Nuclear Magnetic Resonance

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 relaxationTROSY (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‚ Polysaccharides

4.) Drug Design ‚ Structure Activity Relationships by NMR

5) 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

A Basic Concept in ElectroMagnetic TheoryA Basic Concept 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

B.) Theory of NMR:

1. Quantum Description

i. Nuclear Spin (think electron spin)a) Nucleus rotates about its axis (spin)b) 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 fieldc) NMR “active” Nuclear Spin (I) = ½:

1H, 13C, 15N, 19F, 31P biological and chemical relevance 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

Information in a NMR SpectraInformation in a NMR Spectra

1) Energy E = h

h is Planck constant is NMR resonance frequency 10-10 10-8 10-6 10-4 10-2 100 102

wavelength (cm)

-rays x-rays UV VIS IR -wave radio

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

ii. 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)

iii. Energy Levels in a Magnetic Fielda) 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

2. Classical Description

i. 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

ii. Net Magnetization

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

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.


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

iii. Absorption of RF Energy or NMR RF Pulse

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


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.


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

NMR Probe (antenna)

NMR Signal Detection - FIDNMR Signal Detection - FIDThe 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 TransformNMR Signal Detection - Fourier Transform

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 TransformNMR Signal Detection - Fourier Transform

After 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

iv. NMR Relaxationa) No spontaneous reemission of photons to relax down to ground state

1) Probability too low cube of the frequencyb) Two types of NMR relaxation processes

1) spin-lattice or longitudinal relaxationi. transfer of energy to the lattice or

solvent materialii. 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

iv. Relaxation time (T1) exponential decay

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

Please Note: General practice is to wait 5xT1 for the system to have fully relaxed.

2) spin-spin or transverse relaxationi. exchange of energy between excited

nucleus and low energy state nucleusii. randomization of spins or magnetic

moment in x,y-planeiii. related to NMR peak line-widthiv. relaxation time (T2)

Mx = 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 per ~64 excess spins per million in lower statemillion in lower state

Low energy gap


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) B1

2 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.

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 !!

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 !!


• 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


Increase in Magnet Strength is a Major Means to Increase Sensitivity


But at a significant cost!

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

Chemical ShiftChemical Shift

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:

v. Chemical Shifta) Small local magnetic fields (Bloc) are generated by electrons as

they circulate nuclei.1) Current in a circular coil generates a magnetic field

b) These local magnetic fields can either oppose or augment the external magnetic field1) Typically oppose external magnetic field2) Nuclei “see” an effective magnetic field (Beff) smaller then

the external field3) – magnetic shielding or screening constant

i. depends on electron density

ii. depends on the structure of the compoundBeff = 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

c) Effect of Magnetic Anisotropy1) external field induces a flow (current) of electrons in system – ring current effect2) 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

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.

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

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

vi. Spin-Spin Splitting (J-coupling)a) 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)b) 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

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

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 interact2. 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.

Karplus Equation – Coupling Constants Karplus Equation – Coupling Constants

Relates coupling constant toTorsional angle.

Used to solve Structures!

J = const. + 10Cos

vii. Nuclear Overhauser Effect (NOE)a) Interaction between nuclear spins mediated through empty

space (5Å) like ordinary bar magnetsb) Important: effect is time-averagedc) Gives rise to dipolar relaxation (T1 and T2) and specially to

cross-relaxation

the 13C signals are enhanced by a factor1 + = 1 + 1/2 . (1H)/(13C) ~ max. of 2

Perturb 1H spin populationaffects 13C spin population NOE effect

Example 21: The proton NMR spectrum is for a compound of empirical formula C4H8O. Identify the compound

Strong singlet at ~2.25 ppm methyl next to carbonyl

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

O

CH2

H3C

CH3

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

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

3. NMR Instrumentation (block diagram)

sample lift

NMR Tube

RF coilscryoshims

shimcoils

Probe

Liquid He

Liquid N2

i. Superconducting Magneta) solenoid wound from superconducting niobium/tin or niobium/titanium wireb) kept at liquid helium temperature (4K), outer liquid N2 dewar

1) near zero resistance minimal current lose magnet stays at field for years without external power source

c) electric currents in the shim coils create small magnetic fields which compensate inhomogenieties

Cross-section of magnet

Superconducting solenoidUse up to 190 miles of wire!

spinner

magnet

ii. Lock System a) NMR magnetic field slowly drifts with time.b) Need to constantly correct for the field drift during data collectionc) Deuterium NMR resonance of the solvent is continuously irradiated and

monitored to maintain an on-resonance condition1) changes in the intensity of the reference absorption signal controls a feedback circuit2) a frequency generator provides a fixed reference frequency for the lock signal3) if the observed lock signal differs from the reference frequency, a small current change occurs in a room-temperature shim coil (Z0) to create a

small magnetic field to augment the main field to place the lock-signal back into resonance d) NMR probes contains an additional transmitter coil tuned to deuterium frequency

Lock Feedback CircuitField Drift over 11 Hrs (~ 0.15Hz/hr

Lock Changes From

Off-resonance to On-resonance

iii. Sample Probea) Holds the sample in a fixed position in the magnetic fieldb) Contains an air turbine to spin, insert and eject the samplec) Contains the coils for:

1) transmitting the RF pulse2) detecting the NMR signal3) observing the lock signal4) creating magnetic field gradients

d) Thermocouples and heaters to maintain a constant temperature

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

iv. Pulse Generator & Receiver Systema) Radio-frequency generators and frequency synthesizers produce a signal of

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

1) produces bandwidth (1/4) centered around single frequency2) shorter pulse width broader frequency bandwidth

i. Heisenberg Uncertainty Principal: t

FT

* =tp

Pulse length (time, tp)

The Fourier transform indicates the pulse covers a range of frequencies

iv. Pulse Generator & Receiver Systemc) A magnetic field perpendicular to a circular loop will induce a current in the

loop.d) 90o NMR pulses places the net magnetization perpendicular to the probe’s

receiver coil resulting in an induced current in the nanovolt to microvolt rangee) preamp mounted in probe amplifies the current to 0 to 10 V f) no signal is observed if net magnetization is aligned along the Z or –Z axis

4. NMR Data Detection and Processing

i. Fourier Transform NMRa) Instead of sequentially scanning through each individual frequency,

simultaneously observe absorption of all frequencies.1) frequency sweep (CW), step through each individual frequency is very slow (1-10 min)2) short RF pulses result in bandwidth that cover entire frequency range3) Fourier Transform NMR is fast (N x 1-10 sec) 4) Increase signal-to-noise (S/N) by collecting multiple copies of FID

and averaging signal.

S/N number of scansb) Observe each individual resonance as it precesses at its Larmor frequency

(o) in the X,Y plane.c) Monitor changes in the induced current in the receiver coil as a function of

time.

FID – Free Induction Decay = Bo(1-)/2RF pulse along Y

Detect signal along X

X

y

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

i. Fourier Transform NMRd) Observed signal decays as a function of T2 relaxation

1) peak width at half-height (½) is related to T2

e) NMR signal is collected in Time domain, but prefer frequency domainf) Transform from the time domain to the frequency domain using the Fourier

function

T2 relaxation

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00t1 sec

SR = 1 / (2 * SW)

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

SR – sampling rate

ii. Sampling the Audio Signala) Collect Digital data by periodically sampling signal voltage

1) ADC – analog to digital converterb) To correctly represent Cos/Sin wave, need to collect data at least twice as fast as the signal frequencyc) If sampling is too slow, get folded or aliased peaks

Correct Spectra

Spectra with carrier offset resulting in peak folding or aliasing

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

iii. Window Functionsa) Emphasize the signal and decrease the noise by applying a mathematical function to the FID.b) NMR signal is decaying by T2 as the FID is collected.

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 peak

Line-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

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

iv. Zero Fillinga) Improve digital resolution by adding zero data points at end of FID

v. NMR Peak Integration or Peak Areaa) 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

5. Exchange Rates and NMR Time Scale

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

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

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

ii. Effects of Exchange Rates on NMR data

6. Multidimensional NMR

i. NMR pulse sequencesa) composed of a series of RF pulses, delays, gradient pulses and phasesb) in a 1D NMR experiment, the FID acquisition time is the time domain (t1)c) more complex NMR experiments will use multiple “time-dimensiona” 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

ii. Creating Multiple Dimensions in NMRa) collect a series of FIDS incremented by a second time domain (t1)

1) evolution of a second chemical shift or coupling constant occurs

during this time periodb) 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

ii. Creating Multiple Dimensions in NMRd) During t1 time period, peak intensities are modulated at a frequency corresponding to the chemical shift of its coupled partner.e) In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or

cross-peaks indicate a correlation between the two diagonal peaks

iii. 2D NOESY NMR Spectraa) basis for solving a structureb) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)c) NOE is a relaxation factor that builds-up during the “mixing-time” (m) d) relative magnitude of the cross-peak is related to the distance (1/r6) between the protons (≥ 5Å).

2D NOESY NMR Pulse Sequence

iv. 3D & 4D NMR Spectraa) similar to 2D NMR with either three or four time domains.b) additional dimensions usually correspond to 13C & 15N chemical shifts.c) primarily used for analysis of biomolecular structures

1) disperses highly overlapped NMR spectra into 3 & 4 dimensions, simplifies analysis.

d) view 3D, 4D experiments as collection of 2D spectra.e) one experiment may take 2.5 to 4 days to collect.

1) diminished resolution and sensitivity

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

Nuclear Magnetic Resonance

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