KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
Institut für Organische Chemie / Institut für Biologische Grenzflächen 2
www.kit.edu
W.E.Heraeus Seminar in Bad Honnef
KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
Institut für Organische Chemie / Institut für Biologische Grenzflächen 2
www.kit.edu
W.E.Heraeus Seminar in Bad Honnef
Accommodation free, just travel costs!
Up to 65 participants, deadline April 21!
Details: www.ioc.kit.edu/luy/315.php
KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
Institut für Organische Chemie / Institut für Biologische Grenzflächen 2
www.kit.edu
Analytical coherence transfer functionsBurkhard Luy, Oliver Schedletzky, Steffen J. Glaser
4 03.05.2013
Effective Hamiltonian
TOCSY1HHEHAHA1H
HEHAHA13C
Multiple pulse sequences
Isotropic Mixing
Planar Mixing
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Coherence Transfer and Spin System
Coherence Transfer depends on:
- effective mixing conditions- spin system
CC COOH
BrBr
HH
H
1
3
2J12
J13 J23
Coherence Transfer Functions
6 03.05.2013
Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23
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Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23
0
0
m = 3/2
m = 1/2
m = -1/2
m = -3/2
Block structureLargest sub-block: 3x3
Analytical diag. possible!!
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Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23Eigenvectors
Eigenvalues
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Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23Coherence Transfer Function
withInitial spin density
Target spin density
Propagator
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Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23Coherence Transfer Function
Trick: Treat Eigenvalues and Eigenvector components as variables!
with
11 03.05.2013
1
3
2J12
J13 J23
Eigenvalue Differences
Eigenvector components
12 03.05.2013
Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23
13 03.05.2013
Analytical Coherence Transfer FunctionsExample: Planar Mixing for 3-Spin System
1
3
2J12
J13 J23
14 03.05.2013
Surprise: Transfer in the plane1
3
2J12
J13 J23Two Spin Case:
0
Three Spin Case:
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Surprise: Transfer in the plane1
3
2J12
J13 J23
16 03.05.2013
Surprise: Transfer in the plane1
3
2J12
J13 J23
Experimental verification
17 03.05.2013
Four Isotropically Coupled Spins!
1
4
2
3
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Four Isotropically Coupled Spins!
1
4
2
3
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Four Isotropically Coupled Spins!
1
4
2
3
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Four Isotropically Coupled Spins!
1
4
2
3
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Four Isotropically Coupled Spins!
1
4
2
3
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Spin 1 + Spin ½ under Isotropic Mixing
1 1/2J12
23 03.05.2013
Spin 1 + Spin ½ under Isotropic Mixing
1 1/2J12
Negative Coherence Transfer?
24 03.05.2013
Spin 1 + Spin ½ under Isotropic Mixing
1 1/2J12
CDCl3
Indeed!
25 03.05.2013
Anisotropic Ising-Heisenberg Model / Cylindrical Mixing
Is a superposition of
Heisenberg-Dirac-VanVleck /Isotropic Mixing
Dipolar Coupling Hamiltonian
with
The General 2-Spin/3-Spin Case
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I SJL+JP
The General 2-Spin Case
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1
3
2J12
J13 J23
The General 3-Spin Case
Anisotropic Ising-Heisenberg Model / Cylindrical Mixing
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T11Z T12
Z T13Z
JL / JP = -2
JL / JP = -1
JL / JP = -1/2
JL = 0
JL / JP = 1
JL / JP = 4
1
3
2J12
J13 J23
XY / Planar Mixing
Heisenberg-Dirac-Van Vleck / Isotropic mixing
Dip. Coupl.
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T11Z T12
Z T13Z T11
X T12X T13
X
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JL/JP=-0.5
JL/JP=-2
JL=0
JL/JP=-1.5
JL/JP=5 JL/JP=1 JL/JP=0.5
JL/JP=-5
JL/JP=-1
1
3
2J12
J13 J23
T12Z
Maximum transfer efficiency:
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JL/JP=-0.5
JL/JP=-2
JL=0
JL/JP=-1.5
JL/JP=5 JL/JP=1 JL/JP=0.5
JL/JP=-5
JL/JP=-1
1
3
2J12
J13 J23
T12X
Maximum transfer efficiency:
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Conclusion
Analytical Coherence Transfer functions are available for
- Ising / longitudinal mixing: any spin system- XY Model / Planar mixing: three spins ½,
two spins 1- Dipolar Coupling: three spins ½- Heisenberg-Dirac-Van Vleck / Isotropic mixing:
four spins ½spin 1 – spin ½
- General anisotropic Ising-Heisenberg / Cylindrical mixing:three spins ½
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• B. Luy, S. J. Glaser, "Transverse Magnetization Transfer under Planar Mixing Conditions in Spin Systems Consisting of Three Coupled Spins 1/2", J. Magn. Reson. 164, 304-309 (2003).• B. Luy, S. J. Glaser, "Analytical planar mixing transfer functions for two coupled spin-1 nuclei", J. Magn. Reson.,153, 210-214 (2001).• B. Luy, S. J. Glaser, "Superposition of Scalar and Residual Dipolar Couplings: Analytical Transfer Functions for Three Spins 1/2 under Cylindrical Mixing Conditions", J. Magn. Reson. 148, 169-181 (2001).• B. Luy, S. J. Glaser, "Negative Polarization Transfer between a Spin 1/2 and a Spin 1", Chem. Phys. Lett. 323, 377-381 (2000).• B. Luy, S. J. Glaser, "Analytical Polarization and Coherence Transfer Functions for Three Dipolar Coupled Spins 1/2", J. Magn. Reson. 142, 280-287(2000).• B. Luy, O. Schedletzky, S. J. Glaser, "Analytical Polarization Transfer Functions for Four Coupled Spins 1/2 under Isotropic Mixing Conditions", J. Magn. Reson. 138, 19-27 (1999).• O. Schedletzky, B. Luy and S. J. Glaser, "Analytical Polarization and Coherence Transfer Functions for Three Coupled Spins 1/2 under Planar Mixing Conditions", J. Magn. Reson. 130, 27-32 (1998).
Thank you!
35 03.05.2013
W.E.Heraeus Seminar in Bad Honnef
36 03.05.2013
W.E.Heraeus Seminar in Bad Honnef
Accommodation free, just travel costs!
Up to 65 participants, deadline April 21!
Details: www.ioc.kit.edu/luy/315.php
37 03.05.2013
Collaborations on Anisotropic NMR ParametersHorst Kessler (TU Munich)Murray Coles (Tübingen)Stephan Grage (KIT)Andreas Lendlein (GKSS Teltow)Thomas Paululat (Siegen)Peter Spiteller (Bremen)Stefan Kirsch (Wuppertal)Stefan Bräse (KIT)Michael John (Göttingen)Jochen Klages (Bruker)Svetlana Simova (Sofia)Roberto Gil (Pittsburgh)Armando Navarro-Vazquez (Vigo)Jagadeesh Bharatham (Hyderabad)Ilya Kuprov (Oxford)Sabine Laschat (Stuttgart)Harald Schwalbe (Frankfurt)Julien Furrer (Bern)Norbert Sewald (Bielefeld)…
Forschergruppe 934Michael Reggelin (Darmstadt)Christina Thiele (Darmstadt)Robert Berger (Darmstadt)Christian Griesinger (Göttingen)Markus Zweckstetter (Göttingen)Uwe Reinscheid (Coburg)Matthias Köck (Bremen)
€€€DFG Forschergruppe 934DFG Heisenberg-ProfessurHGF Biointerfaces
Industry
38 03.05.2013
Thank you!
Formerly:Kyryl Kobzar
Christoph FreudenbergerJulien Furrer
Felix HalbachMassimiliano Tittarelli
Grit KummerlöweIgor Jakovkin
Alexander HoyerUlrich Sternberg
Currently:Sebastian Ehni
Silke BüchlerChristian Merle
Benjamin GörlingMartin Koos
Claudia Muhle-GollTony Reinsperger
David Schulze Sünninghausen
Pavleta TzvetkovaEminé SagerSummer 2011
39 03.05.2013