1. NMR of Paramagnetics
Paramagnetic materials will cause one or more of the following in NMR spectra:
1) Shortening of T1
(relaxation agents)
2) Broadening of NMR lines (shortening of T2)
(broadening agents)
3) Contact Shifts
4) Pseudocontact shifts
(shift reagents)

2. Relaxation Agents
Electrons have spin 1/2 and a gyromagnetic ratio 658 times that of a proton, and thus are very efficient at inducing intermolecular dipole-dipole relaxation (T1).
Even low concentrations of paramagnetic species can severely reduce relaxation rate, which eliminates NOE enchancement.
Reducing relaxation rate (at least to a certain point) can be good.
Since T1 times are sometimes seconds to hundreds of seconds (quarternary carbons), it is unreasonable to wait that long between scans.
Using shorter pulse widths is one way around this problem (recall the discussion of repetition rate and the Ernst angle); an alternative is adding paramagnetic species
If paramagnetic species are added for this purpose, they are relaxation agents.

3. Relaxation Agents
All paramagnetic species are not good relaxation agents.
The ideal paramagnetic ion to use is one that acts on the whole molecule, reducing T1 without severe line broadening and without significant change in chemical shifts
The molecule most commonly used as a relaxation agent is chromiumacetylacetonate (Cr(acac)3) or simply chromium acac.
Loss of heteronuclear NOE
C13 peak integration
Significant problems to the addition of relaxation reagents include: effects on the sample (degradation, precipitation, etc.), solubility of the relaxation agent, and difficulty controlling the amount of T1 reduction.

4. Shorten the relaxation time T1
13C Spectrum of camphor
With Cr(acetyl acetonate)
No Cr(acetyl acetonate)

5. Broadening agents/Paramagnetic Relaxation Enhancement Agents (PREs)
Paramagnetic material with long electron relaxation times induce large variation in nuclear relaxation times without affecting chemical shift much.
These also normally have little effect on general T1 times, and are usually site specific
To use properly, you need to have an idea of the concentration range (nM- M) where the shortening of T1/T2 is local; that way, there is broadening of resonances specifically near where the paramagnetic agent is interacting.
Included in paramagnetics with long electron relaxation times: Mn(II), Cu(II), and Gd(III).

6. Broadening agents
Titration of Mn (II) into RNA sample (~2 mM). Imino portion of 1D spectrum of RNA; several iminos broaden before others, indicating metal ion binding site.

7. Contact Shifts
Paramagnetic compounds such as radical anions of aromatic hydrocarbons can lead to Fermi contact shifts.
This interaction leads to a hyperfine splitting of the electron signal in electron spin resonance spectroscopy (ESR), while shifting the NMR signal of the ligand to higher or lower field.
a = Q
a = the hyperfine coupling constant for the scalar interaction between the electron and nuclear spin,
Q = proportionality constant (in Gauss)
r = unpaired spin density at the atom under consideration.
The hyperfine coupling constant is essentially the same as the scalar coupling constant (J) of the NMR signal.

8. Contact Shifts
The signal of the unpaired electron is split by magnetic nuclei within the radical.
If the paramagnetic compound is in low concentration relative to the diamagnetic compound, the paramagnetic spin density can be spread over the large number of molecules- it is diamagnetically diluted.
If electron spin relaxation is fast, then the NMR lines are observable.
Spin-spin coupling is effectively removed because the electron relaxation is fast and the exchange of electrons cause the diamagnetic compound to see an average.
You might expect to see an average NMR signal, essentially independent of the paramagnetic ion- that is not what is observed, as there is a contact shift.
Since the energy difference of the ESR signal is much different than the NMR signal, there is a population difference and the one state is favored in the time averaged signal.

9. Contact Shifts B/B0 = ae2/(4pkT) B = the contact shift
B0 = magnetic field
a = the hyperfine splitting
e = gyromagnetic ratio of the electron
p = gyromagnetic ratio of the proton
Additionally, the line width is proportional to the hyperfine coupling constant, and 1/r6 where r is the distance between the nucleus and the radical center.

10. 1-propylnapthalene in the presence in varying concentrations of radical anion

11. Pseudocontact Shifts (Shift Reagents)
Shift reagents are pseudocontact shifts of proton resonances induced by a strongly anisotropic paramagnetic center, such as the unpaired electrons in the valence orbitals of rare earth metals [also low spin iron (III) and Cobalt (II) normally].
This is a dipolar interaction between the paramagnetic center and the nucleus through space.
The magnitude of the dipolar interaction is proportional to:
(3cos2 - 1)/r3
r = distance between the paramagnetic center and the nucleus
= angle between the effective symmetry axis of the paramagnetic moment and the distance vector to the nucleus.

12. Pseudocontact Shifts
Lanthanides are often used as shift reagents, particularly europium, because they induce only slight line broadening.
Primary use of shift reagents is to spread complicated spectral regions over a much larger chemical shift range.
The pseudocontact shift results from complex formation between the shift reagent, where the reagent has free coordination sites, and the substrate.
There is structural information based upon the amount of shift.
 = *(3cos2 - 1)/r3
 = empirical constant for the complex being studied.
D = shift
r = distance between the paramagnetic center and the nucleus

13. 2-adamantanol (with and without EuIII complex)

14. Chiral Shift Reagents ~ ()2/2k
NMR cannot distinguish enantiomers.
However, by forming diastereomers by reaction with an enantiomer pure substance, the diastereomers are distinguishable by NMR.
The reaction can be in fast equilibrium, as NMR will detect the average chemical shift value.
In fast equilibrium, the line width is proportional to the frequency difference between the two resonances.
Lanthanides can induce very large shifts causing the resonance to broaden significantly.
~ ()2/2k
 = line width
 = frequency difference (in Hz)
k = exchange rate

15. Chiral Shift Reagents  ~ B02(exp(G/RT))
Since the frequency difference in Hz is correlated to the magnetic field
 ~ B02(exp(G/RT))
Thus, the lines are broader on high field instruments as the line width is proportional to the square of the applied field.
However, the lines will be narrower at high temperature as the line width is inversely proportional to absolute temperature.
Ideally, use the lowest field instrument at the highest temperature possible.

17. 1H/13C NMR on Paramagnetic Compounds
Pascal Roquette; Astrid Maronna; Matthias Reinmuth; Elisabeth Kaifer; Markus Enders; Hans-Jörg Himmel; Inorg. Chem.  2011, 50,
Désirée C. Sauer; Matthias Kruck; Hubert Wadepohl; Markus Enders; Lutz H. Gade; Organometallics  2013, 32,
Désirée C. Sauer; Matthias Kruck; Hubert Wadepohl; Markus Enders; Lutz H. Gade; Organometallics  2013, 32,

18. Contact and Pseudocontact Shifts in Fe-S Proteins

19. Magnetic Susceptibility
Evans Method
1D spectrum- measure shift from paramagnetic
Sample in 5mm tube, paramagnetic solution in capillary
(n0 – ni)/no = (-4p/3)( Ci – Co)
no = Frequency of Resonance in outer tube
ni = Frequency of Resonance in inner tube
= Volume susceptibility

21. Diffusion NMR
Diffusion NMR or Diffusion Ordered Spectroscopy (DOSY) is the study of molecular diffusion in solution which is correlated to molecular size, shape, and aggregation state.
Diffusion NMR can be used to study molecular diffusion or be used as a basis for separating out NMR spectra of molecules in a mixture.
The study of diffusion rates depends upon application of pulsed field gradients.
The gradients are used to identify the physical location of a molecule in solution.
The molecular diffusion is then analyzed in the direction of the gradient (most likely the Z-axis, but could be X or Y-axis).

22. The sequence applied is a PFG spin-echo; the first pulse rotates the magnetization from the Z-axis to the Y-axis and the chemical shift evolves in the X-Y plane for time .
Without the gradient pulse, the chemical shift information will be refocused by the 180º pulse, and another time  period as in a standard spin-echo experiment.
The only intensity change of the resonances should be due to T2 relaxation.

23. If the gradient pulses are added into the sequence, complete refocusing of the chemical shift will only occur if the molecule has not moved, as the gradients will selectively defocus and refocus magnetization according to position in the magnet.
If a molecule moves (diffuses), then the intensity of the resonance detected will be weaker depending how far it moved.
The amount the molecule moved will be dependent upon its diffusion coefficient and the length of the time it is allowed to move for.

24. I = I0 exp(-2/T2 - (G)2D( - /3))
The intensity detected is defined by:
I = I0 exp(-2/T2 - (G)2D( - /3))
I0 is the signal intensity without gradients (or with power of gradients = 0)
G is the gradient strength
D is the Diffusion coefficient
 and  are the experimental delays in the pulse sequence
Plotting ln(I/I0) vs. G2 will yield a linear plot with a slope proportional to the Diffusion coefficient.

25. PFG Spin-Echo of mixture of Acetone, CDCl3, TMS, Isomenthol
Temp = 298K,  = 30 ms, gradient strengths were increased from T/m to 0.25 T/m

26. ln(I/I0) vs G2
The slopes indicate relative mobility rates of 1:1.3:1.5:1.6 (isomenthol:TMS:Acetone:CHCl3)

27. Signal intensity at increasing gradient strength

28. Plot of ln(I/I0) vs. Gradient2

29. Diffusion Study
Sturlaugson, Fayer, et al., J.Phys.Chem (2010)

30. Diffusion Study of Ion Pairing
Solvent dependence of the diffusion coefficient D (10−10 m2 s−1) and hydrodynamic radius rH (Å) of representative Au(I) complexes
Complex Solvent D rH
[IPrAu(NCPh)]BAr4F CDCl3 Cation
Anion
CD2Cl2 Cation
Anion
[IPrAu(NCMe)]SbF6 CDCl3 Cation
CD2Cl2 Cation
Diffusion coefficients (D) obtained from PFGSE data with Stejskal-Tanner plots.
Hydrodynamic radii (rH) calculated from Stokes-Einstein equation
Lau, Gorin, and Kanan, Chemical Science, 5: (2014)

31. DOSY
DOSY is a 2D experiment sort of; there is no t1, but the results are plotted as a 2D.
Plot of chemical shift vs. Diffusion coefficient
Used to identify compounds in a mixture based upon chemical shift and diffusion coefficient
The relative intensities of the resonances can be extracted out, and then identifying the ratio of compounds in the mixture becomes possible.
Real 2D sequences can be incorporated to create a 3D sort of.
The pseudo 3D can have one dimension of 13C one of 1H and one of diffusion coefficient (or you could have a Diffusion Coefficient Edited COSY, so a 3D COSY ...)]

32. DOSY

33. Diffusion Measurement of Polymer
Polydispersity index of polymers revealed by DOSY NMR, Justine Viéville a, Matthieu Tanty, Marc-André Delsuc, Journal of Magnetic Resonance 212 (2011) 169–173

34. Diffusion Measurement of Polymer
Polydispersity index of polymers revealed by DOSY NMR, Justine Viéville a, Matthieu Tanty, Marc-André Delsuc, Journal of Magnetic Resonance 212 (2011) 169–173