Transcript Slide 1

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 MOST Routinely used Analytical Techniques
NMR History
1937
1946
1953
1966
1975
1985
Rabi predicts and observes nuclear magnetic resonance
Bloch, Purcell first nuclear magnetic resonance of bulk sample
Overhauser NOE (nuclear Overhauser effect)
Ernst, Anderson Fourier transform NMR
Jeener, Ernst 2D NMR
Wüthrich first solution structure of a small protein (BPTI)
from NOE derived distance restraints
1987
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 prizes
1944 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 History
First NMR Spectra on Water
1H
NMR spectra of water
Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment.
Physical Review (1946), 70 474-85.
NMR History
First Observation of the Chemical Shift
1H
NMR spectra ethanol
Modern ethanol spectra
Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. 19: p. 507.
O
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
O
O
NH
O
O
OH
O
OH
HO
O
O
O
O
O
Taxol (natural product)
NMR Structure of MMP-13
complexed to a ligand
Each NMR Observable Nuclei Yields a Peak in the Spectra
“fingerprint” of the structure
2-phenyl-1,3-dioxep-5-ene
1H
NMR spectra
13C
NMR spectra
A 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 I
l
2) 2I + 1 states:
I, I-1, I-2, …, -I
3) identical energies in absence of external magnetic field
c) 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
Information in a NMR Spectra
g-rays x-rays UV VIS
1) Energy E = hu
h is Planck constant
u is NMR resonance frequency 10-10
Observable
Name
10-8
IR
m-wave radio
10-6 10-4
10-2
wavelength (cm)
Quantitative
100
102
Information
d(ppm) = uobs –uref/uref (Hz)
chemical (electronic)
environment of nucleus
peak separation
(intensity ratios)
neighboring nuclei
(torsion angles)
Peak position
Chemical shifts (d)
Peak Splitting
Coupling Constant (J) Hz
Peak Intensity
Integral
unitless (ratio)
relative height of integral curve
nuclear count (ratio)
T1 dependent
Peak Shape
Line width
Du = 1/pT2
peak half-height
molecular motion
chemical exchange
uncertainty principal
uncertainty in energy
ii. Magnetic Moment (m)
a) spinning charged nucleus creates a magnetic field
Magnetic moment
Similar to magnetic field
created by electric current
flowing in a coil
b)
magnetic moment (m) is created along axis of the nuclear spin
m = gp
where:
p – angular momentum
g – 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
Magnetic alignment
= g h / 4p
Bo
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 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:
DE = g h Bo / 2p
where:
Bo – external magnetic field  units:Tesla (Kg s-2 A-1)
h – Planck’s constant 
6.6260 x 10-34 Js
g – gyromagnetic ratio 
unique value per nucleus
1H:
26.7519 x 107 rad T-1 s2p (observed NMR frequency)
c)
Frequency of absorption:
n = g Bo /
d)
From Boltzmann equation:
Nj/No = exp(-ghBo/2pkT)
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
Frequency of absorption:
n = g Bo / 2p
2. Classical Description
i.
Spinning particle precesses around an applied magnetic field
a)
Angular velocity of this motion is given by:
wo = gBo
where the frequency of precession or Larmor frequency is:
n = gBo/2p
Same as quantum mechanical description
ii.
Net Magnetization
z
z
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
Mo
x
y
x
y
Bo
Bo
Quantum Description:
- Nuclei either populate low
energy (a, aligned with field)
or high energy (b, aligned
against field)
- Net population in a energy
level.
- Absorption of radiofrequency promotes nuclear
spins from a  b.
b
DE = h n
Bo > 0
a
Bo
An NMR Experiment
We have a net magnetization precessing about Bo at a frequency of wo
with a net population difference between aligned and unaligned spins.
z
z
Mo
x
y
x
y
Bo
Bo
Now What?
Perturbed the spin population or perform spin gymnastics
Basic principal of NMR experiments
An NMR Experiment
resonant condition: frequency (w1) of B1 matches Larmor frequency (wo)
energy is absorbed and population of a and b states are perturbed.
z
Mo
B1
w1
z
x
B1 off…
x
(or off-resonance)
y
y
Mxy w
1
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.
Right-hand rule
Classical Description
•
Observe NMR Signal

Need to perturb system from equilibrium.


Net magnetization (Mo) now precesses about Bo and B1




B1 field (radio frequency pulse) with gBo/2p frequency
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
Mz
RF pulse
B1 field perpendicular to B0
Mxy
iii.
Absorption of RF Energy or NMR RF Pulse
z
Classic View:
90o pulse
- 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 w1
--
z
Mo
B1
w1
x
B1 off…
x
(or off-resonance)
y
w1 = gB1
precession stops when B1
turned off
Mxy w
1
y
b
Quantum Description:
- enough RF energy has been
absorbed, such that the
population in a/b are now
equal
- No net magnetization along
the z-axis
DE = h n
a
Bo > 0
Please Note: A whole variety of pulse widths are possible, not quantized dealing
with bulk magnetization
An NMR Experiment
What Happens Next?
The B1 field is turned off and Mxy continues to precess about Bo at frequency wo.
z
x
y
Mxy
Receiver coil (x)
wo
 NMR signal
FID – Free Induction Decay
Mxy is precessing about z-axis in the x-y plane
y
Time (s)
y
y
An NMR Experiment
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 - FID
The FID reflects the change in the magnitude of Mxy as
the signal is changing relative to the receiver along the y-axis
Detect signal along X
RF pulse along Y
Again, the signal is precessing about Bo at its Larmor Frequency (wo).
NMR 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 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 Relaxation
a) No spontaneous reemission of photons to relax down to ground state
1) Probability too low  cube of the frequency
b) Two types of NMR relaxation processes
1) spin-lattice or longitudinal relaxation
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
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 relaxation
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-width
iv. 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 Sensitivity
The applied magnetic field causes an energy
difference between aligned(a) and unaligned(b) nuclei
b
Low energy gap
DE = h n
Bo > 0
a
Bo = 0
The population (N) difference can be determined from
Boltzmman distribution: Na / Nb = e DE / kT
The DE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol
Na / Nb = 1.000064
Very Small !
~64 excess spins per
million in lower state
NMR Sensitivity
NMR signal depends on: signal (s) % g4Bo2NB1g(u)/T
1)
2)
3)
4)
5)
Number of Nuclei (N) (limited to field homogeneity and filling factor)
Gyromagnetic ratio (in practice g3)
Inversely to temperature (T)
External magnetic field (Bo2/3, in practice, homogeneity)
B12 exciting field strength
DE = g h Bo / 2p
Na / Nb = e DE / kT
Increase energy gap -> Increase population difference -> Increase NMR signal
DE
≡
Bo ≡
g
g - Intrinsic property of nucleus can not be changed.
(gH/gC)3
1H
for 13C is 64x (gH/gN)3 for 15N is 1000x
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 Sensitivity
•
Relative sensitivity of 1H, 13C, 15N and other nuclei NMR spectra depend on

Gyromagnetic ratio (g)

Natural abundance of the isotope
g - Intrinsic property of nucleus can not be changed.
(gH/gC)3
1H
for 13C is 64x (gH/gN)3 for 15N is 1000x
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 !!
1H
NMR spectra of caffeine
8 scans ~12 secs
13C
NMR spectra of caffeine
8 scans ~12 secs
13C
NMR spectra of caffeine
10,000 scans ~4.2 hours
NMR Sensitivity
Increase in Magnet
Strength is a Major Means
to Increase Sensitivity
NMR Sensitivity
But at a significant cost!
~$800,000
~$2,00,000
~$4,500,000
Chemical 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
The chemical environment for each nuclei results in a unique local
magnetic field (Bloc) for each nuclei:
Beff = Bo - Bloc --- Beff = Bo( 1 - s )
s is the magnetic shielding of the nucleus
v.
Chemical Shift
a) 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 field
1) Typically oppose external magnetic field
2) Nuclei “see” an effective magnetic field (Beff) smaller then
the external field
3) s – magnetic shielding or screening constant
i. depends on electron density
ii. depends on the structure of the compound
Beff = Bo - Bloc --- Beff = Bo( 1 - s )
HO-CH2-CH3
s – reason why observe
three distinct NMR peaks
instead of one based on
strength of B0
n = gBo/2p
de-shielding
high shielding
Shielding – local field opposes Bo
c)
Effect of Magnetic Anisotropy
1) external field induces a flow (current) of electrons in p 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
The NMR scale (d, ppm)
Bo >> Bloc
-- MHz compared to Hz
Comparing small changes in the context of a large number is cumbersome
d=
w - wref
wref
ppm (parts per million)
Instead use a relative scale, and refer all signals (w) in the spectrum to the
signal of a particular compound (wref ).
IMPORTANT: absolute frequency is field dependent (n = g Bo / 2p)
CH 3
Tetramethyl silane (TMS) is a common reference chemical
H3C
Si
CH 3
CH 3
The NMR scale (d, ppm)
Chemical shift (d) 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 (n = g Bo / 2p)
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 Trends
For protons, ~ 15 ppm:
For carbon, ~ 220 ppm:
Carbon chemical shifts have similar trends, but over a larger sweep-width range (0-200 ppm)
Chemical Shift Trends
Acids
Aldehydes
Alcohols, protons a
to ketones
Aromatics
Amides
Olefins
Aliphatic
ppm
15
C=O in
ketones
10
7
5
Aromatics,
conjugated alkenes
Olefins
2
0
TMS
Aliphatic CH3,
CH2, CH
ppm
210
150
C=O of Acids,
aldehydes, esters
100
80
50
0
TMS
Carbons adjacent to
alcohols, ketones
CHARACTERISTIC PROTON CHEMICAL SHIFTS
Common Chemical Shift Ranges
Carbon chemical shifts have
similar trends, but over a
larger sweep-width range
(0-200 ppm)
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
Coupling Constants
Energy level of a nuclei are affected by covalently-bonded neighbors spin-states
1
H
13
1
1
H
H
three-bond
C
one-bond
Spin-States of covalently-bonded nuclei want to be aligned.
+J/4
I
-J/4
bb
S
ab
J (Hz)
ba
S
+J/4
I
aa
I
S
The magnitude of the separation is called coupling constant (J) and has units
of Hz.
vi.
1
11
121
1331
14641
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
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 (a) and excited states (b) of observed nuclei
3) Coupling pattern and intensity follows Pascal’s triangle
Common NMR Splitting Patterns
singlet doublet triplet quartet
1:1
1:2:1 1:3:3:1
pentet
1:4:6:4:1
Coupling Rules:
1.
2.
3.
4.
5.
6.
equivalent nuclei do not interact
coupling constants decreases with separation ( typically # 3 bonds)
multiplicity given by number of attached equivalent protons (n+1)
multiple spin systems  multiplicity  (na+1)(nb+1)
Relative peak heights/area follows Pascal’s triangle
Coupling constant are independent of applied field strength
IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
Karplus Equation – Coupling Constants
J = const. + 10Cosf
Relates coupling constant to
Torsional angle.
Used to solve Structures!
vii.
Nuclear Overhauser Effect (NOE)
a) Interaction between nuclear spins mediated through empty
space (#5Å)  like ordinary bar magnets
b) Important: effect is time-averaged
c) Gives rise to dipolar relaxation (T1 and T2) and specially to
cross-relaxation
Perturb 1H spin population
affects 13C spin population
NOE effect
the 13C signals are enhanced by a factor
1 + h = 1 + 1/2 . g(1H)/g(13C) ~ max. of 2
Example 21: The proton NMR spectrum is for a compound of empirical formula C4H8O.
Identify the compound
Absence of peak at ~9.7 ppm
eliminates aldehyde group
And suggests ketone
Triplet at ~1.2 ppm suggests a
methyl group coupled to a
methylene group
Strong singlet at ~2.25 ppm
methyl next to carbonyl
Quartet at ~2.5 ppm suggests
a methylene next to a carbonyl
coupled to a methyl
3. NMR Instrumentation (block diagram)
i.
Superconducting Magnet
a) solenoid wound from superconducting niobium/tin or niobium/titanium wire
b) 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
magnet
spinner
sample lift
NMR Tube
RF coils
cryoshims
shimcoils
Probe
Superconducting
solenoid
Use up to 190
miles of wire!
Liquid N2
Liquid He
ii.
Lock System
a)
b)
c)
d)
NMR magnetic field slowly drifts with time.
Need to constantly correct for the field drift during data collection
Deuterium NMR resonance of the solvent is continuously irradiated and
monitored to maintain an on-resonance condition
1) changes in the intensity of the reference absorption signal controls a
feedback circuit
2) a frequency generator provides a fixed reference frequency for the lock
signal
3) if the observed lock signal differs from the reference frequency, a small
current change occurs in a room-temperature shim coil (Z0) to create a
small magnetic field to augment the main field to place the lock-signal
back into resonance
NMR probes contains an additional transmitter coil tuned to deuterium frequency
Lock Feedback Circuit
Field Drift over 11 Hrs (~ 0.15Hz/hr
Lock Changes From
Off-resonance to Onresonance
iii.
Sample Probe
a) Holds the sample in a fixed position in the magnetic field
b) Contains an air turbine to spin, insert and eject the sample
c) Contains the coils for:
1) transmitting the RF pulse
2) detecting the NMR signal
3) observing the lock signal
4) creating magnetic field gradients
d) Thermocouples and heaters to
maintain a constant temperature
iv.
Pulse Generator & Receiver System
a) Radio-frequency generators and frequency synthesizers produce a signal of
essentially a single frequency.
b) RF pulses are typically short-duration (msecs)
1) produces bandwidth (1/4t) centered around single frequency
2) shorter pulse width  broader frequency bandwidth
i. Heisenberg Uncertainty Principal: Du.Dt ~ 1/2p
A radiofrequency pulse is a
combination of a wave (cosine) of
frequency w o and a step function
*
=
tp
Pulse length (time, tp)
The Fourier transform indicates the
pulse covers a range of frequencies
FT
iv.
Pulse Generator & Receiver System
c) 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 range
e) preamp mounted in probe amplifies the current to 0 to 10 V
f) no signal is observed if net magnetization is aligned along the Z or –Z axis
4. NMR Data Detection and Processing
i.
Fourier Transform NMR
a) 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 range
3) 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.
b)
c)
S/N % rnumber of scans
Observe each individual resonance as it precesses at its Larmor frequency
(wo) in the X,Y plane.
Monitor changes in the induced current in the receiver coil as a function of
time.
X
y
Detect signal along X
RF pulse along Y
n = gBo(1-s)/2p
FID – Free Induction Decay
i.
Fourier Transform NMR
d) Observed signal decays as a function of T2 relaxation
1) peak width at half-height (n½) is related to T2
e) NMR signal is collected in Time domain, but prefer frequency domain
f) Transform from the time domain to the frequency domain using the Fourier
function
T2 relaxation
Fourier Transform is a mathematical procedure that
transforms time domain data into frequency domain
ii.
Sampling the Audio Signal
a) Collect Digital data by periodically sampling signal voltage
1) ADC – analog to digital converter
b) To correctly represent Cos/Sin wave, need to collect data at least twice as fast
as the signal frequency
c) If sampling is too slow, get folded or aliased peaks
The Nyquist Theorem says that we have
to sample at least twice as fast as the
fastest (higher frequency) signal.
Sample Rate
- Correct rate,
correct frequency
SR = 1 / (2 * SW)
-½ correct rate, ½
correct frequency
Folded peaks!
Wrong phase!
SR – sampling rate
Correct Spectra
Spectra with carrier offset resulting
in peak folding or aliasing
Sweep Width
(range of radio-frequencies monitored for nuclei absorptions)
iii.
Window Functions
a) 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.
Good stuff
Mostly noise
Sensitivity
Resolution
F(t) = 1 * e - ( LB * t ) – line broadening
Effectively adds LB in Hz to peak
Line-widths
Can either increase S/N
or
Resolution
Not
Both!
LB = 5.0 Hz
Increase Sensitivity
FT
LB = -1.0 Hz
Increase Resolution
FT
iv.
Zero Filling
a) Improve digital resolution by adding zero data points at end of FID
8K data
8K FID
No zero-filling
8K zero-fill
16K FID
8K zero-filling
v.
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.
Relative peak areas = Number of protons
3
Integral trace
HO-CH2-CH3
2
1
5. Exchange Rates and NMR Time Scale
i.
Time Scale
Slow
Intermediate
Fast
NMR time scale refers to the chemical shift time scale
a) remember – frequency units are in Hz (sec-1)  time scale
b) exchange rate (k)
c) differences in chemical shifts between species in exchange indicate the
exchange rate.
Range (Sec-1)
Chem. Shift (d)
k << dA- dB
k = dA - dB
k >> dA - dB
0 – 1000
Coupling Const. (J)
k << JA- JB
k = JA- JB
k >> JA- JB
0 –12
T2 relaxation
k << 1/ T2,A- 1/ T2,B
k = 1/ T2,A- 1/ T2,B
k >> 1/ T2,A- 1/ T2,B
1 - 20
d) For systems in fast exchange, the observed chemical shift is the average
of the individual species chemical shifts.
dobs = f1d1 + f2d2
f1 +f2 =1
where:
f1, f2 – mole fraction of each species
d1,d2 – chemical shift of each species
ii.
Effects of Exchange Rates on NMR data
k = p Dno2 /2(he - ho)
k = p Dno / 21/2
k = p (Dno2 - Dne2)1/2/21/2
k = p (he-ho)
k – exchange rate
h – peak-width at half-height
n – peak frequency
e – with exchange
o – no exchange
ii.
Effects of Exchange Rates on NMR data
40 Hz
No exchange:
With exchange:
W1/ 2 =
1
1

pT2 pt ex
k=
1
t ex
slow
k = 0.1 s-1
k = 5 s-1
Increasing Exchange Rate
W1/ 2
1
=
pT2
k = 10 s-1
k = 20 s-1
k = 40 s-1
coalescence
k = 88.8 s-1
k = 200 s-1
k = 400 s-1
k = 800 s-1
fast
k = 10,000 s-1
6. Multidimensional NMR
i.
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-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 NMR
a) 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 period
b) the normal acquisition time is t2.
c) Fourier transformation occurs for both t1 and t2, creating a twodimensional (2D) NMR spectra
Relative appearance of each
NMR spectra will be modulated
by the t1 delay
ii.
Creating Multiple Dimensions in NMR
d) 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
Collections of FIDs
with t1 modulations
Fourier Transform t1
obtain 2D NMR spectra
Fourier Transform t2
obtain series of NMR
spectra modulated by t1
Looking down t1
axis, each point
has characteristics
of time domain FID
Peaks along diagonal are
normal 1D NMR spectra
Contour map (slice at
certain threshold) of 3D
representation of 2D NMR
spectra. (peak intensity is
third dimension
Cross-peaks correlate two
diagonal peaks by J-coupling
or NOE interactions
iii.
2D NOESY NMR Spectra
a) basis for solving a structure
b) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)
c) NOE is a relaxation factor that builds-up during the “mixing-time” (tm)
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 Spectra
a) 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