1. NMR Spectroscopy
Part I. Origin of NMR

2. 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 = g p
: magnetic moment
p: angular momentum
g: magnetogyric ratio

3. 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

4. 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

5. Nuclei in Magnetic Field
In a magnetic field B (in z direction) there are 2I+1 orientations of nucleus with different energies.
B0: magnetic field in z direction
nL: Larmor Frequency

6. Nuclei in Magnetic Field
For I=1/2 nucleus : mI = 1/2 and –1/2

7. Nuclei in Magnetic Field

8. Nuclei in Magnetic Field

9. Nuclei in Magnetic Field

10. Nuclei in Magnetic Field

11. Nuclei in Magnetic Field
Distribution between two states

12. Nuclei in Magnetic Field

13. 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)

14. Nuclei in Magnetic Field
Two spins
All spins  Sum
Bulk Magnetization
excess
facing
down Ho
anti-parallel
parallel

15. Effect of a radio frequency
hn = DE H1
2. pump in energy p ap
1. equilibrium DE p ap
3. non-equilibrium
hn = DE
4. release energy (detect) p ap
5. equilibrium

16. Effect of a radio frequency

17. Effect of a radio frequency

18. NMR Signals

19. Relaxation- Return to Equilibrium
x,y plane
z axis
Transverse
Longitudinal 1 1 t t 2 2
E-t/T2
1-e-t/T1 8 8
Transverse always faster!

20. NMR Spectroscopy
Part II. Signals of NMR

21. 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.

22. Fourier Transform
The Fourier transform relates the time-domain f(t) data with the frequency-domain f(w) data.

23. Fourier Transform

24. Fourier Transform

25. NMR line shape
Lorentzian line
A amplitude
W half-line width

26. 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.

27. Resolution

28. Resolution-digital resolution

29. Resolution Measurement half-height width:
10~15% solution of 0-dichlorobenzene (ODCB) in acetone
Line-shape:
Chloroform in acetone

30. 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

31. Sensitivity Definition signal to noise-ratio
A : height of the chosen peak
Npp : peak to peak noise

32. Sensitivity Measurement 1H 0.1% ethyl benzene in deuterochloroform
13C ASTM, mixture of 60% by volume deuterobenzene and dioxan or 10% ethyl benzene in chloroform
31P 1% trimehylphosphite in deuterobenzene
15N 90% dimethylformamide in deutero-dimethyl- sulphoxide
19F 0.1% trifluoroethanol in deuteroacetone
2H, 17O tap water

33. Sensitivity Factors affect sensitivity Probe: tuning, matching, size
Dynamic range and ADC resolution
Solubility of the sample in the chosen solvent

34. Spectral Parameters Chemical Shift Spin-spin Coupling
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 spin-spin coupling constant J.
Intensity of the signal

36. Chemical Shift Origin of chemical shift s shielding constant
Chemically non-equivalent nuclei are shielded to different extents and give separate resonance signals in the spectrum

37. Chemical Shift

38. Chemical Shift
d – scale or abscissa scale

39. Chemical Shift Shielding s CH3Br < CH2Br2 < CH3Br < TMS
90 MHz spectrum

40. Abscissa Scale

41. 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 ~ 220 ppm
d of F ~ 800 ppm
d of P ~ 300 ppm

42. Chemical Shift Charge density Neighboring group Anisotropy
Ring current
Electric field effect
Intermolecular interaction (H-bonding & solvent)

43. Chemical Shift – anisotropy of neighboring group
c susceptibility
r distance to the dipole’s center
Differential shielding of HA and HB in the dipolar field of a magnetically anisotropic neighboring group

44. Chemical Shift – anisotropy of neighboring group
d~2.88
d~9-10

45. 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.

46. 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

47. Ring Current
The ring current is induced form the delocalized p 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.

48. Ring Current -- example

49. Spin-spin coupling

50. Spin-spin coupling

51. AX system

52. AX2 system

53. Spin-spin coupling

54. AX3 system

55. 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

56. Example AX4 system
I=1; n=3
AX4

57. Order of Spectrum Zero order spectrum only singlet
First order spectrum
Dn >> J
Higher order spectrum
Dn ~ J

58. AMX system

59. Spin-spin coupling Hybridization of the atoms
Bond angles and torsional angles
Bond lengths
Neighboring p-bond
Effects of neighboring electron lone-pairs
Substituent effect

60. JH-H and Chemical Structure
Geminal couplings 2J (usually <0)
H-C-H bond angle
hybridization of the carbon atom
substituents

61. Geminal couplings 2J bond angle

62. Effect of Neighboring p-electrons
Geminal couplings 2J
Effect of Neighboring p-electrons
Substituent Effects

63. Vicinal couplings 3JH-H
Torsional or dihedral angles
Substituents
HC-CH distance
H-C-C bond angle

64. Vicinal couplings 3JH-H dihedral angles
Karplus curves

65. Chemical Shift of amino acid

67. Chemical Shift Prediction
Automated Protein Chemical Shift Prediction
BMRB NMR-STAR Atom Table Generator for Amino Acid Chemical Shift Assignments

71. Example 1

72. Relaxation Time Phenomenon & Application
NMR Spectroscopy
Relaxation Time
Phenomenon & Application

73. Relaxation- Return to Equilibrium
x,y plane
z axis
Transverse
Longitudinal 1 1 t t 2 2
E-t/T2
1-e-t/T1 8 8
Transverse always faster!

74. magnetization vector's trajectory
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- and y- magnetizations.

75. 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.

76. Relaxation time – Bloch Equation

77. Relaxation time – Bloch equation

78. 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

79. 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.

80. Longitudinal Relaxation time T1
Inversion-Recovery Experiment
180y (or x)
90y tD

82. T1 relaxation

83. Range of interaction (Hz)
relevant parameters
Dipolar coupling
- abundance of magnetically active nuclei - size of the magnetogyric ratio
Quadrupolar coupling
- size of quadrupolar coupling constant - electric field gradient at the nucleus
Paramagnetic
concentration of paramagnetic impurities
Scalar coupling
size of the scalar coupling constants
Chemical Shift Anisotropy (CSA)
- size of the chemical shift anisotropy - symmetry at the nuclear site
6- Spin rotation

84. 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

85. 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)

86. Spin-spin relaxation (Transverse) T2
90y
180y (or x) tD tD
signal width at half-height (line-width )= (pi * T2)-1

87. Spin-spin relaxation (Transverse) T2

88. Spin-Echo Experiment

89. Spin-Echo experiment

90. MXY =MXYo e-t/T2

91. Carr-Purcell-Meiboom-Gill sequence

92. 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.

94. Relaxation and correlation time
For peptides in aqueous solutions the dipole-dipole spin-lattice and spin-spin relaxation process are mainly mediated by other nearby protons

95. 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)

96. Application

98. Characterizing Protein Dynamics: Parameters/Timescales
Relaxation

99. 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

100. Linewidth is Dependent on MWA B
Small
(Fast)
Big
(Slow) 1H
15N
Linewidth determined by size of particle
Fragments have narrower linewidths

111. Nuclear Overhauser Effect

112. 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.

113. Nuclear Overhauser Effect

115. 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

116. Nuclear Overhauser Effect Brownian motion and NOE

117. When 1/tc >>w0 (or tc2 w02 <<1 ) extreme narrowing limit

118. When 1/tc >> w0 (or tc2 w02 <<1 )
extreme narrowing limit
For homo-nuclear hmax = 0.5
For hetro-nuclear hmax = 0.5 (gs/gi)

119. When 1/tc ~ w0 (or tc w0 ~ 1 ) M.W.~ 103
W2 and W0 effect are balanced.  max ~ 0
improvement:
Change solvent ofr temperature
Using rotating frame NOE

120. When 1/tc < w0 (or tc w0 >> 1 ) M.W. > 104
W0 dominant ,  max = -1
application
Useful technique for assigning NMR spectra of protein

121. Nuclear Overhauser Effect & distance

122. citraconic acid
mesaconic acid