concentration

The Analog to Digital Converter (ADC) has a maximum range of integers

Clipped Fid

Dynamic Range Problem

Clipped FID

Continuous Wave (CW) vs. Pulse/Fourier TransformContinuous 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)

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

NMR Pulse

a) In FT-NMR, how are all the individual nuclei excited simultaneously?b) RF pulses are typically short-duration (secs)

- produces bandwidth (1/4) centered around single frequency

- shorter pulse width broader frequency bandwidth

Heisenberg Uncertainty Principal: t

FT

* =tp

Pulse length (time, tp)

The Fourier transform indicates the pulse covers a range of frequencies

NMR PulseNMR Pulse

z

x

Mxy

y

z

x

y

Mo

B1

ttp

t = * tp * B1

NMR pulse length or Tip angle (tp)

The length of time the B1 field is on => torque on bulk magnetization (B1)

A measured quantity – instrument and sample dependent.

NMR PulseNMR Pulse

z

x

Mxy

y

z

x

y

Mo / 2

Some useful common pulses

90o

Maximizes signal in x,y-planewhere NMR signal detected

z

x

-Moy

z

x

y

Mo

180o

90o pulse

180o pulse

Inverts the spin-population.No NMR signal detected

Can generate just about any pulse width desired.

NMR Data Detection and Processing

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

time ~ (number of scans) x (recycle delay)

/S N number of scans

Correct Spectra

Spectra with carrier offset resulting in peak folding or aliasing

Sweep Width (range of radio-frequencies monitored for nuclei absorptions)

Proper Spectral WidthNeeds to be large enough to capture all the NMR resonances

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)

Digital Resolution – number of data points

Want to maximize digital resolution:

Proper Acquisition TimeNeeds to be long enough to allow FID to Completely Decay

Sinc Wiggles

Truncated FID

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

Improve digital resolution by adding zero data points at end of FID

Window Functions

Emphasize the signal or decrease the noise by applying a mathematical function to the FID.

0 0.10 0.20 0.30 0.40 0.50t1 sec

Good stuff Mostly noise

F(t) = 1 * e - ( LB * t ) – line broadening

Effectively adds LB in Hz to peakLine-widths

Sensitivity Resolution

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 Hz

Can either increase S/N or Resolution Not Both!

Increase Sensitivity Increase Resolution

Baseline Correction

Need a flat baseline – prefer to fix experimentally

Xi & Roche BMC Bioinformatics (2008) 9:234

Apply any number of mathematical functions:

linearPolynomial (upwards of 6-orders)FID reconstructionPenalized parametric smoothing Etc.

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

Phase Correction

Need a flat baseline – phase all peaks to be pure absorptive in shape

Xi & Roche BMC Bioinformatics (2008) 9:234

Improper phasing can cause severedistortions in the baseline

Phase is due to difference in actual time and the zero-time point of FID (sin + cosines)

NMR Peak Integration or Peak Area

a) The relative peak intensity or peak area is proportional to the number of protons associated with the observed peak.

b) Means to determine relative concentrations of multiple species present in an NMR sample.

HO-CH2-CH3 12

3

Relative peak areas = Number of protons

Integral trace

i. NMR time scale refers to the chemical shift time scalea) remember – frequency units are in Hz (sec-1) time scaleb) exchange rate (k)c) differences in chemical shifts between species in exchange indicate the exchange rate.

d) For systems in fast exchange, the observed chemical shift is the average of the individual species chemical shifts.

Time Scale Chem. Shift ( Coupling Const. (J) T2 relaxationSlow k << A- B k << JA- JB k << 1/ T2,A- 1/ T2,B

Intermediate k = A - B k = JA- JB k = 1/ T2,A- 1/ T2,B

Fast k >> A - B k >> JA- JB k >> 1/ T2,A- 1/ T2,B

Range (Sec-1) 0 – 1000 0 –12 1 - 20

obs = f11 + f22

f1 +f2 =1where:

f1, f2 – mole fraction of each species1,2 – chemical shift of each species

Exchange Rates and NMR Time ScaleExchange Rates and NMR Time Scale

ii. Effects of Exchange Rates on NMR data

k = (he-ho)

k = (o2 -  e

2)1/2/21/2

k = o / 21/2

k = o2 /2(he - ho)

k – exchange rateh – peak-width at half-height – peak frequencye – with exchangeo – no exchange

coalescence

NMR Dynamics and ExchangeNMR Dynamics and Exchange

k = 0.1 s-1

k = 5 s-1

k = 200 s-1

k = 88.8 s-1

k = 40 s-1

k = 20 s-1

k = 10 s-1

k = 400 s-1

k = 800 s-1

k = 10,000 s-1

40 Hz

Incr

easi

ng E

xcha

nge

Rat

e

slow

fast

22/1

1

TW

No exchange:

With exchange:

exTW

11

22/1

ex

k1

Equal Population of Exchange Sites

Multidimensional NMR

NMR pulse sequences

a) composed of a series of RF pulses, delays, gradient pulses and phases

b) in a 1D NMR experiment, the FID acquisition time is the time domain (t1)

c) more complex NMR experiments will use multiple “time-dimensional” to obtain data and simplify the analysis.

d) Multidimensional NMR experiments may also use multiple nuclei (2D, 13C,15N) in addition to 1H, but usually detect 1H)

1D NMR Pulse Sequence

Creating Multiple Dimensions in NMR

a) collect a series of FIDS incremented by a second time domain (t1)

b) the normal acquisition time is t2.

c) Fourier transformation occurs for both t1 and t2, creating a two- dimensional (2D) NMR spectra

Relative appearance of each NMR spectra will be modulated by the t1 delay

Collections of FIDs with t1 modulations

Fourier Transform t2 obtain series of NMR spectra modulated by t1

Looking down t1 axis, each point has characteristics of time domain FID

Fourier Transform t1 obtain 2D NMR spectra

Peaks along diagonal are normal 1D NMR spectra

Cross-peaks correlate two diagonal peaks by J-coupling or NOE interactions

Contour map (slice at certain threshold) of 3D representation of 2D NMR spectra. (peak intensity is third dimension

Creating Multiple Dimensions in NMR

In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or cross-peaks indicate a correlation between the two diagonal peaks

Diagonal peaks corresponds to 1D NMR spectra

Cross peaks correlate diagonal peaks by NOEs

2D 1H-1H NOESY Experiment

Diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)

Relative magnitude of cross-peak is related to distance (1/R6) between protons (≥ 5Å)

2D 1H-13C HSQC Experiment

Correlates all directly bonded 13C-1H pairs

generally requires 13C-labeling (1.1% natural abundance)

2D 1H-1H TOCSY Experiment

Correlates all 3-bonded 1H-1H pairs in a molecules

3D & 4D NMR Spectra

a) additional dimensions usually correspond to 13C & 15N chemical shifts.b) primarily used for analysis of biomolecular structures

- disperses highly overlapped NMR spectra into 3D & 4D c) view 3D, 4D experiments as collection of 2D spectra.d) one experiment may take 2.5 to 4 days to collect.

Spread peaks out by 15N chemical shift of amide N attached to NH

Further spread peaks out by 13C chemical shift of C attached to CH