NMR spectroscopy

Terms:
NMR nuclei magnetic Resonance
Magnetic field: a field produced by moving electric charges,
Static magnetic field: the currents are steady (not changing with time)
External magnetic field B0
Nuclear angular moment (P)
Magnetic moment μ
quantum chemistry
Spin quantum number I
Nuclear Angular moment (P) and the
Magnetic Moment (μ)

Problems and solutions
1. the chemical shift is the resonant frequency of a nucleus, The variations of nuclear magnetic resonance frequencies of the same kind of nucleus, due to variations in the electron distribution, is called the chemical shift.
Reports the value in ppb



The chemical shift of a nuclear reports the local chemical environment : magnetic field caused by other nuclei and electrons.
2. Spin-Spin Coupling occurs: 
- the hydrogen  nuclei of an organic molecule are spinning , and the axis of rotation may be with or against the applied magnetic field
3. COSY (COSY – Correlation spectroscopy) experiment provides which protons are J-coupled with other (correlate protons that are J-coupled) Homonuclear 2D experiment; plot of chemical shift vs. chemical shift identifies spin-coupled resonances. Many variations permit measurements of J coupling constants, long-range connectivities, suppression, and enhancement of selected resonances
To interpret  a COSY plot
Diagonal peaks are equivalent to those observed in ID spectrum.
Cross peaks provide evidence of coupling between correlated spins
4. Longitudinal relaxation R1 and transverse relaxation R2
Relaxation of the NMR signal
After the excitation the system will go back to the equilibrium state.
This is called relaxation, which is caused by small fluctuating magnetic
fields within the sample caused by thermal motion of the molecules.
• There are two types of relaxation processes,
longitudinal relaxation, R1, and
transverse relaxation, R2.
• R1 re-establish the Mz magnetization through fluctuating magnetic
fields in the xy-plane. The time of this process is described by
T1=1/R1.
• R2 describes how the signal disappears in the xy-plane by small
fluctuating magnetic fields both in the xy-plane but also in the z-direction.
T2=1/R2.
COSY is a homonuclear 2D technique that is used to correlate the chemical shifts of 1 H nuclei which
are J-coupled to one another. The original COSY experiment is the easiest of all 2D experiments as it
only consists of two 90-degree pulses. The first pulse, the preparation pulse applied along the x-axis,
creates transverse magnetization components for all allowed transitions. This is followed by the
evolution period t1 during which the various magnetization components are labeled with their
characteristic precession frequencies (including chemical shift and homonuclear J-coupling). The
mixing pulse (also applied along the x-axis) then transfers magnetization between protons that are Jcoupled
with each other. The final distribution of magnetization components is detected by
measuring their precession frequencies during the detection period t2 . The
COSY spectrum is produced by a 2D Fourier transform with respect to both t1 and t2 , and
its cross peaks indicate which 1H nuclei are J-coupled.
The fourier transform with respect to t2 yields four different peaks for a simple A-B spin system.
Two of them represents a doublet centered at chemical shift of proton A and the other two represents
the doublet centered at the chemical shift of proton B. The cross peaks observed in the 2D COSY
spectrum is a result of the fourier transform with respect to t1. The amount of magnetization that is
transferred for example from proton B to proton A by the mixing pulse depends on the preciession of
B during time t1. As a result, the observed signal from A is modulated during t1 by the chemical shift
of B and the second fourier transform will thus result in a cross peak between A and B.
A more thorough explanation of the origin of cross peaks requires the use of the product operator
formalism (not introduced on this course).
Nuclear Overhauser Spectroscopy. Just as in the COSY experiment, we also get diagonal peaks and
cross-peaks but the cross-peaks arises from a completely different mechanim. Here we have dipoledipole
relaxation between protons close in space. Consider 2 protons A and B close in space. During
the experiment, we will have a population transfer from proton A to proton B and the amount of
magnetization that is transferred depends on the checmial shift of proton A. Therefore, we get 2
peaks at the chemical shift of proton B, one at the diagonal (same chemical shift in both dimensions)
and one cross-peak at the chemical shift of B on the x-axis and the chemical shift of proton A on the
y-axis. The intensity of the cross-peak is related to how effective the dipole-dipole relaxation is and
thus by the distance between the protons.
In a NOESY experimet we have a mixing time when the cross-peaks will have time to evolve. This
is usually set to around 50ms for protein where we have very efficient dipole-dipol relaxation and to
about 500ms for smaller molecules. In a NOESY spectrum of a small molecule (up to about 2kDa)
the cross-peaks have opposite sign compared to the diagonal peaks but for larger molecules all peaks
have the same sign.