Download NMR Spectroscopy

NMR Spectroscopy
Part I. Origin of NMR
Nuclei in Magnetic Field

Nucleus rotate about an axis -- spin
Nucleus bears a charge, its spin gives rise to a magnetic
field . The resulting magnetic moment is oriented
along the axis of spin and is proportional to angular
momentum
m=gp
m: magnetic moment
p: angular momentum
g: magnetogyric ratio
Nuclei in Magnetic Field

Spin Quantum Number I
a characteristic property of a nucleus. May be an
integer or half integer
# of protons
# of neutrons
I
even
even
0
odd
odd
integer 1,2,3…
even
even
half integral
odd
odd
half integral
Nuclei in Magnetic Field

Properties of nucleus with spin quantum
number I
1. An angular momentum of magnitude {I(I+1)}1/2ħ
2. A component of angular momentum mIħ on an arbitrary
axis where mI=I, I-1, … -I (magnetic quantum number)
3. When I>0, a magnetic moment with a constant magnitude
and an orientation that is determined by the value of mI.
m = g mI ħ
Nuclei in Magnetic Field

In a magnetic field B (in z direction) there are 2I+1
orientations of nucleus with different energies.
EmI =  mB0 = gB0 mI = mI hvL
B0: magnetic field in z direction
nL: Larmor Frequency
v = gB / 2
Nuclei in Magnetic Field

For I=1/2 nucleus : mI = 1/2 and –1/2
E1/ 2 = gB0 mI = 
g
B0
2
g
E1/ 2 = gB0 mI =  B0
2
E = gB0
Nuclei in Magnetic Field
Nuclei in Magnetic Field
Nuclei in Magnetic Field
Nuclei in Magnetic Field
Nuclei in Magnetic Field
Distribution between two states
N 1
N 1
2
2
gB0
E
 gB0 
= exp( 
) = exp  
  1
kT
kT
 kT 
Nuclei in Magnetic Field
Nuclei in Magnetic Field
Magnetizaton
The difference in populations of the two
states can be considered as a surplus in
the lower energy state according to the
Boltzmann distribution
A net magnetization of the sample is
stationary and aligned along the z axis
(applied field direction)
Nuclei in Magnetic Field
Two spins
All spins
 Sum
Ho
parallel
anti-parallel
excess
facing
down
Bulk
Magnetization
Effect of a radio frequency
p
E
1. equilibrium
H1
hn = E
ap
2. pump in energy
p
ap
3. non-equilibrium
hn = E
p
5. equilibrium
ap
4. release energy (detect)
Effect of a radio frequency
Effect of a radio frequency
a = gB1
NMR Signals
Relaxation- Return to Equilibrium
t
t
x,y plane
Transverse
0
Longitudinal
1
1
t
t
2
2
8
E-t/T2
1-e-t/T1
Transverse always faster!
8
0
z axis
NMR Spectroscopy
Part II. Signals of NMR
Free Induction Decay (FID)
• FID represents the time-domain
response of the spin system following
application of an radio-frequency pulse.
• With one magnetization at w0, receiver
coil would see exponentially decaying
signal. This decay is due to relaxation.
Fourier Transform
The Fourier transform relates the
time-domain f(t) data with the
frequency-domain f(w) data.
Fourier Transform
Fourier Transform
NMR line shape
Lorentzian line
y=
AW
2
W  4x0  x 
2
A
amplitude
W
half-line width
2
Resolution

Definition
For signals in frequency domain it is the deviation of the
peak line-shape from standard Lorentzian peak. For time
domain signal, it is the deviation of FID from exponential
decay. Resolution of NMR peaks is represented by the
half-height width in Hz.
Resolution
Resolution-digital resolution
Resolution

Measurement
half-height width:
10~15% solution of 0-dichlorobenzene
(ODCB) in acetone
Line-shape:
Chloroform in acetone
Resolution

Factors affect resolution
Relaxation process of the observed nucleus
Stability of B0 (shimming and deuterium locking)
Probe (sample coil should be very close to the sample)
Sample properties and its conditions
Sensitivity

Definition
signal to noise-ratio
A
s / n = 2.5
N pp
A:
height of the chosen peak
Npp : peak to peak noise
Sensitivity
Measurement
1H
0.1% ethyl benzene in deuterochloroform
13C
ASTM, mixture of 60% by volume deuterobenzene

31P
15N
and dioxan or 10% ethyl benzene in chloroform
1% trimehylphosphite in deuterobenzene
19F
90% dimethylformamide in deutero-dimethylsulphoxide
0.1% trifluoroethanol in deuteroacetone
2H, 17O
tap water
Sensitivity

Factors affect sensitivity
Probe: tuning, matching, size
Dynamic range and ADC resolution
Solubility of the sample in the chosen solvent
Spectral Parameters

Chemical Shift
Caused by the magnetic shielding of the nuclei by their
surroundings. d-values give the position of the signal relative to
a reference compound signal.

Spin-spin Coupling
The interaction between neighboring nuclear dipoles leads to a
fine structure. The strength of this interaction is defined as spinspin coupling constant J.

Intensity of the signal
Chemical Shift

Origin of chemical shift
Beff = B0  sB0 = 1  s B0
s
shielding constant
g
g
1  s B0
n =
Beff =
2
2
'
Chemically non-equivalent nuclei are shielded to different
extents and give separate resonance signals in the spectrum
Chemical Shift
Chemical Shift

d – scale or abscissa scale
gB0
1  s 1 
n 1 ==
2
gB0
1  s 2 
n 2 ==
2
gB0
s 2  s 1 
n 2 n 1 =
2
n 2 n 1
 s 2 s1
n1
Chemical shift parameter d = s 2  s 1  10 6
Chemical Shift
n
6
d=
10
observing frequency
Shielding s
CH3Br < CH2Br2 < CH3Br < TMS
d CHBr 3  =
90 MHz spectrum
614
90  10 6
 10 6 = 6.82 (ppm)
Abscissa Scale
Chemical Shift



d is dimensionless expressed as the relative
shift in parts per million ( ppm ).
d is independent of the magnetic field
d of proton
0 ~ 13 ppm
d of carbon-13
0 ~ 220 ppm
d of F-19
0 ~ 800 ppm
d of P-31
0 ~ 300 ppm
Chemical Shift
s


local
= s dia
s
local
para
s N s R s e si
Charge density
Neighboring group
Anisotropy
Ring current
Electric field effect
Intermolecular interaction (H-bonding & solvent)
Chemical Shift –
anisotropy of neighboring group
sN =
1
3r 3 4
 //    1  cos2 
 susceptibility
r distance to the dipole’s center
Differential shielding of HA and HB in
the dipolar field of a magnetically
anisotropic neighboring group
Chemical Shift –
anisotropy of neighboring group
d~2.88
d~9-10
• Electronegative groups are "deshielding" and tend to move NMR signals from
neighboring protons further "downfield" (to higher ppm values).
• Protons on oxygen or nitrogen have highly variable chemical shifts which are
sensitive to concentration, solvent, temperature, etc.
• The -system of alkenes, aromatic compounds and carbonyls strongly deshield
attached protons and move them "downfield" to higher ppm values.
•Electronegative groups are "deshielding" and tend to move NMR signals
from attached carbons further "downfield" (to higher ppm values).
•The -system of alkenes, aromatic compounds and carbonyls strongly
deshield C nuclei and move them "downfield" to higher ppm values.
•Carbonyl carbons are strongly deshielded and occur at very high ppm
values. Within this group, carboxylic acids and esters tend to have the
smaller values, while ketones and aldehydes have values 200.
Ring Current

The ring current is induced form the delocalized 
electron in a magnetic field and generates an additional
magnetic field. In the center of the arene ring this
induced field in in the opposite direction t the external
magnetic field.
Ring Current -- example
Spin-spin coupling
Spin-spin coupling
AX system
AX2 system
Spin-spin coupling
AX3 system
Multiplicity Rule
Multiplicity M (number of lines in a multiplet)
M = 2n I +1
n equivalent neighbor nuclei
I spin number
For I= ½
M=n+1
Example
AX4
AX4 system
I=1; n=3
Order of Spectrum
Zero order spectrum
only singlet
First order spectrum
n >> J
Higher order spectrum
n ~ J
AMX system
Spin-spin coupling






Hybridization of the atoms
Bond angles and torsional angles
Bond lengths
Neighboring -bond
Effects of neighboring electron lone-pairs
Substituent effect
JH-H and Chemical Structure

Geminal couplings 2J
(usually <0)
H-C-H bond angle
hybridization of the carbon atom
substituents
Geminal couplings J
2
bond angle
Geminal couplings J
2
Substituent Effects
Effect of Neighboring
-electrons
Vicinal couplings JH-H
3




Torsional or dihedral angles
Substituents
HC-CH distance
H-C-C bond angle
Vicinal couplings JH-H
3

3
Karplus curves

  
1 3
1 3
J = 2 J g 
Jt =
3
3
dihedral angles
Chemical
Shift of
amino acid
http://bouman.chem.georgeto
wn.edu/nmr/interaction/chems
hf.htm
Chemical Shift Prediction
Automated Protein Chemical Shift Prediction
http://www.bmrb.wisc.edu:8999/shifty.html
BMRB NMR-STAR Atom Table Generator for
Amino Acid Chemical Shift Assignments
http://www.bmrb.wisc.edu/elec_dep/gen_aa.html
http://bouman.chem.georgetown.edu/nmr/interaction/chemshf.htm
Example 1
NMR Spectroscopy
Relaxation Time
Phenomenon & Application
Relaxation- Return to Equilibrium
t
t
x,y plane
Transverse
Longitudinal
1
1
t
t
2
2
-t/T2
E
8
0
-t/T1
1-e
Transverse always faster!
8
0
z axis
Relaxation
magnetization vector's
trajectory
The initial vector, Mo, evolves
under the effects of T1 & T2
relaxation and from the influence
of an applied rf-field. Here, the
magnetization vector M(t)
precesses about an effective field
axis at a frequency determined
by its offset. It's ends up at a
"steady state" position as
depicted in the lower plot of x- http://gamma.magnet.fsu.edu/info/tour/blo
and y- magnetizations.
ch/index.html
Relaxation
The T2 relaxation causes the horizontal (xy) magnetisation to
decay. T1 relaxation re-establishes the z-magnetisation. Note
that T1 relaxation is often slower than T2 relaxation.
Relaxation time – Bloch
Equation

Bloch Equation
Relaxation time – Bloch
equation
Spin-lattice Relaxation time
(Longitudinal) T1
Relaxation mechanisms:
1. Dipole-Dipole interaction "through space"
2. Electric Quadrupolar Relaxation
3. Paramagnetic Relaxation
4. Scalar Relaxation
5. Chemical Shift Anisotropy Relaxation
6. Spin Rotation
Relaxation


Spin-lattice relaxation converts the
excess energy into translational,
rotational, and vibrational energy of the
surrounding atoms and molecules (the
lattice).
Spin-spin relaxation transfers the
excess energy to other magnetic nuclei
in the sample.
Longitudinal Relaxation time
T1
Inversion-Recovery
Experiment
180y (or x)
90y
tD
T1 relaxation
Interaction
Dipolar coupling
Range of
relevant parameters
interaction (Hz)
104 - 105
Quadrupolar coupling
106 - 109
Paramagnetic
107 -108
Scalar coupling
10 - 103
Chemical Shift
Anisotropy (CSA)
6- Spin rotation
10 - 104
- abundance of magnetically
active nuclei
- size of the magnetogyric ratio
- size of quadrupolar coupling
constant
- electric field gradient at the
nucleus
concentration of paramagnetic
impurities
size of the scalar coupling
constants
- size of the chemical shift
anisotropy
- symmetry at the nuclear site
Spin-spin relaxation (Transverse)
T2


T2 represents the lifetime of the signal in
the transverse plane (XY plane)
T2 is the relaxation time that is responsible
for the line width.
line width at half-height=1/T2
Spin-spin relaxation (Transverse)
T2
Two factors contribute to the decay of
transverse magnetization.
molecular interactions

( lead to a pure pure T2 molecular effect)

variations in Bo
( lead to an inhomogeneous T2 effect)
Spin-spin relaxation (Transverse)
T2
90y
180y (or x)
tD

tD
signal width at half-height (line-width )= (pi * T2)-1
Spin-spin relaxation (Transverse)
T2
Spin-Echo Experiment
Spin-Echo experiment
MXY =MXYo
-t/T2
e
Carr-Purcell-Meiboom-Gill sequence
T1 and T2


In non-viscous liquids, usually T2 = T1.
But some process like scalar coupling
with quadrupolar nuclei, chemical
exchange, interaction with a
paramagnetic center, can accelerate the
T2 relaxation such that T2 becomes
shorter than T1.
Relaxation and correlation
time
For peptides in aqueous solutions the dipole-dipole spin-lattice and spinspin relaxation process are mainly mediated by other nearby protons
1
T1


2g 
1
4
=
II  1 c 

6
2 2
2 2
5 r
1  w  c 1  4w  c 
1
T2


1 g 4 2
5
2
=
II  1 c 3 

6
2 2
2 2
5 r
 1  w  c 1  4w  c 
4 2
Why The Interest In Dynamics?

Function requires motion/kinetic energy

Entropic contributions to binding events

Protein Folding/Unfolding

Uncertainty in NMR and crystal structures

Effect on NMR experiments- spin relaxation is
dependent on rate of motions  know dynamics to
predict outcomes and design new experiments

Quantum mechanics/prediction (masochism)
Application
Characterizing Protein Dynamics:
Parameters/Timescales
Relaxation
NMR Parameters That Report On
Dynamics of Molecules

Number of signals per atom: multiple signals for
slow exchange between conformational states

Linewidths: narrow = faster motion, wide = slower;
dependent on MW and conformational states

Exchange of NH with solvent: requires local
and/or global unfolding events  slow timescales

Heteronuclear relaxation measurements



R1 (1/T1) spin-lattice- reports on fast motions
R2 (1/T2) spin-spin- reports on fast & slow
Heteronuclear NOE- reports on fast & some slow
Linewidth is Dependent on
MW
A
B
A
B
Big
Small
(Slow) (Fast)
15N
Linewidth
determined by
size of particle
15N
15N
Fragments
have narrower
linewidths
1H
1H
1H
Nuclear Overhauser Effect
Nuclear Overhauser Effect
(NOE)

A change in the integrated NMR absorption
intensity of a nuclear spin when the NMR
absorption of another spin is saturated.
Effect
I  I0
W2  W0
i s  =
=
I0
2W1i  W2  W0
Macromolecules or in viscous solution
W0 dominant, negative NOE at i due to s
Small molecules in non-viscous solution
W2 dominant, positive NOE at i due to s
Nuclear Overhauser Effect
Brownian motion and NOE
W1i

r 6 1  w i2 c2
2 c


 
12

r 1  w  w   
W0 
W2

3 c
r 1 
6
2 2
wi  w s  c
c
6
i
2 2
s
c
When 1/c >>w0 (or c2 w02 <<1 ) extreme narrowing limit
W1 
3 c
r
6
W0 
2 c
r
6
W2 
12 c
r6
When 1/c >> w0 (or c2 w02 <<1 )
extreme narrowing limit
W1 
3 c
r6
W0 
2 c
r6
W2 
12 c
r6

I  I0
W2  W0
12  2 c / r 6
i s  =
=
=
= 1/ 2
i
6
I0
2W1  W2  W0 6  12  2 c / r
For homo-nuclear
max = 0.5
For hetro-nuclear
max = 0.5 gs/gi)
When 1/c ~ w0 (or c w0 ~ 1 ) M.W.~ 103
W2 and W0 effect are balanced.  max ~ 0
improvement:
• Change solvent ofr temperature
• Using rotating frame NOE
When 1/c < w0 (or c w0 >> 1 ) M.W. > 104
W0 dominant ,  max = -1
application
Useful technique for assigning NMR spectra of protein
Nuclear Overhauser Effect & distance
 1 
NOE   6   f  c 
r 
citraconic acid
mesaconic acid