1. An Introduction to Parahydrogen Projects in the Pines Lab David Trease Special Topics... March 20 2007 Chip Crawford

2. NMR and MRI Versatile, non-destructive but low sensitivity!

3. Quantum Description of Magnetic Resonance. Various Polarization Techniques PASADENA Parahydrogen Creation Pines Lab Projects Summary

4. Quantum Description: No fieldB 0 applied E General Ket

5. Hamiltonians The Hamiltonian is rather simple in form, assuming you have a simple magnetic field and spin state!

6. Radio Frequency Hamiltonians rf

7. Time Evolution & Rotating Frame Time evolution operator can be derived from the Schrodinger equation (see Sakurai). rf

8. Quantum-Classical Connection How do these equations relate to the pretty classical picture that David painted? An individual spin has a magnetic moment proportional to the spin: We measure the ensemble of these magnetic moments in a sample. This ensemble measurement corresponds to the vectors to which David referred. The effect that the time evolution operators have on the bulk magnetization is to rotate it, such as simple MRI experiments. Radio Frequency Pulse

9. Transverse Magnetization X up=1/root(2) up + down y In the basis defined by the magnetic field the transverse magnetization of a spin is a linear combination of the basis kets. y x z y x z

10. Nuclear magnetic moment vector E No field Quantum Description B0B0 B 0 applied

11. Nuclear magnetic moment vector B0B0 E No fieldB 0 applied Quantum Description

12. Nuclear magnetic moment vector Ensemble of nuclear spins Pure ensemble; population Mixed ensemble; coherences

13. Ensemble of nuclear spins Coherent ensemble; Time evolution of an ensemble:

14. Thermal polarization Initially; After application of field; At 11 Tesla, population difference ~ 1 in 100,000!    H =  B 0 I z ; ;

15. Relaxation: T 1 Corresponds to a spin aligned against the field flipping to align with it. + -

16. Relaxation: T 2 No single spin correspondence. It is the loss of coherence between the ensemble of spins in the system. Corresponds to a spread in the phase of individual spins.

17. Methods to increase NMR polarization –Large magnetic fields –DNP (Dynamic Nuclear Polarization) –Optical pumping –Polarization transfer –Algorithmic cooling –PASADENA Increasing polarization

18. HPHP Simplest: INEPT Used for polarization transfer from nuclei with high  to nuclei with low  ‘Swaps’ polarization between nuclei via J-coupling INEPT Polarization:a3a a Polarization transfer

19. PASADENA Pauli principle:  fermion  fermion Exchange of nuclei  hyd  =  trans  vib  elec  nuc  rot +++ +/   nuc :     +        +    Exchange + + +  (Para-hydrogen And Synthesis Allow Dramatically Enhanced Net Alignment) 

20. J = 0 J = 1 J = 2 E PASADENA: H 2 rotational wavefunctions + +   nuc  +  Para- hydrogen Para- hydrogen Ortho- hydrogen

21.     Chemical shift     Chemical shift PASADENA The PASADENA experiment Standard two-spin NMR Rh H

22. The PASADENA experiment Rh H Before

23. The PASADENA experiment Rh H After

24. Selection Rules Hamiltonian in low field is just the J-coupling Hamiltonian: How do we convert from triplet to singlet? Natural Conversion happens very slowly We “Catalyze” the conversion with a strong magnetic field Molecule scale gradient breaks the magnetic equivalence of the protons. Must span the strength of the J-coupling - tens of Hertz, ~150 kG/cm. Paramagnetic solids achieve these gradients.

25. Selection Rules

26.  00a Limits on polarization transfer in a compression experiment Limits on the size of a; Sorenson unitary bound; |a| max = 0.87 (for  = 0.5) Shannon entropy bound; |a| max = 0.98 (for  = 0.5)

27. Limited by  and spin resetting time (ratio of relaxation times) Algorithmic cooling PP HH HH 00a HH HH a-  00b Overcomes Sorenson and Shannon entropy bounds Compress Wait for relaxation Compress Wait for relaxation, etc short relaxation time

28. UV LASER pulse removes H 2 molecule from complex RF pulse transfers polarization from para-hydrogen atoms to phosphorus atoms Polarization transfer Polarization transfer The vacant coordination site is filled by para-hydrogen from the bulk solution Less polarized More polarized P P P Ru C Polarization building experiment H atoms

29. UV LASER pulse removes H 2 molecule from complex RF pulse transfers polarization from para-hydrogen atoms to phosphorus atoms Polarization transfer Polarization transfer The vacant coordination site is filled by para-hydrogen from the bulk solution Less polarized More polarized P P P Ru C Polarization building experiment H atoms

30. UV LASER pulse removes H 2 molecule from complex RF pulse transfers polarization from para-hydrogen atoms to phosphorus atoms Polarization transfer Polarization transfer The vacant coordination site is filled by para-hydrogen from the bulk solution Less polarized More polarized P P P Ru C Polarization building experiment H atoms

31. UV LASER pulse removes H 2 molecule from complex RF pulse transfers polarization from para-hydrogen atoms to phosphorus atoms Polarization transfer Polarization transfer The vacant coordination site is filled by para-hydrogen from the bulk solution Less polarized More polarized P P P Ru C Polarization building experiment H atoms

32. Bulk solvent polarisation enhancement

33. Laser setup

34. –10 mm tube –Airtight –Ports for gas entry and vent –Symmetrically spaced capillary tubes –Fit 8 mm quartz rod longitudinally –Fit 2.5 cm wide bore Bubbling apparatus

35. Dr Sabieh Anwar Scott Burt David Trease Helen Hoyt (Bergman lab) Professor Alex Pines All the Pinenuts Acknowledgements Funding: LBNL and DOE