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

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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

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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

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1

3

2J12

J13 J23

Eigenvalue Differences

Eigenvector components

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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

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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

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Surprise: Transfer in the plane1

3

2J12

J13 J23

Experimental verification

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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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Four Isotropically Coupled Spins!

1

4

2

3

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Spin 1 + Spin ½ under Isotropic Mixing

1 1/2J12

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Spin 1 + Spin ½ under Isotropic Mixing

1 1/2J12

Negative Coherence Transfer?

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Spin 1 + Spin ½ under Isotropic Mixing

1 1/2J12

CDCl3

Indeed!

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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

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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