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
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
NMR: “fingerprint” of the compound’s chemical structure
2-phenyl-1,3-dioxep-5-ene
1H
NMR spectra
13C
NMR spectra
Protein Structures from NMR
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
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)
Some Suggested NMR References
“Spin Dynamics – Basics of Nuclear Magnetic Resonance” M. H. Levitt
“Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin
“Modern NMR Techniques for Chemistry Research” Andrew E. Derome
“NMR and Chemistry- an introduction to the
fourier transform-multinuclear era” J. W. Akitt
“Nuclear Magnetic Resonance Spectroscopy” R. K Harris
“Protein NMR Spectroscopy: Principals and Practice”
John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother
“Biomolecular NMR Spectroscopy” J. N. S. Evans
“NMR of Proteins and Nucleic Acids” Kurt Wuthrich
“Tables of Spectral Data for Structure Determination of Organic Compounds”
Pretsch, Clerc, Seibl and Simon
“Spectrometric Identification of Organic Compounds”
Silverstein, Bassler and Morrill
Some NMR Web Sites
Integrated Spectral Data Base System for Organic Compounds
http://www.aist.go.jp/RIODB/SDBS/menu-e.html
The Basics of NMR
Hypertext based NMR course
http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm
Educational NMR Software All kinds of NMR software
http://www.york.ac.uk/depts/chem/services/nmr/edusoft.html
NMR Knowledge Base
A lot of useful NMR links
http://www.spectroscopynow.com/
NMR Information Server
News, Links, Conferences, Jobs
http://www.spincore.com/nmrinfo/
Technical Tidbits
Useful source for the art of shimming
http://www.acornnmr.com/nmr_topics.htm
BMRB (BioMagResBank)
http://www.bmrb.wisc.edu/
Database of NMR resonance assignments
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
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
Basic NMR Spectrometer
Superconducting Magnet
a)
b)
c)
solenoid wound from superconducting niobium/tin or niobium/titanium wire
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
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
Theory of NMR
1. Quantum
i.
Description
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
2) 2I + 1 states:
I, I-1, I-2, …, -I
l
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
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)
2. Classical
i.
Description
Spinning particle precesses around an applied magnetic field
a)
Angular velocity of this motion is given by:
wo = gBo
where the frequency of precession of Larmor frequency is:
n = gBo/2p
Same as quantum mechanical description
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)
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
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
NMR Relaxation
a)
b)
No spontaneous reemission of photons to relax down to ground state
1) Probability too low  cube of the frequency
Two types of NMR relaxation processes
1) 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
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 (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-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
Na / Nb = e
DE = g h Bo / 2p
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
is ~ 64x as sensitive as
13C
15N
is 1000x
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
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 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
Chemical Shift
a)
b)
Small local magnetic fields (Bloc) are generated by electrons as
they circulate nuclei.
1) Current in a circular coil generates a magnetic field
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.
NMR Spectra Terminology
TMS
CHCl3
7.27
increasing d
low field
down field
high frequency (u)
de-shielding
Paramagnetic
600 MHz
1H
0
decreasing d
high field
up field
low frequency
high shielding
diamagnetic
150 MHz
13C
ppm
92 MHz
2H
Increasing field (Bo)
Increasing frequency (u)
Increasing g
Increasing energy (E, consistent with UV/IR)
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
Predicting Chemical Shift Assignments
Numerous Experimental NMR Data has been compiled and general trends identified
• See:
 “Tables of Spectral Data for Structure Determination of
Organic Compounds” Pretsch, Clerc, Seibl and Simon
 “Spectrometric Identification of Organic Compounds”
Silverstein, Bassler and Morrill
• Spectral Databases:
 Aldrich/ACD Library of FT NMR Spectra
 Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)
Ongoing effort to predict chemical shifts from first principals (quantum
mechanical description of factors contributing to chemical shifts)
Predicting Chemical Shift Assignments
Empirical Chemical Shift Trends (Databases) Have Been Incorporated Into A
Variety of Software Applications
Example: ChemDraw
• Program that allows you to generate a 2D sketch of any compound
• can also predict 1H and 13C chemical shifts
 matches sub-fragments of structure to structures in database
Fulvene
Protocol of the H-1 NMR Prediction:
5.22
H
H5.22
Node
Shift
Base + Inc.
H
6.44
H
6.44
H
6.44
H
6.44
H
5.22
H
5.22
5.25
1.24
-0.05
5.25
-0.05
1.24
5.25
1.24
-0.05
5.25
-0.05
1.24
5.25
-0.03
5.25
-0.03
6.44
H
H6.44
H
6.44
H
6.44
Estimation Quality: blue = good, magenta = medium, red = rough
6
5
4
PPM
3
Comment (ppm rel. to TMS)
1-ethylene
1 -C=C gem
1 -C=C trans
1-ethylene
1 -C=C trans
1 -C=C gem
1-ethylene
1 -C=C gem
1 -C=C trans
1-ethylene
1 -C=C trans
1 -C=C gem
1-ethylene
2 -C=C c + t
1-ethylene
2 -C=C c + t
2
1
0
Predicting Chemical Shift Assignments
How Does the Predicted Results Compare to Experimental Data?
Parameter
D(A)
D(B)
D(C)
Experimental ( ppm)
6.22
6.53
5.85
Predicted (ppm)
6.44
6.44
5.22
Typical accuracy
A number of factors can affect prediction:
Similarity of structures in reference database
 Solvent
 Temperature
 structure/conformation
 additive nature of parts towards the whole

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.
Coupling Constants
a)
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
b)
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 (a) and excited states (b) of observed nuclei
3) Coupling pattern and intensity follows Pascal’s triangle
Pascal's triangle
b
a
Common NMR Splitting Patterns
Multiplets consist of 2nI + 1 lines
I is the nuclear spin quantum number (usually 1/2) and
n is the number of neighboring spins.
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!
Nuclear Overhauser Effect (NOE)
a)
b)
c)
Interaction between nuclear spins mediated through empty
space (#5Å)  like ordinary bar magnets
Important: effect is time-averaged
Gives rise to dipolar relaxation (T1 and T2) and specially to
cross-relaxation
Perturb 1H spin population
affects 13C spin population
NOE effect
Nuclear Overhauser Effect (NOE)
Nuclear Overhauser Effect (NOE, h) – the change in intensity of an NMR
resonance when the transition of another are perturbed, usually by saturation.
hi = (I-Io)/Io
where Io is thermal equilibrium intensity
Saturation – elimination of a population difference between transitions
(irradiating one transition with a weak RF field)
irradiate
bb
ab
N
N-d
X
A
ba
X
aa
N+d
N
A
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)
Saturated
(equal population)
ab
N-½d
saturate
bb N-½d
I
S
ba
I
aa
N+½d
N+½d
S
Saturated
(equal population)
Observed signals only occur
from single-quantum transitions
Populations and energy levels immediately
following saturation of the S transitions
bb
ab
W1A
N-½d
W1X
N-½d
W2
W0
aa
W1X
N+½d
ba
W1A
Relaxation back to equilibrium can occur through:
Zero-quantum transitions (W0)
Single quantum transitions (W1)
Double quantum transitions (W2)
N+½d
The observed NOE will depend on the “rate” of these relaxation pathways
Nuclear Overhauser Effect (NOE)
Mechanism for Relaxation
• Dipolar coupling between nuclei
local field at one nucleus is due to the presence of the other
– depends on orientation of the whole molecule
• Dipolar coupling, T1 and NOE are related through rotational
correlation time (tc)
– rotational correlation is the time it takes a molecule to rotate
one radian (360o/2p).
• Relaxation or energy transfers only occurs if some frequencies of
motion match the frequency of the energy of transition
– the available frequencies for a molecule undergoing Brownian
tumbling depends on tc
–
W1A 
3t c
3t c

r 6 (1  w A2t c2 )
r6
3t c
2t c
W0  6
 6
2 2
r (w A  w X ) t c )
r
W2 
12t c
12t c

r 6 (1  (w A  w X ) 2t c2 )
r6
NOE is dependent on the
distance (1/r6) separating the
two dipole coupled nuclei
Important: the effect is time-averaged!
2D NOESY (Nuclear Overhauser Effect)
Relative magnitude of the cross-peak is related to
the distance (1/r6) between the protons (≥ 5Ǻ).
NOE is a relaxation factor that builds-up during
The “mixing-time (tm)
NMR Structure Determination
NOE Data Is the Fundamental Piece of Information to Determine Any Structure
(DNA, RNA, Protein, small molecule)
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
Continuous Wave (CW) vs. Pulse/Fourier Transform
NMR Sensitivity Issue
A frequency sweep (CW) to identify resonance is very slow (1-10 min.)
Step through each individual frequency.
Pulsed/FT collect all frequencies at once in time domain, fast (N x 1-10 sec)
Increase signal-to-noise (S/N) by collecting multiple copies of FID
and averaging signal.
S/N
% r number of scans
NMR Data Detection and Processing
i.
NMR Pulse
a) In FT-NMR, how are all the individual nuclei excited simultaneously?
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)
FT
The Fourier transform indicates the
pulse covers a range of frequencies
NMR Pulse
NMR pulse length or Tip angle (tp)
z
Mo
z
x
qt
tp
x
B1
y
y
Mxy
qt = g * tp * B1
The length of time the B1 field is on => torque on bulk magnetization (B1)
A measured quantity – instrument and sample dependent.
NMR Pulse
Some useful common pulses
z
z
90o pulse
Mo
Maximizes signal in x,y-plane
where NMR signal detected
x
p/2
90o
y
x
y
z
180o pulse
Inverts the spin-population.
No NMR signal detected
Mo
Mxy
z
x
y
Can generate just about any pulse width desired.
p
180o
x
y
-Mo
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.
Quadrature detection
a) Frequency of B1 (carrier) is set to the center of the spectra.
1) Small pulse length to excite the entire spectrum
2) Minimizes folded noise
b) How to differentiate between peaks upfield and downfield from carrier?
1)
observed peak frequencies are all relative to the carrier frequency
c) If carrier is at edge of spectra, then peaks are all positive or negative relative to
carrier
1) Excite twice as much noise, decrease S/N
carrier
How to differentiate between
magnetization that precesses
clockwise and counter clockwise?
carrier
same frequency relative to
the carrier, but opposite sign.
PH = 0
B
B
PH = 90
Use two detectors
90o out of phase.
F
w (B1)
F
PH = 0
F
S
F
S
Phase of Peaks
are different.
PH = 90
iv.
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
v.
NMR data size
a) Analog signal is digitized by periodically monitoring the induced current in the
receiver coil
b) How many data points are collected? What is the time delay between data points
c) 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)
d) Dwell Time (DW) – constant time interval between data points.
SW = 1 / (2 * DW)
e) From Nyquist Theorem, Sampling Rate (SR)
SR = 1 / (2 * SW)
f)
Dependent Valuables
TD
Total Data Acquisition Time (AQ):
AQ = TD * DW= TD/2SWH
Should be long enough to
allow complete delay of FID
Higher Digital Resolution requires longer acquisition times
Dwell time DW
vi.
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
vii.
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
Exchange Rates and NMR Time Scale
i.
Time Scale
Slow
Intermediate
Fast
Range (Sec-1)
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.
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
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.
Example: 2D NOESY NMR Spectra
a) diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)
b) NOE is a relaxation factor that builds-up during the “mixing-time” (tm)
c) relative magnitude of the cross-peak is related to the distance (1/r6)
between the protons (≥ 5Å).
2D NOESY NMR Pulse Sequence
Indirect (second)
1H chemical
evolves during t1
Direct (observed)
1H chemical
evolves during t2
NOE intensity
evolves during tm
Cross peaks correlate diagonal
peaks by J-coupling or NOEs
Diagonal peaks corresponds
to 1D NMR spectra
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
Protein NMR
How do you assign a
protein NMR spectra?
A collection of “COSY”-like
experiments that sequentially
walk down the proteins’
backbone
3D-NMR experiments that
Require 13C and 15N labeled
Protein sample
Detect couplings to NH
Protein NMR
Assignment strategy
We know the primary
sequence of the protein.
Correlation of the Cai & Cai-1
and Cbi & Cbi-1 sequentially
aligns each pair of NHs in the
protein’s sequence.
Amide “Strips” from the 3D
CBCANH (right) and CBCA(CO)NH
(left) experiment arranged in
sequential order
Connect the overlapping correlation between NMR experiments
Protein NMR
Molecular-weight Problem
Higher molecular-weight –> more atoms –> more NMR resonance overlap
More dramatic:
NMR spectra deteriorate with increasing
molecular-weight.
MW increases -> correlation time increases
-> T2 decreases -> line-width increases
NMR lines broaden to the point of not being detected!
With broad lines, correlations (J, NOE) become less-efficient
Protein NMR
How to Solve the Molecular-weight Problem?
1) Deuterium label the protein.
• replace 1H with 2H and remove efficient relaxation paths
• NMR resonances sharpen
• problem: no hydrogens -> no NOEs -> no structure
• actually get exchangeable (NH –NH) noes can
augment with specific 1H labeling
2) TROSY
• line-width is field dependent